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# Ratios and mass; reaction calculation problem
I have come across the following problem:
One method used to inflate air bags in cars is to use nitrogen produced chemically from the decomposition of sodium azide. The sodium formed reacts with potassium nitrate to give more nitrogen.
$$\ce{2NaN3(s) -> 2Na(s) + 3N2(g)}$$
$$\ce{10Na(s) + 2KNO3(s) -> K2O(s) + 5Na2O(s) + N2(g)}$$
a) In what ratio by mass must the sodium azide and potassium nitrate be mixed in order that no metallic sodium remains after the reaction?
b) Calculate the total mass of the solid mixture needed to inflate a $60.0\ \mathrm{dm^3}$ air bag at room temperature and atmospheric pressure.
I have a solution to part a), which is 1:0.311, but this differs from the given answer (1:3.11). Here is my solution:
For every 10 moles of $\ce{NaN3}$, 2 moles of $\ce{KNO3}$ is needed i.e. ratio in moles is 5:1. Mass of $5\ \mathrm{mol}$ of $\ce{NaN3}$ is $5 \times 65.0 = 325$ and mass of 1 mol of $\ce{KNO3}$ is 101.1. So, ratio = 325:101.1 = 1:0.311. Is this incorrect?
I also have a solution to part b), but again this differs from the given answer $(40.9\ \mathrm g)$. Here is my solution: Using ideal gas law to find how many moles of $\ce{N2}$ needed to inflate air bag: $n=\frac{PV}{RT}=\frac{101000\times 0.06}{8.31\times293}=2.49\ \mathrm{mol}$ If the first equation is rewritten as $\ce{10NaN3(s) -> 10Na(s) + 15N2(g)}$, then there are $\frac{15}{16}\times2.49=2.33$ moles of $\ce{N2}$ from the decomposition of sodium azide, and $\frac{1}{16}\times2.19=0.156$ moles of $\ce{N2}$ from the second reaction. Using these values gives $101\ \mathrm g$ of $\ce{NaN3}$ and $31.5\ \mathrm g$ of $\ce{KNO3}$, which clearly does not give the answer. What's incorrect here?
• I suspect you're using the wrong gas equation. There is a much simpler one relating the number of moles of a gas directly to the volume. – Beerhunter Nov 11 '15 at 19:36
• @Beerhunter, I assume your referring to the fact that 1 mole of gas always has a volume of 24 decimetres cubed at rtp, but this gives the same value as mine for the number of moles of nitrogen . – Ambler Nov 11 '15 at 20:15 |
# Is it Regular Language?
According to Wikipedia, Regular Language is Recognized by Some DFAs, or expressed by Regular Expression .. and all finite Language are regular but, not all regular is finite ..
that's mean it may be infinite language is regular ?
my example is L = {a^n b^n+1, n >0 } is it regular ? it generate infinite set of strings how to represent it as DFA or a regular expression (can represent this language using RegExp ?).. i can guarantee the exact number, how to automata to maintain the exact number of a's or b's
i tried some grammar, i do not get the regular grammar .. my grammar looks like
S -> AB
A -> aA | e
B -> bbB | e
final question, how the language is regular and infinite in the same time ?
• To answer a question in your text: $\{a^n, n\geq 0\}$ is infinite and regular. It is described by the regular expression $a^*$, so it can also be described by a finite automaton. – reinierpost Jan 19 '15 at 7:41
## 1 Answer
Here's a derivation in your grammar, assuming that your 'e' denotes the empty string: $$S\Rightarrow AB\Rightarrow B\Rightarrow bbB\Rightarrow bb$$ This is clearly not in $L=\{a^nb^{n+1}\mid n>0\}$. There is, however, a non-regular grammar for your language: \begin{align} S&\rightarrow AB\\ A&\rightarrow aAb\mid ab &\text{generates a^nb^n}\\ B&\rightarrow b &\text{generates the b on the right} \end{align} There is no regular grammar that will generate $L$, since $L$ is not a regular language.
For your last question, "how can a language be regular and infinite?", you appear to be confused by your observation that any finite language is regular. This is true: logically we'd write this as "If a language is finite, then it is regular."
This does not, however, imply the converse: "If a language is regular, then it is finite." To see this, consider the true statement "If a number is a multiple of 6, then it is even". That's certainly true: 42 is a multiple of 6 and is also even. However, the converse, "If a number is even, then it is a multiple of 6" is certainly false sometimes, since 10 is even but not a multiple of 6. In logical notation, we have that the truth of $P\rightarrow Q$ does not guarantee that $Q\rightarrow P$.
The statement "If a language is finite, then it is regular" just says that the set consisting of finite languages are a subset of the set of regular languages, not that the two sets are the same. For example, the language $\{a^n\mid n\ge 0\}$ is regular (since that language is denoted by the regular expression $a^*$ and also generated by the grammar $S\rightarrow aS\mid \epsilon$) but is obviously not finite.
• can i say that every language that has for example a^n b^m whatever the value of n or m equal or not is not regular language ?? its looks like silly question sorry ... – Yassine Jan 18 '15 at 20:28
• There are ways to determine whether a language is regular, for example the Pumping Lemma or the Nerode Relation. – Jasper Jan 18 '15 at 20:46
• @Yassine. It's not a silly question at all. The answer, though, isn't simple, even for languages of the form $a^nb^m$ where there's some relation between $n$ and $m$. For example, if $n=2m$ the language isn't regular, but if we just require $n+m$ to be even, then the language is regular. I suspect you'll learn a lot more about this and similar questions shortly. – Rick Decker Jan 18 '15 at 21:50 |
# Taking On Too Much?
### Help Support The Rocketry Forum:
#### SecretSquirrel
##### Well-Known Member
My niece is going to have a baby any day now. Last night I was told she's taking Le Mans classes in preparation. I think it's awesome that even though she's in a delicate condition, she still finds time to practice for a 24 hour auto endurance race. I still don't see how it helps the kid, but it's cool.
#### Gillard
##### Well-Known Member
My niece is going to have a baby any day now. Last night I was told she's taking Le Mans classes in preparation. I think it's awesome that even though she's in a delicate condition, she still finds time to practice for a 24 hour auto endurance race. I still don't see how it helps the kid, but it's cool.
thanks, funniest thing i've read all week
#### Peartree
##### Cyborg Rocketeer
Staff member
Global Mod
Thanks SS, I needed that today.
#### shrox
##### Well-Known Member
My niece is going to have a baby any day now. Last night I was told she's taking Le Mans classes in preparation. I think it's awesome that even though she's in a delicate condition, she still finds time to practice for a 24 hour auto endurance race. I still don't see how it helps the kid, but it's cool.
So, she's taking classes to learn to be "Da Man"?
#### troj
##### Wielder Of the Skillet Of Harsh Discipline, Potent
Wow! My wife is impressed!
Deb also wants to know how your niece is going to fit behind the wheel -- "Those cars are awfully small!"
-Kevin
#### JoeG
##### Well-Known Member
At least she'll be able to get to the hospital quickly.
#### Evo666
##### Well-Known Member
Le Mans! She's cool in my book
#### MarkII
##### Well-Known Member
And she already has her substitute driver with her. Which factory team is she on? When is she due to meet the pit crew?
Mark K.
#### JDcluster
##### Well-Known Member
I don't think they make a firesuit with a trap door built into them....
JD
#### Pat_B
##### Well-Known Member
In a somewhat related matter, I had a friend who told me one time that his sister was moving into a new condo*. You get the idea.
#### luke strawwalker
##### Well-Known Member
My niece is going to have a baby any day now. Last night I was told she's taking Le Mans classes in preparation. I think it's awesome that even though she's in a delicate condition, she still finds time to practice for a 24 hour auto endurance race. I still don't see how it helps the kid, but it's cool.
Yeah, those childbirth classes are something else... I went with my wife to humor her...
They start talking about all this stuff WE GUYS are supposed to do to "help" our wife give birth...
I'm like, "I learned the basics in the police academy-- if I wanted to "help" my wife give birth I'd just "help" her give birth in a barn, trapped in an elevator, or in a broken down car on the side of the road and save the $20,000 bucks you guys charge for me "helping" her do this in the hospital... My wife starts talking on the ride home about what I'm supposed to do in the delivery room... I'm like "back the truck up... I'm not going to BE in the delivery room-- if God had wanted husbands in the delivery room, he wouldn't have made that nice waiting room just down the hall with the TV and comfy couches!" After enduring a stony stare, we "discussed" the matter. I truly argued the case well that it's tradition; men stay in the waiting room, pacing and nervous (or eating, watching TV, or asleep on the couches, but I left out that part!) waiting for news of the birth, upon receiving said news to hand out cigars and shake hands with the assembled strangers waiting patiently for their own news. It would be breaking tradition, er, impossible, um... darn near SACRILEGE for me, a male, to be present in the delivery room! Alas, my argument fell on deaf ears... As Dr. McCoy once put it, "in short, Captain Sir, they drafted me!" So, the momentous day arrives... So, after she was induced and she laid around half the day, gradually getting worse and worse and finally laying in bed crying while singing church hymns to her ipod, I went searching for a nurse to administer more drugs... (to her preferably, but either one of us would do-- one or the other of us had to have some relief!) After hornswoggling a nurse in the hallway and extracting a promise that she'd deliver more drugs (how much am I paying for this lousy service again-- I mean, heck, even at the Chinese restaurant, the waiter comes around a couple times during the day to ask if I need more tea... seems like the nurses would check in more than at 10 and 2... ) the nurse finally arrives after a half hour and injects something into said victim (oh, sorry, my wife) and glances at some monitory-pulsey type stuff and splits... the doctor decides on a C-section an hour later... So, now Jeff gets the deluxe tour-- including the operating room! (Oh boy, like I really wanted to see that!) So, after a search for some scrubs that would actually fit a 6-1 350 pound fatboy like me, (well, they SAID they fit-- THEY LIED!!!!) I help push the wifey into surgery (how much is this costing again??). Now, I've helped critically injured and dying folks at accidents; I've been hurt on the farm myself a few times and usually so long as it doesn't involve looking for detached body parts, I usually just wrap something around it and keep on working-- the best band-aids are made from shop towels and electrical tape doncha know... but I don't do well as a spectator at such things... when you're "doing something" the adrenaline kicks in and you just do what needs doing. Standing there watching, though, is another matter-- like when we had a "film night" in the academy after a week or so of first aid training-- guess who nearly passed out?? Yet I've helped people who were in their final moments (or nearly so) and not been freaked out... So, I get the front row seat while they cut away on my wife... I turn my back to the table, stand by her head patting her head and holding her hand while they do their thing... shortly the Doctor asks "Would you like to cut the cord??" and I reply curtly, "no thank you; that's what YOU guys are getting paid for!". After a short clean-up and check out, they hand me a wiggling 10 pound 4 ounce baby girl, whom momma wants to see, so I lean down a bit so she can see. I kid you not, the baby turns her head and nearly lifts her head off my arm to look at momma, and then the baby is whisked away by the nurses to the nursery to do all that medical mumbo-jumbo they do to newborns... I stay with my wife (who is finished being sown up and looks rather like a deflated balloon laying on the gurney) as we're escorted to recovery... Later, in the hallway, looking in the nursery window with my brother, we can hear Keira screaming and crying LOUDLY on the other side of the glass-- I comment that 'she has a good set of lungs'... my brother said, "man, she is MAD about something!--she takes after YOU!" That sinks in a minute, and I facepalm myself and go, "oh, s#!t... what have I got myself into??" It's been all uphill from there... Best wishes to your family Don... OL JR #### SecretSquirrel ##### Well-Known Member Whoa, whoa, whoa.... where's the obligatory story about driving a bus or cutting hay??? :roll: #### MysticalRockets ##### Well-Known Member Excuse me... There is a reason why men were always sent to "go get hot water" by the midwives. It takes time to get the water, get the kettle, get the firewood, build a fire, and heat up the water. By the time the water is hot, the baby has arrived. #### luke strawwalker ##### Well-Known Member Excuse me... There is a reason why men were always sent to "go get hot water" by the midwives. It takes time to get the water, get the kettle, get the firewood, build a fire, and heat up the water. By the time the water is hot, the baby has arrived. IG-ZACK-LEE!!!! Why, back in my day, men-folks didn't go nowhere near any darn delivery rooms-- that was strictly for the women-folks. Right as rain! Men folks stayed in the waiting room where they belonged! Why, even when I was hatched, way back in '71, my Dad did the right thing and stayed in the waiting room where he belonged! In fact, they only let him in to see me and my mom after about 2 days, and even then he had to wear surgical scrubs, gloves, and a mask like he was about to do brain surgery! After all, I might have been exposed to a germ or something if he didn't wear a spacesuit... Mom got out of the hospital after 4-5 days I think... Even after all that, my delivery only cost something like$500 or so.
When my sister came along in 76, men-folks still waited in the waiting room where they belonged. They let us in to see her the next day, sans the surgical outfits... but by now the cost had increased to $1,500. She got out of the hospital after 3-4 days IIRC... My brother was hatched in 80. Men folks COULD come into the delivery room by that point, but no REAL MEN did... only hippies and guys who were whipped. Most men contented themselves in the waiting room. We were let in later that afternoon and could actually touch the baby. The cost had skyrocketed to like$6,000 or so, but by then we had insurance... Of course they ran you off after 2-3 days at most...
Nowdays, no waiting room, men EXPECTED to do everything, lousy service, and they shove you out the door as soon as the bleeding stops... and it costs \$20,000 IF YOU'RE LUCKY!
Hmmm... and people wonder what's wrong with medicine...
Later! OL JR
#### slogfilet
##### Well-Known Member
Centrifugal birthing... I wonder...
#### Gillard
##### Well-Known Member
As i have expained to the wife, my job was that of the planner, i provided the blue prints (well half of them anyway) the relatively simple job of building the baby and then delivering the baby was in her department, as is the next twenty or so years, i will be there when the boy is a man and wants to go for a beer!
(not true really, i don't know if its a good or bad thing, but my best friend is five years old and calls me daddy)
both my kids delivery my C section, first was an emergency after 30 hours of labour, 13lb 10, wife just wasn't big enough in the pelvis to delivery him naturally. both kids had complications, first was in special care for a week with fluid on the lungs, hole in the heart, an infection etc, second was fine for the first few days and then had a tumour appeared and continued to grow, which took over about 20% of her face, gots of chemo and treatments later (max was 17 hospital visits to four different hospitals in three different counties) and she's healthy and about to take over the world- she's one tough cookie, and about to turn three.
on the plus side, did not cost a thing in medical bills (british national health service), and her treatment was ground breaking and is now used to help others in similiar situtions.
#### MysticalRockets
##### Well-Known Member
Centrifugal birthing... I wonder...
I have to learn to stop drinking soda while I read these things...
##### Well-Known Member
Oh, come on now. I was at the birth of all four of my children and I was glad to be there. I did not miss a minute of any of their births. No dizziness either.
The first one (my darling daughter) was by C-section. The rest were VBAC. Each was truly a miracle.....Then they grow up:shock:
#### luke strawwalker
##### Well-Known Member
Oh, come on now. I was at the birth of all four of my children and I was glad to be there. I did not miss a minute of any of their births. No dizziness either.
The first one (my darling daughter) was by C-section. The rest were VBAC. Each was truly a miracle.....Then they grow up:shock:
That's good... truly happy for you...
But there are certain things that I just have no need or desire to ever see... and kids hatching is one of them... especially my kid...
I see enough of it dealing with cattle here on the farm... every so often I get stuck pulling a calf-- MAN I HATE THAT! I can do it and it doesn't bother me but it's just DARN HARD WORK, and messy and nasty as can be. Fortunately I haven't had to deal with a prolapsed uterus in a few years-- what a mess...
Did have a cow two years ago that couldn't deliver-- we checked on her at sundown and everything looked fine, but she ran off to the far end of the pasture. Next morning, we checked, dead calf halfway out. We finally got her under the trees and managed to pull the calf, but then she got pretty messed up in her pelvis or spine and couldn't get up. We carried her water, hay, and cattle cubes every day for a few days, shot her full of antibiotics and B-12, and hoped for the best. Of course she'd laid down in a low spot, and all 40 gallons of amniotic fluid pooled around her, and she worked it up into a slimy mud trying to get up while her back legs wouldn't work. The third day the flies got REAL bad, so we KNEW we had to move her or we'd lose her. We used the tractor loader and hay ropes to make a sling under her and get her up, sorta, though she slipped out of the makeshift "sling" and got rope burns on her hips that took all the hair off (which later grew back white), but we did get her moved over about 50 feet under another shade tree on clean ground; brought her more water and hay and cubes, and shot her full of antibiotics and B-12 again. I was frankly amazed she was still alive, and wondered every day what I'd find when I made the trek to the back pasture.
On the fourth day, I noticed a ring had been grazed around her; she'd been eating every blade of grass down to a half-inch tall, and since she couldn't get up, she just sorta ambled around in a circle. The next day she'd drug herself over a little further and eaten the ring into a peanut shape-- she was trying to get up but by this time the soreness and stiffness in her legs, and weakness in her legs and ankles were hampering her more than the nerve problems were. She'd try to get up, but her ankles were turned back (trying to stand on the FRONT of the hoof instead of the bottoms) so we took a wait and see approach, but the next day she'd get 95% of the way up but couldn't quite make it, and fall back down. So, we used the rope sling trick again and used the loader to hoist her up and lower her down on her back legs, moving her legs forward a bit to encourage the circulation and get her hooves stretched back on straight instead of turned under. We kept her hoisted for about an hour, and she was finally able to stand. We let the loader down and she could tentatively walk. We took the rope slings off and she wandered around a bit, but her hind end didn't really want to follow her front end. She finally got pretty well straightened out, and was doing better. After our daily treks to feed and water her and tend to her rehabilitation, my wife dubbed her "Queenie" since we waited on her like a Queen.
Next was the wondering whether she'd be able to conceive and deliver a calf, or whether she'd been too torn up. If she couldn't deliver a calf, she'd get a trip to the sale barn in short order. She conceived and delivered a heifer, but she didn't have much milk and didn't mother the calf very long, but the calf lived, and given that it was less than a year since her 'incident' I figure I'll give her another chance...
Still don't have any interest in HUMAN birth or medicine though... OL JR |
# Tag Info
## New answers tagged soft-question
2
I'd like to perhaps a slightly different viewpoint to your question and maybe turn it around a little. Probability is hard. Very hard. Defining the foundations of probability and statistics so that they are altogether sound and rigorous is actually a work in progress. It definitely is not complete. On the other hand Quantum mechanics is easy. Very easy! I'm ...
0
It doesn't make sense that satellites cannot detect radiation on the ground. They can detect visible light which is far less penetrating than gamma radiation from a decaying radioisotope. Remember, we are talking about MASSIVE amounts of radioactive isotopes in the atmosphere. They have fingerprints, I'm confident, which can be detected from space. Also, ...
0
You can also use PLotly, a collaborative, web-based graphing platform with APIs in Python, R, MATLAB, Julia, and Perl. You you can find the code to make these examples in their documentation. .
2
Let me try to give you a kitchen-table explanation. I can't help you with statistics vis-a-vis quantum mechanics, but probability is very basic. The underlying "real stuff" in quantum mechanics are numbers that, when squared, produce probabilities of seeing things. Typically, these numbers are complex, but they don't always have to be. These numbers are ...
3
I'm going to explain roughly what the Born Rule, following Stan Liou's comment. One of the Postulates of Quantum Mechanics relates a mathematical quantity, the wave function (or state $\psi$ of a Hilbert space, $\mathcal{H}$) to a measurable entity, the probability of a given event to happen. The idea goes like this: if you want to measure a quantity ...
1
What science tries to do is paint as complete and consistent of picture in the language of mathematics as possible. This in practice means figuring out how pieces fit together rather than tackling questions like why is there a puzzle to begin with.
1
anna v wrote in her answer: The only answer to "why" is this "because", data says so. I'd like to provide another example. Consider the question "How does matter move through space". In trying to answer this, Aristotelian arguments could satisfy someone of the answer. Prodding further, Aristotelian arguments don't hold up and we need to use Newtonian ...
2
Physics is concerned with abstract, mathematical models that describe the behaviour of particles, space, time etc and that are tested with observations and experiments. If a model is in agreement with experiments, under certain conditions and up to a certain accuracy, then it is accepted (for situations where those conditions hold). But a theory remains an ...
1
Here are my two cents of the euro: Physics is a science that has a large body of observations, and a limited number of mathematical models/theories that aim to organize and explain those observations and , very important, get validated by predicting the behavior of new observations. Mathematical theories start with axioms and some tools that develop ...
3
"Why" is the fundamental scientific question, the question regarding cause and effect. "How" already implies that certain things cause others, and sometimes it seems that cause and effect are not that easy to distinguish. You can't do any science without "why". Take, for example, the question: "How does CO2 contribute to climate change?" This is a ...
5
No, I do not regret getting my (forthcoming) PhD. I do sometimes regret changing subject areas from my MS to my PhD (MS is on theoretical condensed matter, PhD is on computational astrophysics) but only because it's added 2 or 3 years to my academic career. I have never had anyone ask me any of those questions, but Likely not going to happen in our ...
6
I agree with the others that physics is fundamentally a "hard science" which is (or should be) concerned exclusively with physical, empirical facts, but I have to disagree with the assertion that "How?" is a scientific question while "Why?" is not. Moreover, philosophy is central to scientific research despite not being itself the end goal. This discussion ...
6
In English, asking 'why' is a request for an explanation of, reasons for, or purpose of something. Physics does provide explanations and some types of reasons, but doesn't concern itself will questions of purpose at all, at least not in any teleological sense. So physics answers some types of why questions but not others, because in English usage 'why' is ...
4
"Why" is the question for philosophers. "How" is the question for physicists. The task of a physical scientist is to find a model that adequately describes "how" nature behaves. When more than one model fits, see Occam's Razor. The question of "why" nature is described by one model or another is best left to the philosopher and, be aware, that path leads ...
13
English is pretty imprecise and asking questions of the form "Why does ..." feels natural even when "How does ..." would suffice. "Why" has philosophical overtones because it goes beyond just "How". Physics is a science and the scientific method is tried-and-true method for gaining knowledge about how things work. I'd suggest that in any place you have a ...
0
Yes, a particle can have potential energy in one dimension as potential energy depends upon the configuration of the body. We can have configuration in one dimension as in hook's law and hence potential energy.
2
Sure, a particle can have potential energy in one dimension. Just look at Hooke's Law or the gravitational force. Both of those are conservative forces in one dimension ($x$ and $r$, respectively) that have a corresponding potential energy. In higher dimensions, nothing has to change, but it is possible to have potential energies which depend on the value ...
3
All our sophisticated mathematical tools - Derivatives and Integrals, Fourier Transforms, Groups and Representations, Riemann Tensors, Kähler manifolds, etc. are merely descriptive techniques. What exists is what exists, independent of how we try to describe it. New mathematical ideas often help us see known phenomena more clearly, or deal with the ...
7
this is a broad, complex, somewhat tricky question with many angles that an entire survey or book could be written on but unfortunately it seems one hasnt yet. heres a "grab bag" of some deep parallels noticed over the years that such a book might cover & "research leads" for further inquiry. Modelling and simulation. as computing capability has ...
3
The link between Computer Science and Physics can be very subtle sometimes. For example, consider this article: http://arxiv.org/abs/1010.0128 The point is the following. Consider a quantum algorithm in order to solve an NP-complete problem (i.e.: a hard problem, which is conjectured not to be solvable in polynomial time). Now, consider a classical ...
5
There are numerous examples of people using genetic algorithms, for example, to optimize some output where an actual solution of the equation would be otherwise impossible. Information entropy, which is a generic computing concept, has some hold on statistical physics. But I cannot think of a case I have seen where a concept from cutting edge computer ...
0
For electric circuits, CircuitLab is a nice online editor and simulator. There are some restrictions to what you can do without an account or with a free account - I can't remember the details - but you can use print-screen to get nice pictures out of it. I like it because it is really at the level of simplicity I need: if I'm explaining a basic ...
1
Gerard 't Hooft certainly thinks so. What if you are older, and you are not at all looking forward to join those noisy crowds of young students ? It should be possible, these days, to collect all knowledge you need from the internet. [...] This way, the costs of becoming a theoretical physicist should not exceed much the price of a computer with ...
0
If you do not yet master calculus, I recommend the book Zeldovich Ya.B., Yaglom I.M.: Higher Math for Beginners, Mir 1988 which is great. Then, you need to understand 1) ordinary differential equations of 1st and 2nd order and have some idea about 2) many-variable calculus and 3) linear operators and matrices. If you want to understand Hamilton's ...
0
In the UK, Lagrangian mechanics would normally be taught to first or second year undergraduate students who have a solid understanding of Newtonian dynamics and calculus with multiple variables. For an idea of the kind of texts you might need you could look at university syllabuses such as: University of Manchester: ...
-1
I think it's useful to think about space-time as being like a foam ball. The point of unifying space and time comes from relativity. Consider that when lengths contract, times also dilate. This is a bit like squishing our foam ball in the middle, causing it to bulge at the top and bottom. In other words, the bending of space-time is fundamentally a ...
3
Here's a useful link. For me, it's helpful to think there are clocks and rulers. The clock I have is the only one I have to measure time, and the ruler I have is the only one I have to measure distance, but you can think of space as being spanned by a big lattice of rulers, and if some of them get shortened or lengthened relative to others, there's no way ...
8
According to Wikipedia: In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. [My emphasis.] And according to Wikipedia's entry on Dirac: He was the first to develop quantum field theory, which underlies all theoretical work on ...
5
QFT was formulated over many decades, from the 20's to the 70's, by many people from the USA, Europe and the USSR, amongst others. Although QFT is an active research topic, QFT was demonstrated to be consistent by 't Hooft in the 70's. Whilst particular achievements and developments are attributable to specific individuals, QFT was the result of innumerable ...
1
Basically, the universe has a speed limit. No object can ever exceed the speed of light. Now imagine you decide to prove Einstein wrong by building a train capable of nearly reaching the speed of light, and then shooting a bullet forward in that train, so that the bullet will break the speed of light. In order to preserve this speed limit, time for you and ...
1
Both approaches are equally correct in this case. $F = mv^2/R$ is just a consequence of the law for rotational motion, which says $\tau = I\alpha$ (Torque = Moment of Inertia * Angular acceleration). The former formula may be used in case the objects in consideration are point masses. But the latter, more general version of the formula is applicable for ...
1
There will always be solutions that can't be analytical. For example, any model of more than two bodies without any special constraints, cannot be solved analytically. From the gravitational interactions between three planets to three particles interacting (electromagnetically or otherwise) in quantum theory. To have mathematically analytical solutions, ...
7
No. There is nothing wrong with perturbation theory, or with theories with known, restricted accuracy. The point of theory is to explain the results of observation from as simple an initial theoretical standpoint as possible. Therefore: Since experiment always has a finite uncertainty, one can only ask that theory match the experimental value within its ...
4
The whole volume XVII of the Proceedings of the Cambridge Philosophical Society is available on the Internet Archive at the url https://archive.org/details/proceedingsofcam1718191316camb It is p.43 as marked in the text and p.60 in the document. It is available in pdf, ePub, Kindle, Daisy and DjVu formats, as well as a dedicated (very nice) online ...
3
Muons are single-particle excitations (states) of the $e-\mu-\tau$ quantum field, except that these states don't have definite values of energy (they are in a superposition of states that have definite energy). Because states with different energies change at different rates, this superposition changes with time. After some time has elapsed, the ...
1
What I think you're trying to get at is the vaccum energy. Weight is always associated with a force, so on earth we feel the force of gravity on our body and we call that our weight. Now Einstein showed us that there is an equivalence between mass and energy. What we know from Quantum Field Theory is that there is some underlying amount of energy just ...
3
OK, I watched the video. It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space. He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles ...
4
My suggestion, don't waste your time on it. Only from this Not only does the helical particle wave concept explain all the characteristics of light, etc., by means of a single model, but it allows one to calculate the exact position, velocity and spin of any relativistic particle without the need for such dubious concepts as: Einstein's time ...
0
Yes, he did. There's a press release at UCSB that acknowledges it as his second win: http://www.ia.ucsb.edu/pa/display.aspx?pkey=3161 The reason for this is, presumably, that the committee is considering giving him the bigger "2014 Fundamental Physics Prize." In essence, the Physics Frontiers prize is a nomination for that. (This is based on the ...
1
We do exercise a force on Earth. Let's say that the force in question is F. When F acts on you it provides an acceleration of F/m (where m is your mass) and when the same force F acts on the earth it provides an acceleration of F/M (where M is the mass of the Earth). As M >>>>>> m, the acceleration provide does not create some perceptive change in the ...
4
Let's say you got fatter and fatter until you were the same mass as the earth, and, at the same time, the earth got smaller and smaller until it was only as massive as you were to start with. Now after this has happened, you must agree that you are now exerting a gravitational force on the earth (since you and the earth have now effectively switched roles, ...
5
There is no significance in the choice between upper- and lower-case $\psi$ (or $\Psi$) to denote a system's wavefunction. The two are used interchangeably and it is the author's discretion to use either symbol. (On the other hand, of course, one shouldn't use the two symbols interchangeably within the same text; if both are used they would refer to ...
1
You're looking for experimental particle physics on a big detector at a national lab: There's no end to the custom electronics and embedded systems associated with the data acquisition, Computer science is definitely required (analysis of big data sets), and Plenty of really interesting fundamental physics. If you are still at the university go talk ...
0
I love Alonzo Church, but not for his contributions to Physics. The connection between algorithms and the real physical world can never be more than approximate. Noise is essential to the concept of probability, and probability is now essential to Physics via Quantum Mechanics. But Wiener saw this even classically, so I will go classical. No finite ...
Top 50 recent answers are included |
# Is the identity I came up with for sin(x) ^ 2 correct?
1. Aug 18, 2009
### pro.in.vbdnf
I noticed that the graphs of sin(x) and sin(x) ^ 2 are very similar. So I offset sin(x) ^ 2 to exactly match sin(x):
$$sin(x) = 2 sin^{2}\left(\frac{x}{2} +\frac{\pi}{4}\right) - 1$$
Is this right, or is it an illusion? I haven't been able to find any identity that this is based on.
If it is right, then:
$$sin^{2}(x) = \frac{sin(2x - \frac{\pi}{2}) + 1}{2}$$
Thanks,
pro.in.vbdnf
Last edited: Aug 18, 2009
2. Aug 18, 2009
### arildno
That is certainly true!
Remember that $$sin(2x-\frac{\pi}{2})=-\cos(2x)$$
and therefore, your identity is a rewriting of the half-angle formula.
3. Aug 18, 2009
### Elucidus
You have indeed hit on something true. You are exploiting several trig identities. Namely:
Cofunction (for cosine): $\cos(x)=\sin\left( \frac{\pi}{2}-x \right)$
Symmetry (for sine): $\sin(-x) = \sin(x)$
Double Angle (for cosine): $\cos(2x)=1-2\sin^2(x)$
So:
$$\frac{\sin \left( 2x - \frac{\pi}{2} \right)}{2}= \frac{-\sin \left( \frac{\pi}{2} - 2x \right)}{2} = \frac{-\cos(2x)+1}{2} = \frac{-(1-2\sin^2x)+1}{2}= \frac{2\sin^2(x)}{2} = \sin^2(x)$$
Incidently there is also the Half Angle (or Power Reducing) Identity
$$\sin^2(x) = \frac{1-\cos(2x)}{2}$$
which is closely related to what we have here.
--Elucidus
4. Aug 18, 2009
### pro.in.vbdnf
Thanks for your help! The identities I was missing putting together were $$sin^{2}(x) + cos^{2}(x) = 1$$ and $$cos(2x) = cos^{2}(x) - sin^{2}(x)$$.
So $$cos^{2}(x) = \frac{cos(2x) + 1}{2}$$. I'll have to remember that.
Last edited: Aug 18, 2009
5. Aug 18, 2009
### pro.in.vbdnf
Does that mean $$\sqrt{cos(x)}$$ has an identity in terms of cos(x)?
6. Aug 18, 2009
### Elucidus
I believe you meant $\sin^2(x) + \cos^2(x) = 1$. The latter equation above is the Half Angle (or Power Reducing) Identity for cosine.
I do not think so, but $$\sqrt{1 \pm \cos(x)}$$ does:
$$\sqrt{1+ \cos(x)}=\sqrt{\frac{2(1+\cos(2x/2))}{2}}=\sqrt{2\cos^2(x/2)}=\sqrt{2}\left| \cos(x/2) \right|$$
$$\sqrt{1-\cos(x)}=\sqrt{2}\left| \sin(x/2) \right|$$
Both of these are handy for certain types of methods in calculus.
--Elucidus
7. Aug 18, 2009
### pro.in.vbdnf
(Yes, I meant $\sin^2(x) + \cos^2(x) = 1$.)
What are their names?
By the way, is there a difference between the $$and $tags? And is there a way to vertically center the LaTeX images with the text? 8. Aug 18, 2009 ### arildno 1. The itex-tag can be used to generate Latex within the ordinary sentence structures, like the equation: [itex]2x-1=3$, rather than [tex]2x-1=3$$
2. Note that the half-angle formula gets rid of a square root!!
Thus, the right-hand side is easily integrated, the left-hand side would seem a hopeless target for integration without that nifty identity.
9. Aug 18, 2009
### pro.in.vbdnf
$$\sqrt{cos(x)} = \sqrt{2 cos^{2}\left(\frac{x}{2}\right) - 1}$$
So there is no way to get rid of the right hand radical?
10. Aug 18, 2009
### arildno
Sure, by squaring both sides.
11. Aug 18, 2009
### pro.in.vbdnf
..while keeping the left radical? I wonder if there is an identity of the form $$\sqrt{cos(x)} = ... cos(x) ...$$? |
# 9.3: Two indistinguishable particles with spin 1/2
If we have two identical fermions of spin 1/2, confined in the same region, what is the appropriate wavefunction? In the scattering case we could measure spins far from the interaction, and if we knew that the total spins is conserved, spins can be associated with each particle. In the bound state we cannot tell which particle we are measuring, so the ket must contain both spin and spatial wavefunctions of both particles.
Assuming the spins do not interact, we can separate the two-particle spin wavefunction into $$\sigma (1, 2) = \sigma_1\sigma_2$$. We also know the appropriate one particle basis states $$\uparrow_1, \downarrow_1, \uparrow_2, \downarrow_2$$, where $$\uparrow_1$$ represents “particle 1” in spinor state $$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$$. The combinations for indistinguishable particles are then:
$\uparrow_1\uparrow_2, \quad \downarrow_1\downarrow_2, \quad (\uparrow_1\downarrow_2 + \downarrow_1\uparrow_2)/ \sqrt{2}, \quad (\uparrow_1\downarrow_2 − \downarrow_1\uparrow_2)/ \sqrt{2} \nonumber$
Operating on these with $$\hat{P}_{12}$$ yields eigenvalues 1, 1, 1 and -1 respectively. $${\bf S}^2 = S(S + 1)$$ yields 2, 2, 2 and 0, $$S_z$$ yields 1,-1,0 and 0. Thus the demands of indistinguishability couples the spins of two identical particles into a triplet (S=1) and a singlet (S=0). The spin-1 vector has three possible $$M_s$$ component values - hence the triplet.
This page titled 9.3: Two indistinguishable particles with spin 1/2 is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Graeme Ackland via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. |
# rblock attribute command
Syntax
rblock attribute keyword ... <range>
Primary keywords:
Set the value of rigid block attributes. This command is a synonym for the rblock initialize command. Individual attributes can be listed with the rblock list command and all attributes can be visualized.
Note
• Modification of the rigid block geometry will fail if the resulting rigid block would not fall entirely within the model domain.
• Rigid block attributes are characteristics of the rigid blocks such as position or size. These are distinct from rigid block properties (assigned with the rblock property command) that are surface properties of the rigid blocks that are used to fill contact model properties.
damp f [rbmodblock]
Rigid block local damping coefficient where f > 0. By default, f = 0.
density f [rbmodblock]
Rigid block density where f > 0. By default f = 0.
displacement v [rbmodblock]
Accumulated rigid block displacement vector as a result of cycling.
displacement-x f [rbmodblock]
The $$x$$-component of the accumulated rigid block displacement as a result of cycling.
displacement-y f [rbmodblock]
The $$y$$-component of accumulated displacement as a result of cycling.
displacement-z f (3D ONLY) [rbmodblock]
The $$z$$-component of accumulated displacement as a result of cycling.
euler v (3D ONLY) [rbmodblock]
Current orientation of Euler angles following the X,Y,Z convention (e.g., rotation about the $$x$$-axis followed by rotation about the y’-axis followed by rotation about the z’‘-axis) in degrees. The orientation is updated only when orientation tracking has been enabled (see model orientation-tracking command). When active, the current rigid block orientation can be visualized.
euler-x f (3D ONLY) [rbmodblock]
The $$x$$-euler angle (in degrees) of the current rigid block orientation. See the euler keyword for further details.
euler-y f (3D ONLY) [rbmodblock]
The $$y$$-euler angle (in degrees) of the current rigid block orientation. See the euler keyword for further details.
euler-z f (3D ONLY) [rbmodblock]
The $$z$$-euler angle (in degrees) of the current rigid block orientation. See the euler keyword for further details.
force-applied v [rbmodblock]
Force vector applied to rigid blocks.
force-applied-x f [rbmodblock]
The $$x$$-component of the applied force.
force-applied-y f [rbmodblock]
The $$y$$-component of the applied force.
force-applied-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the applied force.
force-contact v [rbmodblock]
Sum of the contact force accumulated to the rigid blocks during the previous force-displacement update. This value will be modified during the next force-displacement update.
force-contact-x f [rbmodblock]
The $$x$$-component of the contact force.
force-contact-y f [rbmodblock]
The $$y$$-component of the contact force.
force-contact-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the contact force.
fragment i
Fragment ID (see “Fragment”).
moi-11 f [rbmodblock]
11 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-12 f [rbmodblock]
12 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-13 f [rbmodblock]
13 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-22 f [rbmodblock]
22 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-23 f [rbmodblock]
23 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-33 f [rbmodblock]
33 component of the rigid block real moment of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moi-principal fprin11 fprin22 fprin33 (3D ONLY) [rbmodblock]
Real principal moments of inertia. When modified, only the rigid block principal moments of inertia are modified and the other rigid block attributes are not changed. The specification of the rigid block principal moments of inertia via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fix state can be modified in FISH (see the rblock.moi.fix intrinsic).
moment-applied fx fy fz (y- and z- components are 3D ONLY) [rbmodblock]
Moment applied to rigid blocks.
moment-applied-x f (3D ONLY) [rbmodblock]
The $$x$$-component of the moment applied to rigid blocks.
moment-applied-y f (3D ONLY) [rbmodblock]
The $$y$$-component of the moment applied to rigid blocks.
moment-applied-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the moment applied to rigid blocks.
moment-contact fx fy fz (y- and z- components are 3D ONLY) [rbmodblock]
Sum of the contact moments accumulated to the rigid blocks during the previous force-displacement update. This value will be modified during the next force-displacement update.
moment-contact-x f (3D ONLY) [rbmodblock]
The $$x$$-component of the contact moment.
moment-contact-y f (3D ONLY) [rbmodblock]
The $$y$$-component of the contact moment.
moment-contact-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the contact moment.
position v [rbmodblock]
Location of rigid block centroid.
position-x f [rbmodblock]
The $$x$$-component of the location of rigid block centroids.
position-y f [rbmodblock]
The $$y$$-component of the location of rigid block centroids.
position-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the location of rigid block centroids.
rotation f (2D ONLY) [rbmodblock]
Current rigid block orientation. The orientation is updated only when orientation tracking has been enabled (see model orientation-tracking command).
spin fspinx fspiny fspinz (y- and z- components are 3D ONLY) [rbmodblock]
Rigid block angular velocity in radians per second.
spin-x f (3D ONLY) [rbmodblock]
The $$x$$-component of the rigid block angular velocity in radians per second.
spin-y f (3D ONLY) [rbmodblock]
The $$y$$-component of the rigid block angular velocity in radians per second.
spin-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the rigid block angular velocity in radians per second.
velocity v [rbmodblock]
Rigid block translational velocity vector.
velocity-x f [rbmodblock]
The $$x$$-component of the rigid block velocity.
velocity-y f [rbmodblock]
The $$y$$-component of the rigid block velocity.
velocity-z f (3D ONLY) [rbmodblock]
The $$z$$-component of the rigid block velocity.
volume f [rbmodblock]
Rigid block volume. When modified, only the rigid block mass and real mass are modified and the other rigid block attributes based on volume are not changed. The specification of the volume via the command line or via FISH results in the principal moments of inertia being in a fixed state so that they will not be automatically updated when scaling a rigid block, changing the volume, or changing the density. The fixity state of the inertia can be modified in FISH (see the rblock.moi.fix intrinsic).
rblock attribute Keyword Block
Add f to the existing value.
Apply a linear gradient in each of the axes directions starting at the origin.
Apply a linear gradient in the $$x$$-direction starting at the origin.
Apply a linear gradient in the $$y$$-direction starting at the origin.
Apply a linear gradient in the $$z$$-direction starting at the origin.
multiply f
Multiply the existing value by f.
replace f
Replace the existing value with f.
Usage Examples
Set attributes for a rigid block.
rblock attribute density 2650 damp 0.7
[in specimendoc from Simple Rigid Block Bonded-Block Modeling (BBM)]
Set rigid block $$y$$-velocity along a gradient specified with inline FISH.
rblock attribute velocity-z 0.0 gradient 0 0 [-2.0 ＊ nvel / specHeight]
[in testsdoc from Simple Rigid Block Bonded-Block Modeling (BBM)]
Set the $$z$$-velocity of a single 3D rigid block by specifying its ID with a range.
rblock attribute vel-z 1 range id 31
Set multiple attributes (density and damping) for the range of rigid blocks not in the group “arch”.
rblock attribute density 0.0025 damp 0.7 range group 'arch' not
[in buttressdoc from Rigid Block Model of Flying Buttresses] |
# Bayes formula
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
A formula with which it is possible to compute a posteriori probabilities of events (or of hypotheses) from a priori probabilities. Let be a complete group of incompatible events: , if . Then the a posteriori probability of event if given that event with has already occurred may be found by Bayes' formula:
(*)
where is the a priori probability of , is the conditional probability of event occurring given event (with ) has taken place. The formula was demonstrated by T. Bayes in 1763.
Formula (*) is a special case of the following abstract variant of Bayes' formula. Let and be random elements with values in measurable spaces and and let . Put, for any set ,
where and is the indicator of the set . Then the measure is absolutely continuous with respect to the measure () and , where is the Radon–Nikodým derivative of with respect to .
#### References
[1] A.N. Kolmogorov, "Foundations of the theory of probability" , Chelsea, reprint (1950) (Translated from Russian) |
# Talk:Sarah Palin/Archive 64
## Swastika
I asked Courcelles to remove the swastika and the section it's in at the bottom of the article. --Kenatipo (talk) 04:01, 10 January 2011 (UTC)
Where? I can't see it. AndyTheGrump (talk) 04:07, 10 January 2011 (UTC)
Template was vandalised. Now fixed. CIreland (talk) 04:10, 10 January 2011 (UTC)
It was in the Fox contributor template. I think Courcelles fixed it. Now I know how to fix it myself, next time! --Kenatipo (talk) 04:22, 10 January 2011 (UTC)
Correction: the vandalism was fixed by CIreland. (Ireland, why is that IP still allowed to edit?) --Kenatipo (talk) 19:39, 10 January 2011 (UTC)
## Sarah Palin's blood libel
Why is there no mention of this? http://tpmdc.talkingpointsmemo.com/2011/01/sarah-palin-accuses-journalists-of-blood-libel-calls-loughner-apolitical-video.php -- why is this excluded? Merrill Stubing (talk) 16:33, 12 January 2011 (UTC)
If we added information to this article every time she is in the news, this articles would be begin to get too big. If you think it should be in the article, then add a mention with a citation in the appropriate section.--Jojhutton (talk) 16:39, 12 January 2011 (UTC)
I cant, it appears protected to remove any reference of the crosshairs map/Giffords for conservative POV reasons. — Preceding unsigned comment added by Merrill Stubing (talkcontribs) 16:42, 12 January 2011 (UTC)
It is a censored article.Sayerslle (talk) 17:37, 12 January 2011 (UTC)
Come to the sub-article about her image. That's the appropriate place to discuss it.Anythingyouwant (talk) 17:41, 12 January 2011 (UTC)
So we conceal negative info in sub articles? OK. Merrill Stubing (talk) 21:16, 12 January 2011 (UTC)
I must say, I haven't been to this article in a while, and after giving it a quick glance, I feel like it's been oversanitized. I understand the need for subarticles, but reading this article, I don't get the sense that she is nearly as divisive a figure as she is. --Muboshgu (talk) 21:38, 12 January 2011 (UTC)
I imagine that a lot of folks feel the same way about the Barack Obama article - he's a pretty divisive figure himself. So was George W. Bush. But it's not the place of a BLP to detail every controversy. Kelly hi! 21:49, 12 January 2011 (UTC)
No, it isn't. However, to exclude a topic entirely where Palin herself has commented, and this commentary in turn has attracted significant media attention (abroad as well as in the US [1]), is dubious, if not a breach of WP:NPOV. AndyTheGrump (talk) 21:56, 12 January 2011 (UTC)
Did I say it should be excluded? Kelly hi! 22:03, 12 January 2011 (UTC)
(ec) Obama is not divisive in the way Palin is. There is a fundamental difference in their respective oppositions, both in terms of how they inspire it and how they respond to it. Obama's page is similiarly devoid of crucial details there. Most casual readers don't go to subarticles. More info should make its way in here, and some in Obama's page as is relevant there. --Muboshgu (talk) 22:07, 12 January 2011 (UTC)
In part because Wikipedia isn't a newspaper. Give this (non-?) story a week to settle down. Maybe even (gasp!) a whole month. There's enough about Palin that's over a month old, isn't there? -- Hoary (talk) 10:55, 14 January 2011 (UTC)
In my opinion, Ms Palin's use of the term "blood libel" does not really belong in an article about Ms. Palin -- this situation isn't notable because Ms Palin, as distinct from some other person, said "blood libel." Nor is the controversy itself particularly notable, at not yet. So I don't think a discussion of her use belongs in her article. (I think it may belong in either the current "blood libel" article or a new article about contemporary usage of "blood libel.") Agnosticaphid (talk) 21:13, 14 January 2011 (UTC) (edited by Agnosticaphid (talk) 06:49, 15 January 2011 (UTC))
## 2011 Tucson shooting
Not to be a pain in the whatever, but this article should at least mention the fact that she/the Tea Party is part of it. There should be at least one reference to the entire event. I've read the entire page, an not even ONE word refers to it. Leaving it out really is POV. I really hope you can fix this. (PS Mind you, though, that I am neutral in this overheated discussion! I just reckon it peculiar, to say the least, that anyone wanting to know more about that subject, can't seem to find anything about it on the page of the woman who is been named a lot throughout this drama. Mentioning it DOES NOT immediately mean that she did/didn't do anything/nothing; it's just mentioning that she has been named a lot.) Robster1983 (talk) 19:49, 12 January 2011 (UTC)
It's the sub-article about her public image. Kelly hi! 19:53, 12 January 2011 (UTC)
With all do respect: one really has to dig into the articles (Sarah Palin & Public Image of Sarah Palin) before one finds anything about it. I'm especially worried about not even one line being about the Tucson drama on the Sarah Palin article (or at least a reference to it all on the 'Public Image...' article). Would it really be a bad idea to add a line to it? Saying that she has been named a lot, that she doesn't recognise the critique towards her, and then referring to the 'Public Image...' article? I really reckon it would do the article some good, because right now there isn't even a notion to anyone that this can be found in the sub-article (if you hadn't old me, I wouldn't have found it). It's just... as if it just doesn't exist. :s Robster1983 (talk) 20:07, 12 January 2011 (UTC)
(rephrase [...]a reference to it all on the 'Public Image...' article[...]: a reference about the drama in this article to point out that further reading can be done about this subject on the sub-article)Robster1983 (talk) 20:10, 12 January 2011 (UTC)
Yes, it would. The shooting has no connection to Sarah Palin, and including it at all is simply recentism. Do you think in a month or a year this will be such an important factor in Sarah Palin's history and identity that it should be in an encyclopedia article about her? Prodego talk 20:13, 12 January 2011 (UTC)
Why has she deigned to comment on it at all then? its not about a connection, its about her part in the 'debased , exaggerated and vitriolic' American public discourse. Giffords herself objected to her target map after her office was vandalised.I see comments like yours, I don't think , wise admin, I think one of the zeros in her 00000's of admirers. Sayerslle (talk) 22:09, 12 January 2011 (UTC)
There's lots of stuff in the sub-articles that you wouldn't have any idea about from reading this article. We're having difficulty figuring out what to say in the sub-article, so please come there and help.Anythingyouwant (talk) 20:18, 12 January 2011 (UTC)
I'd really love to. The fact that a sub-article is needed shows how much stuff there is to tell about Palin. But about the Tucson drama: both US and foreign media literally referred to Palin and the 'hit list'. So it really does have a certain impact. And about RECENTISM: merely mentioning that Palin is named by the media in this all, though she didn't recognise herself in all the critique (refering to the sub-article wouldn't hurt, either), is way different than "inundated with day-by-day facts". Mind you: we don't want this page to be part of the 'he said-she did' discussion! And it is blocked in a way so that that won't happen. So even if people want to drag the entire discussion on this page, they cán't even make it RECENTISM. Anyhow, I really believe that at this moment simply mentioning the whole drama (again, it's NOT about blaming anyone) wouldn't hurt. Robster1983 (talk) 20:46, 12 January 2011 (UTC)
It's mentioned in both 2011 Tucson shooting and Public image of Sarah Palin. I imagine if the accusations have any sticking power (they normally don't) some brief summary will eventually end up here. Kelly hi! 20:50, 12 January 2011 (UTC)
I've asked you before to stop commenting about me. Kelly hi! 22:04, 12 January 2011 (UTC)
I was commenting about your post. AndyTheGrump (talk) 22:10, 12 January 2011 (UTC)
@Robster1983 Please note that this article cannot be edited by anyone other than administrators. So far no administrator has come forward willing to include information related to the Tucson shootings and any pertinent, notable, verifiable tie in to Sara Palin. There are many editors willing and able to create entries that would be acceptable to all but, sadly, that is not currently possible. Stay tuned, maybe the protective status will change. Buster Seven Talk 22:12, 12 January 2011 (UTC)
Even admins shouldn't edit the article except to make minor and necessary corrections or consensus edits. You can propose draft text here until the protection expires, currently scheduled for January 15. Will Beback talk 01:30, 13 January 2011 (UTC)
We have a significant section on ""Pink Elephant" Movement and 2010 endorsements". Her targeting of House Democrats who voted for the Health Care bill is also notable and we should include at least a sentence or two on that aspect of her 2010 activities. Will Beback talk 00:49, 13 January 2011 (UTC)
That may be, however it is being shown more and more that there is absolutely no connection in the least between the two events. That the (now without any shread of doubt liberaly biased) media has jumped the shark and made a connection where none existed matters little towards the long term view. If anything this would be a good example of how the media has been biased against Palin. Future inclusion, if any, should be based on that. Arzel (talk) 01:14, 13 January 2011 (UTC)
I'm not talking about the shooting. I'm talking about Palin's campaign against the House Democrats, which has received considerable attention, before and after January 8, 2011. Will Beback talk 01:27, 13 January 2011 (UTC)
My concern is that it would quickly turn into a section about this incident. Arzel (talk) 01:45, 13 January 2011 (UTC)
It has not been "shown more and more that there is absolutely no connection in the least between the two events". To actually demonstrate that conclusively, you'd have to show that the (alleged) shooter had never seen any of Palin's posters etc. I doubt any responsible source is going to claim that. It may very well be that any possible connection is seen as less credible with time, but as of now, the issue is still being discussed. Personally, I think the Palin camp might have come out of this a lot better if they'd not claimed to be part of a media plot, and instead acted with a bit more dignity, but while they are making statements denying any connection, they are in no position to complain that others take such self-serving spin with the scepticism it deserves. AndyTheGrump (talk) 01:39, 13 January 2011 (UTC)
More dignity? When you have Krugman, Oblmerman, Mathews, and basically all of the MSM basically saying that Palin has blood on her hands, I think she is well within her rights to claim a media plot against her. You even have Sanders trying to use this event as a campaign (military term by the way) tool, where is the dignity there? As to your primary point, you have to prove that the connection exists, this absurd notion that she must prove the negative is ridiculous. Arzel (talk) 01:45, 13 January 2011 (UTC)
I don't have to prove anything beyond the fact that the possible connection between inflammatory political rhetoric and the shooting is still being discussed in the media (which you seem to have noted yourself). This is my point - it isn't for us to decide that any connection is right, wrong or just plain irrational, but instead to note that the connection is being made, and take this into consideration when composing articles. AndyTheGrump (talk) 01:52, 13 January 2011 (UTC)
(Undent) In my opinion, the subject is being covered adequately and briefly in articles like the Palin image sub-article. In a few days, I may support removal from there, per WP:NOTNEWS, if current trends continue. For example see this story today in the CS Monitor: "As portrait of Jared Loughner sharpens, 'vitriol' blame fades".Anythingyouwant (talk) 02:05, 13 January 2011 (UTC)
Can I assume from this that the default Wikipedia policy on Palin is now that nothing she says, does, or is involved in is worthy of comment, as it will rapidly become 'old news'? If so, one would have to ask why we have an article on her at all? AndyTheGrump (talk) 02:27, 13 January 2011 (UTC)
I'm fairly certain Wikipedia could eliminate at least one data centre if we simply deleted and salted all Palin articles (and, especially, their associated talk pages). I'll support a deletion nomination if you wish to move forward. ;) jæs (talk) 02:30, 13 January 2011 (UTC)
Would it be possible to keep the article and delete Sarah Palin, or do we need to wait for a software upgrade? --FormerIP (talk) 02:35, 13 January 2011 (UTC)
You should go see Tron: Legacy. jæs (talk) 02:39, 13 January 2011 (UTC)
The Palin damage control team is sweeping everything into the rug (aka sub-articles). Please just stick to mentioning that she was the conservative grizzly/hockey mamma governor of a state and 2008 vice prez candidate. Anything else goes under the rug. Likeminas (talk) 02:56, 13 January 2011 (UTC)
My god, inbetween my last post and now, it seems that things really have semi-exploded on this talk page. :| Maybe I can contribute to anything. Here goes: after reading the entire Sarah Palin article, I have to agree with those who reckon this article to be out of balance. I, not able to vote in the US, not even part of the entire political system of the US, really only get the feeling that this Sarah Palin is the best thing on the planet. There doesn't seem to be even one letter of criticism. Personally, I could care less about both people who are pro-Palin and people who are anti-Palin (sort of speak). My only care is how we can make this page representable to the entire world. Because make no mistake, I'm from the Netherlands, but I prefer the English-language Wiki WAY more than the Dutch, exactly because on the English-language Wiki most articles seem to be more balanced and packed with the necessary sources. But at the same time (back to this specific subject) both the Dutch, Belgian, UK, and German press (all state press, I might add) named Palin and the 'hit list' ('named' her, meaning: without blaming her!). If it was Obama being named, than I (and I guess a lot of other people with me) would like to see that being added to his article also. Not because I'd like to see anyone being punished or something like that, but because it IS relevant! It's all over the place, and yet here we are, pretending that nothing happens around Palin, except how wonderful her latest TV-show is? That ISN'T balanced!
At the same time, however, I'm also a big supporter of NOT putting the blame on anyone, in this case Palin. Simply because thát ISN'T balanced either! Stating that Palin created a hateful environment is not only hard to proove (finding a independent and reliable source that ONLY states Palin as the cause of it all won't be out there), but is also not true (following the heated discussion, it is obvious that the political climate per sé is, sort to say, poisoned, and both left and right endulged in it).
So I really hope that we all are done acting like Ramesses/Cleopatra; king/queen of denial (small joke to lighten the mood, I hope :)), and add some info about the shooting on this page without pointing a finger to anyone, while keeping in mind that this ISN'T about right vs. left/ Palin vs. Obama or whatever. This is just about presenting this page as one that teachers from around the globe consider a legit source of information! Robster1983 (talk) 18:40, 13 January 2011 (UTC)
Goed Gadaan, mijn Dutch vriend!Buster Seven Talk 19:38, 13 January 2011 (UTC)
## Tuscon proposal
Option #1:
• In the wake of the Giffords shooting Palin faced criticism for her website inclusion of a graphic that included a crosshair over Giffords's district. Palin defended the graphic, saying that "Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them," controversially calling accusations against her "blood libel".
Anyone have a problem with this?--Louiedog (talk) 19:30, 13 January 2011 (UTC)
Just as a point of reference to aid the upcoming discussion (per above thread, protection is expected to expire Jan 15)on the Tucson propasal, the following is the proposal from January 11 by Editor:off2riorob that had some growing support and was moved to Public image of Sarah Palin. Lets call it Option #2:
• In the immediate aftermath of the 2011 Tucson shootings in which Congresswoman Gabrielle Giffords was critically wounded, Palin was the subject of a degree of press and political criticism, that her style of political rhetoric had helped to create a climate that fostered political violence. The criticism was specifically related to her campaign's use of a campaign graphic portraying what were interpreted by some to represent gunsight crosshairs to mark the districts of Giffords' and twenty other political districts as the focus for 2010 Congressional election. In a twitter post Palin said they were, "bullseye" and not gun sights.${\displaystyle Insertformulahere}$
It had references at the time but I failed to hold on to them. The references are easily replaced. Once it got to the public imaage article it went thru extensive changes and discussion. It is only being brought back to life as a possible starting point for a new consensus. Buster Seven Talk 19:55, 13 January 2011 (UTC)
Yes Loodog, I have a problem with that proposed edit. It is an extremely POV proposal (intentionally or not) because it omits the fact that the gunman was not motivated the least bit by anything Palin said or did. He was threatening Giffords in 2007 when Palin was unknown outside Alaska; moreover, he wasn't a right-winger (e.g. he despised religion, burned the American flag on YouTube, was a registered Independent, was a pothead, etc). The sources cited in the Palin image sub-article confirm what I have said. Why should the main Palin article suggest the opposite?Anythingyouwant (talk) 20:15, 13 January 2011 (UTC)
It omits the fact that the gunman was not motivated by Palin, as well as the fact that pundits claimed he was. It leaves the discussion at a very general level. How would you modify my proposal?--Louiedog (talk) 21:37, 13 January 2011 (UTC)
See below, where I suggest that we summarize the sub-article Public image of Sarah Palin once it stabilizes.Anythingyouwant (talk) 21:48, 13 January 2011 (UTC)
@ Anythingyouwant: we now know that you don't approve thís proposal, that's obvious. But we don't know about what you might approve of concerning this matter. What are your ideas? Please help us to come to a proper way to solve this tough cookie. We could really use your constructive criticism! Robster1983 (talk) 20:25, 13 January 2011 (UTC)
The only point of reference here ought to be the sub-article Public image of Sarah Palin. Per WP:Summary style, this article should either summarize the sub-article or else not say anything about it. Right now, the sub-article remains unstable on this point, so my recommendation would be to stabilize the sub-article before thinking about summarizing it here.Anythingyouwant (talk) 20:30, 13 January 2011 (UTC)
This article 'should not say anything about it'. She has herself spoken about it - its part of her biography. Sayerslle (talk) 21:39, 13 January 2011 (UTC)
Not as support but only as a point of reference to aid future discussion, here is the current section from Public image on Jan 13 @ 2;15. I suggest we call it Option #3:
• In March 2010, Palin posted to her Facebook page to seek contributions to SarahPAC to help defeat 20 House Democrats in the 2010 Congressional election. Her post featured a graphic that used gunsight crosshairs to mark the Democrats' districts.[1] She promoted the Facebook posting with a tweet that urged her followers, "Don't Retreat, Instead - RELOAD!"[2] Palin critics said she was inciting violence.[3][4] One of the targeted Democrats, Representative Gabrielle Giffords of Arizona, objected to the graphic, saying, "we're in the crosshairs of a gun sight over our district. When people do that, they've got to realize that there are consequences to that action."[5] Palin referred to the targets as "a bullseye icon" in a post-election tweet.[6][7]
In the immediate aftermath of the 2011 Tucson shootings, Palin was the subject of press and political criticism about her style of political rhetoric,[8][9] which was countered by defenders of Palin in the media.[10][11][12][13] No link has been found between Palin and the gunman's actions. According to the Washington Post, martial rhetoric and imagery like Palin's is common on both sides of the American political spectrum.[14]InOn the Glenn Beck Show, an e-mail said to be from Palin was read, saying "I hate violence. I hate war. Our children will not have peace if politicos just capitalize on this to succeed in portraying anyone as inciting terror and violence."[15]
• @louieondog, with your permission, may I tag your suggestion Option #1...? I can then tag the other two as #2 and #3, and we will have a level starting point.Buster Seven Talk 21:26, 13 January 2011 (UTC)
• Sure. And if anyone has a problem with it, please have them propose modifications along the lines of "1a", "1b", etc..--Louiedog (talk) 21:35, 13 January 2011 (UTC)
DoneBuster Seven Talk 21:42, 13 January 2011 (UTC)
I agree with anything, just as long as at least a reference to the Tucson shooting article is made, and no foul überheated reactions are placed (for they only end up in a right vs. left status quo). If the link of the shooting is added, then people may or may not click on it, to read more about it. This article here is purely about Palin, and anything that makes her wo she is. Which mean the good and the bad. But that's my personal opinion. Robster1983 (talk) 20:51, 13 January 2011 (UTC)
@atyw and Robster and louiedog. There is a lot going on here at WP and in the RealWorld about this issue. Since this is the main Palin article, lets begin to make sense of everything. I know that for me, in the past, as discusions ebbed and flowed in an attempt to achieve consensus, I got lost. Which one were they talking about? And does the new suggestion include the changes that Editor:soandso suggested two hours ago. Twisting and turning and getting more and more confusing. so that is why I hope we can continue the Option tagging so that everyone , participants and observers, don't get lost.Buster Seven Talk 21:10, 13 January 2011 (UTC)
I think it's about option #1 and option #2, if I'm not mistaken. :s Robster1983 (talk) 21:46, 13 January 2011 (UTC)
OK, so we have three options at this moment, being in bold in the above text. How to continue with this? Should we invite others to come with other possible options, should this come to a vote...??? Robster1983 (talk) 21:50, 13 January 2011 (UTC)
Be bold, Robster. Maybe you can create (option #4 or #5) using the previous ones as a template at a sandbox that you create. We need a skeleton to put some meat onto or put on a diet, as the case maybe.Buster Seven Talk 01:07, 14 January 2011 (UTC)
As always, this summary article should summarize the substance of the sub-article where the meat of content will exist rather than introducing new sources and ideas. I believe this article is still fully-protected anyway. Perhaps we could focus on finalizing the content in the sub-article and prepare a summary from that once it settles fully, in order to have a proposal ready when the article comes out from protection (or sooner, if we're ready and have an admin handy to make the change). Fcreid (talk) 22:02, 13 January 2011 (UTC)
I have no dog in this race. If Options #1, #2 and #3 are determined to be old news by the germinating consensus, so be it. Admin:Will Beback stated somewhere above that protection MAY end on January 15. Whenever protection is lifted, I predict there will be a race to the Assayers Office to get first claim on the position. If that is the Readers Digest version of the existing wording at Public image, again, so be it. But, at the very least, there will be an option that is created here, outside the firestorm of who or which group is in charge. Lets just say we are getting the room ready for visitors. So we are setting out the tables and chairs. Its a BIG room.Buster Seven Talk 22:43, 13 January 2011 (UTC)
Concur, Buster, and I certainly wasn't trying to throw a wet blanket on your efforts to keep sanity here. Honestly, I didn't even digest the proposals earlier, but I will. I did drop by the Public Image sub-article today, and was discouraged to see there still seems to be contention about the content. Anyway, I appreciate your preparedness and evenhandedness, and I agree it will be a rush to get something in here once protection is lifted. Again, I might be the only one not closely following the fracas in the sub-article, so I'll likely stay on the sidelines anyway. Fcreid (talk) 22:51, 13 January 2011 (UTC)
Ty, Fc, as usual, I would hope you don't get too comfortable on the sidelines...(although I may be tempted to join you). I am confident you will advocate for all voices on all sides of the debate. Buster Seven Talk 23:04, 13 January 2011 (UTC)
### Tucson courtesy break
We could open with a Glen Beck quote, balance that with the Donald Sutherland quote, title it "Media Circus" and the call it a wrap! :) Fcreid (talk) 23:18, 13 January 2011 (UTC)
The video released by Palin on January 12 has received considerable attention.[2][3] Shouldn't it be mentioned as well? Will Beback talk 23:19, 13 January 2011 (UTC)
I have read interesting secondary sources on this which run the gamut in interpretation (Washington Times vs. Washington Post), as you'd expect. I also saw an interesting article that dissected (yet again) her effective use of the social media to capture national attention. Is it being treated in the sub-article yet? Fcreid (talk) 23:25, 13 January 2011 (UTC)
It's not in the "public image" article yet. However this is something that Palin did, so it's more biographical in nature. The public image article is more about what people say about her. Inevitably, there'll be overlap. As for this article, we should at least mention the video. I'm not sure if there's a consensus reaction to it sufficient for us to characterize it easily yet, but that may develop in the next few days. Will Beback talk 23:49, 13 January 2011 (UTC)
The video and the "blood libel" issue are now in the sub-article on her image.Anythingyouwant (talk) 00:10, 14 January 2011 (UTC)
Here are the Washington Times and Washington Post articles that discuss the "blood libel" video. I've found these two reliable sources, when combined, can usually ferret out most relevant facts and help formulate commonsense opinion on most things political. Fcreid (talk) 00:36, 14 January 2011 (UTC)
I was just rereading this and found it ironic that I even need to caveat things this way, but there's so much crap out there disguised as truthful reporting. 30-40 years ago, at a time when we were limited to three major news networks, I never gave a second thought as to whether what I was being told on the evening news was actually the truth! But I digress... :) Fcreid (talk) 00:53, 14 January 2011 (UTC)
The sub-article uses an LA Times article by James Oliphant which seems quite comprehensive. But feel free to add more footnotes to the sub-article if you like.Anythingyouwant (talk) 00:40, 14 January 2011 (UTC)
Editor:Will. Maybe someone, I'm not saying who, should/could/would start a rough draft...an Option #4. Someone knowledgeable about WP:RULEBOOK and the editors wants and needs. I don't have anyone in mind (nudge, nudge). Maybe you know an admin that could start the ball rolling.Buster Seven Talk 00:49, 14 January 2011 (UTC)
(Undent) Looking at Public image of Sarah Palin, maybe this would properly summarize, or at least be the basis for a shorter summary: This is Option #4
Incidentally, did you notice that Obama said political rhetoric "did not" cause the Tucson tragedy?Anythingyouwant (talk) 02:15, 14 January 2011 (UTC)
'Palin critics suggested that the gunman might have been influenced by her...' straw man. maybe this would properly summarise...no it would not..all it properly summarizes is the style of a crap wikipedia editor.Sayerslle (talk) 03:12, 14 January 2011 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
Discussions should remain civil and cordial. Buster Seven Talk 22:20, 14 January 2011 (UTC)
### construction zone
@Editor:Sayerslle. It is extremely important that we begin this process with a certain social decorum that is expected anywhere in every workplace among adults. We (emphasis on WE) are in the earliest stages of construction. Ive asked you to refrain from attacking other editors at your talkpage. I didnt think I would also need to do it here. Do not attack your fellow workers. It only serves to sidetrack the discussion and delay consensus. if you are a serious editor you might consider constructing your own proposal. But I would advise you not be to attached to it. WE all edit with the fore-knowledge that our proposals will more than likely be edited and changed for the better it is hoped. Buster Seven Talk 03:34, 14 January 2011 (UTC)
@Editor:Buster. It is extremely important if you give advice like 'Name calling is never a good thing' on a talk page , and want to be respected for your advice you try and follow your own advice, and do not then call people 'crapmeister' shortly afterwards. A certain social decorum is extremely important anywhere in every place among adults. You've asked me to refrain from attacking other editors, (and I shall,) - but feel free to attack other editors yourself. C'est vraiment dégueulasse, ça..Sayerslle (talk) 16:41, 14 January 2011 (UTC)
You can't be overly thin-skinned around here, Sayerslle. Sometimes, a submitted idea is, in fact, crap. You can't take it personally. There are editors here who are willing to help you formulate your idea into something acceptable, but the degree of cooperation you receive will be directly proportional to the cooperation you elicit. You'll find few editors more respected, more helpful and more fair than Buster, so if you really want to participate, he's a good guy to have in your corner. Fcreid (talk) 16:53, 14 January 2011 (UTC)
Blimey if an editor who will/would do whatever is required to 'silence' me, is one of the most respected, helpful , i'm likely to find it re-doubles my need to clear off from SPalin articles. I don't like her, her followers,- I never intended to say anything about her but was surprised when all mention of the recent discussion in the media was absent from her page. I do believe mention of it will appear in time on her page, but there is not the rush I felt there was at first - I just hope critics are left with their own words left in their mouths and it is not left to the demagogues followers to phrase their words. Sayerslle (talk) 18:31, 14 January 2011 (UTC)
Honestly, it's absurd to say User:Buster7 is trying to "silence" you, because he's not. He's just recommending a tad bit more of a collaborative spirit on your part, which is quite the opposite from trying to "silence" you. I can't say I necessarily expected to (ever) be coming to Buster's defense, but he's really trying to do you a favour here. Now, if you'll excuse me, I need to find my mittens. It's a tad bit chilly here in Hell today. jæs (talk) 19:03, 14 January 2011 (UTC)
The above wording struck me at the time as framed from the first to last words as a piece of POV pushing. How sincere editors are about NPOV is surely as important as the odd lack of decorum - I don't go around endlessly using intemperate language but if the paragraph I objected to is looked at with any degree of concern for NPOV it will be found wanting I believe. why are POV templates not passed around as quickly as civility ones.. Anyway, if I see such like again, I shall indeed look away, I believe though if everyone always does that when faced with such blatant POV wp will degenerate further on political articles.Sayerslle (talk) 11:08, 14 January 2011 (UTC)
Ever consider the possibility that it's you pushing a POV? Fcreid (talk) 11:36, 14 January 2011 (UTC)
yes, sometimes - I think the critical view should be put, with full, decent quotes, not maimed ones for POV reasons, as 'Palin was/is irresponsible..' not 'Palin was/is responsible..' which I don't think anyone claimed. Sayerslle (talk) 12:12, 14 January 2011 (UTC)
You'll find this BLP to be unusually politically-charged, and we rigidly enforce the BLP watchwords of "extraordinary claims require extraordinary sources" when considering content. I'm sure you understand there are polarizing views expressed about this person. So, while not dismissing the politics of an issue that produce such polarizing opinion, we must be extremely circumspect when "fringe" opinion expressed as fact. Many content disputes of this type have been referred to BLP Noticeboard for exactly this reason. Thus, some non-notable person (like Donald Sutherland, for example) who makes a claim that Palin's "irresponsibility" contributed to the Tucson shootings will almost surely take that same route. Fcreid (talk) 14:23, 14 January 2011 (UTC)
again, your paraphrase of his opinion is bad - people should be left to speak for themselvs with what they say, your paraphrase is unhelpful - your idea of who is entitled to be considered notable when describing the public sodding image of this woman is not mine etc.I'm totally sick of the crass misrepresentation of things here. I am definitely leaving all Palin articles now - I hope Sutherland will forgive me dragging his august presence onto this deranged talk page. Sayerslle (talk) 15:35, 14 January 2011 (UTC)
That's obviously your prerogative. I'm not predicting or prejudicing your ultimate contributions to this article, or the ensuing outcome, but rather just preparing you for a different standard used here than in the daughter articles, such as Political Positions and Public Image. This is a BLP, which not only is held to a higher standard on content but is also organized in more rigid summary style. If you compare the corresponding sections in the BLP to their respective sub-articles, you'll quickly see what that means. There are few, if any, lengthy quotes here, and those are limited to the most notable. Significant content is encapsulated, with niggling detail relegated to the appropriate sub-article. Most "battles" fought here resulted from differences on relative weight of specific content that supported either a positive or negative viewpoint, so what's here represents that balance that's been struck by many editors during more than two years. There's always room for significant new information, and I suspect the recent events in Tucson meet that threshold. There's probably also some trivia that now needs to be stored in the attic. Fcreid (talk) 17:18, 14 January 2011 (UTC)
The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.
## Unprotect a disruptive article
The sheen of protectionism needs cleaning. Merrill Stubing (talk) 06:09, 14 January 2011 (UTC)
I'll forewarn you that editors who arrive here with a stated objective of making the article content match their personal positive or negative opinion of the subject always seem to leave here dissatisfied. It's entirely up to you whether your intent is to collaborate or to disrupt. Fcreid (talk) 09:49, 14 January 2011 (UTC)
Articles are rarely disruptive, editors often are. Sheens don't need cleaning. If you think the article needs improvement, please say clearly, coolly and concisely what this improvement is, citing sources etc. -- Hoary (talk) 10:42, 14 January 2011 (UTC)
Well said.-- KeithbobTalk 21:32, 14 January 2011 (UTC)
## Previously discussed Options prior to Jan15
Obviously these options are just a composite of many possible choices from prior discussions. Feel free to add your own or modify an existing one. When making modifications to an existing option please use the option # as a reference guide for fellow editors and designate your change as "1a", "2c", etc.
• 'Option #1
• In the wake of the Giffords shooting Palin faced criticism for her website inclusion of a graphic that included a crosshair over Giffords's district. Palin defended the graphic, saying that "Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them," controversially calling accusations against her "blood libel".
• Option #2
• In the immediate aftermath of the 2011 Tucson shootings in which Congresswoman Gabrielle Giffords was critically wounded, Palin was the subject of a degree of press and political criticism, that her style of political rhetoric had helped to create a climate that fostered political violence. The criticism was specifically related to her campaign's use of a campaign graphic portraying what were interpreted by some to represent gunsight crosshairs to mark the districts of Giffords' and twenty other political districts as the focus for 2010 Congressional election. In a twitter post Palin said they were, "bullseye" and not gun sights.
• Option #3
• In March 2010, Palin posted to her Facebook page to seek contributions to SarahPAC to help defeat 20 House Democrats in the 2010 Congressional election. Her post featured a graphic that used gunsight crosshairs to mark the Democrats' districts.[1] She promoted the Facebook posting with a tweet that urged her followers, "Don't Retreat, Instead - RELOAD!"[16] Palin critics said she was inciting violence.[17][18] One of the targeted Democrats, Representative Gabrielle Giffords of Arizona, objected to the graphic, saying, "we're in the crosshairs of a gun sight over our district. When people do that, they've got to realize that there are consequences to that action."[19] Palin referred to the targets as "a bullseye icon" in a post-election tweet.[20][21]
In the immediate aftermath of the 2011 Tucson shootings, Palin was the subject of press and political criticism about her style of political rhetoric,[22][23] which was countered by defenders of Palin in the media.[10][24][25][26] No link has been found between Palin and the gunman's actions. According to the Washington Post, martial rhetoric and imagery like Palin's is common on both sides of the American political spectrum.[14]InOn the Glenn Beck Show, an e-mail said to be from Palin was read, saying "I hate violence. I hate war. Our children will not have peace if politicos just capitalize on this to succeed in portraying anyone as inciting terror and violence."[27]
• Option #4
• In 2010, Palin used gun-related political rhetoric and imagery of a sort that is common in American politics, such as a map targeting political opponents. Following the 2011 Tucson shootings, Palin critics suggested that the gunman might have been influenced by her, but that became less likely as more was learned about the gunman; Palin called the suggestion a blood libel.
• In March 2010, Palin posted to her Facebook page to seek contributions to SarahPAC to help defeat 20 House Democrats in the 2010 Congressional election. Her post featured a graphic that used gunsight crosshairs to mark the Democrats' districts.[1] She also said to her supporters, "don't retreat, reload."[28] Palin critics said she was inciting violence.[29][30] One of the targeted Democrats, Representative Gabrielle Giffords of Arizona, objected to the graphic, saying, "we're in the crosshairs of a gun sight over our district. When people do that, they've got to realize that there are consequences to that action."[31] Palin referred to the targets as "a bullseye icon" in a post-election tweet.[32][33]
In the immediate aftermath of the 2011 Tucson shooting, Palin was the subject of press and political criticism about her style of political rhetoric,[34][35][36] which was countered by defenders of Palin in the media.[10][37][38][39] According to the Washington Post, martial rhetoric and imagery like Palin's is common on both sides of the American political spectrum.[14] On the Glenn Beck Show, an e-mail said to be from Palin was read, saying "I hate violence. I hate war. Our children will not have peace if politicos just capitalize on this to succeed in portraying anyone as inciting terror and violence."[40] Following the 2011 Tucson shooting, a Palin aide stated that death threats against the former Alaska governor had risen to "an unprecedented level".[41] As more details of the shooting emerged, Patrik Jonsson of the Christian Science Monitor wrote: "The suggestion that the shooting of Rep. Gabrielle Giffords Saturday might have been influenced by political 'vitriol' seems less likely as more becomes known about suspect Jared Loughner".[42][14] Palin released a video denying any link between her rhetoric and the shooting, controversially referring to such suggestions as a blood libel,[43][44]
• Synopsis is best, so #1 would be my choice. Fcreid (talk) 23:47, 14 January 2011 (UTC)
@Fcreid. I added Option #4 after your choice. Is it still #1?Buster Seven Talk 00:03, 15 January 2011 (UTC)
I think #4 would have to identify that the metaphor identified Giffords to make the connection on the controversy, but I'll let others have a chance to comment and contribute. Fcreid (talk) 00:16, 15 January 2011 (UTC)
Fcreid Buster7, thank you for taking the time to create this set of options. It is very helpful in moving the process along. Cheers!-- KeithbobTalk 16:34, 16 January 2011 (UTC)
Thanks, Buster. I didn't see that earlier, and it is certainly your doing and not mine to wrangle in options for ultimate inclusion of this point. Fcreid (talk) 14:22, 17 January 2011 (UTC)
Thanks for the correction. Buster, you rock! [and Fcreid is OK too :-)]-- KeithbobTalk 17:40, 17 January 2011 (UTC)
• Although I don't think any mention of this media kerfuffle belongs in this BLP I vastly prefer #1 to any of the other alternatives.--Paul (talk) 00:20, 15 January 2011 (UTC)
First of all: sorry I was absent the last few days, but blame it on one of the worst flus I ever experienced (hail to the one who can create something that bans this simple, though rubbish disease :P) Anyhow, I saw/ read all the options, and I would go for option #1-b. It's short (thus easy to add), it refers to other articles (very important on Wiki), it doesn't point fingers to anyone (knowing how delicate this matter is, that's a great thing, also), and I think this might be the option of which most people might be content with... So #1-b has my vote, for sure. Robster1983 (talk) 17:33, 16 January 2011 (UTC)
### Options submitted after Jan 15
• Option 1-a (submitted Jan 16)
• In the wake of the January 8th, 2011 shooting of Rep. Giffords, Palin faced criticism for her SarahPAC website's inclusion of a graphic that included a crosshair over Giffords's district. Palin defended the graphic, saying that "Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them," controversially calling accusations against her "blood libel".
Perhaps "deflected criticism of the graphic" would describe it better than "defended the graphic" and "controversially equating the accusations of her role in the shooting to a "blood libel"? Fcreid (talk) 12:15, 16 January 2011 (UTC)
note- Option #1-b is in response to Fcreid's suggestion Buster Seven Talk 15:05, 16 January 2011 (UTC)
• Option #1-b (submitted Jan 16)
• In the wake of the January 8th, 2011 shooting of Rep. Giffords, Palin faced criticism for her SarahPAC website's inclusion of a graphic that included a crosshair over Giffords's district. Palin deflected criticism of the graphic, saying that "Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them," controversially equating the accusations of her role in the shooting to a "blood libel".
Just to make sure: this option has my vote. See my explanation in the above section. Robster1983 (talk) 17:40, 16 January 2011 (UTC)
I think this should read 'Palin responded to the criticism...', but this seems to be the most factual representation of what occurred, and on that basis, should go in. AndyTheGrump (talk) 22:18, 16 January 2011 (UTC)
• Option #1-c (submitted Jan 16 PM)
• In the wake of the January 8th, 2011 shooting of Rep. Giffords, Palin faced criticism because the SarahPAC website had used a graphic that included crosshairs over Giffords's district. Palin responded, saying that, 'Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them,' calling accusations against her 'blood libel.
• Option 2-a (submitted Jan 16)
• "In the aftermath of the 2011 Tucson shootings in which Congresswoman Gabrielle Giffords was critically wounded, the press reported criticisms that Palin's style of political rhetoric had helped foster a climate of political violence. The criticisms were specifically in reference to her campaign's use of a graphic portraying, what critics interpreted as, gunsight crosshairs to mark twenty political districts (including Giffords') as the campaign focus for the 2010 Congressional election."
I believe Option 2 comes closest to telling the whole story in a balanced way. However, I have further refined it in an attempt to make it more succinct and more neutral in tone.-- KeithbobTalk 16:32, 16 January 2011 (UTC)
• I agree. I also oppose 1-b as using the words "deflected" which is a non-neutral word choice, and "controversially" which is also a non-neutral word choice. 2-a is about as neutral as one could expect. Collect (talk) 17:55, 16 January 2011 (UTC)
• I also prefer this version. (2a) clear and concise. Although you could ad the totally correct comment from Palin that, Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them,' Off2riorob (talk) 17:54, 17 January 2011 (UTC)
I'm not trying to be the Concensus Traffic Cop but I think we are close. Option #1-b with Andys change (which may allay some of Collects non-neutral concerns) would now read, and become....
• Option #1-d
• In the wake of the January 8th, 2011 shooting of Rep. Giffords, Palin faced criticism for her SarahPAC website's inclusion of a graphic that included a crosshair over Giffords's district. Palin responded to the criticism of the graphic, saying that "Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them," controversially equating the accusations of her role in the shooting to a "blood libel".
Can we assume that it carries with it the positive affirmations toward Option #1-b which is almost the same??? Collect...are you OK with this one?Buster Seven Talk 00:31, 17 January 2011 (UTC)
• Support Robster1983 (talk) 15:07, 17 January 2011 (UTC)
• Neutral-- I like my version better (what a surprise!) but I have not strong objections to this version if it has the consensus of others and moves things forward.-- KeithbobTalk 17:44, 17 January 2011 (UTC)
Keithbob, if every Wikipedian had your positive and constructive attitude, then by god, what a great Wikipedia that would be! _O_ Anyhow, I think it goes without saying that this would 'just' be the 'first version', and that other changes may not only be desirable, but are also required after some time. But like you said: first thing's first; it would already be great if there IS anything about this all in the article! Robster1983 (talk) 20:50, 17 January 2011 (UTC)
### Placement and polishing
Just to be clear, whichever version is chosen, it would go in the section on her public image, right? Also, once a version is chosen, I'd suggest we briefly discuss how it could be polished before inserting. I'll support #1a because it's short and very descriptive, but (like the other proposals) it ought to be polished (e.g. to clarify that the graphic preceded the shooting, making crosshair plural, maybe changing "defended the graphic" to "responded to the criticism", and maybe removing the word "controversially" as Collect suggested). So: "In the wake of the January 8th, 2011 shooting of Rep. Giffords, Palin faced criticism because the SarahPAC website had used a graphic that included crosshairs over Giffords's district. Palin responded, saying that, 'Acts of monstrous criminality stand on their own. They begin and end with the criminals who commit them,' calling accusations against her 'blood libel.'" To hurry things along, how about if we worry about inserting Wlinks after the new text is inserted? I don't think we need to insert any illustrative image for this text.Anythingyouwant (talk) 18:14, 16 January 2011 (UTC)
Agreed. It seems that two variations of option #1 and option #2-a are getting support. While there is no rush, we probably should get one in place before Jan 17 just to allay criticisms that the article lacks timeliness. I could go with either knowing that they can all be edited once in place. Buster Seven Talk 22:07, 16 January 2011 (UTC)
I don't like 2a because it omits both Palin's denial of a link and also the denial of a link by neutral news reports (e.g. WaPo and CS Monitor), not to mention the assertion by Obama that rhetoric "did not" cause the tragedy. We need to include at least one of these, or else we are presenting an uncontradicted accusation. Version 1 does not have this problem.Anythingyouwant (talk) 00:29, 17 January 2011 (UTC)
The trouble with this reasoning is that we'll end up with all the detail that's now in Public image of Sarah Palin#Campaign imagery. That section will inevitably be more informative than what we put in here. Pursuant to WP:SS, therefore, I suggest that whatever ends up in this main bio article be accompanied by a wikilink to the applicable section of the image article. JamesMLane t c 23:12, 17 January 2011 (UTC)
I disagree. As far as I know, none of the material summarized in this Palin article includes a link to a specific subsection of a sub-article, and we shouldn't start now. This is especially important because that subsection of the sub-article is currently subject to edit-warring in violation of article probation.Anythingyouwant (talk) 00:06, 18 January 2011 (UTC)
Then the result here will be that you and other pro-Palin editors won't be satisfied with a straightforward statement that Palin's been criticized on this score. You'll insist on adding every fact, spin, or wild tangent that puts Palin in a better light. Some of us will try to balance the article by adding contrary facts and opinions, which you'll remove (and you'll then accuse us of edit warring when we dare to restore material we consider appropriate). Thus, the summary here will turn into a passage as long as (indeed, pretty much identical to) what's being summarized. JamesMLane t c 02:49, 18 January 2011 (UTC)
I am not pro-Palin, I think the present material in this article about Tucson is fine, and I have no intention of adding to it, much less edit-warring more stuff into the article. Being anti-anti-Palin is not the same as being pro-Palin.Anythingyouwant (talk) 02:56, 18 January 2011 (UTC)
I believe that our article should not be pro-Palin, anti-Palin, or anti-anti-Palin. It should be pro-truth. That might sometimes seem to verge on being anti-Palin, but only because reality has a well-known liberal bias. JamesMLane t c 05:08, 18 January 2011 (UTC)
Nope, truth is but a byproduct of otherwise getting it right: it should be verifiable and neutral. Palin being "criticized" ought to be in there, but so should some commentary (from reliable sources) that there was a rush to judgment before all the facts were in shortly after the shooting. That's why the Washington Post and Christian Science Monitor pieces are relevant and need to be included to some degree. I'm actually less concerned about Palin's direct response, because I think having her article here be a sort of "call and response" on every question, controversy, or "scandal" isn't encyclopedic. (And we'd run out of space.) jæs (talk) 05:32, 18 January 2011 (UTC)
I haven't tried to remove the Washington Post or Christian Science Monitor quotations from the image article. I've merely noted that the "everybody does it" meme has some opponents, and argued that that POV deserves to be reported, too. Similarly, in the main bio, we should present both those POV's or neither. The easy solution, per WP:SS, is to present neither POV in this article, leave all the detail of that type to the daughter article, and include a wikilink. JamesMLane t c 06:23, 18 January 2011 (UTC)
I disagree, because I think that then leaves readers with the impression that the speculation immediately after the shooting was never disputed, which it obviously was (both by Palin and by notable commentators in reliable sources). The solution isn't to leave out important details, because that leaves us with content that is just as lacking in neutrality as would overloading the article with too many details (wp:undue). It would not be neutral to intentionally fail to mention that there was notable commentary dismissing/refuting/criticizing the early speculation. jæs (talk) 07:07, 18 January 2011 (UTC)
Per WP:SS, the solution is to leave out important details. This one article can't contain everything important about Sarah Palin's life. It's an encyclopedia article, not a book-length bio. That's why we have daughter articles and wikilinks. We can simply state the fact of the controversy (without implying that either side was right, and without presenting supporting evidence and arguments used by either side) and include the wikilink for the reader who wants those important details.
One way to approach the problem is to look at the current text in the image article (three paragraphs long as of this writing) and decide what in there is not important. If you end up concluding that some supporting argumentation for the side you prefer is important and the other side's drivel is not important, go back to the beginning and try again. JamesMLane t c 16:30, 19 January 2011 (UTC)
## Thomas Sowell's article
Under the political positions section, the seventh item has an external link in the text. Is this just a simple error? I'm too scared to edit any part of this article. : )--Banana (talk) 01:07, 17 January 2011 (UTC)
Removed and tweaked, the inline link was unnecessary as the comment was already cited. Off2riorob (talk) 18:13, 17 January 2011 (UTC)
## Sarah Palin is a politician
Can't believe I had to type that sentence. It's not the only thing she is. She's also a pundit, and a mother, and etc. Just because she isn't holding any office doesn't mean she isn't a politician (see Newt Gingrich). Whether or not she runs for office again, her greatest claims to notability are her governorship and candidacy for VP. Everything she has said has had a political connotation. Ergo, she is a politician. --Muboshgu (talk) 20:20, 21 January 2011 (UTC)
[4] –noun 1. a person who is active in party politics. Sarah Palin is clearly active in party politics.--Cube lurker (talk) 20:23, 21 January 2011 (UTC)
Exactly. it is silly to argue otherwise, which is what I wrote in my original edit summary. If User:Tryggvi bt has a problem with me using the word, he should maybe raise this elsewhere, but to get into an edit-war over this seems utterly pointless. AndyTheGrump (talk) 20:25, 21 January 2011 (UTC)
Please see the Wikipedia entry for Politician. I see no evidence that Sarah Palin meets the criteria that are listed there for being considered a politician. Perhaps it needs to be redefined to accommodate Ms. Palin.Tryggvi bt (talk) 20:34, 21 January 2011 (UTC)
I think you need to re-read the definition provided by Cube lurker. You seem to be trying to push a POV on her. --Muboshgu (talk) 20:37, 21 January 2011 (UTC)
From the Wikipedia politician article. Any person influencing group opinions in his or her favor can be termed a politician.--Cube lurker (talk) 20:42, 21 January 2011 (UTC)
Okay. I didn't realize that we were talking about "politician" in the sense that someone vying for prom queen is a politician. I guess I can agree with that.Tryggvi bt (talk) 21:33, 21 January 2011 (UTC)
You know that's not what we're talking about. You're just making yourself appear less than neutral in relation to the articles subject.--Cube lurker (talk) 21:36, 21 January 2011 (UTC)
Note: "can be termed a politician" doesn't mean they should. I think the important thing is that there is no evidence that Sarah Palin does have, or has recently had, any meaningful influence on decision-making nor that she intends to seek a position in the near future that would allow her to do so. And what's wrong with being a former politician anyway? She did her stuff, left her legacy, and then called it quits. No big deal.Tryggvi bt (talk) 21:52, 21 January 2011 (UTC)
She's putting out feelers in Iowa. That shows she's active. --Muboshgu (talk) 21:56, 21 January 2011 (UTC)
So, by the same token, we should call Donald Trump a politician? — Preceding unsigned comment added by Tryggvi bt (talkcontribs) 22:05, 21 January 2011 (UTC)
Sarah Palin wears many hats, one of which is office seeker. Ergo, she is a politician. Buster Seven Talk 21:11, 21 January 2011 (UTC)
Please provide evidence that Palin is seeking office.Tryggvi bt (talk) 21:33, 21 January 2011 (UTC)
Please see below.Buster Seven Talk 02:49, 22 January 2011 (UTC)
If we want to keep going we have SarahPAC Palins still active Political Action Comittee.--Cube lurker (talk) 21:48, 21 January 2011 (UTC)
Right, I forgot about that. Her 2010 efforts certainly count as political, and she'll likely do the same in 2012 whether or not she runs. --Muboshgu (talk) 21:56, 21 January 2011 (UTC)
By that token, many organizations would count as "politicians" because many organizations operate PACs. I guess I always thought of a "politician" as a human individual. I may be wrong. Furthermore, SarahPAC has not supported Sarah Palin in seeking political office. Only other candidates. If you have contrary evidence, please present it.Tryggvi bt (talk) 22:21, 21 January 2011 (UTC)
An outsider's view - I'm Australian. Not American. So I'm the sort of guy who will come here to learn about Palin, but whose opinion makes no difference in US elections. We do get a lot of coverage of Presidential elections here, but nothing on Gubernatorial elections (with one exception that I can recall - Arnie). Naturally the first I heard of Palin was in August 2008. Why? Because of her VP candidacy. I just did a very rough count of Edits to her article. It was created in October 2005 because of her candidacy for Governor of Alaska. There were around 750 updates until her VP candidacy. After that there have been around 14,000 updates to this article. Now, it seems to me that 1. She got an article because she was a politician, and 2. It got much busier because she became a higher profile politician. My guess would be that without her political activities she wouldn't even have an article. I don't have an article, but I'm not a politician. Do you get it yet? That she is not currently in office is irrelevant. Aiming for office was the only reason we care. The fact that much of the media sees her as a viable candidate for 2012 is why this article continues to be of interest. For the purposes of Wikipedia she is a politician, pure and simple. HiLo48 (talk) 22:57, 21 January 2011 (UTC)
Please provide evidence that any non-partisan media sees her as a "viable 'candidate'" for 2012. I'd hate for us to be misinforming foreigners (of which I am one - sort of...).Tryggvi bt (talk) 23:11, 21 January 2011 (UTC)
What a strange request. I've explained my position. The media of which I speak is Australian media describing the fact that her possible candidacy is still a big topic in the US. I don't think partisanship of Australian media in relation to US politics is an issue here. Almost all of ours would be a fair bit to the left of the Democratic Party. HiLo48 (talk) 23:20, 21 January 2011 (UTC)
"Non-partisan media"? Would The Guardian do: "She remains the only star of a Republican party which, despite recent election successes, is still struggling to find a heavyweight contender to take on Obama in 2012. For all Palin's faults she remains a significant contender – as even Dick Cheney acknowledged this week in a rare interview." [5] AndyTheGrump (talk) 23:36, 21 January 2011 (UTC)
Hey, I just realised that I don't even know which direction of media partisanship is being blamed here. Is it, by American definitions, the left wing or right wing (presumably extreme in either case) which is being "blamed" for the view that she is a politician? HiLo48 (talk) 00:11, 22 January 2011 (UTC)
Yes. And while we're at it, if I'm going to be accused of "misinforming foreigners" can I point out that as a Brit, in this context so am I. I didn't revert Tryggvi out of any partisan sympathies one way or another, but simple because the suggestion that Palin had retired from politics seemed so ridiculous. Still at least Tryggvi's edit has achieved on positive thing - a rare consensus on the Palin article talk page the he/she is wrong. AndyTheGrump (talk) 02:06, 22 January 2011 (UTC)
It's worth saying that a lot Australians have an interest in the Palin phenomenon because of its obvious parallels with a populist, female, right wing politician of ours by the name of Pauline Hanson. She emerged on the national stage in the mid 1990s to cause trouble all over the place, ultimately more on her own side of politics. While she isn't in any elected position at this stage, I suspect all Australians would still describe her as a politician. (And that's despite a brief period of fame on the local version of Dancing with the Stars! Has Palin tried that yet?) HiLo48 (talk) 03:30, 22 January 2011 (UTC)
(I was brought here by your condescending edit summary) There is no comparison between Hansen and Palin, other than the fact that they are both right-of-center women. Horologium (talk) 03:49, 22 January 2011 (UTC)
Apologies. Wasn't meant to be condescending. It reflected the fact that I was neither expecting nor demanding that most Americans would have heard of Hanson. If a lot do, I take back that view too. In the eyes of many who are aware of both, including me, there are a lot parallels. But that's politics in democracies. We are allowed to disagree. :-) HiLo48 (talk) 03:55, 22 January 2011 (UTC)
I think your ongoing pursuance of this pointless debate has reached the point of beating a dead horse. --Muboshgu (talk) 23:15, 21 January 2011 (UTC)
For a reliable source, simply check any dictionary. (Wikipedia definitions don't work for these purposes.) I once thought the same thing in a previous, similar discussion, but was proven wrong about the definition. I don't foresee that consensus changing any time soon. Zaereth (talk) 23:27, 21 January 2011 (UTC).
See [6]. There are 1104 related articles. This is not the first discussion of her role as a politician or the media defining her as a politician. Check the archives. Her role in the recent mid-term elections defines her as a politician. Buster Seven Talk 02:49, 22 January 2011 (UTC)
Now, see? If you folks had just started by presenting the evidence that I was asking for from the outset we wouldn't have had to go through this. I'll still reserve my right to disagree since I would not consider "sending out feelers" to be actively seeking office. But, I'm just such a stickler for detail - it can get obnoxious at times. This has been a learning experience though, and that has to have some value in and of itself, right? We've learned that "politically active" equates with "politician" (yay, we're all politicians!). We've learned that users come to Wikipedia to see what they expect to see instead of learning something new. And finally, we've learned that consensus can be reached on Wikipedia by turning something that no one gives a crap about into a debatable issue.Tryggvi bt (talk) 15:46, 22 January 2011 (UTC)
I'm curious. It's possible she will be a candidate at the next Presidential election. (Certainly more likely than you or me.) So then she will be a politician, right? So, you would then have her defined as a politician for a while, then not a politician, then a politician. I still maintain that the only reason she is notable is because of political activities, a lot in the past, a little bit since the last Presidential election, and the possibility that she could be a candidate again. Have I got that wrong? Is she notable for anything else? HiLo48 (talk) 22:14, 22 January 2011 (UTC)
Palin is notable for being a former politician, right? Latecomers to the discussion might not realize that it started because I changed the Palin entry from stating that she is a "politician" to stating that she is a "former politician". I don't see what's wrong with that nor that there's anything problematic with being a former politician that becomes a politician again in the future. Grover Cleveland, the 22 and 24 president of the U.S., was a former president during Benjamin Harrison's term and then became president again, right? No one would say that Cleveland was president while Harrison was president, would they? I really don't see what the problem is here. Take Eliot Spitzer for example - he's a former politician as is stated in his Wikipedia entry. This doesn't preclude him from becoming a politician again later, does it? It seems reasonable to say the same of Palin. But, apparently, as Muboshgu points out, we're just flogging a dead horse here.Tryggvi bt (talk) 22:45, 22 January 2011 (UTC)
But Palin is still getting a lot of media attention, even here in Australia. That's not because of her past (well, it is partly), but because she is seen by many as a potential candidate for President next time round. It really doesn't matter what she says. (I'm sure others have told little fibs at this stage of the "campaign" in the past anyway.) It's clear that many Americans want her to be a candidate. The media would love it too. My point is that her current media attention isn't because of being a former politician. It's because of her potential. If you don't want to see her described as a "current" politician, maybe we need to be a bit more descriptive, and describe her as something like "Former politician and presently the great white hope of the masses". I'm deliberately being a little ironic with my words there. I certainly don't mean those exact words. But I hope you get my drift. HiLo48 (talk) 23:05, 22 January 2011 (UTC)
• One engaged in politics, especially (but not exclusively) an elected or appointed government official.
• A politically active or interested person.
I think she quite clearly meets those particular definitions of the term. I believe this has been the consensus at other biographies, as well. jæs (talk) 23:17, 22 January 2011 (UTC)
AndyTheGrump (talk) 23:37, 22 January 2011 (UTC)
I agree with Jaes' definition. She still is very much engaged in political influence. Even if she was not, people usually refer to notable persons by the profession for which they are most widely known. She will always be known for being a politician. People still refer to her as "Governor Palin," just as people still call Jimmy Carter "Mr. President." It's common to call him the 39th President, but rarely the former president. Paul Hogan will always be considered an actor, even though he hasn't starred in a movie in a few years. Stephen King will always be known as a writer, just as Robinson Risner will always be known as a fighter pilot. Since I still do not see why it would be necessary to place the label "former" on Mrs. Palin, I too find myself leaning toward the "dead horse" conclusion. Zaereth (talk) 23:58, 22 January 2011 (UTC)
So you'll be changing Eliot Spitzer's and other noted "former politician's" entries then?Tryggvi bt (talk) 00:53, 23 January 2011 (UTC)
No, I usually steer clear of political articles. Military aviation is more my cup of tea. Zaereth (talk) 01:22, 23 January 2011 (UTC)
Who? Sorry, but never heard of him. Yes, I know I can look at the article (and will now), but I don't have to look at Palin's to know who she is. The points I've been making are that she is notable (more notable than Eliot obviously) because news of her past and possible future tilts at Office has travelled the world. HiLo48 (talk) 01:16, 23 January 2011 (UTC)
Can someone please provide verification that what is displayed above is, in fact, a horse. Due to the mountainous background it may well be a donkey (which are often used as pack-animals). It could even be a mule. I think we need to be sure before we commit to a definite determination. Also, the caption says "dead" horse. I know it looks dead but feigning death has long been a survival trick of many varied species. Plus, if it is dead...is it still a horse? Buster Seven Talk 00:17, 23 January 2011 (UTC)
This may well be an ass, also. Strange that we don't have any definitive photographs of dead horses being flogged. Nonetheless, even if the mule is no longer active, it's still a mule. jæs (talk) 08:19, 23 January 2011 (UTC)
An outsider's two cents regarding an interesting issue - while both sides have valid points, if you do a cursory search of other one time public servants (Ahhhnold, Jesse Ventura, Steve Forbes) you'll find that Politician is listed. I think that this is likely divided along political lines, and I've got no love for the subject at hand, but she's known for, among other things, being a governor and vice presidential candidate, ergo, she is a politician. Hope this helps a teeny bit.--Williamsburgland (talk) 23:48, 24 January 2011 (UTC)
That's right, although (unless I missed something) the article on Steve Forbes does not say he is a politician, though I think it could. He is an interesting case because he has never held elective office, though he has run for President twice. Since then he has been actively supporting other candidates for various offices, so broadly speaking he is a "politician" rather than a "former politician." To my thinking, "former politician" should be reserved for someone who has actively taken themselves (or been definitively taken out of) the political realm. The aforementioned Elliot Spitzer would be an example of the former; when he resigned as governor, he said he was leaving politics. (Although lately he is starting to sound like he wants back in.) The latter category is exemplified by former Israeli Prime Minister Ariel Sharon. He did not leave politics voluntarily, and at the time of his massive and disabling stroke, was in office and preparing to run for re-election as leader of his newly formed party. Now he is permanently and completely disabled, making it reasonable to call him a "former politician." In contrast, nothing has happened that would make Sarah Palin a "former" politician, as opposed to a politician. Neutron (talk) 00:55, 25 January 2011 (UTC)
This edit claims to remove bias, but instead introduces it. Most public officials who resign due to ethics complaints are guilty. Therefore, to avoid false impression she resigned due to well founded complaints or due to a finding of ethical violations, we need to to mention that the ethics complains were cited by her as frivolous and had all been dismissed. Also, I believe it should be mentioned that she resigned from the Commission job which is an influential position in a state with rich natural resources such as Alaska. A longer term such as 3 to 5 years would be expected, and stating she left after one year, without indicating that she resigned, again leaves the false impression that she was ousted. KeptSouth (talk) 12:07, 28 January 2011 (UTC)
## Christian Science Monitor quiz
per editor request
The following discussion has been closed. Please do not modify it.
.
Woot! 10 out of 10! Now I can counter the wife when she says I've wasted two and a half years here on Wikipedia! :) Fcreid (talk) 09:21, 15 January 2011 (UTC)
You're a lucky man. I also scored 10 out of 10 and my girlfriend was completely unimpressed. JamesMLane t c 14:21, 15 January 2011 (UTC)
Drats! I thought I saw her in Omaha w/ a trombone. So...9 out of 10. I realize now it was probably Tina Fey.Buster Seven Talk 17:00, 15 January 2011 (UTC)
Editor:Jasper Deng wishes to delete this thread. He has made two attempts and they have been reverted. Since I instituted the thread I thought I might comment. Any long-time editor that edits under the Sarah Palin umbrella of articles is sadly aware that, at times, it can be an extremely contentious and confrontational arena. This was merely an attempt to reduce the level of Us vs Them meme that prevails. It doesnt need to stay or, at worst, it will be archived soon. Rather than fight against it I challenge Editor:Jasper Deng to take the test...and post his results. Or would that be too much FUN at an encyclopedia back room??? Lighten up. This isn't the British Museum. Buster Seven Talk 03:52, 31 January 2011 (UTC)
## Source
Might come in handy: http://www.huffingtonpost.com/2011/02/05/palin-america-reagan_n_819073.html
Particularly the statements by Reagan's son might be able to be used in a later version. WikiManOne 18:19, 6 February 2011 (UTC)
## More on Palin's Prior Knowledge of Witch Hunting and funding it
Previous talk page discussions about Palin's knowledge of Thomas Muthee's witch hunting activities pointed out the absence of a reliable source being cited about Palin's knowledge. Therefore unless such a source could be cited about Palin, Muthee matters should only be in the article on Muthee, not Palin. But here is a source not cited at the time of that talk page discussion. According to CBS, Palin saw the video as early as 2000. - “‘What a blessing that the Lord has already put into place the Christian leaders, even though I know it's all through the grace of God,’ she wrote in March 2000 to her former pastor. She thanked him for the loan of a video featuring a Kenyan preacher who later would pray for her protection from witchcraft as she sought higher office.” – CBS News. Here is the link[7] This is information about Palin, not just Muthee. This responds to previous arguments that there is not yet a reliable source on this that is about Palin, but only about Muthee. HkFnsNGA (talk) 21:20, 22 December 2010 (UTC)
I'm not see anything saying that the video was on his witch hunting. Am I missing that?--Cube lurker (talk) 21:35, 22 December 2010 (UTC)
I don't see anything about witch hunting either. And I also don't see how having once watched a video is significant to a biography. Kelly hi! 22:02, 22 December 2010 (UTC)
Cub lurker and Kelly are both right about the video content not being mentioned in the CBS article, but so as not to overwhelm the paragraph in the Palin article, I put the Muthee link so interested readers can go to the linked Muthee article. HkFnsNGA (talk) 22:20, 22 December 2010 (UTC)
Regarding Kelly's second comment, CBS News found her having written what she did about it as being significant enough to be one of the few early Palin quotes they report. HkFnsNGA (talk) 22:20, 22 December 2010 (UTC)
The press reports, and has since she was announced as VP candidate, everything she says or doesn't say, and everything she does and doesn't do. Kelly hi! 22:52, 22 December 2010 (UTC)
Kelly's second comment is correct, too, in that just watching "a video" featuring Muthee and writing praise for it, without a reliable source as to the video being about Muthee's witch hunting, is not significant. It is unlikely that the video is other than the well known 1999 video on Muthee's witch hunting, but the source is ambiguous on this. Another problem with my edit that Kelly deleted is that the CBS News story does not specify that Palin actually watched the video. HkFnsNGA (talk) 23:28, 22 December 2010 (UTC)
I recall from news sources a couple of years back, that before she ran for vp, Palin saw a witch hunting video and then later supported and funded the hunter. If it was not Palin, this would incontrovertably merit placement in an article about a major national level politician. But I do not want to do the work chasing down RS for this if it is not going to end up in the article anyway. So I ask now for objections to including this in the article if there are RS for it. PPdd (talk) 16:57, 3 February 2011 (UTC)
Difficult to answer without seeing what the source actually says. My best advice would be to take a look at this thread, and some of the archived threads on the same topic. Then ask yourself if you think you can find a source that counters the previous objections that have kept this out of the article to this point. My personal belief is that if there was a source that would show that this incontrovertably merited placement in the article we would have seen it by now, but I could be proven wrong.--Cube lurker (talk) 17:16, 3 February 2011 (UTC)
I don't know how to search archives for additional threads. The search software on the history page does not work.
Talk2Action was considered to be NRS by many, but I find that it is meticulously researched (in anticipation of minutea based objections), and I recall stuff on this there, but I also recall hearing about it in mainstream media (although maybe not with all of seeing the Muthee video, and funding Muthee, in one place). PPdd (talk) 17:29, 3 February 2011 (UTC)
About half way down the headers of this talk page there's a search box specifically for this pages talk archives. It's right above the FAQ header.--Cube lurker (talk) 17:34, 3 February 2011 (UTC)
Is there a way to put such a search box on other pages? The issue has come up for me in articles other than this one. PPdd (talk) 17:38, 3 February 2011 (UTC)
Looks like this template does it. `{{Round In Circles|search=yes}}`. There may be others with different wording as well. Not 100% sure.--Cube lurker (talk) 17:50, 3 February 2011 (UTC)
If you just want a simple search box for any web page, (not specifically for archives), I often find control+F to be very useful. Zaereth (talk) 17:55, 3 February 2011 (UTC)
### Montreal Radio DJ Prank Sarkozy Call to Palin
I have changed the reference for this from one of the many youtube recordings of it to an MNSBC mainstream news report that also includes the recording. I wonder whether a CBS official youtube channel recording would have filled the bill ? The Johnny Halliday and the baby phoques are highlights that should maybe get particular mention ?--— ⦿⨦⨀Tumadoireacht Talk/Stalk 08:42, 5 February 2011 (UTC)
There was a lengthy discussion on this in the past, please see here. Consensus strongly indicated the content, while amusing, was not biographical. I think time has only reinforced that determination. jæs (talk) 20:46, 6 February 2011 (UTC)
Agree w/ Editor/jaes. Buster Seven Talk 20:53, 6 February 2011 (UTC)
I have now read that discussion-Consensus indicated nothing of the sort-the Naysayers simply wore down the Inclusionists as so often happens elsewhere on this site. Mentioned worldwide in National Newspapers and coming on the heel of several disaster interviews and crushing parodies,it forms part of the tapestry of the tale of her fall from grace and is again particularly relevant after the recent gun sights and blood libel fiascos. I suggest that the revert be undone to allow the consideration of its impact over time to take place as suggested in the original debate. Time has reinforced some determination( to conceal it ?) alright but I am suspicious of what prompts it and the wobbly rationale proffered--— ⦿⨦⨀Tumadoireacht Talk/Stalk 01:45, 7 February 2011 (UTC)
[citation needed]jæs (talk) 04:26, 7 February 2011 (UTC)
It's been reported on by the telegraph as well. just sayin WikiManOne 19:20, 7 February 2011 (UTC)
Sourcing that the event occurred wasn't the issue in the prior discussion. The issue was that there was no sourcing indicating the prank has had a lasting biographical impact on Palin or her public image. Time hasn't resulted in any significant additional coverage, as best as I can tell. jæs (talk) 19:25, 7 February 2011 (UTC)
## Recent attempts to add Category
Discussion is going nowhere, and has already been addressed at two noticeboards.
The following discussion has been closed. Please do not modify it.
Editor:Userpd has pursued Admin:Horologium and brought up charges at AN/I and NPOV/N. At both venues it was suggested to bring the conversation to talk:Sarah Palin. Here are some facts.Buster Seven Talk
1. Initial attempt by Userpd to add Category.[8]
2. Revert by Editor:Collect w/ clear edit summary. [9]
3. userpd reverts Editor:Collect. Provides questionable source. [10]
4. Editor:Buster7 reverts userpd. Radio Netherlands not reliable. [11]
5. userpd reverts Editor:Buster7. userpd questions B7's Good Faith. [12]
6. Editor:Fcreid reverts userpd. "no mention of membership or affiliation". [13]
7. userpd reverts Editor:Fcreid. [14]
• Retreaved from userpd's talk. Outreach by Editor:Buster7 to create consensus. Userpd was not interested.
[16]
• Retreaved from Editor:Fcreids talk. Note timestamp. Courtesy notification following Fcreid's revert.
[17]
Seems like userpd might deserve a block of some sort... WikiManOne 20:23, 6 February 2011 (UTC)
Beyond that I disagree vehemently in principle with your quest to categorize people having "anti-Islam" sentiment, coupled with the fact that this quest apparently leads you only to the Sarah Palin article, there is actually a very simple solution which I and others have advised you multiple times. If this claim is true, it should be sourced in multiple places. Palin is a major American political figure. Not a day goes by without an article about her in the media. Find a source for this claim in a mainstream U.S. news outlet. I doubt a single person here would even consider this claim using the source you've provided. Fcreid (talk) 21:18, 6 February 2011 (UTC)
So you're against if I'm listing people to this category because it won't suit them (allegedly) due to personal interests of some editors? If you really against people being listed to this category, then why don't you go there and start removing them from it?, apparently you're not going to do that, as if this category exists for such a long time, that means people can be added here. If I had other sources, I'd provide it, the WP: Notability guideline however doesn't state that it's required, it's required for the source to be reliable, yes and the source is pretty much reliable. Userpd (talk) 21:26, 6 February 2011 (UTC)
Oh yeah, I should get block now? Why shouldn't get block these two (Buster7 and his "friend" Fcreid) that didn't bother to tell exactly why this source is unreliable? Maybe you would have a point if I reverted the admin's edit and continued further without providing arguments, but none of these had taken place. Every my edit is with summary. And after admin's Horologium edit (who turns out doesn't care if the same sort of information is in Wilder's article) I grasped my willingness and tried to sort out this case. here. Note, I couldn't catch up with the time to reply to the latter posts till this case was closed. Here it's clear you're biased to their side and look from their point of view, hence you're not to judge this case. You're not neutral at all. Userpd (talk) 21:04, 6 February 2011 (UTC)
Let's go over this, again:
the source: "the organisation Stop Islamization of America, which is supported by a number of conservative US politicians including Newt Gingrich and Sarah Palin". Now, according to WP: Notability Radio of the Netherlands has appeared on many mainstream publications, in books and in BBC. Okay, even if we assume that it's not reliable, the admin Horologium who wanted this category to be removed from here, was totally ok of the same information being in Wilders' article. He, as an admin, should approach to the same content in two different articles equally. He didn't do that. He only removes it from here, I understand, maybe this article is in his watchlist or he monitors it, but he's an admin hence should be hold accountable. That's why I'm not questioning Fcreids and Buster7 neutrality and responsibility before wikipedia, because they're not obliged to be neutral as much as admin. Userpd (talk) 21:19, 6 February 2011 (UTC)
It has nothing to do with neutrality, but with standards. As jæs states below, I expect near unanimity in opposition based solely on this source, and people of every political bent monitor this page. If your gripe is with Horologium, work that out on talk, but it appears your issue with him already failed to gain traction on the noticeboards. If your goal is to find a basis for categorizing this and other persons as "anti-Islamic", find better sources and be sincere in your editorial objectives and standards. (For example, I see that you've never attempted to categorize Newt Gingrich using this same source, although he's mentioned in the same breath... why not?) Fcreid (talk) 22:10, 6 February 2011 (UTC)
Including this category will require multiple reliable sources quite explicitly stating what it is you're trying to add, and the sources above don't seem to establish that anywhere near the level that would be required. You've been advised of this, so I don't see any path forward for you without sourcing, and I really don't see that sourcing out there today.
That being said, I think there should be some sort of barnstar award created here. First for your brazen, fearless edit warring, clearly in contravention of wp:blp on an article covered by article probation. Second, for uniting the folks who edit this article from virtually every viewpoint against your edit warring. That's an incredible accomplishment in and of itself. jæs (talk) 21:29, 6 February 2011 (UTC)
Hear! Hear!Buster Seven Talk 21:39, 6 February 2011 (UTC)
Have you read my post right above your post? Let's assume it's not enough, where am I not right when I said that an admin should treat equally the same content in two different articles? Admin can't be careless! He should be interested in keeping articles clean and neutral. He only selectively kept it neutral when removed the content based on this source only from this article and did nothing about it in another article Userpd (talk) 21:45, 6 February 2011 (UTC)
You may as well drop it, Userpd. The sources aren't reliable enough. And even if they were, the mere fact that someone wants to stop or prevent Islamization of America doesn't necessarily mean they're anti-Islam; it could instead mean they support peaceful coexistence and mutual respect, instead of conquest by one religion (Islam) over another.Anythingyouwant (talk) 22:12, 6 February 2011 (UTC)
How is it unreliable? Radio Netherlands Worldwide is one of the top five international broadcasters alongside the BBC, Voice of America, Radio France Internationale and Deutsche Welle, is a key partner of BBC. and has a long standing history. Userpd (talk) 12:45, 7 February 2011 (UTC)
Categorization of living persons must be done with exceeding care. The attempt here was not done with care or regard for WP:BLP and the persistence of the person insisting on the categorization is a potential problem for WP, especially considering the person appears quite alone. I would also note that David Cameron would fit the same "category" using Userpd's rationale. In short, the category has zero support among other editors. Collect (talk) 22:38, 6 February 2011 (UTC)
This is from what I wrote at NPOVN: If Category:Anti-Islam sentiment is applied to an article about person X, what does that tell us about X? X once said something that someone interpreted as expressing anti-Islam sentiment? X frequently makes such statements? X has devoted a significant part of their life towards expressing anti-Islam sentiments? Once we settle that, what is an "anti-Islam sentiment"? Essentially, a category like that is meaningless (or has such a wide range of possible interpretations that the result is unhelpful). Also, there is no useful technique to decide which people should get this label (because it is a category invented on Wikipedia and so cannot be verified by reliable sources, meaning that applying this category would always involve OR where an editor interprets what a reliable source says as meaning "anti-Islam sentiment"). Johnuniq (talk) 23:13, 6 February 2011 (UTC
Userpd is an obvious special purpose account who appears through the accounts editing history is only trying to pervert some sort of POV into the project. We don't add a category that Palin hates Muslims just like we don't add a category that Obama is socialist. Neither is appropriate. Userpd should be reprimanded and if the POV pushing continues, should be blocked.--Jojhutton (talk) 23:19, 6 February 2011 (UTC)
I tend to agree fully with Johnuniq, and other sentiments, that catagorization of people is nothing more than a perfect venue for McCarthyism. I don't think, as editors, it is our place to put labels on people. I also agree that such a claim would require some extraordinary sourcing, and even then, a really good argument as to why it would be biographicial in nature. The burden is on those who want it in, and not the other way around.
To Userpd, I'm not sure that you understand exactly what an admin actually is or does. In essense, an admin is just an editor like you and me, who happens to have a few extra buttons they can push. Horologium has been an editor on this article even before he became an admin, and so a conflict of interest prevents him from using his admin tools here. To my knowledge, he never has, and so in this capacity, he is just another editor just like the rest of us. Zaereth (talk) 23:34, 6 February 2011 (UTC)
From Wikipedia:Advice for new administrators: "Paying careful attention to our core policies, Neutral point of view...". Clearly, having granted an adminship he has to be neutral, which means he should have deleted this inappropriate (by his opinion) sort of information from both articles, not just from this only. Userpd (talk) 12:45, 7 February 2011 (UTC)
To add such a cat would need to be a major part of her notability and there would need to be content in the article that supported the claim. There is nothing that supports this cat at all. So she opposes the construction of Park5, this clearly is barely worthy of any discussion at all. I also support User:Jojhutton comments that the Userpd needs to stop pushing for this inclusion, and notice that there is no support for it at all. Off2riorob (talk) 23:47, 6 February 2011 (UTC)
You have wrong interpretation of what this category is. It doesn't necessarily list people who "hate muslims". For example, Geert Wilders is listed there because he's opposed to Islam, not to muslims. Although, he has made anti-Muslim statements in the past. But that's out of the question here. As for your baseless accusation that I'm doing something which is in violation to the rules, I would ask you to refrain from it. That's not the proper way of conduct at talkpages. Userpd (talk) 18:41, 7 February 2011 (UTC)
I agree with Userpd's desire to include this category-the arguments offered against it keep shifting their ground and also stray frequently into ad hominem attempts to undermine his compellingly well presented evidence for inclusion. Recommending blocks for calmly advanced reasoning is counter to the spirit of the project and is tantamount to bullying.
The similar argument just above about including a short sentence referencing Palin's performance on a Montreal radio show prank call,is ongoing and trots out the same tired and misinformed references to the same selected bits of policy articles. Let us give readers some credit for being able to make up their own minds about what is significant and let us assemble articles unpruned by the partisan--— ⦿⨦⨀Tumadoireacht Talk/Stalk 02:06, 7 February 2011 (UTC)
────────────────────────────────────────────────────────────────────────────────────────────────────
As best as I can tell, the two of you are very much trying to push readers to make up their minds in one direction, by stating as fact that Palin is inherently a part of "anti-Islam sentiment" — with ridiculously flimsy sourcing. I can give you more than a few "bits" of more than a few policies that make it pretty clear that's unacceptable. You might notice that's why every other editor here isn't jumping on your particular bandwagon. jæs (talk) 04:33, 7 February 2011 (UTC)
I would add my name to the list of editors above who feel that the single source being presented does not provide a clear basis for including SP in the anti Islam category. I would also add that there seems to be a clear consensus on this issue.-- KeithbobTalk 16:22, 7 February 2011 (UTC)
Include me in the consensus too: an utterly inadequate source for the claims being made. AndyTheGrump (talk) 16:38, 7 February 2011 (UTC)
Well, the source is reliable, so at least it deserves a one-sentence mention in the article. Userpd (talk) 18:27, 7 February 2011 (UTC)
No it doesn't. And there is no such thing as a 'reliable source' in the abstract. Reliability can only be judged on what the source says about a particular thing. The overwhelming consensus here is clearly that this is far too poorly sourced for such a contentious claim. It isn't going to be included unless this is repeated in mainstream sources, so stop wasting everyone's time here. AndyTheGrump (talk) 18:36, 7 February 2011 (UTC)
I disagree with the whole concept of such a category, but as long as you're going to have it, it seems pretty clear Sarah Palin should be on it. I don't see why this is such an issue. [18] [19] WikiManOne 18:42, 7 February 2011 (UTC)
AndyTheGrump, as you might notice, I wasn't the one who started this discussion. I made a section at admin's neutral point of view noticeboard where provided the evidence of the admin Horologium's non-neutrality in approach to the same content in two different articles. Seeing how reluctant other admins there (none has responded to this section), I just lost a bit of willingness to do next step in this case (which would have been an attempt to reason here so that this information would have been put into article) Userpd (talk) 18:57, 7 February 2011 (UTC)
It's pretty clear Sarah Palin contributes to anti-Islam phobia. I don't see why this is an issue, add the damn category. WikiManOne 18:58, 7 February 2011 (UTC)
Actually, I think the category might well be potentially libellous. What is the correct procedure to move it for deletion? AndyTheGrump (talk) 19:11, 7 February 2011 (UTC)
──────────────────────────────────────────────────────────────────────────────────────────────────── Start a category for deletion discussion. As long as such a category exists though, Palin should be on it. WikiManOne 19:14, 7 February 2011 (UTC)
Unless Palin moves clearly in anti Muslim or Islam direction and it becomes part of her notability there is no chance at all of adding it here. None at all. Off2riorob (talk) 19:19, 7 February 2011 (UTC)
Did you even read my two sources? People are listed in categories with much less sources than that. There are now three mainstream sources that list her as anti-islam, she already is anti-muslim and it is part of her notability. WikiManOne 19:22, 7 February 2011 (UTC)
Not wanting your country taking over by another race or religion doesn't mean you don't like them, its just normal. add her to American politicians that are against the Islamification of America - Off2riorob (talk) 19:26, 7 February 2011 (UTC)
But trying to create a phobia that such a take over is occurring when it clearly isn't is just called anti-islam sentiment. I feel very tempted to break Godwin's law right now as the parallels are obvious. WikiManOne 19:28, 7 February 2011 (UTC)
WikiManOne, you originally suggested that Userpd should be blocked for trying to add this category and now you go and add it anyway yourself against concensus and probably against WP:BLP? Just exactly what point are you trying to make? Arzel (talk) 19:33, 7 February 2011 (UTC)
Let's see if we can make this clearer: if either of you add the category, it will be removed as being clearly unsupported by reliable sources and against firm consensus. Unless or until you bring forward more compelling sourcing, I don't see any reason in continuing to go around and around in circles. If you disagree, begin an RfC. Best of luck. jæs (talk) 19:31, 7 February 2011 (UTC)
She's against Islam as a whole, she's against Mosques in the streets (Stop Islamization America's goal is to stop construction of mosques and everything related to Islam). It's not like she's against "islamic terrorism", she's against Islam. Besides the category "Anti-Islam sentiment" isn't that libelous because of the word "sentiment". If it was just "Anti-Islam", then it would be more libelous. Why are you so afraid of her image? If she possesses herself and participates in actions against "Islamization" (veiled messages such as: America to stay Christian etc.) Userpd (talk) 21:33, 7 February 2011 (UTC)
Here is a remarkable statement from AndytheGrump: 'Reliability can only be judged on what the source says about a particular thing ' -Corollary -we only reference statements we like from the NYT ?--— ⦿⨦⨀Tumadoireacht Talk/Stalk 22:05, 7 February 2011 (UTC)
Ahh, the accusation of bad faith, what would SP talk be without you? I too find the claim that a single line in a radio broadcast saying "Sarah Palin supports this organization" means that she has anti-islam sentiment to be remarkably weak even for this page, and believe me, we have seen some really weak RS claims on this page. I firmly disagree with the inclusion of the category in question on this page, and, if anyone puts that cat up for deletion, please let me know, i will happily argue for deleting such a vague and dubious category. Bonewah (talk) 22:21, 7 February 2011 (UTC)
Yes, it is up to us, the community, to determine the reliability of any source. We can reference an article from the NYT, but not an opinion piece. We can also compare sources for accuracy and trace them back to the original. A reliable source will properly attribute any opinion. We must also determine which source is more reliable for a particular subject. For instance, a newspaper article about gravity will almost assuredly be less reliable that a book on astrophysics regarding the same subject. A tour guide book of the Chesapeake Bay Area may be a good source for articles about that area, but not so much for articles about aerial combat.
Once again, you'll need to provide sourcing that explicitely states this opinion. I assume we're not mind-readers here, and are incapable of knowing another's personal thoughts, so, unless she has stated so directly, this opinion would need to be attributed properly to satisfy the reliability requirements.
The significance requirements for this article are pretty high, so anything brought in must be compared for relative wieght. In other words, has it recieved as much coverage as, say, troopergate or the other stuff in here. This is an extraordinary claim, and would need to be backed up with some extraordinary sources.
Any claim like this should be related to factual representation, and not personal opinion as to motive. For instance, in the Elvis article, it would be rather presumptuous to say he liked peanut-butter and banana sandwiches unless he stated so directly. It would be factual, though, to state that he was known to eat such sandwiches. (I don't like salad, but I eat it.)
Upon satisfying the requirements for verifiability, reliability, significance, and weight, you will then need to show relevance, not only as to why this opinion is particulary relevant to the subject as a whole, (as opposed to all of the other opinions out there), but also as to why it is appropriate for a biography and not to, say, the "political positions" or some such article. As has been previously stated, it is up to you to do this leg-work, provide the sources, and garner consensus for it. So far, we're not even close. Zaereth (talk) 22:42, 7 February 2011 (UTC)
(out) Just wanted to drop in and "not vote" my own opposition to the tagging of this inflammatory category on the SP article. In particular, I'd like to respond to the following argument by Userpd:
"Material from reliable non-academic sources may also be used, particularly if it appears in respected mainstream publications. Radio of the Netherlands had appeared on many respected mainstream publications, examples: book, bbc, external link"
Now, read literally, and, I think, correctly, this policy seems to state that material from reliable non-academic sources may be used if the specific material itself, and not merely the non-academic source in general, has appeared in respected mainstream publications. In other words, the fact that Radio Netherlands itself has been referenced by respected mainstream publications on other subjects does not mean that it's rubber stamped as a reliable source. Rather, if the actual Radio Netherlands material which alleges the negative connection with Palin – upon which her purported membership in the category is based – has appeared in respected mainstream publications, it may be eligible to be considered reliable. But if that were the case, I don't think this debate would be taking place, because you'd have yourself a reliable source. Thus, without having parsed every word of this talk page discussion and related noticeboard/userpage comments, I feel pretty confident in agreeing with the apparently vast majority of other editors here who think that the fitness for inclusion of this category remains unsubstantiated by the satisfactory reliable sourcing which would be required for such a potentially inflammatory or libelous claim. Cheers all. Factchecker atyourservice (talk) 23:45, 7 February 2011 (UTC)
I think it's time we bring Hitler into the conversation. Let's pretend, for arguments sake only, that Sarah Palin liked the stylized apparel of the SS Stormtroopers. Would we then be obligated to include her in the Category:Nazi Sympathizers? Surely, this would be slanderous as well as libelous. Unless there was evidence of more than just an eye for fashion. We, the wikipedia editors, would need an enormous amount of factual documentation in order to permit such an outrageous claim. For our times, this desire to categorize Palin as anti-Islamic carries a burden of proof that is more than ordinary. It is clear that a sizable and abundant plurality of editors that have chosen to comment are against inclusion of this category.Buster Seven Talk 00:09, 8 February 2011 (UTC)
What defines the reliability of the source? And how RNW isn't being applied to these definitions. Userpd (talk) 11:32, 8 February 2011 (UTC)
────────────────────────────────────────────────────────────────────────────────────────────────────We don't even need to Godwinize the debate; we can go over the top in a much more relevant way, tailored to the particular discussion in a way that I think that some of the editors who support the inclusion can understand. The article states that Palin supports a group which supports Wilders, therefore Palin is just as much an anti-Islamist as Wilders. Hmmmm...Barack Obama appointed Van Jones, who is a truther, to a high-level staff position, so we should add Barack Obama to Category:9/11 truth. That is exactly what is being pushed here, and it's just as preposterous. FWIW, a quick search for "Palin" at the link in the RNW article that is ostensibly being used to support the addition of the category to Palin's BLP returns no results at all. Note also that there is still absolutely no mention at all of this issue in the article on Palin, which is an ironclad requirement to add any category (especially a contentious or potentially libelous category) to a BLP. You cannot add categories which are not discussed in the article for any reason whatsoever, and a mention on the article on Geert Wilders does not give Userpd carte blanche to use it here. He is either unwilling or unable to grasp this simple concept, since he has been told this on no fewer than three separate pages (AN/I, NPOVN, and this page), and yet he is still arguing the same point.
As for his fatwa against me because I am an admin, it doesn't matter at all because I am not (and have not) acted as an admin on this page, except for the one time where I restored semi-protection after full protection expired. I am far too involved as a regular editor to act in an administrative capacity, and his tedious attempts to try to impose the standards of an uninvolved admin on me are singularly unproductive and unrealistic, a total red herring used to obscure his attempts to push a PoV on this article with no solid sourcing. (Note that I am not in any way questioning RNW as a source; I am stating that the source does not make the conceptual leap he is making to tie Palin to the category.) Horologium (talk) 01:11, 8 February 2011 (UTC)
Therefore? That's your own point. Not necessarily, but the fact that she supports the same organization as this prominent anti-Islam politician indicates that she is anti-Islamic as well. Above were provided reliable sources wherein she had been making anti-Islamic remarks. And hey, look from the bright side, maybe SP's opposition to Islam isn't a bad thing? It will definitely help her gain votes among conservatives / people who sympathize with some aspects of conservatism if she's to run for presidency again. Userpd (talk) 11:28, 8 February 2011 (UTC)
"the fact that she supports the same organization as this prominent anti-Islam politician indicates that she is anti-Islamic as well". Really? Well since Godwin's Law has already been invoked, let's apply this 'logic' elsewhere: Hitler liked dogs. Barack Obama likes dogs. Therefore Obama is a Nazi! Brilliant! And BTW, please don't imply that those opposing your ridiculous campaign to include the dubious category as 'conservative' or 'Palin suppporters': I for one am anything but. AndyTheGrump (talk) 12:17, 8 February 2011 (UTC)
That's a red herring, it depends on what one supports not just "likes". And there are many related aspects such as her previous anti-Islamic views or criticism or else. Uhm, campaign? Put off your tinfoil hat. And no, it's not as dubious as "conservative" or "Palin supporters". The latter don't even exists as a category, and unlikely will be. Userpd (talk) 15:14, 8 February 2011 (UTC)
@ Userpd. The reliability of a source depends on context. Each source must be carefully weighed to judge whether it is reliable for the statement being made and is the best such source for that context. In general, the more people engaged in checking facts, analyzing legal issues, and scrutinizing the writing, the more reliable the publication. Sources should directly support the information as it is presented in an article, and should be appropriate to the claims made. Go to Wikipedia:Identifying reliable sources for more education. If you continue to reject and dismiss what represents a large portion of Wikipedia thought, your career here will be quite unhappy...unless rejection and dismissal is what you're after. Change your mind and you will change your experience. Also, BTW, contrary to what you have implied, I am also not a Palin supporter. Buster Seven Talk 12:41, 8 February 2011 (UTC)
Buster7, use wiki-markup while replying at discussions properly, because it looks as you're responding to AndyTheGrump, you should've used one ":" less in the beginning of your text. No, reliability of the source doesn't depend on that. You probably wanted to say: to include an (controversial?) info from a reliable source, this info should also appear on other reliable sources. Userpd (talk) 15:14, 8 February 2011 (UTC)
This is going nowhere Userpd clearly doesn't understand WP:V and consensus, and should read WP:NOT#FORUM too. I tried to collapse this section, but can't seem to get it to work. can someone else do the honours. (Userpd, if you are unhappy with this, take the argument elsewhere - you are wasting your own time as well as everyone else's here). AndyTheGrump (talk) 15:31, 8 February 2011 (UTC)
And you can't read what your opponents say. See above, I already told you regarding your link "NOT FORUM". at 8:57, 7 February 2011, if you've overlook it, I will make you a courtesy and quote myself: "AndyTheGrump, as you might notice, I wasn't the one who started this discussion." Userpd (talk) 16:15, 8 February 2011 (UTC)
Note: I started this discussion at the request of Administrators at prior discussions at AN/I and NPOV/N. I now end it.Buster Seven Talk 18:12, 9 February 2011 (UTC)
## For general consumption
For any future confrontations and/or wranglings this may come in handy. Clear, concise, precise.
Thanks Buster. Also, for some more detailed information on evaluating sources, the book Reference service and sources gives some good information. See section seven, eight and part 2. Zaereth (talk) 22:29, 9 February 2011 (UTC)
## Is it time we had a project for Conservatism?
You Betcha! Click here -- Lionel (talk) 22:39, 12 February 2011 (UTC)
## Bogosity check
The infobox lists Palin as the 5th mayor of Wasilla. You might want to double check that. Wasilla had at least 4 mayors prior to those which are listed on the Wasilla page. Wasilla started out as a second-class city, which elects its mayors from amongst the city council membership. About ten years later, it became a first-class city, which popularly elects its mayors. I believe that Bumpus was the first popularly-elected mayor. I previously pointed this out on Wasilla's talk page in May of last year, but I suppose that people quit paying attention once Palin's association with Wasilla wasn't so flavor-of-the-month.RadioKAOS (talk) 03:12, 24 February 2011 (UTC)
The article on Dorothy Page states that she was mayor of Wasilla, which isn't reflected in the list or anywhere else on Wikipedia that I've seen. I believe Bumpus died while in office. Page could have been acting mayor. Once again, it appears that the Google wizards have no clue about any of this. I'll see what time I have to dig up non-web-based sources.RadioKAOS (talk) 07:01, 2 March 2011 (UTC)
## Resignations
Prior to Editor:Kenatipo's Feb 17 changes, the article stated that Palin was the only elected governor to have resigned from every governmental position {that she had held) prior to the expiration of the various offices tenure. The Kenatipo changes shifted the focus from repeated resignations by one governor to a history of resignations from the Office of Governor of Alaska by many (5, 6, maybe more). The insertion of one should not have cancelled out the other as it really is two seperate observations. Both facts should be included. The edit summary for the change speaks to "putting it in historic context". That may well be, but it is not necessary to hide other historic facts (ie, the repeated resignations by a single ex-governor) in order to inumerate how many Alaskan governors have quit. Both observations should be shared with the reader. Buster Seven Talk 15:02, 17 February 2011 (UTC)
Upon further reflection , I thought to myself, "How can Alaska have 5 or 6 Governors that resigned since it has only been a state since 1959?" If we leave the article in its present state, the reliability of facts that readers/teachers/students get from this WP article will be questionable. There have been 2 individuals that resigned from the office of Governor of the STATE of Alaska. That is not what the article states. Buster Seven Talk 15:29, 17 February 2011 (UTC)
I agree that the resignation of territorial governors and state governors is an apples and oranges comparison. Alaskan territorial governors were appointed by the President of the United States. As political appointees, it was expected that they would offer their resignation to a newly elected president so that the incoming administration could appoint someone better aligned with the goals of the incoming administration. State governors are elected by the residents of the state. As a result, they are answerable to their local population and not to the sitting U.S. President and would not be expected to resign with a change of administration in Washington D.C. --Allen3 talk 16:08, 17 February 2011 (UTC)
Note:See [20] for reversion of both lede mentioning of resignations.Buster Seven Talk
At least we agree that the prior statement was factually incorrect: Sarah Palin was the second governor of the state of Alaska to resign since statehood. Don't agree that it's apples and oranges; a governor is a governor whether appointed, elected, of a territory, protectorate, state or whatever. I also wonder about the POV of insisting that SP resigns frequently. Bottom line, I like the current version. --Kenatipo speak! 19:07, 17 February 2011 (UTC)
Off topic: is it just my computer and ISP, or is it taking the SP article page a long time to reload? --Kenatipo speak! 19:11, 17 February 2011 (UTC)
Not sure but I think the length of time has to do with the sheer volume of info, history, etc. that has to be dragged with it. Buster Seven Talk 19:34, 17 February 2011 (UTC)
Thanks. Glad to know it's not just me! --Kenatipo speak! 20:38, 17 February 2011 (UTC)
The "apples and oranges" difference comes into play because the "prior to statehood" governors were appointees that were expected to resign with the change in Washington DC administrations. After 1959, Governors were elected not appointed. Apples and oranges. Buster Seven Talk 19:41, 17 February 2011 (UTC)
The facts seem to keep intruding here: #1 resigned because of "fraud", #2 because he was Canadian, #3 because he was "unhappy", #4 to run for US Senate, #5, Wally Hickel, to be Sec'y of Interior, and #6 because she was hounded out by political enemies. None of the first 4 (except, possibly #3 ??) were pro-forma resignations of appointees. --Kenatipo speak! 20:38, 17 February 2011 (UTC)
I personally don't see either characterization as significant, especially in the lead. The original edit was an attempt to "invent a category" that suited a POV, i.e. to substantiate the "Quitta from Wasilla" mantra that permeates in some parts. From any perspective, that presentation of facts in the originally edit was purely WP:OR. (The only person to quit all government positions? C'mon!) The second set of facts was a conspicuous attempt to place that resignation in an historical context by qualifying with facts that others have resigned the office previously (before or after Alaskan statehood). Neither points belongs in the lead or, possibly, the article... and both points, absent secondary sources, are pretty clearly OR. Fcreid (talk) 23:49, 17 February 2011 (UTC)
I agree. As I said earlier, I like the lead the way it is, without either "first to resign" or "sixth to resign". Which brings up another point: the lead should be a summary of article contents. Was the claim that SP was the first to resign in the body of the article, or only in the lead? --Kenatipo speak! 00:33, 18 February 2011 (UTC)
I concur with Fcreid's reasoning about both sides of the debate. Palin is far from the first official to have resigned from high office (see John N. Irwin for an example of an official who resigned as governor twice and in such an ethical manner that it caused troubles for the U.S. Treasury). As for the "historical perspective" addition, the choice of 1906 (during the middle of the District of Alaska period) seems to be a highly unusual start for a sampling period. --Allen3 talk 00:52, 18 February 2011 (UTC)
There's no mystery about the starting point of the sampling period. I went to List of Governors of Alaska. Alaska has had a governor since 1884 as District, Territory and now State. According to the note in the chart, Brady was the first governor of Alaska to resign. I also concur with Fcreid; neither point belongs in the lead. --Kenatipo speak! 02:11, 18 February 2011 (UTC)
The first governor of the District of Alaska to resign was John Henry Kinkead, not John Green Brady. --Allen3 talk 04:07, 18 February 2011 (UTC)
Damned Wikipedia! You just can't trust it! --Kenatipo speak! 16:49, 18 February 2011 (UTC)
So that makes SP at least the 7th governor of Alaska to resign! I think (and I'm guessing here) that the Notes in that article, insofar as they involve appointees, are about resignations that were not pro-forma. (I like the lead the way it is regarding this issue.) --Kenatipo speak! 04:24, 18 February 2011 (UTC)
A comment on process, mostly directed to Locke's Ghost: Ideally, the place to start with your addition of "first elected governor" would have been the Resignation of Sarah Palin article. If it flies there, then it can be in the relevant subsection of this article, and, if it's notable enough it can be mentioned in the lead of this article. Ideally speaking, of course. --Kenatipo speak! 16:49, 18 February 2011 (UTC)
### courtesy break/hagiographic
• This debate is kinda twiddly. Fact: She resigned before her term ended. Fact: It is very, very notable that she did so. Fact: She is also the only governor of the STATE of Alaska to resign without continuing on in some other aspect of government service. Fact: This is also notable. I am not seeing any debate on these issues as being grounded in fact.If they are not grounded in fact, then what are they grounded in? Will restore text tomorrow or so. Thank you for your time and trouble. GlitchCraft (talk) 10:08, 6 March 2011 (UTC)
• Get a consensus for doing such first. At this point, I would suggest that your proposal lacks consensus. Collect (talk) 11:27, 6 March 2011 (UTC)
• Wikipedia:Verifiability trumps WP:CONSENSUS, lest we become hagiographic – as we are indeed doing. Will restore text as per WP:V tomorrow or so. Thank you so much for sharing. GlitchCraft (talk) 13:08, 6 March 2011 (UTC)
• I think your misconstruing WP:V. Just because its verifiable, doesn't mean that it should go in, especially without a consensus. Canyou imagine how huge these article would get if anything that was ever printed was allowed to go in to the articles against consensus?--Jojhutton (talk) 13:24, 6 March 2011 (UTC)
• You are the one who misconstrues Wikipedia policy. You are patently advancing a straw man argument. WP:UNDUE and WP:TRIVIA are the filters against your implied reductio ad absurdem. Indeed, the latter are so clearly applicable to your objections (and so clearly irrelevant to the present case) that your reductio ad absurdem is, well, absurd... The details of her resignation are patently notable, obviating any recourse to UNDUE or TRIVIA; and WP:V still (and always and everywhere) trumps WP:CONSENSUS... Will restore text tomorrow or so, lest we become hagiographic. Thank you so much for sharing. GlitchCraft (talk) 14:18, 6 March 2011 (UTC)
• I don't usually do this, but the temptation in this instance is just too tempting that I simply can't help myself. I'll take my three years experience and 22,000+ edits over your 19 edits as a pretty good indication that I may know a bit more about wikipedia policy and how it is implemented than you do. But who know, I may be wrong.--Jojhutton (talk) 14:55, 6 March 2011 (UTC)
• What have we here. A new way of indenting? @ User:Glitch Craft. Thanks for the new word in my lexicon. But, I suggest you take your boxing gloves off and 'set a spell'. I had the same response as Editor:Jojhutton and I'm sure we 2 are not alone. Collaboration is the operative word at this article. You might want to hold back on your threat to re-introduce material without collaborating with your fellow editors...just as a gesture of good faith. Buster Seven Talk 15:12, 6 March 2011 (UTC)
I'll break the ice is this is actually a legitimate discussion and not just trolling... Fact: She resigned before her term ended. Agreed. Fact: It is very, very notable that she did so. Agreed. Fact: She is also the only governor of the STATE of Alaska to resign without continuing on in some other aspect of government service. Maybe. What sources do you provide to proclaim so, as others above have provided differing sources above? Fact: This is also notable. Disagree. You'll need to demonstrate why this is notable, e.g. did it receive extensive media coverage, has it been key to her overall notability, etc. What's makes it any more notable than, say, being the only Alaska governor to do so with size 6 shoes? Fcreid (talk) 16:01, 6 March 2011 (UTC)
• If a Governor resigns without cause, that is so inherently notable, that merely questioning its notability passes the sniff test for POV-based editing. I'll play along with this discussion for another day or so, but the text belongs in the article and in the WP:LEDE. As for calling me a troll... please do not make such accusations unless you can make them stick. As for pointing out that my indenting habits differ from yours, thank you for your kind assistance, but you might be better off spending time looking at File:Graham's Hierarchy of Disagreement.svg, and determining where on the pyramid that sort of comment belongs GlitchCraft (talk) 23:45, 6 March 2011 (UTC)
The article already covers the resignation prominently, with even greater detail provided in the resignation sub-article where details on that topic belongs. In addition, the reason (or "cause") for her resignation is also presented in both articles. I've requested you not only provide reliable sources for the specific claims you're making, but also that you explain the notability for inclusion of what seems, at least on the surface, a contrived categorization that I've never seen discussed in mainstream sources. I don't think that's an unreasonable threshold for inclusion. Fcreid (talk) 00:05, 7 March 2011 (UTC)
Oh, as to my "trolling" comment, your presentation here smacks of it... you returned after contributing nothing to the ensuing discussion after you first raised the issue, only to decree today that you deemed all contrary opinion as "twiddly" (probably not the word you wanted) and, thus, intended to restore the controversial text despite the obvious majority opinion to the contrary. Frankly, I expected you to disappear yet again after making your comment today, which is why I introduced my own comments as a possible waste of breath. Fcreid (talk) 00:19, 7 March 2011 (UTC)
(ec, in response to User:GlitchCraft) I don't think anyone is questioning the notability of her resignation. We have a whole damned article on it, as a matter of fact. The issue is that consensus has tended to find that "she resigned in July 2009" with a brief mention of her "logic" is sufficient for the lede here. I don't see any compelling editorial reason to try to say she was or was not the first governor, territorial or otherwise, to resign her office with or without continuing on to some other form of government service. That sounds awfully convoluted when we look at it carefully, does it not? jæs (talk) 00:07, 7 March 2011 (UTC)
• The article as it originally stood placed her resignation in close context with her candidacy for VP. It would not be strange at all to conclude that she resigned to run – but she did not. She resigned, essentially, because she didn't feel like doing her job. Now, if that isn't notable, what is? And it certainly must go in the WP:LEDE. The reason we need to make up a new category for her is because, you know, no other elected governor (at least not of Alaska) has ever just "up and quit" (i.e., take your ball and bat and go home) for that reason. It sounds profoundly notable. :-) She is unique and needs a new category for that reason, whether we like it or not... The article as it currently stands goes through a breathless list of her "firsts", all of which are positive. Why is it that her status as the first governor to simply walk away from the job without any really reasonable explanation is not listed among her "firsts"? It strikes me as being particularly POV-laden to list her "positive firsts" and neglect her "negative first (and only)" – especially since the latter is much more indicative of what she can and (especially) will do in the future. A person who quits for no reason is a person who quits for no reason, and there must be some reason why she is the first person in this job who quit for no reason ... that reason is, the job is a serious one, and quitting it for no reason is a very grave matter. She is the first (and only) to do so. It should be listed among her other firsts.. GlitchCraft (talk) 07:45, 7 March 2011 (UTC)
It already states her rationale for resigning pretty clearly. Adding that she was the first grandmother, first left-handed person or first female caribou hunter to do so is simply contrived categorization to embellish the point without purpose. Even if it were more than trivial, it belongs in the respective sub-article. (Have you worked on the resignation article?) Fcreid (talk) 09:56, 7 March 2011 (UTC)
## Track Palin birthdate
I added the birthdate of Track Palin, April 20 1989, to the "family life" section. I note that this was deleted. The information is discussed at various places on the web; it would be useful to have it in Wikipedia as a source, instead of just in various blogs and commentaries. A search for "track palin birthday" gives, for example, 50,000 hits: (Track Palin Birthday search) Some of which are:
Geoffrey.landis (talk) 17:41, 6 March 2011 (UTC)
The exact date of birth of Palin's offspring is of little significance to the article, and there may be privacy issues involved in such cases, so policy discourages such details: see WP:DOB. AndyTheGrump (talk) 17:49, 6 March 2011 (UTC)
This material is well sourced; it is all over the web. There are no privacy issues in material that is publicly available. You may think that there is no "significance" to the information, however, I will comment that 50,000 google hits make a prima facia case that it is significant to at least some fraction of the Wikipedia readers. Geoffrey.landis (talk) 23:13, 6 March 2011 (UTC)
Is Track Palin notable? Not according to Wikipedia policy (notability isn't inherited). Am I right in assuming that the reason you see his birthday as relevant is in relation to the suggestion that he was possibly conceived out of wedlock? This seems to be the reason for the large number of Google hits you find. If indeed this is the case, then we should debate the issue openly, and determine whether it is correct to disclose such questionable (and perhaps unverifiable) speculation about a non-notable person. If this isn't the reason you wish to include Track's DoB, I think you will have to explain why you wish to ignore a clearly-stated policy: "If the subject complains about the inclusion of the date of birth, or the person is borderline notable, err on the side of caution and simply list the year." (WP:DOB) AndyTheGrump (talk) 23:28, 6 March 2011 (UTC)
If you want to add a section about the controversy about Track Palin, please go ahead and do so. Otherwise, please stop deleting sourced material on the basis of spurious arguments. WP:DOB simply is not an issue here. The information is simply information. It is a controversy if you want to make it a controversy; do so if you think it would enhance the value of the article.
You mention: "If the subject complains about the inclusion of the date of birth" -- as far as I know, this is not an issue. If Track Palin has complained about the inclusion of his date of birth, this would be relevant-- please cite this complaint can be found. If not, the argument is irrelevant. Geoffrey.landis (talk) 00:52, 7 March 2011 (UTC)
Several editors have given very valid reasons as to why this should not be in the article, and the only response you have really given is "I found it on the internet, I am going to put it in here because I can." Not gonna happen. Tarc (talk) 01:05, 7 March 2011 (UTC)
"Several editors have given very valid reasons as to why this should not be in the article" : By the word "several," you apparently mean "one." If you had included a reason why it should not be in the article-- and I note that you didn't-- that would have been "two." Geoffrey.landis (talk) 01:40, 7 March 2011 (UTC)
Geoffrey.landis, I quoted the relevant sentence from WP:DOB in its entirety - the significant clause is clearly the one relating to the question of "borderline" notability. You have given no reason to suggest that Track Palin is notable at all. Now, will you please explain why you think WP:BLP policy should be ignored in this case. It is standard Wikipedia procedure that when inclusion of any data is contested, the person wishing to include it must provide justification. So far, you have given none whatsoever. AndyTheGrump (talk) 01:10, 7 March 2011 (UTC)
You did not quote WP:DOB in its entirety; the crucial sentence part you left out is this one: "Wikipedia includes full names and dates of birth that have been widely published by reliable sources." I will assert that Sarah Palin's book Going Rogue counts as a reliable source, but if it doesn't, I can quote numerous other sources.
The "justification" for including this material was given in the first paragraph above: because the material is of interest. One demonstration that the material is of interest is that the question draws 50,000 hits on Google. So, the question is, should Wikipedia editors be deleting material that is of interest, in fact, material that people specifically go to Wikipedia to look up (note that there are 77 pages (corrected link: [21]) that specifically mention the fact that Wikipedia "omits" Track Palin's birthday)? Geoffrey.landis (talk) 01:40, 7 March 2011 (UTC)
Why is it of interest? (Your 77 pages link doesn't work. Please put it in your own words.)HiLo48 (talk) 01:47, 7 March 2011 (UTC)
Geoffrey.landis, you've not even bothered to quote the sentence from WP:DOB in its entirety - it is clearly referring to the DoB of the subject of the biography.
You were the one who brought up WP:DOB. If you are now saying that WP:DOB is not in fact relevant here because it "clearly refers" to the DoB only of the subject of the article, why did you quote it in the first place? For reference, the complete sentence (which I quoted only up to the word "or") is: "Wikipedia includes full names and dates of birth that have been widely published by reliable sources, or by sources linked to the subject such that it may reasonably be inferred that the subject does not object." Geoffrey.landis (talk) 03:59, 9 March 2011 (UTC)
Now, I'm sure there are lots of things that might be of interest to Wikipdia readers that we could include, but don't - we have policies regarding notability, relevance, privacy etc that exclude much, and we have a specific policy that discourages giving the exact DoB of people of borderline notability, never mind no notability at all. If you want to override this policy, you will have to provided a better argument than 'some people are interested'. How about giving one? Or are you suggesting the policy needs amending - if so, this is the wrong place to argue for it. AndyTheGrump (talk) 01:53, 7 March 2011 (UTC)
Some good points above. If you want to write a paragraph on the born out of wedlock issue, GL, then be straight about it. If you want to include this info soley because it is interesting to you, consider that you have not provided RS (even though you have asserted that you have) and that others see reason to be cautious. Also, you should not have reverted based on BRD and you should not have then again reverted. Coming close to 3/rr.Cptnono (talk) 02:06, 7 March 2011 (UTC)
Is that what this is about? That typical gestation periods with her eldest child are close enough to her marriage date that it introduces the potential for speculation that this woman (in her mid-20s at the time) *may* have engaged in premarital intercourse? :) Fcreid (talk) 09:52, 7 March 2011 (UTC)
I've seen this pattern before on other articles—it's a trick to skirt the content guidelines. Suppose you want an article to make point A, but you can't muster an acceptable source, so you instead find point B, for which you do have a source, and which insinuates point A. In this case, the dream is two layers deep: A user wants to say that Palin is a hypocrite (point A), but that would violate NPOV, so they find a point which invites readers to that conclusion without stating it outright (point B), and add the insinuating point C, for which they have a source. The telltale sign is the insistence on adding a factoid that is sourced but, taken by itself, utterly mundane. Insistent editing + facial irrelevance = insinuation. - Simon Dodd { U·T·C·WP:LAW } 15:06, 7 March 2011 (UTC)
I'm just putting in the factual information. I am receiving enough machine-gun fire from partisans simply for the attempting to insert sourced facts into the article that I do not have the time to fight the battle you propose. Thanks, but no thanks. @HiLo48: I'm sorry the google link doesn't work for you. It works on my end of the link; feel free can go to Google.com and do the search yourself.Geoffrey.landis (talk) 13:37, 7 March 2011 (UTC)
• Ah, the last refuge of wikiscoundrels: "But, but, I'm just putting in the truth! And if I have a source!" What is always forgotten is that the threshold for inclusion in Wikipedia is verifiability; it is a necessary condition, not a sufficient one. A number of users have explained to you why this stays out, and it's apparent that policy and consensus go against you, so at this point, it's time to drop the stick and back away from the dead horse.- Simon Dodd { U·T·C·WP:LAW } 14:29, 7 March 2011 (UTC)
A point of information: if I am a 'partisan' for anything, it is for high standards in Wikipedia articles. I am no supporter of Sarah Palin, never have been, and hopefully never will be. When I reverted the initial edit giving Track's exact birthdate I was unaware that there was any controversy attached to it, and maybe if this had been made clearer, I might have been prepared to take part in a discussion as to whether it was actually significant (though I'm not sure I could have been convinced, without evidence that mainstream sources also saw it as relevant). However, I think that in such circumstances, the intentions of editors needs to be made clear, rather than hiding behind 'facts' that are only seen as significant in an undisclosed context. Geoffrey.landis, I suggest that the next time somebody disputes an edit, you assume good faith, and make your motivations clear. AndyTheGrump (talk) 15:39, 7 March 2011 (UTC)
I have been continuously accused of partisanship here, and now accused of "hiding behind facts." I will assert that "the facts" is what Wikipedia is, in fact, about. Geoffrey.landis (talk) 03:59, 9 March 2011 (UTC)
My position is exactly the same as Andy's. I don't support Palin, but do support quality content here. I ask again, "Why is it of interest?" At least try to tell us why it interests you, and we might get somewhere. HiLo48 (talk) 16:18, 7 March 2011 (UTC)
I ask again, "Why is it of interest?" I'm sorry, but I have to assert that the question "why is it of interest" is irrelevant. It is not the purview of an encyclopedia (at least, not of Wikipedia) to ask the motivations of people reading an article. Let me ask you a different question: why do you think it is of interest to ask why it is of interest? If you are suggesting "some of the people reading the articles probably have partisan opinions, and may be trying to gather facts to either support or refute their opinions"-- well, so? I would have though that giving the facts would be the purpose of an encyclopedia. You would say not? Geoffrey.landis (talk) 04:06, 9 March 2011 (UTC)
Oh that's easy. I suspect that you want to show the date of birth as part of the process of scoring political points against Palin, presumably around the subject of having conceived a child out of wedlock. If so, say so. Don't beat about the bush. Do the math for people. Explain that she was a naughty girl. Don't just leave a date of birth sitting there like a shag on a rock for no apparent reason. Apart from a reason like that, there is no purpose in showing the child's date of birth. Or is there? HiLo48 (talk) 04:20, 9 March 2011 (UTC)
Actually if you try to argue that she was a 'naughty girl', you'll find people rapidly pointing out that the evidence is rather tenuous - gestation times are only averages. Leave the insinuation in, and nobody can argue... Personally, I think SP could have been 'intimate' (Marge Simpson's euphemism, which I rather like) with the entire adult male population of Alaska, and it wouldn't be relevant to her political career - but then I'm a Brit, and if the leader of the opposition chooses to live 'out of wedlock' with his long-term partner, it is of no particular significance. Evidently, in the US, such things matter, but if they do then say so - explain why you think this matters, what the evidence is, and what we should say about it. Wikipedia isn't just about 'facts', but relevance. AndyTheGrump (talk) 04:34, 9 March 2011 (UTC)
I hope you realise that us outrageous Aussies have gone a step further. It's our PM who's in an "out of wedlock" arrangement. And she's a woman too! And he's a divorcee. And I'm pretty sure his first kid was actually born before he was married. Oh, the disgrace. HiLo48 (talk) 07:08, 9 March 2011 (UTC)
Geoffrey, Andy and HiLo are not Palin partisans, and, even if they were, they've given you valid reasons for not including the birthdate. --Kenatipo speak! 16:34, 7 March 2011 (UTC)
For what it's worth, Obama's kids' birthdays are listed, Joe Biden's and Mitt Romney's only have year of birth and Huckabee's are simply listed as adults. Arguably, presidential children are a special case. Regardless of other considerations, I have a hard time seeing why we would include the date of birth for one child and not the others. --agr (talk) 16:50, 7 March 2011 (UTC)
sigh. Which boring, POV pushing nontroversy in particular would you like to add?- Simon Dodd { U·T·C·WP:LAW } 00:19, 8 March 2011 (UTC)
So I guess if editors reject your proposed additions to an article, the best way to handle that is to make a new section with exactly the same thing as the last time, but with added snark. Id swear we've seen you here before, glitch, but, frankly, all you POV pushers kinda blend together. Bonewah (talk) 01:00, 8 March 2011 (UTC)
• I am not a POV pusher; I am proposing accuracy and adherence to NPOV. This is not the same thing as the earlier thread; it walks completely away from the earlier "first" bit and merely suggests that we put all prominent controversies in the lead, in compliance with WP:LEAD and WP:NPOV. I am not WP:STICK; that's a silly essay, while WP:NPOV is a policy, and WP:LEAD is a guideline. Please adhere to Wikipedia policies and guidelines. Thanks, folks. GlitchCraft (talk) 02:35, 8 March 2011 (UTC)
(EC)Really? This isnt about the same thing as the earlier thread? Are you sure? I only ask because in the earlier thread you are going on about Palin's resignation and how we must mention in the lede that it was 'controversial' and in this thread you also declare that her resignation is controversial and must be mentioned in the lede. To me, that sounds like exactly the same thing. Bonewah (talk) 03:23, 8 March 2011 (UTC)
• I don't agree with the snarky way this editor brings up this point, but I do agree with the underlying point. Sarah Palin is especially notable for her divisiveness, which isn't mentioned at all in the lead. I understand it's difficult to phrase that in a way that is NPOV, but I think it should be done. – Muboshgu (talk) 03:09, 8 March 2011 (UTC)
• Okay, go ahead. Phrase just that point in a way that meets NPOV and other content guidelines. - Simon Dodd { U·T·C·WP:LAW } 03:13, 8 March 2011 (UTC)
• Muboshgu, I agree - the difficulty is that Palin tends to be controversial in general, rather than having specific 'prominent controversies' that have marked her career. As to how to deal with this, I'm not sure - the article certainly downplays this, and suggestions that there are NPOV problems seem valid to me. This needs more thought...AndyTheGrump (talk) 03:26, 8 March 2011 (UTC)
• I understand that that's the problem. If I could easily solve this, I'd be able to run wikipedia. Maybe a phrasing like "Palin is a controversial figure with poll numbers that say..." or "While Palin has a large following, she also has many detractors" could work. Somehow. I dunno. – Muboshgu (talk) 03:30, 8 March 2011 (UTC)
• Putting that into the lede is not going to satisfy NPOV. Even Rush Limbaugh, who is unquestionably more polarizing, doesn't have such a characterization in the lede, and I doubt that you will find such a statement in the lede of the article of any former US politician or political commentator. She's controversial, but not nearly as much as some of the breathless commentary here would have us believe. Horologium (talk) 03:36, 8 March 2011 (UTC)
Controversial to whom? Every politician or political commentator in the US is 'controversial' or 'divisive' to someone. Hell, even Joe Lieberman, a politician know for his bi-partisanship, was considered divisive to some due to his support for the Iraq war. Bonewah (talk) 03:47, 8 March 2011 (UTC)
• As a first effort, how about starting the lede with "Sarah Louise Palin ... is a sometimes-controversial American politician, author, speaker, and political news commentator...". I'm not sure this violates NPOV, given that she has often gone out of her way to be controversial, or at least to distance herself from mainstream politics - it wouldn't be hard to find WP:RS that described her as controversial, in any case. We might do well to look at how she has been characterised in the international media, rather than just with US sources, which tend to be predictably partisan. This might perhaps give a broader perspective. AndyTheGrump (talk) 03:50, 8 March 2011 (UTC)
• That's true, the international media don't have nearly the same partisan divisions. They come down unanimously on one side of it.- Simon Dodd { U·T·C·WP:LAW } 04:13, 8 March 2011 (UTC)
Is she more controversial than Newt Gingrich? His lede doesnt describe him as such despite the fact that he was pretty much the most hated republican in the '90s, at least to the left, anyway. I could find about a million sources that describe Rahm Emanuel as controversial, but his wikipedia lede isnt one of them. On the other hand, check out Ann Coulter's lede, it actually does use the word controversial in it. Bonewah (talk) 04:07, 8 March 2011 (UTC)
### Time out
Folks, we're being riled up by a user that's all-but an SPA in a meaningless challenge to do the impossible. May I suggest that we ignore the interloper, hat the preceding talk section, and return to our regularly-scheduled business?- Simon Dodd { U·T·C·WP:LAW } 04:16, 8 March 2011 (UTC)
I think we're past the SPA and engaging in actual discussion. I know it's hard to pull off without violating NPOV, but something needs to be in the lead about her controversial nature. – Muboshgu (talk) 04:18, 8 March 2011 (UTC)
Yup.Is anyone actually going to argue that Palin hasn't attracted controversy? AndyTheGrump (talk) 04:25, 8 March 2011 (UTC)
Why? And if so, how? Haven't you already demonstrated—by saying it ought to be done yet not being able to articulate a viable text—that doing so requires hitting a pretty difficult target? - Simon Dodd { U·T·C·WP:LAW } 04:30, 8 March 2011 (UTC)
Are you stating that you see no evidence of controversy regarding Sarah Palin? AndyTheGrump (talk) 04:34, 8 March 2011 (UTC)
I'm saying that I see no means of moving from that general observation to a specific text in the lede. Too specific and fail WP:UNDUE; too general and fail WP:NPOV/WP:V/WP:WEASEL ("regarded by many as controversial"); too circumlocutious and it becomes clunky and thus pointy. Some things just won't write. And if you think I'm wrong, write it! - Simon Dodd { U·T·C·WP:LAW } 04:49, 8 March 2011 (UTC)
Like I said, it needs thinking about - but it needs doing, IMO. AndyTheGrump (talk) 04:53, 8 March 2011 (UTC)
And I never said it would be easy. It is a pretty difficult target, but we should practice our aim rather than giving up. – Muboshgu (talk) 05:29, 8 March 2011 (UTC)
• Meh, I'm not a SPA, I'm a new account. Want me to copy edit an article for ya? Point me in the correct direction and I'll try to get it done in the next couple of days, whenever I have free time. Lagniappe... [Oh and calling editors "interlopers" sounds a bit WP:OWN-ish; you might wanna avoid that word]... Meanwhile, there are all those policies and things that we need to follow... as for the too general/too specific problem (above), it isn't really a problem at all. Handling controversies is done all the time in leads. First of all, each controversy (probably) needs only one sentence, so long as that sentence hits the main thrust of the criticism [and perhaps its rebuttal.. if the sentence then gets too long/snake-like, well, another sentence is fine]... Development is done in body text, of course. Secondly, you know, if you don't get it right the first time, this is a wiki, so... GlitchCraft (talk) 13:26, 8 March 2011 (UTC)
It is certainly not impossible to fix the lede - but the amount of material in this article which would not be found in any other BLP is a testament to some serious POV-pushers in the past. Frankly, the article is "too long by half" or more in the first place. Any lede of more than four paragraphs becomes, in itself, a sort of article :). Welcome to Wiki-World! Collect (talk) 13:40, 8 March 2011 (UTC) BTW, the huge amount of the article about "controversies" is definitely some of the first material which should be excised, not adding tons of that "stuff" to the already too-long lede. Collect (talk) 13:43, 8 March 2011 (UTC) .
Regarding "too long by half", that can be corrected by deleting extra references. There are places where multiple references are used to back up the same sentence, and they are never used again. There's no need to cite four sources when one will do. I may go through this later and trim extraneous refs. – Muboshgu (talk) 14:23, 8 March 2011 (UTC)
## Lede revision: a start
Several users have expressed a desire to revise the lede; others have worried that it is already too long. No one has yet offered specifics. While I'm dubious of the particular insertions that have been suggested, I agree the lede is in dire straights, practically dripping with fat and obsolete recentism. I'd like to propose the following revision:
Sarah Louise Palin (pronounced /ˈpeɪlɨn/), née Heath (b. February 11, 1964), is an American politician and commentator. She was the youngest person and the first woman elected Governor of Alaska, an office she held from December 2006 until resigning in July 2009. In the 2008 United States Presidential Election, she was the Republican nominee for Vice President, becoming the first Alaskan on the national ticket of a major party and the first Republican woman nominated for the vice-presidency. Speculation that she would run for the Presidency in 2012 began when it became apparent that the 2008 McCain–Palin ticket would be defeated.
After her resignation, Palin wrote Going Rogue, which has sold more than two million copies, and America by Heart. She has associated herself with the Tea Party movement, endorsing and campaigning for a number of successful candidates in the 2010 midterm elections. Since January 2010, she has providing political commentary for Fox News, and hosted a television show, Sarah Palin's Alaska, which aired between November 2010 and January 2011.
This version strips out an awful lot of information which certainly belongs in the article, but which no less certainly doesn't need to be covered in the lede. In the latter context, it's just fat. I would actually propose this text as a direct replacement, but at very least, I suggest that to the extent it whips the existing text into shape, it serves as a starting point for covering anything that we think should be included. At minimum, it's far better than what's there now. Thoughts?- Simon Dodd { U·T·C·WP:LAW } 16:30, 8 March 2011 (UTC)
• I would strip the "speculation" section as being exactly that. WP is not a crystal ball nor is it in the business of talking about what someone predicts or does not predict. Let's try to winnow this article down to facts directly and specifically related to Palin, and not be the melange of marginally related topics which were inserted in the past. Collect (talk) 16:36, 8 March 2011 (UTC)
• What "speculation" section? You mean the sentence "Speculation that she would run for the Presidency in 2012 began when it became apparent that the 2008 McCain–Palin ticket would be defeated"? I would be okay with removing that. My bet, however, is that most editors would prefer revision to removal; how about moving it to the end of ¶2 and rewording to something like "She is often mentioned as a possible candidate in the 2012 Presidential election"?- Simon Dodd { U·T·C·WP:LAW } 17:13, 8 March 2011 (UTC)
Right - and I doubt anyone really thinks that speculation about future events belongs in any BLP. If she announces a candidacy, then WP can easily include that fact when it becomes a fact. Collect (talk) 17:56, 8 March 2011 (UTC)
Yes cut the "Speculation...defeated" sentence from the lead. And correct "Palin wrote Going Rogue". Lynn Vincent (another anti-choice, anti-gay marriage creationist, natch) did. Writegeist (talk) 18:06, 8 March 2011 (UTC)
Ghostwriters are ubiquitous in politics, so I think characterizing the replacement of the named author with their ghostwriter as "correcting" is a little tendentious. Nevertheless, we don't have to settle that here and now. If there is any place in this article for the kind of "correction" you envision, it is in the body of the article (and not even necessarily there, cf. Barry Goldwater; the right place is in the book's article). The lede—our current occupation—should stick to identifying Palin as the author. - Simon Dodd { U·T·C·WP:LAW } 18:25, 8 March 2011 (UTC)
No we should not. She isn't (except in the broadest, non-writer-specific, sense of author as originator). And your assertion that my post called for the replacement of Palin's name with Vincent's is a fictional concoction. I simply pointed out that your "she wrote Going Rogue" is factually incorrect, and in support I identified the person who did write it. No, we should not "stick to identifying Palin as the author." We should replace it with such as: "Her book Going Rogue, published after her resignation, has sold more than two million copies." (I'm not sure that the sales warrant inclusion in the lead.) Thanks for characterizing my correction of a factual error as POV-pushing ("tendentious"). Not the first time an accusation of POV-pushing has adorned a Dodd response here. Please let it be the last. Writegeist (talk) 19:50, 8 March 2011 (UTC)
I can live with that locution—that's not nearly as awkward a substitute as I expected you to suggest. How is this as a replacement for the sentence in my original proposal: "Her book Going Rogue, published after her resignation, has sold more than two million copies, and a second book, America by Heart, was released in November 2010." If other editors can live with it, I'd support using only Writegeist's test, i.e. dropping the reference to AbH entirely, leaving that sentence to read "Her book Going Rogue, published after her resignation, has sold more than two million copies."
Incidentally, I think a little vaseline on the lens is appropriate for the lede, which is a very brief summary. In articles about people, Wikipedia attributes books and judicial opinions to their purported authors even when it's an open secret that they had help or even a ghostwriter (even when the article on the book itself notes the help), a fortiori in the lede. Since I agree with your proposed revision, we're not going to have that argument here, but if you fancy your chances, take it to the content noticeboard.- Simon Dodd { U·T·C·WP:LAW } 20:05, 8 March 2011 (UTC)
A huge number of books "by" politicians (heck, celebrities in general) have had "assistance" at the very least. Normal practice is to use what the title page says, and not try to do sleuthing about who wrote what part. Collect (talk) 21:37, 8 March 2011 (UTC)
I would also mention that the fact that it was published "after her resignation" is pointless and has no place in the lede of a biography of a living person, except as perhaps a jab at the fact that she resigned from her office, which is already mentioned. Rapier (talk) 22:22, 8 March 2011 (UTC)
Yep. Exactly. It's hard to hear the contrary suggestion over the sound of an axe being ground, but I got the gist and we should reject it. Nevertheless, I do prefer Writegeist's proposed text insofar as it's more concise, and Rapier's for the same reason (I incorporated it into take 3, below).- Simon Dodd { U·T·C·WP:LAW } 00:29, 9 March 2011 (UTC)
### Take 2
Here's a version incorporating the changes proposed above by Collect and Writegeist:
Sarah Louise Palin (pronounced /ˈpeɪlɨn/), née Heath (b. February 11, 1964), is an American politician and commentator. She was the youngest person and the first woman elected Governor of Alaska, an office she held from December 2006 until resigning in July 2009. In the 2008 United States Presidential Election, she was the Republican nominee for Vice President, becoming the first Alaskan on the national ticket of a major party and the first Republican woman nominated for the vice-presidency.
Her book Going Rogue, published after her resignation, has sold more than two million copies. She subsequently associated herself with the Tea Party movement, endorsing and campaigning for a number of successful candidates in the 2010 midterm elections, and is often mentioned as a possible candidate in the 2012 Presidential election. Since January 2010, she has providing political commentary for Fox News, and hosted a television show, Sarah Palin's Alaska, which aired between November 2010 and January 2011.
How is that?- Simon Dodd { U·T·C·WP:LAW } 20:09, 8 March 2011 (UTC)
Even though I loathe the page, you could link all or part of "endorsing and campaigning for" to Mama grizzly. Also fix the tense following "Since January 2010...", and it looks good. Tarc (talk) 20:16, 8 March 2011 (UTC)
• Good catch on "has providing"—shades of Yakov Smirnoff there! I would resist the Mama Grizzly link unless other editors are strongly in favor of it. If that's the ticket price for reforming the lede, fine, but otherwise I'd rather not.- Simon Dodd { U·T·C·WP:LAW } 20:24, 8 March 2011 (UTC)
In parallel construction - try "endorsed and campaigned for" as being grammatically more symmetrical. "Often mentioned" is a waste of "often" as far as the lede is concerned. Collect (talk) 21:37, 8 March 2011 (UTC)
I can handle that. Again, I really don't think that the fact that her book was published after her resignation is necessary, and I'd consider mentioning the channel that "Sarah Palin's Alaska" is on, since we've identified the channel that she acts as a political commentator on. I wouldn't be up in arms over either point if they were ignored. Rapier (talk) 22:43, 8 March 2011 (UTC)
I don't think that works without adding more words. The phrasing below ("take 3") squeezes about as much air from the sentence as I think we'll get.- Simon Dodd { U·T·C·WP:LAW } 00:17, 9 March 2011 (UTC)
### Take 3
Another mod per Rapier and Tarc; I've also collected her political career into the first paragraph (contiguity is next to concision), which I think is better:
Sarah Louise Palin (pronounced /ˈpeɪlɨn/), née Heath (b. February 11, 1964), is an American politician and commentator. She was the youngest person and the first woman elected Governor of Alaska, an office she held from December 2006 until resigning in July 2009. In the 2008 United States Presidential Election, she was the Republican nominee for Vice President, becoming the first Alaskan on the national ticket of a major party and the first Republican woman nominated for the vice-presidency. She has subsequently associated herself with the Tea Party movement, endorsing and campaigning for a number of successful candidates in the 2010 midterm elections, and is a possible candidate in the 2012 Presidential election.
Her book Going Rogue has sold more than two million copies. Since January 2010, she has provided political commentary for Fox News, and hosted a television show, Sarah Palin's Alaska, which aired between November 2010 and January 2011.
- Simon Dodd { U·T·C·WP:LAW } 00:17, 9 March 2011 (UTC)
• I don't suppose anyone would be willing to go one step further and eliminate ¶2 entirely? Is her media empire important enough for the lede? Or have we now boiled the existing lede down to its bare minimum? If so, I propose substituting this in, and then we can talk here about what (if anything)) to add. - Simon Dodd { U·T·C·WP:LAW } 00:31, 9 March 2011 (UTC)
• Perhaps we could fold the second para into the first with something like she is currently a political commenter for Fox news, or some such thing. Is that claim even true? Bonewah (talk) 00:46, 9 March 2011 (UTC)
• No idea. Who here watches Fox?- Simon Dodd { U·T·C·WP:LAW } 01:16, 9 March 2011 (UTC)
• The books seem to be notable - I suppose we could eliminate all books from the lede for J. K. Rowling and others ... Collect (talk) 00:55, 9 March 2011 (UTC)
• Notability is not the criterion for inclusion in the lede, and that's not a good analogy. Here's a better one: The Shining (novel) is notable enough for an article, and it's notable enough to be mentioned six times in Stephen King—but it is not so central to King's career as to merit the prime (and exceedingly limited) real estate of his lede. The lede should concisely summarize the topic, hitting the major points of who or what the subject is and why people care. WP:LEDE offers a helpful guideline about what should be included: "The emphasis given to material in the lead should roughly reflect its importance to the topic, according to reliable, published sources…." So the question becomes, just as whether one can or cannot introduce Stephen King without mentioning The Shining, whether one can or cannot introduce Sarah Palin without mentioning GR and/or AbH. I don't think either are essential, but there is certainly a distinction between the two, and I think it suggests that GR should be mentioned: GR occupies a more prominent place in the Palin narrative, insofar as it established her intention to remain an active part of the political landscape. I could take it or leave it, but I would defend leaving it in while excluding AbH and/or future works.- Simon Dodd { U·T·C·WP:LAW } 01:16, 9 March 2011 (UTC)
• I have to take some issue with a number of successful candidates. The word successful should probably be omitted; a bunch of "her candidates" did end up winning, but there were a substantial amount (possibly close to equal?) who did not, many of whom were some of the most prominent. It seems weird to only refer to the ones that won and not to the others.--Yaksar (let's chat) 01:21, 9 March 2011 (UTC)
It's certainly a logical link, and I wouldn't say it's necessarily a bad idea. But it would seem to omit some of her most notable endorsements, like Joe Miller (who I would consider the most prominent next to Christine O'Donnell), Rand Paul, or Marco Rubio. But considering the phenomenon of "mama grizzlies" she started it might make sense to link to it in the lead.--Yaksar (let's chat) 01:32, 9 March 2011 (UTC)
### Done
I realize that we haven't quite wrapped it up and put a bow on it here on the talk page, but I don't think I am getting too far ahead in saying that there is rough consensus for the changes that we've discussed. At very least, I don't think anyone has even hinted at objections so strong as to revert, to it's close enough that I have boldly moved the current version into the main article (dif); if editors have concerns, please at least mention them here before reverting. I think we have really made an improvement today, and we're in a much better position now than we were 24 hours ago to talk about adding things to the lede. - Simon Dodd { U·T·C·WP:LAW } 03:45, 9 March 2011 (UTC)
• I think you've done pretty well. Good work. GlitchCraft (talk) 08:37, 9 March 2011 (UTC)
Great job. Now, if we can make similar improvements in the rest of the article, we'll be getting somewhere.--Paul (talk) 14:49, 9 March 2011 (UTC)
I like it too. It's certainly better than it was prior. – Muboshgu (talk) 22:39, 9 March 2011 (UTC)
## Willow Palin
Is she notable enough for her own article? The site was unprotected and an article has sprung up. I'm almost instinctively clicked on XFD but we should talk about it here first. – Muboshgu (talk) 22:40, 9 March 2011 (UTC)
I understand your reaction, I had a very similar reaction when I saw the edit summary to this article indicating the article was no longer a redirect. The previously protected redirect was unprotected via a RfPP request that mentioned the discussions the occurred when the redirect was originally created by omitted more recent discussions such as this BLP noticeboard discussion from November 2010 that found insufficient reason to overturn the longstanding protection. I would suggest that based upon the new article's history, Wikipedia:Biographies of living persons/Noticeboard might be a better forum than this talk page to continue this discussion. --Allen3 talk 23:06, 9 March 2011 (UTC)
I usually don't make it to other forums, so I'll leave my response here. So far, I see no evidence of notability. The first source is TMZ, which I seriously question a tabloid-style media source like this one's reliability. Sources number two and three are about her mother, and only mention her once in passing, along with the other children. The fourth source is an opinion piece. The last source references its sources as TMZ. I'm not seeing that as covering the requirements for notability, especially for a BLP. Zaereth (talk) 23:16, 9 March 2011 (UTC)
Yeah, that's why I was thinking AfD might be a better place to discuss notability. I'll start a thread on the BLP noticeboard though, and probably progress to an AfD. – Muboshgu (talk) 23:20, 9 March 2011 (UTC)
Comment away. – Muboshgu (talk) 23:33, 9 March 2011 (UTC)
There is no need to wait that long. I nuked it as an A7. There is nothing notable about a minor private citizen, and it is likely that the article is simply a coatrack to attack the subject's mother. Horologium (talk) 01:12, 10 March 2011 (UTC)
Problem solved: "This page has been deleted. The deletion and move log for the page are provided below for reference. 19:58, 9 March 2011 Horologium (talk | contribs) deleted "Willow Palin" (A7: No explanation of the subject's significance (real person, animal, organization, or web content))"- Simon Dodd { U·T·C·WP:LAW } 01:13, 10 March 2011 (UTC)
Allen3 was right. That was a better route than AfD. – Muboshgu (talk) 01:32, 10 March 2011 (UTC)
## Edit request from 68.56.22.87, 6 March 2011
Exchange "née" for either "born" or "maiden" on the english version of the page.
68.56.22.87 (talk) 14:13, 6 March 2011 (UTC)
Not done: the term "née" is commonly used in English, as you can see here: the French and English-adopted term "née" (pronounced /ˈneɪ/ in English, [ˈne] in French), meaning "born as," can be applied to a woman's family-name at birth that has been replaced for any reason. Salvio Let's talk about it! 14:40, 6 March 2011 (UTC)
Agreed. The term "née" is quite acceptable. Buster Seven Talk 14:46, 6 March 2011 (UTC)
"Nee" is acceptible, but it is not commonly used and it would be better to use the dominant terms.LedRush (talk) 20:27, 10 March 2011 (UTC)
• Née is well-known, traditional, and precise. We should stick with it. And if it is true that some readers don't know it, they should welcome (to paraphrase Fowler's 3d) the enjoyable opportunity of learning something new. <rant>I have had this fight over attempts to banish whence/thence/hence, and of those it may at least be said that they have declined into semi-retirement—in this case, however, it is proposed that the dog be put to sleep while he is still healthy and hunting! It's just too much to bear to see useful words being hounded out of the language by ingrate philistines who don't know how to use them, and the condescending enablers with their infantilizing demand that nothing should ever be written that might make the slightest demand of even one of its readers.</rant> - Simon Dodd { U·T·C·WP:LAW } 23:22, 10 March 2011 (UTC)
Another Fowler reader. Cool.--Paul (talk) 00:04, 11 March 2011 (UTC)
@Dodd. Totally. Writegeist (talk) 23:53, 10 March 2011 (UTC)
Except that noboby ever really uses the term. But other than that...LedRush (talk) 23:58, 10 March 2011 (UTC)
I beg to differ. Anyone with a reasonable intelligence/education knows and uses the word, 'nee'.Mylittlezach (talk) 20:18, 25 March 2011 (UTC)
And, of course, it can be used for name changes of any reason and is therefore less precise than the second choice the editor put forward in his edit request. Other than those two things...LedRush (talk) 00:02, 11 March 2011 (UTC)
## Cite farm
One way to remove some clutter and speed up load time wold be to trim the cite thicket a bit. See forex: "In November 2010 HarperCollins released Palin's second book, titled America by Heart: Reflections on Family, Faith, and Flag.[241][242][243]". OK, there's no reason for three cites there. Choose the best and most reliable one, then delete the other two. Multiple cites should, in general, only be used to back up statements that are so controversial that they attract edit wars... I did see one other triple-cite that might have been legitimate: Her book sold as well as three others. I'm assuming (I didn't look) that the three cites were to list the sales figures for each of the three other books. Even in that case, I would consider a single note which contains all the info rather than 3 separate cites GlitchCraft (talk) 10:13, 10 March 2011 (UTC)
• I very much agree with this, on two levels. First: Generally-speaking, it's a laudable instinct to support statements with citations, but it can be taken to silly extremes. WP:V "requires that all quotations and any material challenged or likely to be challenged be attributed to a reliable published source" (emphasis added); no reasonable editor would challenge the statement that AbH was released in November 2010 by HarperCollins so long as it is in fact accurate, although one might wonder whether giving the publisher is superfluous. Second: Don't multiply citations unless something useful is added. Don't just pile on more citations that say the same thing; as GC said, choose one reliable source that supports the statement, and add more only when add to the article.- Simon Dodd { U·T·C·WP:LAW } 14:35, 10 March 2011 (UTC)
• I made that point a day or so ago, and I was thinking about taking a paring knife to that problem this weekend. If someone wants to beat me to it, they're more than welcome. I ran the dead link checker a few days ago to help. – Muboshgu (talk) 01:57, 11 March 2011 (UTC)
• I'm a troll, an interloper and a SPA. I certainly can't edit this article! I defer to your editing efforts. GlitchCraft (talk) 03:30, 11 March 2011 (UTC)
## kathy griifen/sarah palin.
palin says kathy destroyed her daughters life, palin said pick on me, come to alaska and dont come near my children.
--Cubes4 (talk) 20:16, 10 March 2011 (UTC)
And I don't think any of it is worth including here. Maybe in the "public image" article. – Muboshgu (talk) 01:56, 11 March 2011 (UTC)
i just notices the fight its a idk sorry. --Cubes4 (talk) 12:42, 11 March 2011 (UTC)
## I'll just leave this here.
Whether this becomes notable (I don't think it is as of now) or not should really depend on the mainstream press, I suppose. The parallels to the Obama "birther" conspiracy theories are obvious. Pär Larsson (talk) 16:30, 14 April 2011 (UTC)
Not notable. Not remotely usable. Even the Photoshopped stuff is not worth the paper it is written on. Collect (talk) 17:34, 14 April 2011 (UTC)
It's running in the New York Times and I just read it on BusinessInsider.com. —Preceding unsigned comment added by 173.13.80.114 (talk) 19:41, 14 April 2011 (UTC)
I agree with Collect, this is more fringe nonsense from the Palin obsessed left. Bonewah (talk) 11:57, 15 April 2011 (UTC)
Concur. This fake-pregnancy thing has been flogged again and again, but all one has to do is look at the dates of birth and compare them to the human gestation period to see that it's patently absurd. Mark Shaw (talk) 12:02, 15 April 2011 (UTC)
I disagree, I think this might be worth making a sub-page on. It was a widely known rumor during the election and it seems to have resurfaced with this article. Actually having just recently read the article is what brought me to the wikipedia page; I was looking for some articles with counterpoints. Moreover, the article linked there is actually not total drivel as some seem to be suggesting and it is getting a lot of attention. Part of the reason it is I think is because of the fact that the Obama birther rumor has resurfaced rather prominently lately and the author makes a point about how the Palin story was never latched on to by the mainstream media, despite her being much less forthcoming than Obama. On that note there is an entire multipage article on the Obama "birther" rumor(Barack_Obama_citizenship_conspiracy_theories), and his main article references other misbeliefs, such as that he is a Muslim. I don't agree with those rumors either, but I certainly believe wikipedia should mention them because they are notable, well sourced and it serves to limit misinformation. So yeah, please make a brief article or subsection on this, source it well and save everyone a lot of effort in having to wage a protracted edit war/lock on this page. 174.108.121.250 (talk) 10:31, 17 April 2011 (UTC)
The two matters are not analogs in any respect. More importantly, this is a biography of a living person (with multiple persons, including underage minors, impacted if we were to perpetuate such salacious nonsense). I can envision nothing that could be crafted that would meet the bar for inclusion in this article (or on WP, for that matter), and it certainly would not based on someone's college term paper. Fcreid (talk) 19:50, 17 April 2011 (UTC)
I agree with Fcreid, Collect, Bonewah, and Mark. An encyclopedia should not be a place for spreading rumors. Especially not a BLP.Zaereth (talk) 19:54, 17 April 2011 (UTC)
Add me to Zaereth's list. Not remotely acceptable at present, and even if it were given mainstream media attention, the fact that it involves minors etc would require great care regarding anything said. AndyTheGrump (talk) 19:57, 17 April 2011 (UTC)
Just to be clear wasn't advocating writing something supporting the rumor. To the contrary, wanted something to debunk it if possible (Same as the Obama page). Something in the section about electoral controversies stating something like "It was suggested that Palin was not the mother of her son. (sources) However, this rumor has not been substantiated (counter sources)". Also not to be too nitpicky, but it's "minor", not "minors" right now, as Bristol is 21 and a rather public person at this point. Though I do certainly agree anything about Trig should be handled with kid gloves. Pun retroactively intended. 174.108.121.250 (talk) 09:21, 18 April 2011 (UTC)
I don't know what you're proposing, but I hope you're not suggesting that WP perpetuate a vicious, tasteless and baseless rumor like this simply to extort Palin into releasing personal OB/GYN healthcare records or to stimulate a hospital to violate the HIPAA in order to refute it? There is absolutely no evidence to support this nonsense in the first place. One needs to suspend disbelief even to craft the "conspiracy" in a workable form, i.e. that after Palin assumed the son as her surrogate, that she then "forced" her daughter to become pregnant again to cover it up and that the birth notice of the latter grandchild was delayed several months for the timeline to remain intact. It's utter nonsense, and it belongs in the cesspool at dKos and not on WP. Fcreid (talk) 10:18, 18 April 2011 (UTC)
Yes, that is exactly what I was suggesting. </sarcasm>. Again, I read the article, wanted to read the counter points but found little (when googling "Trig Palin" you get 1) This article 2) a Huffington post article about his birth 3) 50 pages of conspiracy theory stuff). Only thing I found against the theory was 1 piece in 1 article (actually an article supporting the theory) where she said she already released the birth certificate (not sure if this is true or not). I thought wikipedia might be a good place to start because it's usually good about consolidating such sources -for example with the Obama article, and for that matter virtually any other politician, e.g. Silvio Berlusconi, whose article is half about popular conspiracy theories about him- but I found nothing. Seems this topic has been blacklisted by though so I'll drop it. 174.108.121.250 (talk) 21:39, 18 April 2011 (UTC)
I'm certain there are a plethora of conspiracies not given digital ink by WP, and this will be one of them. The "50 pages of conspiracy theory stuff" you encountered was, no doubt, from the blogosphere which does not differentiate between truth and absurdity. The optimist in me would love to believe Professor Scharlott's theory was correct, i.e. that mainstream media sources avoided this indecent assault against Palin as a matter of decency and decorum. However, the realist in me knows that was not the reason. Instead, this was not (and never will be) covered in mainstream sources because the conspiracy is too harebrained and flimsy at its very core, even against the absurd yardstick by which we measure such things. Beyond that the dates simply don't add up, as described above, the sheer number of people who would have been complicit and yet remained silent to this date is staggering. I presume the one thing you did glean in your research is that Palin doesn't know a single person who wouldn't love to talk to the media... seriously, do you believe Levi would have remained silent on this while his star was fading? Fcreid (talk) 22:48, 18 April 2011 (UTC)
## Palin's mayoral tenure
I believe that Palin resigned months in advance of the expiration of her term in order to devote her time to her unsuccessful campaign for Lt. Governor. — Preceding unsigned comment added by Activist (talkcontribs) 17:50, 16 April 2011 (UTC)
Your belief is incorrect. Palin was succeeded as mayor of Wasilla by Dianne Keller, who was sworn on October 14, 2002. This document (Agenda/Minutes) from the Wasilla City Council shows City Council member Dianne Keller attending the meeting (in the "Roll Call" section), and then notes her swearing in as mayor in the "Special Orders" section, after which it notes the presentation of a plaque to outgoing mayor Sarah Palin. Palin's term ended in October because her successor received 43.7% of the votes;[22] there is only a runoff election when no candidate receives more than 40% of the votes,[23] and the mayor is sworn in on the first Monday after the election results are certified.[24] Since there were only 987 ballots cast, certification was not an arduous process.
Some bozo at answers.com claiming that she resigned does not make it so. Horologium (talk) 19:10, 16 April 2011 (UTC)
Municipal officeholders in Alaska are usually sworn in within days or weeks after the election, unless there is a runoff, that is true. Nothing special related to Wasilla or to Palin. Since we're revisiting Palin's tenure as mayor, I wanted to revisit the rankings which were created for Wasilla's mayors. They have all since been removed, including Palin's entry. To recap, the list of mayors of Wasilla that was created, presumably in response to all the media attention given to Palin several years ago, failed to include any mayors from nearly the first full decade of Wasilla's existence as an incorporated city. Leo M. Nunley was the first mayor of Wasilla, as I faintly recall, yet he isn't on the list. Neither is Pat Hjellen, who succeeded Nunley. Dorothy Page is listed in the body of her article as a former mayor of Wasilla, and is listed in Category:Mayors of Wasilla, Alaska, yet is not on the list. In other words, someone created something and just left it with major problems for everyone else to clean up. The response since has been to compound these problems rather than address them. Ultimately, it doesn't help that the City of Wasilla keeps anything of a historical nature found on its website as carefully hidden or non-obvious as possible. To that, I'm pretty sure you Palinistas are to blame, as they're probably afraid of their servers being immobilized every time "Sarah Palin is trending" or whatever and people rush like lemmings to "find out more."RadioKAOS (talk) 02:57, 26 April 2011 (UTC)
How does Sarah Palin qualify for inclusion in Category:State cabinet secretaries of Alaska? Chair of the AOGCC is not a cabinet-level position. If anything, it's one of the more high-profile out of probably hundreds of boards and commissions in Alaska state government, but it has nothing to do with the governor's cabinet, which I presume is the purpose of that category.RadioKAOS (talk) 03:31, 26 April 2011 (UTC)
## Accuracy issue
Regarding the bridge to nowhere section, the Wikipedia page says: "Alaska chose not to return the \$442 million in federal transportation funds.[115]"However, if you check reference 115, it says the amount was \$223 million, not \$442 million. The claim does not match the cited source. —Preceding unsigned comment added by 68.108.124.239 (talk) 02:51, 14 May 2011 (UTC)
## Track Palin marriage
There has been a bit of a back-and-forth over the inclusion of his marriage in this article; consequently, there should be a discussion.
I am of the mind that the information does not belong in the article, because it is about Track, not about his mother. If Track Palin ever gets an article of his own (not likely, but possible) it would belong there, but not here. Just as we have excluded discussions of the activities of Willow Palin, Bristol Palin and Levi Johnston in this article (the first is a redirect to this article; the other two eventually merited articles of their own), we should not be using this article to discuss Track. In this case there is no BLP concern, but its inclusion is simply a case of undue weight: Track's marriage is not relevant to a biography of Sarah Palin.
If someone can demonstrate why this needs to be included, I am open to changing my mind, but as it stands I don't see any valid rationale for its inclusion. Horologium (talk) 02:07, 2 June 2011 (UTC)
I think a bare mention of this fact is useful to the article for sake of comprehensiveness, especially since the subject is not notable and does not have his own article. If someone is looking for facts about Palin's personal life, there is no need to make the reader look elsewhere for this non-controversial data.Jarhed (talk) 02:14, 2 June 2011 (UTC)
It's not relevant to Sarah Palin as an encyclopedic figure, though. Levi Johnston, to use the example of another of her children's beaus, had an impact on Palin. – Muboshgu (talk) 02:16, 2 June 2011 (UTC)
I find that a very odd thing to say. Of course the marriage of Palin's oldest son is relevant to Palin as an encyclopedic figure. This is especially so since his entry into the military was a very public part of the 2008 election. For anyone looking for this data, in Palin's article in the section on her personal life is where he or she would naturally expect to find it.Jarhed (talk) 02:27, 2 June 2011 (UTC)
I don't see how this is relevant to her BLP. I still agree with the previous consensus that mention of family should be limited to immediate family members, and then only by name and relation. If we start listing in-laws, next we'll have cousins, uncles, aunts, and then entire genealogies. The purpose of this article is to provide readers with information about the subject, that is, a better understanding of Palin. Personal information regarding her children does not seem to fulfill that goal.
I am also a firm believer in a private citizen's right to keep their privacy. Being related to a notable person, whether by blood or by marriage, does not make that person notable. Even if the information is found in a reliable source, there is no need to repeat it unless Track becomes notable enough to have his own article, in which case, mention of his immediate family members would be appropriate. Zaereth (talk) 04:51, 2 June 2011 (UTC)
Track is not a notable figure. His wife certainly isn't. Whether or not he has one isn't encyclopedic. It's not relevant to Sarah Palin's BLP. You haven't suggested why it is. – Muboshgu (talk) 04:57, 2 June 2011 (UTC)
Agree with the comments above that the relationships her children engage in (marriage or otherwise) are not relevant to her biography here. For (obvious) reasons stated in the article, Levi Johnston was an exception; Britta Hanson is not. jæs (talk) 07:44, 2 June 2011 (UTC)
## Within this wp article wikilink "mitigation" to Global warming mitigation.
Within this wp article wikilink "mitigation" to Global warming mitigation. 99.181.132.99 (talk) 06:37, 5 June 2011 (UTC)
## Politician?
I was just wondering if the tense used describing her as a politician in the first sentence is correct, "... is an American politician". She was, past tense, a politician. As she doesn't hold a political office, should the tense in that part of her description be changed? Since it's no longer valid, shouldn't it be dropped from the very first sentence of this article and simply documented in the body of the article? 24.189.3.151 (talk) 05:19, 7 June 2011 (UTC)
You don´t have to hold a political office to be considered a politician. The description fits, since when she is mentioned in media it´s mostly in a political context.Gråbergs Gråa Sång (talk) 12:32, 7 June 2011 (UTC)
I agree, plus (even disregarding what the media say) she has continued to try to influence public opinion on issues and candidates and she has a PAC to coordinate such efforts. Not to mention she has run for and held public office and has not ruled out a future run. Clearly a politician. Also please note this has been discussed before, at great length, see Talk:Sarah_Palin/Archive_64#Sarah_Palin_is_a_politician. Neutron (talk) 00:11, 8 June 2011 (UTC)
Agree the term is correct per the two comments above.-- KeithbobTalk 17:54, 10 June 2011 (UTC)
## Add Palin links from Get the Energy Sector off the Dole
Add Palin links from Get the Energy Sector off the Dole. 99.181.132.99 (talk) 06:34, 5 June 2011 (UTC)
And possibly others: Sarah Palin, Tea Partier in Name Only, Defends Big Oil Subsidies from Good (magazine) 4.May.2011, for contrast. 99.181.132.99 (talk) 06:47, 5 June 2011 (UTC)
More discussion on Talk:Tea Party movement. 99.181.129.104 (talk) 05:22, 12 June 2011 (UTC)
## Emails
Does the recent release of "thousands" of Palin emails warrant inclusion? Writegeist (talk) 17:35, 10 June 2011 (UTC)
No, we are not a newspaper. What are we going to say about it right now? That three years after liberal media requested Palin's emails for political purposes that some 24,000 pages of emails were released. Right now it is a political witch hunt and nothing more. Arzel (talk) 17:48, 10 June 2011 (UTC)
Agree with Arzel, that at present its not relevant. If, after some time, it receives significant and lasting coverage and becomes a significant part of her career then its worth a mention.-- KeithbobTalk 17:55, 10 June 2011 (UTC)
I don't like the tone of Arzel's reply ("liberal media"? At least you're not calling it the "lamestream" or "gotcha" media), but I agree with the comment. At this point, we don't know if there is anything encyclopedic in these emails. I imagine there is a good chance that there may be a bombshell or two in there, but there might not be. We should wait for one to come out before adding anything. – Muboshgu (talk) 18:00, 10 June 2011 (UTC)
I wonder if there are any from a certain NY politician.Buster Seven Talk 18:34, 10 June 2011 (UTC)
@Buster: Eew! @ Arzel: Obviously WP is not a newspaper. And to quote Wikidemon on your talk page last month, "Making things into a liberal versus conservative issue is decidedly unproductive." As is talk of a witch hunt. I didn't ask for political commentary. I just asked whether the release of thousands of a person's emails (dating from that person's tenure as a state governor, and released by the Governor's Office under the Freedom of Information Act), might warrant inclusion in that person's BLP. I am unsure. I hoped for responses based on BLP policy etc. Perhaps others, in addition to Muboshgu and Keithbob, will oblige. Meanwhile, as there is no rush, I tend to agree with Muboshgu about waiting. Writegeist (talk) 20:21, 10 June 2011 (UTC)
Somebody mentioned my wikiname? :) My personal opinion, no. The mere fact of the release of emails doesn't seem important. There are quite a few sources on this, which establishes that some people are taking note. But that doesn't establish context, weight, or relevance that it is a noteworthy part of the telling of Palin's life story, which is the subject of this article. It has only been a few hours. If the release of the emails turns out to be a significant event in her life and career, or triggers other events that are (as demonstrated by the weight of the sources), it could merit inclusion someday but we probably won't know that for at least a few days. Meanwhile, no harm in taking a wait and see approach. - Wikidemon (talk) 23:03, 10 June 2011 (UTC)
The release of emails certainly belongs in Governorship of Sarah Palin. I don't see the relevance here. Will Beback talk 23:17, 11 June 2011 (UTC)
Agreed. Writegeist (talk) 23:21, 11 June 2011 (UTC)
## Non-notable POV removed
I did this edit because I do not think the "local gun store owner" is notable. Wasbeer 01:12, 20 June 2011 (UTC)
The owner's personal notability is irrelevant. His comment, which reflects an opinion from someone who lives and works in Wasilla, is cited with an RS. Honestly, if we're going to judge the notability of someone whose comments are cited in a news story, Wikipedia is going to be a really, really bleak place and you will have a lot of work ahead of you. 67.233.238.6 (talk) 06:47, 20 June 2011 (UTC)
He? She is probably female since her name is Nancy. We are judging the notability of every POV on Wiki. Lots of lazy journalists use the opinion of any random passer-by as filler content. Non-notable POV's should be removed. I already have a lot of work ahead of me, offwiki too. Wasbeer 16:25, 20 June 2011 (UTC)
The name was not included here or in the article. In any case, it's not your job to selectively determine which parts of an article are notable or not. 67.233.238.6 (talk) 05:56, 21 June 2011 (UTC)
Correct. I do not get paid to do so. Wasbeer 06:54, 21 June 2011 (UTC)
I support the edit by wasbeer, the opinion of a single person from Wasilla is not encyclopedic content, in my opinion. Bonewah (talk) 21:51, 21 June 2011 (UTC)
In the interests of collegiality, I support the edit too. However, it is a matter of opinion and the original content was ok.--Jarhed (talk) 09:19, 22 June 2011 (UTC) |
# Origami Chains
Models of this type are also automatically listed in: abstract modular, abstract, geometric, modular, multi-sheet, pattern
These are modular origami models which create a one-dimensional structure (as opposed to quilts, which are two-dimensional). Such models can usually be extended to arbitrarily large numbers of units. By connecting the two ends, a chain can be transformed into a closed ring, but structurally I treat this as just a variant of the same model.
I haven’t seen any specific name used for such structures so far, so I introduced my own, origami chains.
This page lists folding instructions for models of a single type. You might be interested in the models themselves instead.
## No matching entries found
No instructions for this model type were found. Perhaps you were looking for models? |
The initial population is 250 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 5 hours?
$p \left(t\right) = 250 \cdot {2}^{\frac{t}{8}}$ where $t$ is measured in hours.
$p \left(5\right) = 250 \cdot {2}^{\frac{5}{8}} \cong 386$ |
# Prove the regular surface with 2 geodesics from p to q, and negative curvature cannot be simply connected.
What ideas/formulas are required to solve this? Exercise: If a and b are two geodesics from point p to q, how do you prove that M is not simply connected? M is a regular surface in R3 and has negative Gaussian curvature K. Points p & q are two distinct points on surface M.
I know surface is simply connected if any simple closed curve can be shrunk to a point continuously in the set. So a sphere is simply connected, and a donut is not simply connected. And I know that since the curvature is negative, and since K=det(Sp)=w*z, so eigenvalues w and z have opposite signs. I also have the formula K=(eg-f^2)/(EG-F^2) based on the 1st fundamental forms and derivatives for solving for E,F,G,e,f,g. Not sure what if anything that is used to solve. And the only geodesic equations I can think of off hand are
d/dt(E u' + F v')=1/2[E_u u'^2 + 2F_u u'v' +G_u v'^2 ], d/dt(Fu'+Gv')=1/2[E_v u'^2 +2F_u u'v' +G_v v'^2 ], and geodesic curvature c=, and Gauss-Bonnet integrals but not sure how that can be applied. If they can be applied, please let me know. Maybe the fact that the normal of any point on the geodesic arc also is on the same normal vector to the surface M at that point helps? What ideas and equations are required to solve the exercise?
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You are calling $a$ and $b$ geodesics, but you are also calling $a$ and $b$ principal curvatures. It would be good to use different notations for these things. – treble Nov 1 '12 at 0:17
thanks @treble, i fixed it to say w and z for principal curvatures. maybe it is not even necessary for me to mention them at all since Will seems to have solved the exercise without them – user47735 Nov 1 '12 at 16:55
## 1 Answer
EDIT, Thursday evening: a good illustration for the bit about negative curvature is the inner circle in the "hole" in a torus of revolution, which is a "closed geodesic" and cannot be contracted continuously to a point. The closed geodesic occurs in the (inner) part of the torus where the Gauss curvature is negative, while the outer portion has positive curvature. Meanwhile, no compact surface in $\mathbb R^3$ can have negative Gauss curvature everywhere, for which Neal gave a simple answer in comments. It is, of course, possible to have noncompact surfaces with negative curvature, such as the catenoid of revolution. However, for any such surface of revolution with negative curvature, the absolute value of the curvature goes to $0$ as we get far from the central axis. So Mariano asked whether there are any infinite surfaces in $\mathbb R^3$ with Gauss curvature that is bounded away from $0,$ and the answer is no, not for a $C^2$ surface. Link to the question MARIANO QUESTION.
ORIGINAL: This is Gauss-Bonnet for polygons on an oriented surface. The familiar case should be this: the area of a geodesic triangle on the unit sphere is $\alpha + \beta + \gamma - \pi,$ where $\alpha, \beta, \gamma$ are the angles at the vertices of the triangle. Next, we define the external angles $\theta_1 = \pi - \alpha, \; \theta_2 = \pi - \beta, \; \theta_3 = \pi - \gamma,$ according to Figure 4-25 of do Carmo:
==========
==========
The unit sphere has curvature $K=1,$ so the integral of $K$ over a polygon is just its area. Furthermore, the boundary arcs are geodesics, with geodesic curvature $k_g = 0.$ So the statement about this area is equivalent to $$\int \int_T \; K d \sigma \; + \theta_1 + \theta_2 + \theta_3 = 2 \pi.$$
Compare this with Gauss-Bonnet, formula (1) here:
==========
===========
You may or may not be told this: in the simply connected hyperbolic plane of constant curvature $-1,$ the area of a triangle is $\pi - (\alpha + \beta + \gamma),$ where $\alpha, \beta, \gamma$ are the angles at the vertices of the triangle. However, because $K = -1,$ this is once again the same as $$\int \int_T \; K d \sigma \; + \theta_1 + \theta_2 + \theta_3 = 2 \pi.$$
For your exercise, you are asked about an (oriented) "diangle" $D,$ with angles $0 \leq \alpha, \beta \leq \pi.$ If an angle is equal to $0,$ that is what the author calls a "cusp," see Figure 4-26, the right half. We take the external angles as before, and get $$\int \int_D \; K d \sigma \; + \theta_1 + \theta_2 = 2 \pi,$$ $$\int \int_D \; K d \sigma \; + (\pi - \alpha) + (\pi - \beta) = 2 \pi,$$ $$\int \int_D \; K d \sigma \; = \alpha + \beta.$$ What does this mean? We have $K < 0.$ The right hand side of the equation is nonnegative. If there is any interior to the "diangle," the integral is strictly negative. The only legal possibility is that the two geodesics are identical, both vertices are cusps, the two geodesic arcs are exactly the same, once out, once back.
Otherwise, and here is where the topology comes in, the two geodesic arcs do not bound a piece of surface as I was assuming, and the loop cannot be deformed homotopically to a single point, thus the surface is not simply connected.
Well, I hope that works for you. There is quite a bit of detail that could be added about orientation. Furthermore, I do not think a closed surface in $\mathbb R^3$ can have negative Gauss curvature. I know that a closed surface in $\mathbb R^3$ cannot have constant negative Gauss curvature.
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A closed surface in $\mathbb{R}^3$ can have negative Gauss curvature at some points (e.g. on the line $s = 0$ of the embedding $(\cos{s}\cos{t},\cos{s}\sin{t},\sin{s})$ of $T^2\hookrightarrow\mathbb{R}^3$). A closed surface must have at least one point of positive Gauss curvature (enclose the surface in a sphere of minimal radius, which must be tangent to the surface at some point; the surface has positive curvature at that point). – Neal Nov 1 '12 at 2:56
@Neal, works for me. Right, the version I recall is the farthest point from the origin. – Will Jagy Nov 1 '12 at 2:58
But I'd guess, for some reason, that a closed surface (closed in that it is a closed subset of $R^3$) can be of negative curcature. I dunno! – Mariano Suárez-Alvarez Nov 1 '12 at 3:03
@MarianoSuárez-Alvarez, I do not see how, but my dissertation was in minimal surfaces, which is a special case and may be too restrictive. I'm thinking Ian Agol would know. If there is an example, it is awfully damn crinkly. – Will Jagy Nov 1 '12 at 3:23
I asked on MO for Ian to answer :-P – Mariano Suárez-Alvarez Nov 1 '12 at 3:35 |
# 009A Sample Final 2, Problem 6
Find the absolute maximum and absolute minimum values of the function
${\displaystyle f(x)={\frac {1-x}{1+x}}}$
on the interval ${\displaystyle [0,2].}$
Foundations:
1. To find the absolute maximum and minimum of ${\displaystyle f(x)}$ on an interval ${\displaystyle [a,b],}$
we need to compare the ${\displaystyle y}$ values of our critical points with ${\displaystyle f(a)}$ and ${\displaystyle f(b).}$
2. To find the critical points for ${\displaystyle f(x),}$ we set ${\displaystyle f'(x)=0}$ and solve for ${\displaystyle x.}$
Also, we include the values of ${\displaystyle x}$ where ${\displaystyle f'(x)}$ is undefined.
Solution:
Step 1:
To find the absolute maximum and minimum of ${\displaystyle f(x)}$ on the interval ${\displaystyle [0,2],}$
we need to find the critical points of ${\displaystyle f(x).}$
Using the Quotient Rule, we have
${\displaystyle {\begin{array}{rcl}\displaystyle {f'(x)}&=&\displaystyle {\frac {(1+x)(1-x)'-(1-x)(1+x)'}{(1+x)^{2}}}\\&&\\&=&\displaystyle {\frac {(1+x)(-1)-(1-x)(1)}{(1+x)^{2}}}\\&&\\&=&\displaystyle {{\frac {-2}{(1+x)^{2}}}.}\end{array}}}$
We notice that ${\displaystyle f'(x)\neq 0}$ for any ${\displaystyle x.}$
So, there are no critical points in the interval ${\displaystyle [0,2].}$
Step 2:
Now, we have
${\displaystyle f(0)=1,~f(2)=-{\frac {1}{3}}.}$
Therefore, the absolute maximum value for ${\displaystyle f(x)}$ is ${\displaystyle 1}$
and the absolute minimum value for ${\displaystyle f(x)}$ is ${\displaystyle -{\frac {1}{3}}.}$
The absolute maximum value for ${\displaystyle f(x)}$ is ${\displaystyle 1}$ and the absolute minimum value for ${\displaystyle f(x)}$ is ${\displaystyle -{\frac {1}{3}}.}$ |
Table 4 reports the results of estimating equation (11). In column 1, we include all affiliates and find a positive and statistically significant point estimate, indicating that affiliates in countries receiving a BTT expanded their employment more than other affiliates in the same industry. Columns 2 and 3 show that this positive effect is entirely driven by affiliates in high-RID industries, where BTTs are most likely to resolve double taxation. The effect in low-RID industries in column 3 is statistically indistinguishable from 0 and is economically small. Columns 4 to 6 introduce the standard controls discussed in section II, along with controls for BTTs in sibling affiliate countries to control for potential spillovers across siblings. We define “Parent-Sibling BTTs” as the share of initial sibling affiliate employment covered by a BTT with the United States in year $t$ and “Affiliate-Sibling BTT” as the share of initial sibling affiliate employment covered by a BTT between country $c$ and the countries in which affiliate $a$ has siblings. In both cases, using the initial shares of employment observed for each firm avoids allowing endogenous shifts in the affiliate weights to affect these controls. These controls have minimal effects on the coefficients of interest. The coefficient estimate of 0.338 in column 5 indicates that in high-RID industries, receiving a BTT increased affiliate employment by 40.2%, on average.25
Table 4.
Foreign Affiliate-Level Analysis: The Effect of BTTs on Offshore Employment
Dependent Variable: Log Affiliate Employment—$ln(mat)$
(1)(2)(3)(4)(5)(6)
SampleAllHigh RIDLow RIDAllHigh RIDLow RID
BTT 0.232*** 0.461*** −0.022 0.132* 0.338*** −0.089
(0.066) (0.077) (0.086) (0.072) (0.083) (0.088)
$ln(GDPus+GDPd)$ 7.062** 6.658* 7.331***
(3.129) (3.451) (2.800)
$ln(GDPus-GDPd)2$ 0.480* 0.512* 0.416*
(0.264) (0.286) (0.244)
$ln(SkillDifference)$ −0.185* −0.173* −0.195**
(0.095) (0.102) (0.087)
$ln(TradeCosts)$ 0.031 0.029 0.033
(0.034) (0.036) (0.032)
BIT −0.548** −0.528* −0.566**
(0.258) (0.279) (0.240)
FTA 0.016 0.075 −0.05
(0.105) (0.099) (0.112)
Exchange Rate −0.00002 −0.00003 −0.00001
(0.000) (0.000) (0.000)
Parent-Sibling BTTs −0.044* −0.046** −0.044
(0.026) (0.021) (0.033)
Affiliate-Sibling BTTs 0.133* 0.173** 0.083
(0.075) (0.081) (0.090)
Affiliate FE YES YES YES YES YES YES
Industry-Year FE YES YES YES YES YES YES
$N$ 342,239 197,116 145,123 342,239 197,116 145,123
$R$-squared 0.0014 0.0047 0.0001 0.0131 0.015 0.0145
$F$-Statistic 12.47 35.58 0.06 7.31 24.31 4.12
Dependent Variable: Log Affiliate Employment—$ln(mat)$
(1)(2)(3)(4)(5)(6)
SampleAllHigh RIDLow RIDAllHigh RIDLow RID
BTT 0.232*** 0.461*** −0.022 0.132* 0.338*** −0.089
(0.066) (0.077) (0.086) (0.072) (0.083) (0.088)
$ln(GDPus+GDPd)$ 7.062** 6.658* 7.331***
(3.129) (3.451) (2.800)
$ln(GDPus-GDPd)2$ 0.480* 0.512* 0.416*
(0.264) (0.286) (0.244)
$ln(SkillDifference)$ −0.185* −0.173* −0.195**
(0.095) (0.102) (0.087)
$ln(TradeCosts)$ 0.031 0.029 0.033
(0.034) (0.036) (0.032)
BIT −0.548** −0.528* −0.566**
(0.258) (0.279) (0.240)
FTA 0.016 0.075 −0.05
(0.105) (0.099) (0.112)
Exchange Rate −0.00002 −0.00003 −0.00001
(0.000) (0.000) (0.000)
Parent-Sibling BTTs −0.044* −0.046** −0.044
(0.026) (0.021) (0.033)
Affiliate-Sibling BTTs 0.133* 0.173** 0.083
(0.075) (0.081) (0.090)
Affiliate FE YES YES YES YES YES YES
Industry-Year FE YES YES YES YES YES YES
$N$ 342,239 197,116 145,123 342,239 197,116 145,123
$R$-squared 0.0014 0.0047 0.0001 0.0131 0.015 0.0145
$F$-Statistic 12.47 35.58 0.06 7.31 24.31 4.12
Documents the effect of newly signed bilateral tax treaties (BTTs) on foreign affiliate employment. “High RID” and “Low RID” refer to firms within industries that exhibit ratios of total payments in royalties, interest, and dividends relative to total industry sales that are above and below the median sector (see appendix A.2 for details). Sample covers 1987 to 2007. Standard errors clustered by both affiliate country and year are in parentheses. Significant at $*$10%, **5%, and ***1%.
Close Modal |
Tag Info
1
In this answer you can find a calculation for how bright "Nemesis" would be at near-infrared wavelengths. This calculation assumed we were looking for a 20 Jupiter mass object with a similar age to the Sun at a distance of 1.4 light years (to fit in with the Nemesis hypothesis). The calculated magnitudes were H=14 and W2=8 (in the WISE infrared satellite ...
2
It's pretty easy to put upper limits on how bright any nearer stars could be. As a rough guide, consider a survey like Hipparcos, which is complete to something like 9th magnitude. If there's another star closer than Alpha Centauri, the brightest possibility is if it's at the same distance. Wolfram|Alpha tells us that a magnitude 9 star at Alpha Centauri's ...
3
It's begining to look like there aren't as many brown dwarfs as was once thought: NASA's Wide-field Infrared Survey Explorer, or WISE, has been turning up a new crowd of stars close to home: ... Previous estimates had predicted as many brown dwarfs as typical stars, but the new initial tally from WISE shows just one brown dwarf for every ...
4
No, black holes are not the only cause of HVSs, although it is thought to be the most common mechanism. Hyper velocity stars are believed to be caused when binary stars come close enough to a supermassive black hole for one of the pair to be captured while the other star is ejected at high velocity. This appears to the main mechanism for HVSs. See for ...
12
Human color vision is based on three types of "cones" in the eye that respond differently to different wavelengths of light. Thus, not counting overall brightness, the human color space has two degrees of freedom. In contrast, the spectra of stars are very close to a black body, which depends only on effective temperature. As one varies the temperature, the ...
1
The European Southern Observatory has catalogues with image data available from http://www.eso.org/qi/, you will have to register before you are able to access them. I'd suggest you look at other observatory's websites for their data. You will have to look past the pages targeted at the general public and find links for data or science, or user portal or ...
1
Yes. If you have the Hipparcos data from ftp (http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=I/239&-to=3), you will have several data files. In hip_main.dat you have a field MultFlag at position 347 that indicates whether the star is a double or multiple star: Note on MultFlag: indicates that further details are given in the Double and ...
1
Basically you need to convert between luminosities (which you can add) and magnitudes using $$M-M_\odot=-2.5\log_{10}(L/L_\odot)$$ Let's call the total luminosity $L_0$ and magnitude $M_0$ and the individual luminosities and magnitudes $L_1$, $L_2$ and $L_3$ and $M_1$, $M_2$ and $M_3$. Then, you have the total luminosity of the system, directly ...
2
In the case of multiple images of a background, distant object, the answer is relatively simple. You take a spectrum of the multiple images or parts of an extended lensed image and you see whether the spectrum looks the same, and in particular whether the redshift of the multiple images are the same. Gravitational lensing affects light of all wavelengths ...
1
Yes, and not only from space but from the Earth surface too. Stars emit in almost all wavelengths depending on their surface temperatures. The hotter the star is the shorter (higher energy) wavelengths it'll emit. You can try this simulator to check this: http://astro.unl.edu/naap/blackbody/animations/blackbody.html
5
The answer is: frequently. There are many amateur astronomers that make it their ambition to discover new supernovae or to observe and report on new variable stars. As an example, let me cite amateurs Robert Evans, who apparently holds the record for most supernovae found by visual observation, or Tom Boles, who holds the record for supernova discoveries by ...
2
I presume what you mean is how does the plane of the orbit compare to the equatorial rotation plane of the star? The answer is, you can sort of estimate this, by using something called the Rossiter-McLaughlin effect (see also Rossiter 1924; McLaughlin 1924). You can find plenty of information on the web - I'll add a couple of links when I have a moment - ...
0
Is there any way to find the angle of the orbital plane of the exoplanet orbiting its parent star? It's unclear what precisely you're asking. The planet will be orbiting (to very good approximation) on a Keplerian orbit (closed ellipse co-focal with the parent star). Such an orbit has two relevant angles. One is the angle between the orbital plane and the ...
1
Stan has essentially answered this in his comment, which I will attempt to spell out a little more laboriously. The significant majority of our Sun's energy output comes from the proton-proton chain. This was advocated by Eddington back in the 1920's, but at that time your basic concern was a very real and major problem. Objects with like electrical ...
-4
Most of the answers I've read to this question seem to come from people that don't have all the facts. If you were to look at our Sun from Pluto, it would look like just another star in the sky. stars have a limit on how far away they can be seen. Most of the stars in our own galaxy are too far away to be seen with the naked eye. what you see in the sky at ...
1
Let's assume that what is falling onto the neutron star is "normal" material - i.e. a planet, an asteroid or something like that. As the material heads towards the neutron star it gains an enormous amount of kinetic energy. If we assume it starts from infinity, then the energy gained (and turned into kinetic energy) is approximately (ignoring GR) $$... 0 The Gliese catalogue can be found at CDS here. Given an RA and Dec then you can use the fortran program found here to get the constellation. 3 This question is very broad - there are very many techniques for estimating temperatures, so I will stick to a few principles and examples. When we talk about measuring the temperature of a star, the only stars we can actually resolve and measure are in the local universe; they do not have appreciable redshifts and so this is rarely of any concern. Stars do ... 1 There is no equation, you need a detailed model of the interior physics of very low mass stars. Very roughly, you can say that hydrogen fusion occurs when the central temperature exceeds about 10^{7}\ K (the density dependence is secondary) and that from the virial theorem, the central temperature is given approximately by T \simeq 1.6\times 10^{7} M/R, ... 1 A proposal for the minimum mass of a gas cloud before collapsing to become a star was made by James Jeans; because of this, it was termed the Jeans mass. It is calculated as$$M=\frac{4 \pi}{3} \rho R^3 where $\rho$ is density and $R$ is the radius of the cloud - one half of the Jeans length, which is dependent on the speed of sound and the density of the ...
2
I think it's an interesting question. The trick would be a sustained fission reaction, faster than half life, but slower than a chain reaction. A chain reaction could hardly be considered "star like" - it would just explode. Lets say you had a planet sized object, maybe 100 parts Iron, basically inert, to 1 part Uranium , which would generate heat ...
2
It is very unlikely with the normal fission process for most of the elements. They can be divided into 2 groups: slow reaction and fast reactions. The elements with slow reactions do not generate enough energy in a short enough time to be able to heat sufficiently to provide light. The elements with fast reactions would disappear before enough accumulated ...
3
The Sun has lots of features "like the red spot", but they are dissimilar too. Similarities: The Sun's photosphere - the bit we can see - is entirely gaseous; the photosphere rotates differentially with solar latitude; the gas is turbulent. There are features that can be seen quite easily - these are the dark magnetic sunspots, typically of size a few ...
1
Ahh got it. The coordinates are given as latitude, longitude. Fortunately, the longitude hardly matters (depending what precision you need), but the latitude does. A star at the zenith will have a declination equal to the latitude on Earth. As far as Right Ascension goes, well around the March equinox then stars with 12 hours in Right Ascension will reach ...
0
There's a couple of celestial coordinate systems you should learn about, which are the most commonly used: Horizontal coordinate system, observer-centered. Equatorial coordinate system, earth-centered. Depending on the system you use, the coordinates of your celestial object will be represented in one way or the other and should be read accordingly.
Top 50 recent answers are included |
## Probability and Computing: Chapter 2 Exercises
Exercise 2.5: If $X$ is a $B(n,1/2)$ random variable with $n \geq 1$, show that the probability that $X$ is even is $1/2$.
$Pr(X=j) = \binom{n}{j}p^{j}(1-p)^{n-j}=\binom{n}{j}p^{n} \qquad (p=1-p)$.
Since $Pr(X = j)$ only depends on $\binom{n}{j}$, all we need to prove is : $\sum_{\text{i is even}}\binom{n}{i} = \sum_{\text{j is odd}}\binom{n}{j}$.
Indeed, we have $0= (1-1)^n=\sum_{k=0}^{n}\binom{n}{k}(-1)^{k}=\sum_{\text{i is even}}\binom{n}{i} - \sum_{\text{j is odd}}\binom{n}{j}$.
Exercise 2.6: Suppose that we independently roll two standard six-sided dice. Let $X_{1}$ be the number that shows on the first dice, $X_{2}$ the number on the second dice, and X the sum of the numbers of two dice.
(a) $E[X\mid X_{1} \text{ is even}] = \sum_{i}iPr( (X=i)\mid (X_{1} \text{ is even}))$
$= 3\cdot\frac{1}{18}+4\cdot\frac{1}{18}+5\cdot \frac{2}{18}+6\cdot\frac{2}{18}+7\cdot\frac{3}{18}+8\cdot\frac{3}{18}+9\cdot\frac{2}{18}+10\cdot \frac{2}{18}+$
$11\cdot\frac{1}{18} +12\cdot\frac{1}{18} = 7.5$
(b) $E[X\mid X_{1} = X_{2}] = \sum_{i}iPr(X=i \mid X_{1} = X_{2})$
$=(2+4+6+8+10+12)\frac{1}{6}=7$.
(c) $E[X_{1}\mid X=9] = \sum_{i}iPr(X_{1}=i \mid X=9)$
$= (3+4+5+6) \cdot \frac{1}{4}=4.5$.
(d) $E[X_{1}-X_{2}\mid X=k]= 0 \qquad (k \in [2,12])$.
Exercise 2.7: Let $X$ and $Y$ be independent geometric random variables, where $X$ has parameter $p$ and $Y$ has parameter $q$.
(a) $Pr(X=Y)=\sum_{i=1}^{\infty}Pr(X=Y=i) = \sum_{i=1}^{\infty}(1-p)^{i-1}p(1-q)^{i-1}q$
$= pq\sum_{i=0}^{\infty}[(1-p)(1-q)]^{i}=pq\cdot \frac{1}{1-(1-p)(1-q)} = \frac{pq}{p+q-pq}.$
(b) $E[max(X,Y)] =?$
First we will calculate $Pr(max(X,Y)=i)$ and $Pr(max(X,Y) \geq i)$.
$Pr(max(X,Y) = i) = Pr(X=i)Pr(Y \leq i) + Pr(Y=i)Pr(X
$= (1-p)^{i-1}p\sum_{j=1}^{i}(1-q)^{j-1}q + (1-q)^{i-1}q\sum_{j=1}^{i-1}(1-p)^{j-1}p$
$= (1-p)^{i-1}pq\sum_{j=0}{i-1}(1-q)^{j}+(1-q)^{i-1}pq\sum_{j=0}^{i-2}(1-p)^{j}$
$=(1-p)^{i-1}pq\frac{1-(1-q)^{i}}{q}+(1-q)^{i-1}pq\frac{1-(1-p)^{i-1}}{p}$
$=(1-p)^{i-1}p[1-(1-q)^{i}] +(1-q)^{i-1}q[1-(1-p)^{i-1}]$
$=(1-p)^{i-1}p+(1-q)^{i-1}q-(1-p)^{i-1}p(1-q)^{i}-(1-q)^{i-1}q(1-p)^{i-1}$
$= (1-p)^{i-1}p+(1-q)^{i-1}q- (1-p)^{i-1}(1-q)^{i-1}[p(1-q)+q]$
$= (1-p)^{i-1}p+(1-q)^{i-1}q- (1-p)^{i-1}(1-q)^{i-1}(p+q-pq)$.
$Pr(max(X,Y) \geq i) = \sum_{j=i}^{\infty}(1-p)^{i-1}p +\sum_{j=i}^{\infty}(1-q)^{i-1}q+$
$\sum_{j=i}^{\infty}[(1-p)(1-q)]^{i-1}(p+q-pq)$
$= p\sum_{j=i-1}^{\infty}(1-p)^{j} + q\sum_{j=i-1}^{\infty}(1-q)^{j}+$
$(p+q-pq)\sum_{j=i-1}^{\infty}[(1-p)(1-q)]^{j}$
$= p\cdot \frac{(1-p)^{i-1}}{p} + q\cdot \frac{(1-q)^{i-1}}{q} +(p+q-pq)\cdot \frac{[(1-p)(1-q)]^{i-1}}{p+q-pq}$
$= (1-p)^{i-1} + (1-q)^{i-1}+[(1-p)(1-q)]^{i-1}$.
Because $max(X,Y)$ is a discrete random variable takes on only nonnegative integer value, we have:
$E[max(X,Y)] = \sum_{i=1}^{\infty}Pr(max(X,Y) \geq i)$
$= \sum_{i=1}^{\infty}[(1-p)^{i-1}+(1-q)^{i-1}+(1-p-q+pq)^{i-1}]$
$= \sum_{i=0}^{\infty}[(1-p)^{i}+(1-q)^{i}+(1-p-q+pq)^{i}]$
$= \frac{1}{1-(1-p)}+\frac{1}{1-(1-q)}+\frac{1}{1-(1-p-q+pq)}$
$= \frac{1}{p}+\frac{1}{q}+\frac{1}{p+q-pq}$.
(c) $Pr(min(X,Y)=k)= Pr(X= k)Pr(Y \geq k) + Pr(Y=k)Pr(X > k)$
$= (1-p)^{k-1}p\sum_{i=k-1}^{\infty}(1-q)^{i}q+(1-q)^{k-1}q\sum_{i=k}^{\infty}(1-p)^{i}p$
$= (1-p)^{k-1}pq\frac{(1-q)^{k-1}}{q}+(1-q)^{k-1}pq\frac{(1-p)^{k}}{p}$
$=p(1-p)^{k-1}(1-q)^{k-1}+q(1-q)^{k-1}(1-p)^{k}$
$= (1-p)^{k-1}(1-q)^{k-1}(p+q-pq)$.
(d) $E[X\mid X \leq Y] =$
Exercise 2.13:
(a) Consider the following variation of the coupon collector’ s problem. Each box of cereal contains one of $2n$ different coupons. The coupons are organized into $n$ pairs, so that coupons 1 and 2 are a pair, coupons 3 and 4 are a pair, and so on. Once you obtained one coupon from every pair, you can obtain a prize. Assuming that the coupon in each box is chosen independently and uniformly at random from the $2n$ possibilites, what is the expected number of boxes you must buy before you can claim the prize?
(b) Generalize the result of the problem in part (a) for the case where there are $kn$ different coupons, organized into $n$ disjoint sets of $k$ coupons, so that you need one coupon from every set.
(a) Let $X$ be the total number of boxes we must buy before we have at least one coupon from every pair, and $X$ the number of boxes we buy until we get a coupon from $i$th pair when we already had coupons from exactly $i-1$ pair.
Certainly we have $X = \sum_{i=1}^{n}X_{i}$.
The probability to get a coupon from a new pair when already had coupons from $i-1$ pairs is $p_{i}=\frac{1}{2n}\cdot (2n-2(i-1))=\frac{n-i+1}{n}$
Since each $X_{i}$ is a geometric random variable with parameter $p_{i}=\frac{n-i+1}{n}$, their expected values are: $E[X_{i}]=\frac{1}{p_{i}}=\frac{n}{n-i+1}$.
Thus $E[X] = E[\sum_{i=1}^{n}X_{i}]= n\sum_{i=1}^{n}\frac{1}{i}$.
Use the same technique described in the text, we can prove $E[X] = \text{ln}n+\Theta (1)$.
(b) Things are essentially the same when we have $kn$ coupons in $k$ different sets. The expected number of boxes we must buy before having at least one coupon from every set is $\text{ln}n +\Theta (1)$. |
## Results (1-50 of 393 matches)
Next
Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim arith $\mathbb{Q}$ self-dual $\operatorname{Arg}(\epsilon)$ $r$ First zero Origin
2-1352-104.3-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.3 $$0.0 0 -0.188 0 0.990912 Modular form 1352.1.n.b.315.3 2-1352-104.3-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 104.3$$ $0.0$ $0$ $-0.345$ $0$ $1.07585$ Modular form 1352.1.n.c.315.2
2-1352-104.3-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.3 $$0.0 0 -0.331 0 1.10937 Modular form 1352.1.n.a.315.1 2-1352-104.3-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 104.3$$ $0.0$ $0$ $-0.466$ $0$ $1.21175$ Modular form 1352.1.n.c.315.3
2-1352-104.3-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.3 $$0.0 0 0.321 0 1.25534 Modular form 1352.1.n.b.315.1 2-1352-104.3-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 104.3$$ $0.0$ $0$ $0.199$ $0$ $1.45920$ Modular form 1352.1.n.b.315.2
2-1352-104.3-c0-0-6 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.3 $$0.0 0 0.145 0 1.73929 Modular form 1352.1.n.c.315.1 2-1352-104.3-c0-0-7 0.821 0.674 2 2^{3} \cdot 13^{2} 104.3$$ $0.0$ $0$ $0.168$ $0$ $2.29428$ Modular form 1352.1.n.a.315.2
2-1352-104.35-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.35 $$0.0 0 -0.145 0 0.698231 Modular form 1352.1.n.c.867.1 2-1352-104.35-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 104.35$$ $0.0$ $0$ $-0.199$ $0$ $0.956653$ Modular form 1352.1.n.b.867.2
2-1352-104.35-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.35 $$0.0 0 -0.321 0 0.962837 Modular form 1352.1.n.b.867.1 2-1352-104.35-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 104.35$$ $0.0$ $0$ $-0.168$ $0$ $1.29676$ Modular form 1352.1.n.a.867.2
2-1352-104.35-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.35 $$0.0 0 0.331 0 1.85795 Modular form 1352.1.n.a.867.1 2-1352-104.35-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 104.35$$ $0.0$ $0$ $0.188$ $0$ $1.94936$ Modular form 1352.1.n.b.867.3
2-1352-104.35-c0-0-6 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.35 $$0.0 0 0.345 0 1.98776 Modular form 1352.1.n.c.867.2 2-1352-104.35-c0-0-7 0.821 0.674 2 2^{3} \cdot 13^{2} 104.35$$ $0.0$ $0$ $0.466$ $0$ $2.85347$ Modular form 1352.1.n.c.867.3
2-1352-104.43-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.43 $$0.0 0 -6.79e-5 0 1.00058 Modular form 1352.1.p.c.147.2 2-1352-104.43-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 104.43$$ $0.0$ $0$ $-0.123$ $0$ $1.00953$ Artin representation 2.1352.6t5.a.a Modular form 1352.1.p.a.147.1
2-1352-104.43-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.43 $$0.0 0 -0.363 0 1.15845 Modular form 1352.1.p.c.147.4 2-1352-104.43-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 104.43$$ $0.0$ $0$ $-0.133$ $0$ $1.43391$ Modular form 1352.1.p.c.147.5
2-1352-104.43-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.43 $$0.0 0 0.351 0 1.62906 Modular form 1352.1.p.c.147.1 2-1352-104.43-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 104.43$$ $0.0$ $0$ $0.408$ $0$ $2.01612$ Modular form 1352.1.p.c.147.3
2-1352-104.43-c0-0-6 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.43 $$0.0 0 0.0699 0 2.11233 Modular form 1352.1.p.c.147.6 2-1352-104.43-c0-0-7 0.821 0.674 2 2^{3} \cdot 13^{2} 104.43$$ $0.0$ $0$ $0.376$ $0$ $2.36510$ Artin representation 2.1352.12t18.a.b Modular form 1352.1.p.b.147.1
2-1352-104.51-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.51 $$0.0 0 -0.121 0 0.429080 Modular form 1352.1.h.a.675.2 2-1352-104.51-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 104.51$$ $0.0$ $0$ $-0.460$ $0$ $0.435783$ Modular form 1352.1.h.a.675.4
2-1352-104.51-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.51 $$0.0 0 -0.254 0 1.26145 Modular form 1352.1.h.a.675.6 2-1352-104.51-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 104.51$$ $0.0$ $0$ $0.460$ $0$ $1.37568$ Modular form 1352.1.h.a.675.1
2-1352-104.51-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.51 $$0.0 0 0.121 0 1.66555 Modular form 1352.1.h.a.675.5 2-1352-104.51-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 104.51$$ $0.0$ $0$ $0.254$ $0$ $1.81236$ Modular form 1352.1.h.a.675.3
2-1352-104.75-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.75 $$0.0 0 -0.351 0 0.159165 Modular form 1352.1.p.c.699.1 2-1352-104.75-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 104.75$$ $0.0$ $0$ $-0.408$ $0$ $0.911332$ Modular form 1352.1.p.c.699.3
2-1352-104.75-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.75 $$0.0 0 0.123 0 1.33459 Artin representation 2.1352.6t5.a.b Modular form 1352.1.p.a.699.1 2-1352-104.75-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 104.75$$ $0.0$ $0$ $-0.376$ $0$ $1.33863$ Artin representation 2.1352.12t18.a.a Modular form 1352.1.p.b.699.1
2-1352-104.75-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.75 $$0.0 0 6.79e-5 0 1.57681 Modular form 1352.1.p.c.699.2 2-1352-104.75-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 104.75$$ $0.0$ $0$ $-0.0699$ $0$ $1.72333$ Modular form 1352.1.p.c.699.6
2-1352-104.75-c0-0-6 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 104.75 $$0.0 0 0.133 0 1.90080 Modular form 1352.1.p.c.699.5 2-1352-104.75-c0-0-7 0.821 0.674 2 2^{3} \cdot 13^{2} 104.75$$ $0.0$ $0$ $0.363$ $0$ $2.17439$ Modular form 1352.1.p.c.699.4
2-1352-8.3-c0-0-0 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 8.3 $$0.0 0 -0.250 0 0.778652 Artin representation 2.1352.12t11.b.b Modular form 1352.1.g.a.339.2 2-1352-8.3-c0-0-1 0.821 0.674 2 2^{3} \cdot 13^{2} 8.3$$ $0.0$ $0$ $0$ $0$ $0.826751$ Modular form 1352.1.g.b.339.1
2-1352-8.3-c0-0-2 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 8.3 $$0.0 0 0 0 0.958699 Modular form 1352.1.g.b.339.2 2-1352-8.3-c0-0-3 0.821 0.674 2 2^{3} \cdot 13^{2} 8.3$$ $0.0$ $0$ $0.250$ $0$ $1.13667$ Artin representation 2.1352.12t11.b.a Modular form 1352.1.g.a.339.1
2-1352-8.3-c0-0-4 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 8.3 $$0.0 0 0 0 1.23776 Artin representation 2.1352.7t2.a.c Modular form 1352.1.g.c.339.1 2-1352-8.3-c0-0-5 0.821 0.674 2 2^{3} \cdot 13^{2} 8.3$$ $0.0$ $0$ $0$ $0$ $1.46715$ Modular form 1352.1.g.b.339.3
2-1352-8.3-c0-0-6 $0.821$ $0.674$ $2$ $2^{3} \cdot 13^{2}$ 8.3 $$0.0 0 0 0 1.55848 Artin representation 2.1352.7t2.a.a Modular form 1352.1.g.c.339.2 2-1352-8.3-c0-0-7 0.821 0.674 2 2^{3} \cdot 13^{2} 8.3$$ $0.0$ $0$ $0$ $0$ $2.21165$ Artin representation 2.1352.7t2.a.b Modular form 1352.1.g.c.339.3
2-1352-1.1-c1-0-0 $3.28$ $10.7$ $2$ $2^{3} \cdot 13^{2}$ 1.1 $$1.0 1 0 0 0.247790 Modular form 1352.2.a.n.1.1 2-1352-1.1-c1-0-1 3.28 10.7 2 2^{3} \cdot 13^{2} 1.1$$ $1.0$ $1$ $0$ $0$ $0.346855$ Modular form 1352.2.a.g.1.1
2-1352-1.1-c1-0-10 $3.28$ $10.7$ $2$ $2^{3} \cdot 13^{2}$ 1.1 $$1.0 1 0 0 0.954139 Modular form 1352.2.a.l.1.1 2-1352-1.1-c1-0-11 3.28 10.7 2 2^{3} \cdot 13^{2} 1.1$$ $1.0$ $1$ $0$ $0$ $1.07183$ Modular form 1352.2.a.m.1.1
Next |
Image text transcribed for accessibility: Euler's equation and orthogonality of sinusoids Euler's equation is very useful not only in obtaining the rectangular and polar forms of complex numbers, but in many other respects as we will explore in this problem. ej theta = cos(theta) + jsin(theta) carefully plot x|n| = e jpin for - infinity < n < infinity is this a real or a complex signal? Suppose you want to find the trigonometric identity corresponding to sin(alpha)sin(beta) Use Euler's equation to express the sines in terms of exponentials, multiply the resulting exponentials, and use Euler's equation to regroup the expression in terms of sinusoids. As we will later on, two periodic signals x(t) and y(t) of period T0 are said to be orthogonal if the integral over a period T0 is For instance, consider. Check first that these functions repeat every (i.e., show that). Thus, can be seen as their period. Then use the representation of a cosine in terms of complex exponentials, to express the integrand in terms of exponentials and calculate the integral cos(theta t) = e beta + e -beta/2 |
# Printing out Pascal's Triangle in row-major format
Here's the problem statement:
Given an integer value, print out Pascal's Triangle to the corresponding depth in row-major format:
Input Sample:
6
Output Sample:
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
I need some practice with recursion, so I tried that approach:
var pascalDepth = parseInt(line, 10); //The input integer is provided on a single line as a text value, so this handles it.
var testTriangle = pascalTriangle(pascalDepth);
var output = [];
for(var i = 0; i < testTriangle.length; i++){
for(var j = 0; j < testTriangle[i].length; j++){
output.push(testTriangle[i][j]);
}
}
console.log(output.join(" "));
function pascalTriangle(totalLines, triangle) {
if (typeof triangle === 'undefined') {
triangle = [];
}
if (triangle.length === totalLines) {
return triangle;
}
if (triangle.length > 0) {
var triangleLine = [];
for (var i = 0; i < triangle.length; i++) {
if (typeof triangle[triangle.length - 1][i - 1] === 'undefined') {
triangleLine.push(1);
} else {
triangleLine.push((triangle[triangle.length - 1][i - 1] + triangle[triangle.length - 1][i]));
}
}
triangleLine.push(1);
triangle.push(triangleLine);
} else {
triangle.push([1]);
}
return pascalTriangle(totalLines, triangle);
}
• Typically, recursive functions should not have side effects. This means you should not be mutating a variable getting passed down through the stack. It should be returned instead and combined with the current result in local variables with each iteration. Also you could I think make the code a little easier to understand by replacing some repeated expressions with variables, e.g.: triangle.length and triangle[triangle.length - 1]. Apr 22 '13 at 14:16
• I don't think this is the sort of problem that suits recursion - an iterative approach makes much more sense. You are doing an operation N times (the depth of the triangle) rather than breaking a problem down into smaller chunks.
– RobH
Apr 22 '13 at 14:58
Like the Fibonacci sequence, calculating Pascal's triangle recursively using a pure functional approach wouldn't be very efficient, since you would repeatedly compute many of the entries.
You've implemented a recursive solution with memoization, which is smarter. However, with memoization, the solution is stylistically iterative. Consider the following function, which behaves identically to yours, but is written in a more straightforward manner:
function pascalTriangle(totalLines) {
var triangle = [];
while (triangle.length < totalLines) {
if (triangle.length > 0) {
var triangleLine = [];
for (var i = 0; i < triangle.length; i++) {
if (typeof triangle[triangle.length - 1][i - 1] === 'undefined') {
triangleLine.push(1);
} else {
triangleLine.push((triangle[triangle.length - 1][i - 1] + triangle[triangle.length - 1][i]));
}
}
triangleLine.push(1);
triangle.push(triangleLine);
} else {
triangle.push([1]);
}
}
return triangle;
}
You could consider your "recursion" to be a fancy goto. Alternatively, you could conclude that Pascal's triangle does not lend itself to recursion.
That said, your implementation could be more compact. Think of deriving the next line this way:
[ , 1, 3, 3, 1]
+ [1, 3, 3, 1, ]
—————————————————
[1, 4, 6, 4, 1]
Then, you can use higher-level thinking: make two arrays with the appropriate offset, and find the sums of the corresponding elements.
function pascalTriangle(totalLines, triangle) {
// Helper function to add corresponding elements of two arrays
function sum(a, b) {
return a.map(function(_, i) {
return a[i] + b[i];
});
};
if (triangle == null) { // Initial call with just one parameter
triangle = [[1]];
}
if (totalLines === triangle.length) { // Final case
return triangle;
}
var prevLine = triangle[triangle.length - 1];
var nextLine = sum([0].concat(prevLine), prevLine.concat([0]));
return arguments.callee(totalLines, triangle.concat([nextLine]));
}
I've used arguments.callee for the function to refer to itself, so that if you rename the function (or make it anonymous), it can still work.
I have this implementation right off the top of my head and it doesn't use recursion. It's a plain loop that creates the current row with the previous row.
Here's the jsPerf results as well, with improvements in performance in some browsers, double especially Safari and Firefox.
//we need our depth input, and our storage array
var depth = 6,
output = [];
//we have a function that calculates the row using the existing triangle
function triangulate(triangle, rowIndex) {
//we declare variables up the top of the scope like how JS sees it
//this also makes clear what variables are in the scope
var previousRow = triangle[rowIndex - 1],
row = [],
i, left, right, length;
//if our row is the first row, the previous should be undefined
//so we return an array containing only 1
if (!previousRow) return [1];
//we cache the limit to a variable to avoid property access overhead
length = previousRow.length;
//we run the loop from the first number to the cell after the last number
for (i = 0; i <= length; i++) {
//we start with the first number in the row and the one before that
left = previousRow[i - 1];
right = previousRow[i];
//loose comparison is used since there are no zeroes in Pascal's triangle
//if we start with the first number, the one before it should be undefined
//thus we push the one at the right, which is our first number
if (!left) {row.push(right);continue;}
//if we end at the cell after the last number, that cell should be undefined
//thus we push the one at the left, which is the last number in the row
if (!right) {row.push(left);continue;}
//if both conditions fail, this means left and right are both numbers
//we add and push them to the current row
row.push(left + right);
}
return row
}
for (var i = 0; i < depth; i++) {
output.push(triangulate(output, i))
}
console.log(output.toString());
Looks long? Take a look at the comment-free version, pure code glory!
var depth = 6,
output = [];
function triangulate(triangle, rowIndex) {
var previousRow = triangle[rowIndex - 1],
row = [],
i, left, right, length;
if (!previousRow) return [1];
length = previousRow.length;
for (i = 0; i <= length; i++) {
left = previousRow[i - 1];
right = previousRow[i];
if (!left) {row.push(right);continue;}
if (!right) {row.push(left);continue;}
row.push(left + right)
}
return row;
}
for (var i = 0; i < depth; i++) {
output.push(triangulate(output, i))
}
console.log(output.toString());
Try uglifying it, it's a billion times shorter! |
1. ## Find the function
Find a positive, continuous function f(x) which satisfies the integral equation
$f(x) = \pi \left( 2 + \int_{1}^{x} 3f(t) dt \right)$
Hint: start by differentiating each side.
I Have Absolutely NO Idea On How To Do This Problem, I Don't Even Understand The Hint.
Thanks To Anyone Who Helps <3
: )
2. Originally Posted by qzno
Find a positive, continuous function f(x) which satisfies the integral equation
$f(x) = \pi \left( 2 + \int_{1}^{x} 3f(t) dt \right)$
Hint: start by differentiating each side.
I Have Absolutely NO Idea On How To Do This Problem, I Don't Even Understand The Hint.
Thanks To Anyone Who Helps <3
: )
Differentiate both sides of the equation, as it says. The left side will be $f'(x),$ and for the right side, you will need to use the second part of the fundamental theorem of calculus. After that, you should be able to determine a suitable $f(x)$ through integration.
3. i still cant figure out how to differentiate the right side : (
4. $\frac{d}{dx} \left[ \int_a^x f(t) \, dt \right] = f(x)$
5. i know that : (
6. Originally Posted by qzno
i know that : (
Okay, but we aren't mind readers. You need to tell us where you are getting stuck. Can you at least get the derivative? You have a constant (derivative is zero) plus an integral with a variable limit which can be differentiated using the property that skeeter gave; that part should be straightforward.
Show us your attempts so far, and we can guide you in the right direction.
7. I Got It Down To The Following:
$\int \frac{f'(x)}{f(x)} dx = \int 3\pi dx$
What do I do from here : )
8. Originally Posted by qzno
I Got It Down To The Following:
$\int \frac{f'(x)}{f(x)} dx = \int 3\pi dx$
What do I do from here : )
Good. The right side becomes $3\pi x + C\text.$ Now what is $\int\frac{u'}u\,dx?$
Apply the log rule, and then exponentiate both sides.
9. can you do u substitution and do like
u = f(x)
du = f'(x) dx
and then youd get
$\int \frac{1}{u} du$
10. Originally Posted by qzno
can you do u substitution and do like
u = f(x)
du = f'(x) dx
and then youd get
$\int \frac{1}{u} du$
Correct! You've got it.
11. so i got:
$ln (f(x)) + C = 3 \pi x + C$
is that all i do?
12. Originally Posted by qzno
so i got:
$ln (f(x)) + C = 3 \pi x + C$
Good, but the two constants of integration are not necessarily equal; you should either use separate names (like $C_0$ and $C_1$), or combine them as one constant.
is that all i do?
No. You want to find $f(x)$ (i.e., solve for $f(x)$).
Note that in this problem, you want to find a function that satisfies the conditions. There are many choices, depending on what you choose for $C\text.$ Just pick something that works.
13. $f(x) = e^{3 \pi x + c_2} - c_1$
or
$f(x) = e^{3 \pi x + c_2 - c_1}$
Are either of these correct?
14. Originally Posted by qzno
$f(x) = e^{3 \pi x + c_2 - c_1}$
Good. Now choose $c_1$ and $c_2$ so that $f$ satisfies the original equation.
15. how do u choose $c_1$ and $c_2$ ? |
# Chapter 6 Loops and Strings
Computers are often used to automate repetitive tasks, such as searching for text in documents. Repeating tasks without making errors is something that computers do well and people do poorly.
In this chapter, you’ll learn how to use while and for loops to add repetition to your code. We’ll also take a first look at String methods and solve some interesting problems.
## 6.1 The while Statement
Using a while statement, we can repeat the same code multiple times:
int n = 3; while (n > 0) { System.out.println(n); n = n - 1; } System.out.println("Blastoff!");
Reading the code in English sounds like this: “Start with n set to 3. While n is greater than 0, print the value of n, and reduce the value of n by 1. When you get to 0, print Blastoff!”
The output is shown here:
3 2 1 Blastoff!
The flow of execution for a while statement is as follows:
1. Evaluate the condition in parentheses, yielding true or false.
2. If the condition is false, skip the following statements in braces.
3. If the condition is true, execute the statements and go back to step 1.
This type of flow is called a loop, because the last step “loops back around” to the first. Figure 6.1 shows this idea using a flowchart.
The body of the loop should change the value of one or more variables so that, eventually, the condition becomes false and the loop terminates. Otherwise, the loop will repeat forever, which is called an infinite loop:
int n = 3; while (n > 0) { System.out.println(n); // n never changes }
This example will print the number 3 forever, or at least until you terminate the program. An endless source of amusement for computer scientists is the observation that the directions on shampoo, “Lather, rinse, repeat,” are an infinite loop.
In the first example, we can prove that the loop terminates when n is positive. But in general, it is not so easy to tell whether a loop terminates. For example, this loop continues until n is 1 (which makes the condition false):
while (n != 1) { System.out.println(n); if (n % 2 == 0) { // n is even n = n / 2; } else { // n is odd n = 3 * n + 1; } }
Each time through the loop, the program displays the value of n and then checks whether it is even or odd. If it is even, the value of n is divided by 2. If it is odd, the value is replaced by 3n+1. For example, if the starting value is 3, the resulting sequence is 3, 10, 5, 16, 8, 4, 2, 1.
Since n sometimes increases and sometimes decreases, there is no obvious proof that n will ever reach 1 and that the program will ever terminate. For some values of n, such as the powers of two, we can prove that it terminates. The previous example ends with such a sequence, starting when n is 16 (or 24).
The hard question is whether this program terminates for all values of n. So far, no one has been able to prove it or disprove it! For more information, see https://en.wikipedia.org/wiki/Collatz_conjecture.
## 6.2 Increment and Decrement
Here is another while loop example; this one displays the numbers 1 to 5:
int i = 1; while (i <= 5) { System.out.println(i); i++; // add 1 to i }
Assignments like i = i + 1 don’t often appear in loops, because Java provides a more concise way to add and subtract by one. Specifically, ++ is the increment operator; it has the same effect as i = i + 1. And -- is the decrement operator; it has the same effect as i = i - 1.
If you want to increment or decrement a variable by an amount other than 1, you can use += and -=. For example, i += 2 increments i by 2:
int i = 2; while (i <= 8) { System.out.print(i + ", "); i += 2; // add 2 to i } System.out.println("Who do we appreciate?");
And the output is as follows:
2, 4, 6, 8, Who do we appreciate?
## 6.3 The for Statement
The loops we have written so far have three parts in common. They start by initializing a variable, they have a condition that depends on that variable, and they do something inside the loop to update that variable.
Running the same code multiple times is called iteration. It’s so common that there is another statement, the for loop, that expresses it more concisely. For example, we can rewrite the 2-4-6-8 loop this way:
for (int i = 2; i <= 8; i += 2) { System.out.print(i + ", "); } System.out.println("Who do we appreciate?");
for loops have three components in parentheses, separated by semicolons: the initializer, the condition, and the update:
1. The initializer runs once at the very beginning of the loop. It is equivalent to the line before the while statement.
2. The condition is checked each time through the loop. If it is false, the loop ends. Otherwise, the body of the loop is executed (again).
3. At the end of each iteration, the update runs, and we go back to step 2.
The for loop is often easier to read because it puts all the loop-related statements at the top of the loop. Doing so allows you to focus on the statements inside the loop body. Figure 6.2 illustrates for loops with a flowchart.
There is another difference between for loops and while loops: if you declare a variable in the initializer, it exists only inside the for loop. For example:
for (int n = 3; n > 0; n--) { System.out.println(n); } System.out.println("n is now " + n); // compiler error
The last line tries to display n (for no reason other than demonstration), but it won’t work. If you need to use a loop variable outside the loop, you have to declare it outside the loop, like this:
int n; for (n = 3; n > 0; n--) { System.out.println(n); } System.out.println("n is now " + n);
Notice that the for statement does not say int n = 3. Rather, it simply initializes the existing variable n.
## 6.4 Nested Loops
Like conditional statements, loops can be nested one inside the other. Nested loops allow you to iterate over two variables. For example, we can generate a “multiplication table” like this:
for (int x = 1; x <= 10; x++) { for (int y = 1; y <= 10; y++) { System.out.printf("%4d", x * y); } System.out.println(); }
Variables like x and y are called loop variables, because they control the execution of a loop. In this example, the first loop (for x) is known as the “outer loop”, and the second loop (for y) is known as the “inner loop”.
Each loop repeats its corresponding statements 10 times. The outer loop iterates from 1 to 10 only once, but the inner loop iterates from 1 to 10 each of those 10 times. As a result, the printf method is invoked 100 times.
The format specifier %4d displays the value of x * y padded with spaces so it’s four characters wide. Doing so causes the output to align vertically, regardless of how many digits the numbers have:
1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100
It’s important to realize that the output is displayed row by row. The inner loop displays a single row of output, followed by a newline. The outer loop iterates over the rows themselves. Another way to read nested loops, like the ones in this example, is: “For each row x, and for each column y, …”
## 6.5 Characters
Some of the most interesting problems in computer science involve searching and manipulating text. In the next few sections, we’ll discuss how to apply loops to strings. Although the examples are short, the techniques work the same whether you have one word or one million words.
Strings provide a method named charAt. It returns a char, a data type that stores an individual character (as opposed to strings of them):
String fruit = "banana"; char letter = fruit.charAt(0);
The argument 0 means that we want the character at index 0. String indexes range from 0 to n−1, where n is the length of the string. So the character assigned to letter is 'b':
b a n a n a 0 1 2 3 4 5
Characters work like the other data types you have seen. You can compare them using relational operators:
if (letter == 'A') { System.out.println("It's an A!"); }
Character literals, like 'A', appear in single quotes. Unlike string literals, which appear in double quotes, character literals can contain only a single character. Escape sequences, like '\t', are legal because they represent a single character.
The increment and decrement operators also work with characters. So this loop displays the letters of the alphabet:
System.out.print("Roman alphabet: "); for (char c = 'A'; c <= 'Z'; c++) { System.out.print(c); } System.out.println();
The output is shown here:
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Java uses Unicode to represent characters, so strings can store text in other alphabets like Cyrillic and Greek, and non-alphabetic languages like Chinese. You can read more about it at the Unicode website (https://unicode.org/).
In Unicode, each character is represented by a “code point”, which you can think of as an integer. The code points for uppercase Greek letters run from 913 to 937, so we can display the Greek alphabet like this:
System.out.print("Greek alphabet: "); for (int i = 913; i <= 937; i++) { System.out.print((char) i); } System.out.println();
This example uses a type cast to convert each integer (in the range) to the corresponding character. Try running the code and see what happens.
## 6.6 Which Loop to Use
for and while loops have the same capabilities; any for loop can be rewritten as a while loop, and vice versa. For example, we could have printed letters of the alphabet by using a while loop:
System.out.print("Roman alphabet: "); char c = 'A'; while (c <= 'Z') { System.out.print(c); c++; } System.out.println();
You might wonder when to use one or the other. It depends on whether you know how many times the loop will repeat.
A for loop is “definite”, which means we know, at the beginning of the loop, how many times it will repeat. In the alphabet example, we know it will run 26 times. In that case, it’s better to use a for loop, which puts all of the loop control code on one line.
A while loop is “indefinite”, which means we don’t know how many times it will repeat. For example, when validating user input as in Section 5.9, it’s impossible to know how many times the user will enter a wrong value. In this case, a while loop is more appropriate:
System.out.print("Enter a number: "); while (!in.hasNextDouble()) { String word = in.next(); System.err.println(word + " is not a number"); System.out.print("Enter a number: "); } double number = in.nextDouble();
It’s easier to read the Scanner method calls when they’re not all on one line of code.
## 6.7 String Iteration
Strings provide a method called length that returns the number of characters in the string. The following loop iterates the characters in fruit and displays them, one on each line:
for (int i = 0; i < fruit.length(); i++) { char letter = fruit.charAt(i); System.out.println(letter); }
Because length is a method, you have to invoke it with parentheses (there are no arguments). When i is equal to the length of the string, the condition becomes false and the loop terminates.
To find the last letter of a string, you might be tempted to do something like the following:
int length = fruit.length(); char last = fruit.charAt(length); // wrong!
This code compiles and runs, but invoking the charAt method throws a StringIndexOutOfBoundsException. The problem is that there is no sixth letter in "banana". Since we started counting at 0, the six letters are indexed from 0 to 5. To get the last character, you have to subtract 1 from length:
int length = fruit.length(); char last = fruit.charAt(length - 1); // correct
Many string algorithms involve reading one string and building another. For example, to reverse a string, we can concatenate one character at a time:
public static String reverse(String s) { String r = ""; for (int i = s.length() - 1; i >= 0; i--) { r += s.charAt(i); } return r; }
The initial value of r is "", which is an empty string. The loop iterates the indexes of s in reverse order. Each time through the loop, the += operator appends the next character to r. When the loop exits, r contains the characters from s in reverse order. So the result of reverse("banana") is "ananab".
## 6.8 The indexOf Method
To search for a specific character in a string, you could write a for loop and use charAt as in the previous section. However, the String class already provides a method for doing just that:
String fruit = "banana"; int index = fruit.indexOf('a'); // returns 1
This example finds the index of 'a' in the string. But the letter appears three times, so it’s not obvious what indexOf might do. According to the documentation, it returns the index of the first appearance.
To find subsequent appearances, you can use another version of indexOf, which takes a second argument that indicates where in the string to start looking:
int index = fruit.indexOf('a', 2); // returns 3
To visualize how indexOf and other String methods work, it helps to draw a picture like Figure 6.3. The previous code starts at index 2 (the first 'n') and finds the next 'a', which is at index 3.
If the character happens to appear at the starting index, the starting index is the answer. So fruit.indexOf('a', 5) returns 5. If the character does not appear in the string, indexOf returns -1. Since indexes cannot be negative, this value indicates the character was not found.
You can also use indexOf to search for an entire string, not just a single character. For example, the expression fruit.indexOf("nan") returns 2.
## 6.9 Substrings
In addition to searching strings, we often need to extract parts of strings. The substring method returns a new string that copies letters from an existing string, given a pair of indexes:
• fruit.substring(0, 3) returns "ban"
• fruit.substring(2, 5) returns "nan"
• fruit.substring(6, 6) returns ""
Notice that the character indicated by the second index is not included. Defining substring this way simplifies some common operations. For example, to select a substring with length len, starting at index i, you could write fruit.substring(i, i + len).
Like most string methods, substring is overloaded. That is, there are other versions of substring that have different parameters. If it’s invoked with one argument, it returns the letters from that index to the end:
• fruit.substring(0) returns "banana"
• fruit.substring(2) returns "nana"
• fruit.substring(6) returns ""
The first example returns a copy of the entire string. The second example returns all but the first two characters. As the last example shows, substring returns the empty string if the argument is the length of the string.
We could also use fruit.substring(2, fruit.length() - 1) to get the result "nana". But calling substring with one argument is more convenient when you want the end of the string.
## 6.10 String Comparison
When comparing strings, it might be tempting to use the == and != operators. But that will almost never work. The following code compiles and runs, but it always displays Goodbye! regardless what the user types.
System.out.print("Play again? "); String answer = in.nextLine(); if (answer == "yes") { // wrong! System.out.println("Let's go!"); } else { System.out.println("Goodbye!"); }
The problem is that the == operator checks whether the two operands refer to the same object. Even if the answer is "yes", it will refer to a different object in memory than the literal string "yes" in the code. You’ll learn more about objects and references in the next chapter.
The correct way to compare strings is with the equals method, like this:
if (answer.equals("yes")) { System.out.println("Let's go!"); }
This example invokes equals on answer and passes "yes" as an argument. The equals method returns true if the strings contain the same characters; otherwise, it returns false.
If two strings differ, we can use compareTo to see which comes first in alphabetical order:
String name1 = "Alan Turing"; String name2 = "Ada Lovelace"; int diff = name1.compareTo(name2); if (diff < 0) { System.out.println("name1 comes before name2."); } else if (diff > 0) { System.out.println("name2 comes before name1."); } else { System.out.println("The names are the same."); }
The return value from compareTo is the difference between the first characters in the strings that are not the same. In the preceding code, compareTo returns positive 8, because the second letter of "Ada" comes before the second letter of "Alan" by eight letters.
If the first string (the one on which the method is invoked) comes earlier in the alphabet, the difference is negative. If it comes later in the alphabet, the difference is positive. If the strings are equal, their difference is zero.
Both equals and compareTo are case-sensitive. In Unicode, uppercase letters come before lowercase letters. So "Ada" comes before "ada".
## 6.11 String Formatting
In Section 3.5, we learned how to use System.out.printf to display formatted output. Sometimes programs need to create strings that are formatted a certain way, but not display them immediately (or ever). For example, the following method returns a time string in 12-hour format:
public static String timeString(int hour, int minute) { String ampm; if (hour < 12) { ampm = "AM"; if (hour == 0) { hour = 12; // midnight } } else { ampm = "PM"; hour = hour - 12; } return String.format("%02d:%02d %s", hour, minute, ampm); }
String.format takes the same arguments as System.out.printf: a format specifier followed by a sequence of values. The main difference is that System.out.printf displays the result on the screen. String.format creates a new string but does not display anything.
In this example, the format specifier %02d means “two-digit integer padded with zeros”, so timeString(19, 5) returns the string "07:05 PM". As an exercise, try writing two nested for loops (in main) that invoke timeString and display all possible times over a 24-hour period.
Be sure to skim through the documentation for String. Knowing what other methods are there will help you avoid reinventing the wheel. The easiest way to find documentation for Java classes is to do a web search for “Java” and the name of the class.
## 6.12 Vocabulary
loop:
A statement that executes a sequence of statements repeatedly.
loop body:
The statements inside the loop.
infinite loop:
A loop whose condition is always true.
increment:
Increase the value of a variable.
decrement:
Decrease the value of a variable.
iteration:
Executing a sequence of statements repeatedly.
loop variable:
A variable that is initialized, tested, and updated in order to control a loop.
index:
An integer variable or value used to indicate a character in a string.
Unicode:
An international standard for representing characters in most of the world’s languages.
empty string:
The string "", which contains no characters and has a length of zero.
Two or more methods with the same name but different parameters.
## 6.13 Exercises
The code for this chapter is in the ch06 directory of ThinkJavaCode2. See page ?? for instructions on how to download the repository. Before you start the exercises, we recommend that you compile and run the examples.
If you have not already read Appendix A.6, now might be a good time. It describes the DrJava debugger, which is a useful tool for visualizing the flow of execution through loops.
Exercise 1
Consider the following methods (main and loop):
1. Draw a table that shows the value of the variables i and n during the execution of loop. The table should contain one column for each variable and one line for each iteration.
2. What is the output of this program?
3. Can you prove that this loop terminates for any positive value of n?
public static void main(String[] args) { loop(10); } public static void loop(int n) { int i = n; while (i > 1) { System.out.println(i); if (i % 2 == 0) { i = i / 2; } else { i = i + 1; } } }
Exercise 2
Let’s say you are given a number, a, and you want to find its square root. One way to do that is to start with a rough guess about the answer, x0, and then improve the guess by using this formula:
x1 =(x0 + a/x0) / 2
For example, if we want to find the square root of 9, and we start with x0 = 6, then x1 = (6 + 9/6) / 2 = 3.75, which is closer. We can repeat the procedure, using x1 to calculate x2, and so on. In this case, x2 = 3.075 and x3 = 3.00091. So the repetition converges quickly on the correct answer.
Write a method called squareRoot that takes a double and returns an approximation of the square root of the parameter, using this technique. You should not use Math.sqrt.
As your initial guess, you should use a/2. Your method should iterate until it gets two consecutive estimates that differ by less than 0.0001. You can use Math.abs to calculate the absolute value of the difference.
Exercise 3
One way to evaluate exp(−x2) is to use the infinite series expansion:
exp(−x2) = 1 − x2 + x4/2 − x6/6 + …
The ith term in this series is (−1)i x2i / i!. Write a method named gauss that takes x and n as arguments and returns the sum of the first n terms of the series. You should not use factorial or pow.
Exercise 4
A word is said to be “abecedarian” if the letters in the word appear in alphabetical order. For example, the following are all six-letter English abecedarian words:
abdest, acknow, acorsy, adempt, adipsy, agnosy, befist, behint, beknow, bijoux, biopsy, cestuy, chintz, deflux, dehors, dehort, deinos, diluvy, dimpsy
Write a method called isAbecedarian that takes a String and returns a boolean indicating whether the word is abecedarian.
Exercise 5
A word is said to be a “doubloon” if every letter that appears in the word appears exactly twice. Here are some example doubloons found in the dictionary:
Abba, Anna, appall, appearer, appeases, arraigning, beriberi, bilabial, boob, Caucasus, coco, Dada, deed, Emmett, Hannah, horseshoer, intestines, Isis, mama, Mimi, murmur, noon, Otto, papa, peep, reappear, redder, sees, Shanghaiings, Toto
Write a method called isDoubloon that takes a string and checks whether it is a doubloon. To ignore case, invoke the toLowerCase method before checking.
Exercise 6
In Scrabble1 each player has a set of tiles with letters on them. The object of the game is to use those letters to spell words. The scoring system is complex, but longer words are usually worth more than shorter words.
Imagine you are given your set of tiles as a string, like "quijibo", and you are given another string to test, like "jib".
Write a method called canSpell that takes two strings and checks whether the set of tiles can spell the word. You might have more than one tile with the same letter, but you can use each tile only once.
1
Scrabble is a registered trademark owned in the USA and Canada by Hasbro Inc., and in the rest of the world by J. W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc.
Text © Allen Downey and Chris Mayfield. Interactive HTML © Trinket. Both provided under a CC BY-NC-SA license. Think Java 2nd Edition, Version 7.1.0. |
# Difference between revisions of "Main Page"
• Previous documentation was lost, so current wiki is an old version that does not include installation and getting started information. Updated documentation will be made available asap. In the meantime, send any questions to adam dot p dot harrison at gmail dot com if you have any questions on how to get started**
## Introduction
Welcome to LibMIA.
LibMIA is a software library designed to make manipulation of multi-indexed arrays (MIAs) easy. Technical computing packages, such as MATLAB, GNU Octave, and SciPy, support matrix algebra, making code look remarkably similar to what a scientist or practitioner would write on paper. However, matrices are not well-suited to work with and operate on MIAs, such as those found in digital imagery. What's needed is a formalism and supporting software designed for MIAs.
## MIA Formalism
If you're familiar with Einstein notation, then you already know much of MIA formalism. The biggest difference is the use of only one index type. There are other important differences.
An inner product, $c$, between two arrays $a_{i}$ and $b_{i}$, each of dimension $n$, is the summation of the products of all corresponding elements:
\begin{align} c=\sum_{i=1}^{n}a_{i}b_{i} \textrm{.} \end{align} Index notation uses a repeated index to represent an inner product, where the dimensionality is understood from the context:
\begin{align} c=a_{i}b_{i} \textrm{.} \end{align} Index notation also provides a concise convention for outer products. An outer product, $c_{ij}$, of $a_{i}$ and $b_{j}$, with dimensions $\{m,n\}$, is defined as the ordered product of all possible combinations of elements within the two arrays.
\begin{align} c_{ij}=\left( \begin{array}{cccc} a_{1}b_{1} & a_{1}b_{2} & \ldots & a_{1}b_{n} \\ a_{2}b_{1} & a_{2}b_{2} & \ldots & a_{2}b_{n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m}b_{1} & a_{m}b_{2} & \ldots & a_{m}b_{n} \\ \end{array} \right) \textrm{.} \end{align} Index notation simply uses differing indices to represent an outer product, where again the dimensionality is understood from the context:
\begin{align} c_{ij}=a_{i}b_{j} \textrm{.} \end{align} MIA formalism supports another important product - the element-wise or inter product. Performed using two first-order MIAs, it is expressed using an underline:
\begin{align} c_{i}=a_{\underline{i}}b_{\underline{i}} \textrm{.} \end{align} With the inter product defined, an MIA product can consist of any combination of $N$-order inner, inter, and outer products.
\begin{align} c_{lmji}=a_{\underline{i}jkl}b_{\underline{i}mj} \end{align} Note that the order of indices do not have to be same on the left and right-hand sides of the expression. MIA formalism has other benefits, including the ability to represent addition and subtraction, MIA inversions. Inter products also allow ternary or higher inner products to be associated.
## Using LibMIA
<syntaxhighlight lang="Cpp"> DenseMIA<double,3> a(4,6,5); //Could also be sparse DenseMIA<double,3> b(4,2,6); DenseMIA<double,3> c; PRODIND i; PRODIND j; //returns ProdIndex<id,false> PRODIND k; PRODIND l; c(j,l,k)=a(i,!k,l)*b(i,j,!k); //will compile c(j,l,k)=a(i,k,l)*b(i,j,!k); //will cause compilation error </syntaxhighlight> |
#### Howdy, Stranger!
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# Introduction: Susan Potter
edited March 2018 in Chat
At work, I try to solve problems usually by designing, developing, maintaining, troubleshooting, and/or evolving software [distributed] systems. At home, I'm trying to teach my children the wonder of mathematics. Being able to apply the ideas and concepts in category theory to more situations will improve my fluidity in applying these techniques in both my work solutions and provide more accessible examples to my children.
• Options
1.
Hello and welcome to the course. I’m another student and I also have a young child (almost 4 years old). It’s really great you are looking at category theory for novel ways to teach your kids. I think young kids have a lot more capacity for understanding abstract ideas than they are given credit for. I have introduced mine to some basic arithmetic, geometry and set theory. But I don’t yet have a systematic approach or any resources which I have found particularly good. Can I ask what age are your children and if you have found any good resources? Thank you, and good luck with the course!
Comment Source:Hello and welcome to the course. I’m another student and I also have a young child (almost 4 years old). It’s really great you are looking at category theory for novel ways to teach your kids. I think young kids have a lot more capacity for understanding abstract ideas than they are given credit for. I have introduced mine to some basic arithmetic, geometry and set theory. But I don’t yet have a systematic approach or any resources which I have found particularly good. Can I ask what age are your children and if you have found any good resources? Thank you, and good luck with the course!
• Options
2.
Hello Nasos, I'm also very interested in learning, although I don't have children. Piaget did a lot of research on how mathematico-logical structures develop. In later years he was interested in category theory. There is a paper with a learning task that tries to model specifically category theoretic knowledge (https://www.karger.com/Article/Abstract/275811). Unfortunately the task description is a bit cryptic but maybe it can serve as an inspiration to find resources.
Comment Source:Hello Nasos, I'm also very interested in learning, although I don't have children. Piaget did a lot of research on how mathematico-logical structures develop. In later years he was interested in category theory. There is a paper with a learning task that tries to model specifically category theoretic knowledge (https://www.karger.com/Article/Abstract/275811). Unfortunately the task description is a bit cryptic but maybe it can serve as an inspiration to find resources.
• Options
3.
Welcome and good luck, Twitter friend from afar!
Comment Source:Welcome and good luck, Twitter friend from afar! |
Plus One Public Exam March 2019 One Mark Question Paper
11th Standard
Reg.No. :
•
•
•
•
•
•
Chemistry
Time : 01:00:00 Hrs
Total Marks : 100
100 x 1 = 100
1. An element X has the following isotopic Composition 200X = 90%, 199X = 8% and 202X = 2% The Weighted average atomic mass of the element X is closet to
(a)
201 u
(b)
202 u
(c)
199 u
(d)
200 u
2. The equivalent mass of a trivalent metal element is 9 g eq-1 the molar mass of its anhydrous oxide is
(a)
102 g
(b)
27 g
(c)
270 g
(d)
78 g
3. Total number of electrons present in 1.7 g of ammonia is
(a)
6.022 x 1023
(b)
$\frac { 6.022\times { 10 }^{ 22 } }{ 1.7 } \quad$
(c)
$\frac { 6.022\times { 10 }^{ 24 } }{ 1.7 }$
(d)
$\frac { 6.022\times { 10 }^{ 23 } }{ 1.7 }$
4. Identify disproportionation reaction
(a)
CH4 + 2O2 $\longrightarrow$ CO2+ 2H2O
(b)
CH4 + 4Cl2 $\longrightarrow$ CCl4 + 4HCI
(c)
2F2+ 2OH $\longrightarrow$ 2F-+ OF2+ H2O
(d)
2NO2 + 2OH- $\longrightarrow$ NO-2 + NO-3 + H2O
5. Which of the following statement(s) is/are not true about the following decomposition reaction.
2KClO3 $\longrightarrow$ 2KCl + 3O2
(i) Potassium is undergoing oxidation
(ii) Chlorine is undergoing oxidation
(iii) Oxygen is reduced
(iv) None of the species are undergoing oxidation and reduction.
(a)
only (iv)
(b)
(i) and (iv)
(c)
(iv) and (iii)
(d)
All of these
6. Two 22.4 litre containers A and B contains 8 g of O2 and 8 g of SO2 respectively at 273 K and 1 atm pressure, then
(a)
Number of molecules inA and B are same
(b)
Number of molecules in B is more than that in A.
(c)
The ratio between the number of molecules in A= to number of molecules in B is 2:1
(d)
Number of molecules in B is three times greater than the number of molecules in A
7. What is the mass of precipitate formed when 50 ml of 8.5 % solution of AgNO3 is mixed with 100 ml of 1.865 % potassium chloride solution?
(a)
3.59g
(b)
7g
(c)
14 g
(d)
28 g
8. The mass of a gas that occupies a volume of 612.5 ml at room temperature and pressure (250 c and 1 atm pressure) is 1.1g. The molar mass of the gas is
(a)
66.25 g mol-1
(b)
44 g mol-1
(c)
24.5 g mol-1
(d)
662.5 g mol-1
9. Which of the following contain same number of carbon atoms as in 6 g of carbon-12.
(a)
7.5 g ethane
(b)
8 g methane
(c)
both (a) and (b)
(d)
none of these
10. Which one of the following is used as a standard for atomic mass.
(a)
6C12
(b)
7C12
(c)
6C13
(d)
6C14
11. Maximum oxidation state is present in the central metal atom of which compound
(a)
CrO2Cl2
(b)
MnO2
(c)
[Fe(CN)6]3-
(d)
MnO
12. What will be the basicity of H3BO3, which is not a protic acid?
(a)
One
(b)
Two
(c)
Three
(d)
Four
13. Assertion: The ash produced by burning paper in air is lighter than the original mass of paper.
Reason: he residue left after combustion of a chemical entity is always lighter
(a)
Both assertion and reason are correct and reason is the correct explanation for assertion.
(b)
Both assertion and reason are correct but reason is not the correct explanation for assertion
(c)
Assertion is true but reason are false
(d)
Both assertion and reason are false
14. How many grams are contained in 1 gram atom of Na?
(a)
13g
(b)
1 g
(c)
23 g
(d)
1/23g
15. Based on equation E = $-2.178\times { 10 }^{ -18 }J\left( \frac { { Z }^{ 2 } }{ { n }^{ 2 } } \right)$certain conclusions are written. Which of them is not correct?
(a)
Equation can be used to calculate the change in energy when the electron changes orbit
(b)
For n = I, the electron has a more negative energy than it does for n = 6 which means that the electron is more loosely bound in the smallest allowed orbit
(c)
The negative sign in equation simply means that the energy of electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus.
(d)
Larger the value of n, the larger is the orbit radius.
16. Two electrons occupying the same orbital are distinguished by
(a)
azimuthal quantum number
(b)
spin quantum number
(c)
magnetic quantum number
(d)
orbital quantum number
17. Shape of an orbital is given by
(a)
Principal quantum number
(b)
Spin quantum number
(c)
Azimuthal quantum number
(d)
Magnetic quantum number
18. What is the maximum numbers of electrons that can be associated with the following set of quantum numbers? n = 3, I = 1 and m =-1
(a)
4
(b)
6
(c)
2
(d)
= 10
19. The total number of orbitals associated with the principal quantum number n = 3 is
(a)
9
(b)
8
(c)
5
(d)
7
20. How many electrons in an atom with atomic number 105 can have (n + I) = 8 ?
(a)
30
(b)
17
(c)
15
(d)
unpredictable
21. Electron density in the yz plane of 3dxy-y2 orbital is
(a)
zero
(b)
0.50
(c)
0.75
(d)
0.90
22. If uncertainty in position and momentum are equal, then minimum uncertainty in velocity is
(a)
$\frac { 1 }{ m } \sqrt { \frac { h }{ \pi } }$
(b)
$\sqrt { \frac { h }{ \pi } }$
(c)
$\frac { 1 }{ 2m } \sqrt { \frac { h }{ \pi } }$
(d)
${ \frac { h }{4\pi } }$
23. A macroscopic particle of mass 100 g and moving at a velocity of 100 cm S-1 will have a de Broglie wavelength of
(a)
6.6 x 10-29 em
(b)
6.6 x 10-30 em
(c)
6.6 x 10-31 em
(d)
6.6 x 10-32 em
24. Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle?
(a)
$\triangle x.\triangle p\ge \frac { h }{ 4\pi }$
(b)
$\triangle x.\triangle v\ge \frac { h }{ 4\pi m }$
(c)
$\triangle E.\triangle t\ge \frac { h }{ 4\pi }$
(d)
$\triangle E.\triangle x\ge \frac { h }{ 4\pi }$
25. Electronic configuration of species M2+ is 1s2 2s2 2p6 3s2 3p6 3d6 and its atomic weight is 56. The number of neutrons in the nucleus of species M is:
(a)
26
(b)
22
(c)
30
(d)
24
26. Which of the following experiment proves the presence of an electron in an atom?
(a)
Rutherford's $\alpha$-ray scattering experiment
(b)
Davisson and Germer experiment
(c)
J. J. Thomson cathode ray experiment
(d)
G.P. Thomson gold foil experiment
27. de Broglie equation is________________
(a)
E=$h \ \gamma$
(b)
E=mc2
(c)
$\gamma ={E_2-E_1 \over h}$
(d)
$\lambda ={h\over mv}$
28. The idea of stationary orbits was first given by_________.
(a)
Rutherford
(b)
J.J. Thomson
(c)
Niels Bohr
(d)
Max Planck
29. Which of the following statements is correct for an electron that has the quantum numbers n = 4 and in = -2.
(a)
The electron may be in 2p orbital
(b)
The electron may be in 4d orbital
(c)
The electron is in the second main shell
(d)
The electron must have spin quantum number as $+\frac{1}{2}$
30. Period of an element is represented by _____ quantum number
(a)
Principal
(b)
Azimuthal
(c)
Magnetic
(d)
Spin
31. The atomic weight of Au is ______
(a)
195
(b)
197
(c)
198
(d)
196
32. Match the list I with List II and select the correct answer using. the code given below the lists.
List I List II A Metalloid 1 Cerium B Noble gas 2 Nobelium C Trans uranium element 3 Arsenic D Lanthanide 4 Argon
(a)
A B C D 1 3 2 4
(b)
A B C D 4 2 1 3
(c)
A B C D 3 4 2 1
(d)
A B C D 2 1 4 3
33. Which pair of elements has the same characteristic chemical properties?
(a)
Z = 13, Z = 22
(b)
Z = 2, Z =4
(c)
Z = 4, Z = 24
(d)
Z = 3, Z = 11
34. "The relative tendency of a bonded atom in a molecule to attract the shared pair of electrons towards itself" is termed as_____
(a)
electron gain enthalpy
(b)
electronegativity
(c)
electron affinity
(d)
ionisation energy
35. Which orbital diagram gives an insight to the highest ionization energy?
(a)
(b)
(c)
(d)
36. Gadolinium belong to '4f series.Its atomic number is 64. Which of the following is the correct electronic configuration of gadolinium?
(a)
[Xe]4f95s1
(b)
[Xe]4f75d16s2
(c)
[Xe]4f65d26s2
(d)
[Xe]4f8d2
37. Which of the following is the correct electronic configuration of noble gases?
(a)
ns2 np6 nd10
(b)
ns2 np5
(c)
ns2 np6
(d)
ns2 np3
38. On moving from left to right across a period in the periodic table, the metallic character__________.
(a)
increases
(b)
decreases
(c)
remains constant
(d)
first increases and then decreases
39. Various successive ionisation enthalpies (in kJ mol-1) of an element are given below.
IE1 IE2 IE3 IE4 IE5 577.5 1,810 2,750 11,580 14,820
The element is
(a)
phosphorus
(b)
Sodium
(c)
Aluminium
(d)
Silicon
40. Identify the wrong statement.
(a)
Amongst the isoelectronic species, smaller the positive charge on cation, smaller is the ionic radius
(b)
Amongst isoelectric species greater the negative charge on the anion, larger is the ionic radius
(c)
Atomic radius of the elements increases as one moves down the first group of the periodic table
(d)
Atomic radius of the elements decreases as one moves across from left to right in the 2nd period of the periodic table.
41. The element with positive electron gain enthalpy is
(a)
Hydrogen
(b)
Sodium
(c)
Argon
(d)
Fluorine
42. Which of the following orders of ionic radii is correct?
(a)
H- > H+ > H
(b)
Na+ > F- > O2-
(c)
F > O2- > Na+
(d)
None of these
43. Which of the following pairs of elements exhibit diagonal relationship?
(a)
Be and Mg
(b)
Li and Mg
(c)
Be and B
(d)
Be and Al
44. Water gas is
(a)
H2O(g)
(b)
CO + H2O
(c)
CO + H2
(d)
CO + N2
45. Which one of the following statements is incorrect with regard to ortho and para dihydrogen ?
(a)
They are nuclear spin isomers
(b)
Ortho isomer has zero nuclear spin whereas the para isomer has one nuclear spin
(c)
The para isomer is favoured at low temperatures
(d)
The thermal conductivity of the para isomer is 50% greater than that of the ortho isomer
46. Tritium nucleus contains
(a)
1 p+0 n
(b)
2 p+1 n
(c)
1 p + 2 n
(d)
none of these
47. Non-stoichiometric hydrides are formed by
(a)
(b)
carbon, nickel
(c)
manganese, lithium
(d)
nitrogen, chlorine
48. The hardness of water can be determined by volumetrically using the reagent
(a)
sodium thio sulphate
(b)
potassium permanganate
(c)
hydrogen peroxide
(d)
EDTA
49. The cause of permanent hardness of water is due to
(a)
Ca(HCO3)2
(b)
Mg(HCO3)2
(c)
CaCl2
(d)
MgCO3
50. The reaction H3PO2 + D2O ➝ H2DPO2 + HDO indicates that hypo-phosphorus acid is
(a)
tribasic acid
(b)
dibasic acid
(c)
mono basic acid
(d)
none of these
51. Water is a
(a)
basic oxide
(b)
acidic oxide
(c)
amphoteric oxide
(d)
none of these
52. Match the list Iwith List IIand select the correct answer using. the code given below the lists.
List I List II A H2O2 1 SiH4 B D2O 2 PdH C Metallic hydride 3 Bleach D Molecular hydride 4 Study of reaction mechanism
(a)
A B C D 1 3 2 4
(b)
A B C D 4 3 1 2
(c)
A B C D 3 4 2 1
(d)
A B C D 2 1 4 3
53. Choose the incorrect statement:
(a)
The boiling points of both deuterium and tritium are higher than that of protium.
(b)
The inter nuclear distances between the two bonded atoms are different in all the isotopes.
(c)
Enthalpy of dissociation is high in tritium
(d)
both (b) and (c)
54. Which of the following is electron precise hydride?
(a)
B2H6
(b)
NH3
(c)
H20
(d)
CH4
55. Which set of the metals do not have any effect on water?
(a)
Ag, Au, Pt
(b)
Na, Mg, Al
(c)
Fe, Ca, Zn
(d)
Fe, Pb, Na
56. Consider the following statements.
(i) Silver, Gold, Mercury and Platinum do not have any effect on water.
(ii) Carbon, Sulphur and Phosphorous do not react with water.
(iii) Beryllium reacts with water less violently.
Which of the following statements is/are not correct?
(a)
(i) only
(b)
(ii) and (iii)
(c)
(iii) only
(d)
(ii) only
57. Hydrogen resembles halogens in many respects for which several factors are responsible. Of the following factors which one is most important in this respect?
(a)
Its tendency to lose an electron to form a cation
(b)
Its tendency to gain an electron to attain stable electronic configuration.
(c)
Its low negative electron gain enthalpy value
(d)
Its small size
58. Assertion: Permanent hardness of water is removed by treatment with washing soda.
Reason: Washing soda reacts with soluble calcium and magnesium chlorides and sulphates in hard water to form insoluble carbonates
(a)
Both assertion and reason are true and reason is the correct explanation of assertion.
(b)
Both assertion and reason are true but reason is not the correct explanation of assertion.
(c)
Assertion is true but reason is false
(d)
Both assertion and reason are false
59. Which of the following compounds will not evolve H2 gas on reaction with alkali metals?
(a)
ethanoic acid
(b)
ethanol
(c)
phenol
(d)
none of these
60. RbO2 is
(a)
superoxide and paramagnetic
(b)
peroxide and diamagnetic
(c)
superoxide and diamagnetic
(d)
peroxide and paramagnetic
61. Assertion : BeSO4 is soluble in water while BaSO4 is not
Reason : Hydration energy decreases down the group from Be to Ba and lattice energy remains almost constant.
(a)
both assertion and reason are true and reason is the correct explanation of assertion
(b)
both assertion and reason are true but reason is not the correct explanation of assertion
(c)
assertion is true but reason is false
(d)
both assertion and reason are false.
62. The compound (X) on heating gives a colourless gas and a residue that is dissolved in water to obtain (B). Excess of CO2 is bubbled through aqueous solution of B, C is formed. Solid (C) on heating gives back X. (B) is
(a)
CaCO3
(b)
Ca(OH)2
(c)
Na2CO3
(d)
NaHCO3
63. When CaC2 is heated in atmospheric nitrogen in an electric furnace the compound formed is
(a)
Ca(CN)2
(b)
CaNCN
(c)
CaC2N2
(d)
CaNC2
64. Among the following the least thermally stable is
(a)
K2CO3
(b)
Na2CO3
(c)
BaCO3
(d)
Li2CO3
65. Spodumene is the silicate mineral of _____
(a)
lithium
(b)
sodium
(c)
cesium
(d)
francium
66. Dead burnt plaster is ________
(a)
CaSO4
(b)
CaSO4·1/2H20
(c)
CaSO4.H2O
(d)
CaSO4.2H20
67. Several blocks of magnesium are fixed to the bottom of a ship to
(a)
Keep away the sharks
(b)
prevent of rusting of iron ships
(c)
make the ship lighter
(d)
prevent puncturing by under sea rocks
68. Quick lime is:
(a)
CaCO3
(b)
CaO
(c)
CaSO4.2H2O
(d)
Ca(OH)2
69. Which one of the following metal act as co-factor in phosphate transfer of ATP by enzymes?
(a)
Calcium
(b)
Beryllium
(c)
Magnesium
(d)
Sodium
70. Which alkaline earth metal do not import colour to a non-Iuminous flame?
(a)
Beryllium
(b)
Calcium
(c)
Magnesium
(d)
Barium
71. Which of the following is used in photoelectric cells?
(a)
Na
(b)
K
(c)
Li
(d)
Cs
72. The temperatures at which real gases obey the ideal gas laws over a wide range of pressure is called
(a)
Critical temperature
(b)
Boyle temperature
(c)
Inversion temperature
(d)
Reduced temperature
73. A bottle of ammonia and a bottle of HCI connected through a long tube are opened simultaneously at both ends. The white ammonium chloride ring first formed will be
(a)
At the center of the tube
(b)
Near the hydrogen chloride bottle
(c)
Near the ammonia bottle
(d)
Throughout the length of the tube
74. The value of universal gas constant depends upon
(a)
Temperature of the gas
(b)
Volume of the gas
(c)
Number of moles of the gas
(d)
units of Pressure and volume.
75. The table indicates the value of van der Waals constant 'a' in (dm3)2 atm. mol-2.
Gas O2 N2 NH3 CH4 a 1.360 1.390 4.170 2.253
The gas which can be most easily liquefied is
(a)
O2
(b)
N2
(c)
NH3
(d)
CH4
76. If temperature and volume of an ideal gas is increased to twice its values, the initial pressure P becomes
(a)
4P
(b)
2P
(c)
P
(d)
3P
77. Equal moles of hydrogen and oxygen gases are placed in a container, with a pin-hole through which both can escape what fraction of oxygen escapes in the time required for one-half of the hydrogen to escape.
(a)
$\frac { 3 }{ 8 }$
(b)
$\frac { 1 }{ 2 }$
(c)
$\frac { 1 }{ 8 }$
(d)
$\frac { 1 }{ 4 }$
78. If the volume of a fixed mass of a gas is reduced to half at constant temperature, the gas pressure _____________
(a)
remains constant
(b)
doubles
(c)
reduces to half
(d)
becomes zero
79. Match the list - I with List - II and select the correct answer using the code given below the lists.
List-I List-II A. $\frac { { r }_{ 1 } }{ { r }_{ 2 } } =\sqrt { \frac { { M }_{ 2 } }{ { M }_{ 1 } } }$ 1. Boyle's law B. PV = constant 2. Graham's law C. $\frac { V }{ T } =constant$ 3. Ideal gas D. PV=nRt 4. Charle's law
(a)
A B C D 1 2 3 4
(b)
A B C D 4 3 2 1
(c)
A B C D 2 1 4 3
(d)
A B C D 1 3 4 2
80. A gas such as carbon monoxide would be most likely to obey the ideal gas law at
(a)
High temperature and high pressure
(b)
High temperature and low pressure
(c)
Low temperature and high pressure
(d)
Low temperature and high pressure
81. In a closed room of 1000 m3 a perfume bottle is opened up. The room develops smell. This is due to which property of gases
(a)
Viscosity
(b)
Density
(c)
Diffusion
(d)
None
82. Which of the following diagram directly describes the behaviour of a fixed mass of an ideal gas?
(a)
(b)
(c)
(d)
83. The instrument used for measuring the atmospheric pressure is ___________.
(a)
lactometer
(b)
barometer
(c)
electrometer
(d)
ammeter
84. Which one of the following is absolute zero?
(a)
293 K
(b)
273 K
(c)
-273.15o C
(d)
0o C
85. In an adiabatic process, which of the following is true?
(a)
q = w
(b)
q = 0
(c)
ΔE = q
(d)
PΔV= 0
86. An ideal gas expands from the volume of 1 x 10-3 m3 to 1 x 10-2 m3 at 300 K against a constant pressure at 1 x 105 Nm-2. The work done is
(a)
- 900 J
(b)
900 kJ
(c)
270 kJ
(d)
-900 kJ
87. The heat of formation of CO and CO2 are - 26.4 kcal and - 94 kcal, respectively. Heat of combustion of carbon monoxide will be
(a)
+ 26.4 kcal
(b)
- 67.6 kcal
(c)
- 120.6 kcal
(d)
+ 52.8 kcal
88. Given that C(g)+ O2(g) ⟶ CO2(g)ΔHo =-akJ;2CO(g)+O2(g) ⟶ 2CO2(g)ΔHo=-bkJ; Calculate the AHo for the reaction C(g)+ 1/2O2(g) ⟶ CO(g)
(a)
$\frac{b+2a}{2}$
(b)
2a-b
(c)
$\frac{2a-b}{2}$
(d)
$\frac{b-2a}{2}$
89. In an isothermal reversible compression of an ideal gas the sign of q, ΔS and ware respectively
(a)
+,-,-
(b)
-,+,-
(c)
+,-,+
(d)
-, -, +
90. The values of ΔH and ΔS for a reaction are respectively 30 kJ mol-1 and 100 JK-1 mol-1. Then the temperature above which the reaction will become spontaneous is
(a)
300 K
(b)
30 K
(c)
100 K
(d)
200 C
91. For an isothermal process.
(a)
q = 0
(b)
dV = 0
(c)
dT = 0
(d)
dP = 0
92. Which among the following is not a state function?
(a)
Pressure
(b)
Volume
(c)
Temperature
(d)
Work
93. When water freezes in a glass beaker, ΔS of the system _____
(a)
ΔS>0
(b)
ΔS<0
(c)
ΔS=0
(d)
ΔS≥0
94. What is correct about ΔG
(a)
It is zero for reversible reaction
(b)
It is positive for spontaneous reactions
(c)
It is negative for non-spontaneous reaction
(d)
It is zero for non-spontaneous reaction
95. Solve: ΔH=10 k cal mol-1, ΔS=20 cal deg-1 mol-1 and T=300k. Then ΔG=?
(a)
-18,000 cals mol-1
(b)
18,000 cals mol-1
(c)
-16,000 cals mol-1
(d)
4000 cals mol-1
96. Which of the following is a state function?
(a)
q
(b)
$\Delta$q
(c)
w
(d)
$\Delta$S
97. The enthalpy of vapourisation of a liquid is 30 kJ mol -1 and the entropy of vapourisation is 75 JK -1 mol-1. The boiling point of the liquid at 1 atm is:
(a)
250K
(b)
400K
(c)
450K
(d)
600K
98. For the reaction, X2 O4(l) $\rightarrow$ 2 XO2 (g), $\Delta$U=2.1 Kcal, $\Delta$S = 20 cal K-1 at 300 K. Hence,$\Delta$G is:
(a)
2.7 Kcal
(b)
-2.7 Kcal
(c)
9.3 K.=cal
(d)
-9.3 Kcal
99. Hot water in a thermos flask is an example of ______
(a)
closed system
(b)
open system
(c)
isolated system
(d)
isochoric system
100. Which one of the following is not a path function?
(a)
Work
(b)
Heat
(c)
Pressure
(d)
Either (a) or (b) |
# Homogenisation of a curve with another curve.
Find the equation a pair of straight lines through origin which passes through the intersection of curves whose equation are $$L1: x^2+y^2-2x-2y-2=0$$ and $$L2: x^2+y^2-6x-6y+14=0$$.
I know that the curves have to be homogenised, although I don't know how to homogenise a curve with another. All I know is how to homogenise a curve with line, but this is completely different. Please help.
Subtract the two equations $L1-L2$ will give
$x^2+y^2-2x-2y-2-(x^2+y^2-6x-6y+14)=0\rightarrow 4 x + 4 y=16 \rightarrow y=4-x$
Substitute in $L1$
$x^2+(4-x)^2-2x-2(4-x)-2=0\rightarrow 2 x^2-8 x+6=0$
and finally the two points of intersection of the two circles $A(1;\;3),\;B(3;\;1)$
Then is easy to write the equation of the lines that pass through the origin and $A$ and $B$
Hope this helps |
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Polynomial mappings. (English) Zbl 0829.11002
Lecture Notes in Mathematics. 1600. Berlin: Springer-Verlag. vi, 130 p. DM 34.00; öS 265.20; sFr 34.00 (1995).
Let $R$ be an integral domain and $K$ its quotient field. The main purpose of the first part of the book is to study the ring $\text{Int}\left(R\right)=\left\{f\in K\left[X\right]$; $f\left(R\right)\subset R\right\}$. It is well known (G. Pólya, 1915) that, when $R=ℤ$, $\text{Int}\left(R\right)$ is a free $R$-module generated by a family ${\left\{{h}_{n}\right\}}_{n\in ℕ}$ of polynomials with $deg{h}_{n}=n$ (these are in fact the binomial polynomials). An open problem is the determination of all rings $R$ with this property.
The author discusses this problem, in particular in the case when $R={I}_{K}$ is the ring of integers of a number field $K$. Another interesting question is about the algebraic properties of $\text{Int}\left(R\right)$: noetherianity, Skolem property, maximal and prime ideals, Krull dimension, Prüfer property, etc. This first part also deals with the values of the successive derivatives of polynomials or of rational functions.
The second part is devoted to the study of fully invariant subsets of a field by polynomial mappings: if $f\in ℚ\left[X\right]$ and $S\subset ℚ$ satisfy $f\left(S\right)=S$, then either $S$ is finite or $degf=1$. The aim of study is to determine the fields with this property or its analogue in the case of several variables. In particular, is this property stable by purely transcendental extension (yes) or by finite extension? The last chapter deals with polynomial cycles: by a theorem of I. N. Baker (1960) every polynomial of degree $\ge 2$ in $ℂ\left[X\right]$ has cycles of every order with at most one exception. The author considers this question in algebraic number fields.
This nice, short (130 pages) but dense book makes a sound review of the question. As often as possible, concise proofs are given. More technical results or related questions are described and references are given; the text is well supplemented by many exercises given at the end of each chapter. The appendix states a list of 21 open problems and the book contains 11 pages of bibliographical references (from 1895 to 1994). It is interesting to have such a synthesis on questions which are often studied but scattered in the literature.
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# Write a generalization correlating solubility with ionization
Further afield salt in Cheshire and write a generalization correlating solubility with ionization the west Midlands also dissolves underground producing salt springs on wiches, hence the towns with wich name endings such as Droitwich, Nantwich, Middlewich and Northwich.Aug 18, 2008 · what is the general statements correlating solubility to the nature of solute and solvent? Debenedetti. A newer improved empirical model has been published just recently [ 18 ]. Gain understanding today! Asked in Chemistry What is a substance with a low solubility ?
I think low pH means high degree of ionization. 6. Compounds containing the following 4 ionic compounds are generally SOLUBLE. The methodology was applied to the calculation of solubility of two proteins. We have seen that the calculation of [H 3 O+] and pH for a solution of a pure weak acid in water requires write a generalization correlating solubility with ionization solving the K a equilibrium expression for the acid. 1 decade ago. Best Answer.
Seems my ap chem review book is using these two terms interchangeably and I am just plain confused. Chem 116 POGIL Worksheet - Week 10 Weak Bases, Acid Strength and Structure, Common Ion Effect, and Buffers Why? • Use Table G to determine if a solution is saturated, unsaturated, and supersaturated. A generalization of the retention index system including linear temperature programmed gas-liquid partition chromatography, J. which is write a generalization correlating solubility with ionization called an acid-ionization constant.The degree of ionization of a weak electrolyte is the fraction of molecules that react with water to give ions. Similarly, weak acid is absorbed at a faster rate from stomach (pH 1.4 – 2).
Abstract Booklet . You can submit your request write a generalization correlating solubility with ionization and our online homework helpers will provide the solution within the shortest time Chem 116 POGIL Worksheet - Week 10 Weak Bases, Acid Strength and Structure, Common Ion Effect, and Buffers Why? Am I correct to assume that the ionization coefficient is the fraction of the ammonia that has ionized? Further, the original series is not complete as there are plenty of ions available in the simple and complex form (both inorganic and organic) which have not been tested and await generalization.. So the uncharged substances can be passed easily due to its lipid solubility. conjugate acid-base pair--A pair of compounds that differ by the presence of one H+ unit 1970 A comparison of the theories Arrhenius, Bronsted and Lewis shows a progressive generalization of the acid base concept. the atomic number (Z) for the first 20 elements. ) NIST Spectra nist ri 1007 (Program type: Ramp; Column cl.
Moore and Stanitski) Sections 5-2a and 5-3, and/or Chapter 1.3-1.5 and Chapter 2. Mar 01, write a generalization correlating solubility with ionization 2016 · Finding Patterns in Atomic Radius & Ionization Energy A period in chemistry is a complete row of the periodic table. Apr 13, 2007 · The solubility of alcohols in water depends on the formation of hydrogen bond between the OH-group of the alcohol and the H of water;therefore when the …. Together with an avalanche of alternative experimental evidence [5–11], such. May 02, 2016 · Say I have an ion XY. Thanks A 0.1 M solution of phosphoric acid is a better conductor. Mechanism Of Solubilization 5. Degree of ionization?
Ionization potentials depend principally on four main factors: atomic size, nuclear charge, the shielding effect of inner electrons, and the type of electron removed Neutralization reactions are one type of chemical reaction that proceeds even if one write a generalization correlating solubility with ionization reactant is not in the aqueous phase. His collaboration with Payen led to the discovery of diastase and of its presence in human saliva. o Determine the factors that affect the solubility of a solution. 4.11 Molar Solubility and the Common Ion Effect 7:20. INTRODUCTION & APPLICATION OF SOLUBILITY & SOLUBILIZED SYSTEM CONTENT: - 1.
• Calculating the solubility of a slightly soluble salt in a solution of a common ion. Types Of Solubility 4. 13 – 15 January, 2020 . 2. In … 9.6/10 (429) Write A Generalization Relating Solubility With Ionization sesufmattliper.ml/write-a-generalization-relating-solubility-with-ionization.html Writing quality college papers can write a generalization relating solubility with ionization really be such a stress and pressure. The samples were exposed to 254-nm. the bronsted-lowry concept of acids and bases Using this theory, you should be able to write weak acid/base dissociation equations and identify acid, base, conjugate acid and conjugate base. 2. write a generalization correlating solubility with ionization
## With generalization ionization write a solubility correlating
Thus, solubility also depends on the extent of the ionization of the salt Writing is a complex skill for every student. Day 2: Quantum Theory If you have not yet worked through the Introduction, please do so before beginning this section.As you work through this section, if you find that you need a bit more background material to help you understand the topics at hand, you can consult “Chemistry: The Molecular Science” (5th ed. Chemistry – Unit 11 write a generalization correlating solubility with ionization – Worksheet 2 Periodic trends 1. Use group numbers from the periodic table to make generalizations. The solvent particles collide with the solute particles. Find the pH and the degree of ionization for an 0.10 M solution of formic acid: Initial Equilibrium. What is the difference between its dissociation or solubility, or are they the same? 6. A generalization of the procedure derived above, which also will allow determina- tion of less separated pKg values of polyfunctional substances, will be given in another report, Appendix As shown above, the solubility data S, at pH, follow a linear relationship, i.e. Version 2 – 29 November.
For example, the chemical reaction between HCl(aq) and Fe(OH) 3 (s) still proceeds according to the equation 3 HCl(aq) + Fe(OH) 3 (s) → 3 H 2 O(ℓ) + FeCl 3 (aq) even though Fe(OH) 3 is not soluble. Explanation: The solubility of any ionic compound is due to the ionization of the compound and then the strong ion-dipole interactions acting between the ions and the solvent. Solubility rules 1. The question got bumped and I looked at it. A model correlating physico-chemical parameters directly with the solubility of the complexes was also presented . nd British Planetary Sciences Conference . Actually, they need it write a generalization correlating solubility with ionization to be in order to successfully go through college. I dissolve it in a solution.
Write a sentence giving a general description of graph 1. These techniques allow the experiment to distinguish excitations in the ion that occur during and after ionization. Nov 21, 2019 · where did the resume originate from, truck driver helper resumetop report ghostwriting for hire for collegewrite a descriptive essay about the beachuniversity dissertation guidelinestop movie review ghostwriting for hire ca. The rule is "like dissolves like". Likewise silica, SiO 2, has very low solubility in water because its atoms are held together in a 3-dimensional covalent lattice, but will react with bases so it is an acid. It is likely that Lewis Carroll was inspired to write Alice in Wonderland by sinkholes he knew at Ripon and Croft near Darlington. Divide the work among group members to fill in each of the tables in Model 1 Write an equation that represents the second ioniz Which of the following options correctly lists the The first three ionization energies for Ba is give. The developed expressions are exact provided Henry's law is valid Chapter 7 Electronic Configurations and the Properties of Atoms - 3 - In this text, we will arbitrarily assign ms = +½ to electrons represented with an upward arrow (also called “spin up” electrons) and ms = ½ to electrons represented with a downward arrow (also called “spin down” electrons) Acid-base titrations depend on the write a generalization correlating solubility with ionization neutralization between an acid and a base when mixed in solution. university essay guise write a generalization correlating solubility with ionization! Andrew L.
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Six Rules for writing oxidation/reduction reactions so that the products can be predicted when considering the. they approximate to a straight line y, = mx, + a The approximation criterion. The endpoint and the equivalence point are not exactly the same: the equivalence point is determined by the stoichiometry of the reaction, while the endpoint is just the color change from the indicator While it may seem that randomness always increases when a crystal is dissolved into a liquid phase, it does not have to be that way Concerning sugar, the molecule has a large number of hydroxyl groups and is generally rather large when compared with the water molecule around it — much larger than your average sodium or chloride ions Find the pH and the degree of ionization for an 0.10 M solution of formic acid: Initial Equilibrium. Thanks A 0.1 M …. o Predict the solubility of an ionic compound by using the solubility …. The article deals with experimental determination of ionization constants and solubility for the compounds (target products, initial β-lactams, acylating agents and by-products) involved in enzymatic synthesis of some therapeutically used aminopenicillins and aminocephalosporins, write a generalization correlating solubility with ionization namely ampicillin, amoxicillin, cephalexin, cephadroxil, cephaloglycin, cefaclor, cefprozil, cefatrizine o Determine the factors that affect the solubility of a solution. Panagiotopoulos, and Pablo G. If we have a large range of examples, if our observation is constantly directed to seeking the correlation of cause and effect in people's actions, their actions appear to us more under compulsion and less free the more correctly we connect the effects with the causes Highlights An expression for the solubility of proteins as a function of pH is developed. Ferguson*, Athanassios Z.
Nitrogen, which has a half-filled shell, has a higher ionization potential than oxygen, which has one electron more than a …. If the extent of ionization is 20% or more. write a generalization correlating solubility with ionization Chromatogr., 11, 1963, 463-471. On the other hand, ionization reflects if a compound is present in the charged or uncharged state and is at least influenced by two major parameters Background. Model Note: Proceed to Questi HCH3COO …. The article deals with experimental determination of ionization constants and solubility for the compounds (target products, initial β-lactams, acylating agents and by-products) involved in. Persoz studied the solubility of chemical compounds and their molecular volumes. 4.11 2.b and I am going to take a weak acid and write it in this space right here [take a weak acid, and I am going to take a weak acid and write it in this space right here HF for example.] and write it in this space right here HF for example.] And when you shift this reaction here. Recently Viewed. Our online assignment help services are quite extensive and cover all types of homework help needed by students. Highlights An expression for the solubility of proteins as a function of pH is developed.
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What is the difference between its dissociation or solubility, or are they the same? The partition coefficient, abbreviated P, is defined as a particular ratio of the concentrations of a solute between the two solvents (a biphase of liquid phases), specifically for un-ionized solutes, and the logarithm of the ratio is thus log P.: 275ff When one of the solvents is water and the other is a non-polar solvent, then the log P value is a measure of lipophilicity or hydrophobicity Selective Interaction of Ethidium Derivatives with Quadruplexes: An Equilibrium Dialysis and Electrospray Ionization Mass Spectrometry Analysis Article in Biochemistry 42(35):10361-71 · October. The ionization potentials within a period generally increase as you go to the right in that period. As a green material, SCCO2 has desirable properties s. In similar fashion, calculating the. The solubility is calculated with information of the primary protein structure. The article deals with experimental determination of ionization constants and solubility for the compounds (target products, initial β-lactams, acylating agents and by-products) involved in enzymatic synthesis of some therapeutically used aminopenicillins and aminocephalosporins, namely ampicillin, amoxicillin, cephalexin, cephadroxil, cephaloglycin, cefaclor, cefprozil, cefatrizine Apr 18, 2015 · Ksp = ([Positive Ion]^n x [Negative Ion]^n) divide write a generalization correlating solubility with ionization by [Compound] n is the number of moles and most of the time concentration of the compound isn't involved in the equation because solids and liquids are emitted from the Equilibrium equation. Session 3, Talk 3 (1:40 PM) Numerous experimental studies have been conducted to determine the solubility of n-. H-044. Briefly, the pellets were resuspended in 5 m m Tris-HCl (pH 7.5) buffer with 0.5 m m [14 C]halothane, plus or minus 5 m m non-radioactive halothane (higher competing concentrations of halothane were not used because of limited solubility and UV absorption), in 2-ml quartz cuvettes (5-mm path length) at 25 °C. thanks! Every ion is a spectator ion and there is not net ionic equation at all So the uncharged substances can be passed easily due to its lipid solubility.
Definition Of Solubility 3. • Use Table G to determine if a solution is saturated, unsaturated, and supersaturated. Like-Dissolves-Like: A solute is soluble in a given solvent if it has the tendency to make interactions with the molecules of the. write a generalization correlating solubility with ionization Dec 27, 2019 · Free Biology, Chemistry, Geology homework help via qualified mentors. • Predicting whether precipitation will occur • Determining the qualitative effect of pH on solubility. the solubility increases. The methodology was applied to the calculation of solubility of two proteins. ;) Answer Save.
When one realizes that Fe(OH) 3 (s) is a component of rust, this. Most of these investigations considered the “natural” CDs, and generally, models were obtained with sufficient predictive power.. Jun 23, 2011 · Abstract. However, you don’t need to worry about it because you can simply seek our essay writing write a generalization relating solubility with ionization … 9.4/10 (411) Write A Balanced Equation For The Reaction Of Propanoic https://smashingessays.com/write-a-balanced-equation-for-the-reaction-of-propanoic write a generalization correlating solubility with ionization. DEPARTMENT OF LABOR. how to write a book quickly Animetal usa thesis of a cruel angel dos and don'ts of writing a college essay write a generalization correlating solubility with ionization Advertising hot topics to write article best content ghostwriters website for college how to write a very long sentence Ap us history essay on articles of confederation. Lv 7. Supercritical carbon dioxide (SCCO2) is an ecofriendly supercritical fluid that is chemically inert, nontoxic, noninflammable and nonpolluting. Moore and Stanitski) Sections 5-2a and 5-3, and/or Chapter 1.3-1.5 and Chapter 2. 2 Answers. E.g Solubility of NaCl will be: Ksp = [Na^+]^1 x [Cl^-]^1 No dividing by the [Compound] because NaCl is a solid, so it doesn't take part The characteristics that enable us write a generalization correlating solubility with ionization to distinguish one substance from another are called properties.
NdUsing the data in the table on the 2 sheet in the workbook, plot the …. Dec 22, 2013 · The quick answer is that “Like dissolves like”. Journal of the American Chemical Society. 4.11 Molar Solubility and the Common Ion Effect 7:20. Relevance. Abstracts are listed in alphabetical order, by the surname of first author . But, many uncharged drugs can’t be absorbed or they are insufficiently lipid soluble like aminoglycosides Common Ion Effect on Acid Ionization 3 5. Department of Chemical Engineering, Princeton University . Occupational Exposure to 2-Methoxyethanol, 2-Ethoxyethanol and Their Acetates (Glycol Ethers). This is the executive summary, not the resume., apa style format for thesis paper, best curriculum vitae editor service uk, write a generalization correlating solubility with ionization, boutique business plan template, apeejay school saket homeworkBut, are they so really easy that each company is able write a generalization correlating solubility with ionization to cope bel ami robert pattinson resume. ionization in hydrocarbon molecules [4] have used covariance techniques, correlating energies in the photoelectron spectra with the ionic fragments.
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The second ionization potential is greater than the first, and each succeeding ionization potential is, in general, greater than the one before. 4. Aim Of Studying Solubility 2. 4.11 2.b and I am going to take a weak acid and write it in this space right here [take a weak acid, and I am going to take a weak acid and write it in this space right here HF for example.] and write it in this space right here write a generalization correlating solubility with ionization HF for example.] And when you shift this reaction here. The problem is in part asking about the pH of a 0.1 molar ammonia solution. The oxides of phosphorus dissolve in water to produce phosporus acid (H 3 PO 3) and phosphoric acid (H 3 PO 4) Oct 25, 2008 · the solubility of a substance can only tell what about it, when the substance is bean identify e.g the solubility of sugar in water. However frankly speaking, I want to know about the relationship between. Therefore, it is easier to refer to a set of generalizations, sometimes called "solubility rules," that is based upon experimentation. Operational Skills • Writing solubility product expressions • Calculating Ksp from the solubility, or vice versa. Please use the template when requesting help and show your work. Neutralization reactions are one type of chemical reaction that proceeds even if one reactant is not in the aqueous phase.
Most of these investigations considered the “natural”. Using the data in the table of ionization energies, plot the first ionization energy (IE 1) vs. However, it is not easy to estimate write a generalization correlating solubility with ionization the relative magnitudes of these two forces or to quantitatively predict water solubilities of electrolytes. The energy expression for hydrogen-like atoms is a generalization of the hydrogen atom energy, in which Z is the nuclear charge (+1 for hydrogen, +2 for He, +3 for Li, …. In natural environments, bacteria must frequently cope with extremely scarce nutrients. A generalization of the procedure derived above, which also will allow determina- tion of less separated pKg values of polyfunctional substances, will be given in another report, Appendix As shown above, the solubility data S, at pH, follow a linear relationship, i.e. When a solute dissolves in a solvent the individual particles of the solute separate from their neighbours and move between the spaces of the solvent particles. Controllably Interfacing with Metal: A Strategy for Enhancing CO Oxidation on Oxide Catalysts by Surface Polarization. DEGREE OF IONIZATION is the fraction of a ….
Degree of ionization? Differences are mostly within experimental uncertainty. Is it true that low pH means high degree of ionization or high solubility? Familiar examples of physical properties include density, color, hardness, melting and boiling points, and electrical conductivity Assignment Expert is a leading provider of homework help to students worldwide. they approximate to a straight line y, = mx, + a The approximation criterion. A write a generalization correlating solubility with ionization physical property is a characteristic of matter that is not associated with a change in its chemical composition. It's a …. The ionization constant of carboxylic acids (RCOOH) in water (H20) are nearly independent of temperature thus a single constant is used for RCOOH ionization according to reaction 8 in Table 2.
The developed expressions are exact provided Henry's law is valid Here, the green substance has a greater solubility in the lower layer than in the upper layer. The OP seems to use the two terms coefficient of ionization and ionization coefficient interchangeably and assigns the variable $\alpha$. I launched this website in the international year of chemistry (2011) to help novice to advanced level students who pursue this subject either seriously or as a part of their studies and at the same time to contribute to the progress of science and technology by encouraging people to learn and question, especially by participating in the discussions at forums Write the balanced chemical equation for the ionization of each. Factors Affecting Solubility 6. Unit 11: Visit Document. For example, B C O F. Predicting Precipitates Using Solubility Rules. 1970 A comparison of the theories Arrhenius, Bronsted and Lewis shows a progressive generalization of the acid base concept. While it may seem that randomness always increases when a crystal is dissolved into a liquid write a generalization correlating solubility with ionization phase, it does not have to be that way Concerning sugar, the molecule has a large number of hydroxyl groups and is generally rather large when compared with the water molecule around it — much larger than your average sodium or chloride ions Aug 08, 2013 · Nowadays, the solubility data are used to determine pK a values for a wide range of drugs, where the pK a value is of great interest.87 The power of this technique is that poorly soluble drug can be analyzed at very low concentrations, in the order of μM, and with a precision up to ±0.5 in log units.84 A drawback is that for most solubility.
The value\of -11.28 is based on a pK of about 4.9 reported by Bomberger and Smith ' from potentiometric titrailons of actual refinery sour water streams.. Most studies focus on bacterial growth in nutrient replete conditions, while le. A model correlating physico-chemical parameters directly with the solubility of the complexes was also presented [17]. The energy expression for hydrogen-like atoms is a generalization of the hydrogen atom energy, in which Z is the nuclear charge (+1 for write a generalization correlating solubility with ionization hydrogen, +2 for He, +3 for Li, …. I dissolve it in a solution. Likewise silica, SiO 2, has very low solubility in water because its atoms are held together in a 3-dimensional covalent lattice, but will react with bases so it is an acid. Reasons For Insolubilization Of Drugs 8 Day 2: Quantum Theory If you have not yet worked through the Introduction, please do so before beginning this section.As you work through this section, if you find that you need a bit more background material to help you understand the topics at hand, you can consult “Chemistry: The Molecular Science” (5th ed. Use group numbers from the periodic table to make generalizations. DEGREE OF IONIZATION is the fraction of a ….
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Similarly, weak acid is absorbed at a write a generalization correlating solubility with ionization faster rate from stomach (pH 1.4 – 2). o Predict the solubility of an ionic compound by using the solubility …. Common Ion Effect on Acid Ionization 3 5. Outline the essential ideas in each of these theories and select three reactions, one that can be interpreted by all three theories, one that can be interpreted by two of them, and one that can be interpreted by only one. o Distinguish between saturated, unsaturated, and supersaturated solutions. Write the equation for the acid ionization constant, K a, for this acid. How ionized is water? Unit 11: Visit Document. start with: “as compounds become more ionized,…” A Sample Consisting Of 2 Moles He Is Expanded Isothermally At 0 Degrees From A sample consisting of 2 moles He is expanded isothermally at 0 degrees from 5.0dm3 to 20.0dm3..
The oxides of phosphorus dissolve in water to produce phosporus acid (H 3 PO 3) and phosphoric acid (H 3 PO 4) View 24 Common Ion Effect on Acid Ionization - Answers from SCIENCE Chemistry at Evanston Twp write a generalization correlating solubility with ionization High School. A newer improved empirical model has been published just recently [18]. Polar substances tend to dissolve in polar solvents, and nonpolar substances dissolve in nonpolar solvents. 1a. Not only students are intimate to the writing skills a lot of people are also write a generalization correlating solubility with ionization eager to write a good article. o Distinguish between saturated, unsaturated, and supersaturated solutions. B(aq) + H 2 O(l) <==> HB + (aq) + OH-(aq) has a base-ionization constant, K b (the equilibrium constant for. Write a sentence giving a general description of graph 1. Application of Solubility 7. Outline the essential ideas in each of these theories and select three reactions, one that can be interpreted by all three theories, one that can be interpreted by two of them, and one that can be interpreted by only one.
For example, the chemical reaction between HCl(aq) and Fe(OH) 3 (s) still proceeds according to the equation 3 HCl(aq) + Fe(OH) 3 (s) → 3 H 2 O(ℓ) + FeCl 3 (aq) even though Fe(OH) 3 is not soluble. This means in particular that polar solutes will dissolve in polar solvents and. Solubility and Molecular Conformations of n-Alkane Chains in Water . Divide the work among group members to fill in each of the tables in Model 1 Chemistry - how to write balanced ionic equations, Molecular, Complete Ionic, and Net Ionic Equations, examples and step by step solutions, How to write ionic and net ionic equations, How to write a double replacement net ionic equation, what are spectator ions, precipitation reaction, single …. While solubility is an endpoint value indicating the amount of a compound that is soluble in a solvent, dissolution describes the kinetic process of write a generalization correlating solubility with ionization a compound being solved in a solvent . Equilibria involving weak bases are treated similarly to those for weak acids.In general, a weak base B with the base ionization. Help For Personal Statement, cover letter for travel counselor position, organize binder homework, top annotated bibliography ghostwriter sites for school. But, many uncharged drugs can’t be absorbed or they are insufficiently lipid soluble like aminoglycosides Mar 01, 2016 · Finding Patterns in Atomic Radius & Ionization Energy A period in chemistry is a complete row of the periodic table.
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When one realizes that Fe(OH) 3 (s) write a generalization correlating solubility with ionization is a component of rust, this. The conventional approach for correlating this behaviour is to use the Setschenow equation (15 ) to describe the relationship between solubility and electrolyte concentration in terms of a single constant which is essentially the slope of the plot of log of the ratio of solubility in electrolyte solution to that in pure water against molarity May 31, 2009 · This classification arose because of exceptions observed when ions are attempted to fit in the original protein solubility scale of performance. Seems my ap chem review book is using these two terms interchangeably and I am just plain confused. The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H 2 O, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, OH − May 02, 2016 · Say I have an ion XY. Differences are mostly within experimental uncertainty. Write the equation for the acid ionization constant, K a, for this acid. Jun 23, 2011 · Abstract. 1 part in a hundred million, thus written as H₂O or HOH. One could write a molecular equation showing a double-replacement reaction, but both products, sodium chloride and ammonium nitrate, are soluble and would remain in the solution as ions. thanks 4 reading please drop by your answers. interaction of organic substances with CDs [14-16].
We have seen that the calculation of [H 3 O+] and pH for a solution of a pure weak acid in water requires solving the K a equilibrium expression for the acid. The partition coefficient, abbreviated P, is defined as a particular ratio of the concentrations of a solute between the two solvents (a biphase of liquid phases), specifically for un-ionized solutes, and the logarithm of the ratio is thus log P An acid dissociation constant, K a, (also known as acidity constant, or acid-ionization constant) is a quantitative measure of the strength of an write a generalization correlating solubility with ionization acid in solution.It is the equilibrium constant for a chemical reaction ↽ − − ⇀ − + + known as dissociation in the context of acid–base reactions.The chemical species HA is an acid that dissociates into A −, the conjugate base of the. Trevor H. However, in the case of nitrogen and oxygen, the situation is reversed. In similar fashion, calculating the. 29 CFR Part 1910. The solubility is calculated with information of the primary protein structure. Dec 07, 2019 · Home › MoonCraft Forums › Server Announcements › write a future letter This topic contains 0 replies, has 1 voice, and was last updated by KevenMn 1 month ago. > Why is this so? In 1835, in collaboration with Jean-Baptiste Biot, he showed how to follow experimentally the inversion of cane sugar, simply observing with a polarimeter the.
Viewing 1 post (of 1 total) Author write a generalization correlating solubility with ionization Posts November 1, 2019 at 6:47 pm #18684 KevenMnParticipant Dionte Bryant from Lakewood was …. Docket No. |
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Recognitions: Gold Member Science Advisor Staff Emeritus No, amazingly, you are wrong and your teacher is right! Since that integrand does not exist at x= 0, you have to use the definition: $$\int_{-1}^1 \frac{dx}{x}= \lim_{\alpha\to 0^-}\int_{-1}^\alpha \frac{dx}{x}+ \lim_{\beta\to 0^+}\int_\beta^1\frac{dx}{x}$$ and those limits do not exist. You cannot just evaluate the anti-derivative at 1, -1, and then subtract- that's ignoring the whole problem of what happens at 1. |
dc.contributor.author Immel, Thomas J. dc.contributor.author Eastes, Richard W. dc.contributor.author McClintock, William E. dc.contributor.author Mende, Steven B. dc.contributor.author Frey, Harald U. dc.contributor.author Triplett, Colin dc.contributor.author England, Scott L. dc.date.accessioned 2020-10-13T17:18:31Z dc.date.available 2020-10-13T17:18:31Z dc.date.issued 2020-09-30 dc.identifier.citation Immel, T.J.; Eastes, R.W.; McClintock, W.E.; Mende, S.B.; Frey, H.U.; Triplett, C.; England, S.L. Daily Variability in the Terrestrial UV Airglow. Atmosphere 2020, 11, 1046. dc.identifier.uri http://hdl.handle.net/10919/100469 dc.description.abstract New capability for observing conditions in the upper atmosphere comes with the implementation of global ultraviolet (UV) imaging from geosynchronous orbit. Observed by the NASA GOLD mission, the emissions of atomic oxygen (OI) and molecular nitrogen (N$2$) in the 133–168-nm range can be used to characterize the behavior of these major constituents of the thermosphere. Observations in the ultraviolet from the first 200 days of 2019 indicate that the oxygen emission at 135.6 nm varies much differently than the broader Lyman-Birge-Hopfield (LBH) emission of N$2$. This is determined from monitoring the average instrument response from two roughly 1000 km$2$ areas, well separated from one another, at the same time of each day. Variations in the GOLD response to UV emissions in the monitored regions are determined, both in absolute terms and relative to a running 7-day average of GOLD measurements. We find that variations in N$2$ emissions in the two separate regions are significantly correlated, while oxygen emissions, observed in the same fixed geographic regions at the same universal time each day, exhibit a much lower correlation, and exhibit no correlation with the N$2$ emissions in the same regions. This indicates that oxygen densities in the airglow-originating altitude range of 150–200 km vary independently from the variations in nitrogen, which are so well correlated across the dayside to suggest a direct connection to variation in solar extreme-UV flux. The relation of the atomic oxygen variations to solar and geomagnetic activity is also shown to be low, suggesting the existence of a regional source that modifies the production of atomic oxygen in the thermosphere. en dc.format.mimetype application/pdf dc.language.iso en en_US dc.publisher MDPI dc.rights Creative Commons Attribution 4.0 International en dc.rights.uri http://creativecommons.org/licenses/by/4.0/ en dc.title Daily Variability in the Terrestrial UV Airglow en dc.type Article - Refereed en_US dc.date.updated 2020-10-13T13:24:25Z dc.contributor.department Aerospace and Ocean Engineering dc.title.serial Atmosphere dc.identifier.doi https://doi.org/10.3390/atmos11101046 dc.type.dcmitype Text dc.type.dcmitype StillImage
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Vol. 22 - Num. 86
Original Papers
# Impact of the rapid diagnostic test of Streptococcus pyogenes on the consumption of antibiotics in Primary Care
aPediatra. CS Pilarica Circular. Valladolid. España.
bCS Pilarica Circular . Valladolid. España.
dMIR-Medicina Familiar y Comunitaria. CS Pintor Oliva. Palencia. España.
Correspondence: MN Sánchez. E-mail: [email protected]
Reference of this article: Bachiller Luque MR, Sánchez Sierra MN, Ruiz San Pedro AM, Prado Prieto MA, Maté Enríquez T, Melero Guijarro L, et al. Impact of the rapid diagnostic test of Streptococcus pyogenes on the consumption of antibiotics in Primary Care. Rev Pediatr Aten Primaria. 2020;22:153-9.
Published in Internet: 25-05-2020 - Visits: 7261
Abstract
Objective: the aim of the study was to analyse the use of the rapid Streptococcus antigen detection test in primary care paediatrics, its impact on antibiotic prescription and the associated decrease in antibiotic treatment costs.
Material and methods: we conducted a cross-sectional descriptive study in children aged less than 15 years managed in 24 primary care centres between April 2017 and February 2018. We developed a protocol for the use of the rapid strep test (RST). We included patients with a Centor score equal to or greater than 2 points. We collected data on the number of daily defined doses (DDDs) and amount antibiotics prescribed in the study period from the prescription billing system and compared it with the costs corresponding to the previous 12-month period.
Results: 819 TDRS were performed. The results were positive in 250 (30.5%), negative in 557 (68%) and inconclusive in 12 (1.5%). Antibiotics were prescribed to 33% of the patients (all patients with a positive test, 18 with a negative test and 3 with an inconclusive test). Antibiotherapy was not prescribed to 539 of the patients with a negative result (97%). The total number of prescribed DDDs decreased by 21 960 (12%), of which 19 023 (86.6%) corresponded to the most frequently prescribed antibiotics (penicillins, amoxicillin, amoxicillin-clavulanic acid and azithromycin). We found a reduction of €11 320 in antibiotherapy costs (12.5%), while the total cost of rapid testing was € 991, corresponding to total savings of €10 329.
Conclusions: the introduction of the RST in primary care paediatrics has achieved a reduction in the frequency of antibiotherapy. Its use has proven effective in optimising antibiotic use, reducing antibiotic prescription and therefore preventing associated adverse events and reducing unnecessary pharmacotherapy costs.
Keywords
Cost analysis Diagnostic test kit Drug utilization evaluation Primary care Streptococcus pyogenes Tonsillitis
## INTRODUCTION
Acute pharyngotonsillitis (AP) is one of the most common diseases of childhood and generates up to 30% of paediatric primary care (PC) visits.1,2 It is more prevalent in countries with temperate climates, with incidence peaks in winter and spring in the northern hemisphere. It is an inflammatory disease of the mucosae of the pharynx or pharyngeal tonsils, manifesting with redness, swelling, exudate, ulcers or vesicles.
The aetiology is usually infectious, most frequently viral (40%-80% of cases), with a self-limiting course and favourable outcomes of disease.3
Group A beta-haemolytic streptococcus (GABHS), or Streptococcus pyogenes, is the most frequent bacterial causative agent, and is responsible for approximately 15% to 30% of total cases.4 It is usually detected in patients aged more than 3 years and is rare in younger children (6%-10% of cases of GABHS). However, some authors have reported a prevalence of approximately 20% in infants aged less than 1 year and 26% in children aged 2 to 3 years5,6 (possibly including asymptomatic carriers, which may account for up to 12% of the total). Thus, despite its low prevalence, some authors recommend performance of diagnostic tests and contemplating the need for treatment in children aged less than 3 years with close contact with cases of AP due to GABHS in the household or at school to decrease the spread of the bacterium and transmission of the disease.7
More than 50% of patients with a clinical diagnosis of AP receive empirical antibiotherapy.4-8 Antibiotic treatment of pharyngotonsillitis caused by GABHS has been generally recommended to reduce the duration of symptoms and to prevent transmission as well as suppurative and nonsuppurative complications of the disease.8
However, the clinical presentation of pharyngotonsillitis does not suffice to discriminate between a viral and a bacterial aetiology.9 Therefore, the purpose of performing diagnostic tests is to be able to make this differentiation. The introduction of rapid antigen detection tests (RADTs) for detection of streptococcus, known as the rapid strep test (RST) and easy to perform in the primary care setting, allows early diagnosis and initiation of treatment with a high specificity, and therefore could help reduce unnecessary antibiotic use.
The aim of our study was to analyse the use of the RST in PC paediatric clinics for diagnosis of streptococcal pharyngitis, the impact of this test in antibiotic prescription and the associated reduction in the costs associated with the use of antibiotherapy in these patients.
## MATERIAL AND METHODS
We conducted a cross-sectional descriptive study in 34 PC clinics in 24 primary care centres in the Eastern Health District (Área de Salud Este) of Valladolid. The study period ranged from April 2017 to February 2018.
We included all cases of patients aged 14 years or younger that sought care in our clinic for AP of probable streptococcal aetiology. To determine this, we used the Centor score modified by McIsaac (Table 1),10,11 including all cases with a score of 2 or greater. The exclusion criteria were: Centor score of less than 2, that is, patients with a low probability of having streptococcal pharyngotonsillitis, and additional visits related to the same episode of disease.
Table 1. Modified/McIsaac Centor Score
Criteria Score
1. Fever >38° 1
2. Tonsillar swelling or exudate 1
3. Tender/swollen lateral anterior cervical nodes 1
4. Absence of cough 1
5. Age:
• 3-14 years
• >14 years
1
0
Risk of streptococcal infection (%)
• 2%-6% if score = 0-1
• 10%-28% if score = 2-3
• 38%-63% if score = 4-5
We developed a management protocol (Figure 1) based on the age of the patient and the Modified/McIsaac Centor score to select patients that would benefit from performance of a RST and to determine the approach to treatment based on its results.
Figure 1. Pharyngotonsillitis management protocol
In the weeks before starting the study, we held training sessions open to all PC paediatricians and nurses and specific trainings in clinics in which we distributed printed documents featuring the indications for antibiotic prescription and directions for correct performance of RSTs.
The study was approved by the Ethics Committee of the Eastern Valladolid health district. After informing families about the study and obtaining informed consent, paediatricians performed the clinical evaluation and had a nurse collect a throat swab specimen. The specimen was collected by rubbing a cotton swab on the posterior wall of the pharynx and both pharyngeal tonsils with emphasis on the most reddened areas or areas with exudate, avoiding contact with the tongue, uvula or any other part of the mouth to avoid contamination of the sample with the saprophytic flora of the respiratory tract. The RST was subsequently performed by chromatographic immunoassay (Strep A MonlabTest). The result was available 15 minutes later, and subsequent treatment was administered in adherence with the protocol (Figure 1).
We collected data for the following variables: sex, age in years, care setting, signs and symptoms of AP, modified/McIsaac Centor score, use of RST and results, antibiotic prescription and prescribed antibiotic.
We collected data from the CONCYLIA prescription billing system of the Public Health System of Castilla y León (SACYL), documenting the daily defined dose (DDD) and the expenditure in antibiotic prescriptions in the paediatrics sector during the study period, comparing the expenditure with that of the 12 months prior (April 2016-March 2017).
We performed a descriptive analysis of the study variables, expressing quantitative data as mean and standard deviation and qualitative data as absolute frequency and percentage distributions.
## RESULTS
We recruited a total of 819 patients with manifestations compatible with acute pharyngotonsillitis and a modified/McIsaac Centor score of 2 or higher. The mean age was 7.5 years (1-14). We found no difference in the presenting signs and symptoms based on age or sex.
The most frequent presenting complaints were fever, painful swallowing and pharyngeal redness or exudate. We found a scarlatiniform rash in 8% of patients. Less frequent manifestations included abdominal pain (1.5%), headache (1.2%) and vomiting (0.6%).
A RST was performed in all patients. The results were positive in 250 (30.5%), negative in 557 (68%) and inconclusive in 12 (1.5%). Four percent of the tests performed corresponded to patients younger than 3 years. In this subset of younger patients, 17.5% had a positive result. The most frequent indication for the RST in this group of patients was the presence of scarlatiniform rash, found in more than half (53%), followed by exudate in the pharynx or tonsils with fever in absence of cough (32%) and fever of unknown origin (15%).
Antibiotherapy was prescribed to 271 patients (33.1%), including all with a positive result of the RST, 18 with a negative result (3.2%) and 3 with inconclusive results (25%). Antibiotherapy was not initiated in 539 patients with negative results (96.8%). Table 2 and Figure 2 present the antibiotic agents used in the sample.
Table 2. Antibiotic prescription
Antibiotic agent n Percentage
Penicillin 43 15.9%
Amoxicillin 185 68.9%
Amoxicillin–clavulanic acid 8 2.9%
Cefuroxime 3 1.1%
Cefixime 1 0.4%
Azithromycin 5 1.8%
Unknown 26 9.6%
Total 271 100%
Figure 2. Chart of prescribed antibiotic agents
All patients had achieved full resolution of symptoms after completing the course of antibiotherapy, and we did not observe any complications of this treatment.
After analysing the prescription database, we found that the number of DDDs in the study period decreased by 21 960 (12%) compared to the same period a year before, of which 19 023 (86.6%) corresponded to the antibiotic agents used most frequently in PC (penicillins, amoxicillin, amoxicillin-clavulanic acid and azithromycin).
The reduction in antibiotherapy costs was €11 320 (12.5%) while the cost of performing RSTs was €991, which resulted in savings of €10 329 in health care costs (11.4%) in our health district.
## DISCUSSION
Rapid strep tests are easy to do, yield results in a few minutes in the patient care setting, and allow early and individualised initiation of treatment. This reduces disease transmission and the days of missed school and, above all, optimises antibiotic use. These tests offer a specificity of 95% or higher and a sensitivity that ranges from 70% to 90%12-18 for diagnosis of AP caused by GABHS. The main drawbacks of this test is that it cannot detect other serotypes and that a negative result does not fully rule out infection by GABHS. In cases in which the RST is negative but there is a high suspicion of streptococcal AP, a throat swab culture could be useful,19,20 as it has a specificity of nearly 99% and, if the sample has been collected correctly, the sensitivity can be as high as 90% to 95%.12,21 Although the turnaround time for culture is longer (24-48 hours), this method has the advantage that it can identify different bacteria and serotypes and allows assessment of antimicrobial susceptibility and resistance. Neither test can discriminate between AP caused by GABHS or GABHS carrier status. Nevertheless, given the low prevalence of asymptomatic carriage (ranging from 6% to 12%), antibiotherapy is not recommended routinely in patients with negative results,3 but only in select cases.11
Several scales have been proposed to facilitate diagnosis of AP caused by GABHS and identify patients in who some form of testing is indicated. The one used most frequently is the modified/McIsaac Centor score. This score is based on the presence or absence of certain clinical features, while taking age into account: a body temperature greater than 38°C, tonsillar swelling or exudate, tender swollen anterolateral cervical nodes and absence of cough. It has a high negative predictive value,22 so that the probability of a positive result in microbiological diagnostic tests is of 3% or less in patients that meet none of the clinical criteria and of 38% to 63% in patients that meet 4 to 5 criteria.19 Some form of diagnostic testing (RST or culture) is indicated in cases with a score of 2 or greater, unless the clinical presentation were compatible with viral infection, which would invalidate the indication.23
The introduction of the RST in the primary care paediatrics setting has allowed to greatly reduce the prescription of unnecessary antibiotic treatments. As we specified above, the number of total DDDs decreased by 21 960 (12%), of which 19 023 (86.6%) corresponded to the antibiotic agents prescribed most frequently in PC (penicillins, amoxicillin, amoxicillin-clavulanic acid and azithromycin). Our findings were consistent with the previous literature. In 2008, Maltezou et al.24 reported that the use of RSTs achieved a reduction in antibiotic prescription of 61% compared to empirical management of patients based on clinical features. In 2016, Kose et al.25 found that the exclusive use of clinical criteria for diagnosis of streptococcal pharyngotonsillitis led to antibiotic prescription in a high proportion of patients (79.8%), which dropped to 42.6% after performance of rapid testing.
Thus, the use of RSTs in this care setting has proven useful in terms of rational antibiotic use, reducing antibiotic prescription and contributing to preventing the development of drug resistance as well as adverse events.
Another aspect we ought to highlight is that the use of the RST in PC reduces unnecessary drug costs.
Phof et al.26 calculated that the average medical care costs per GABHS case was of $118 (58% of the total cost). Antibiotic treatment amounted to 20% of these costs ($23.60 per case). Kose et al.25 determined that the average cost of empirical antibiotherapy was $7.20 per patient, which decreased by 76.4% ($5.50) with individualisation of treatment following performance of rapid testing. Considering the cost of the RST (of \$1.14 per patient), the cost of treatment per patient decreased by 60.6%.
In our study, the reduction in drug prescription costs was of 11 320 € (12.5%), while the costs of rapid testing amounted to €991, with overall savings of €10 329.
In light of all of the above, the use of rapid streptococcal antigen detection tests seems to be an efficient and advisable intervention in primary care paediatrics clinics.
## CONFLICTS OF INTEREST
The authors have no conflicts of interest to declare in relation to the preparation and publication of this article.
## ABBREVIATIONS
AP: acute pharyngotonsillitis · DDD: daily defined dose · GABHS: group A beta-haemolytic streptococcus · PC: Primary Care · RST: rapid antigen detection test for streptococcus.
## REFERENCES
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24. Maltezou HC, Tsagris V, Antoniadou A, Galani L, Douros C, Katsarolis I, et al. Evaluation of a rapid antigen detection test in the diagnosis of streptococcal pharyngitis in children and its impact on antibiotic prescription. J Antimicrob Chemother. 2008;62:1407-12.
25. Kose E, Sirin Kose S, Akca D, Yildiz K, Elmas C, Baris M, et al. The effect of rapid antigen detection test on antibiotic prescription decision of clinicians and reducing antibiotic costs in children with acute pharyngitis. J Trop Pediatr. 2016;62:308-15.
26. Pfoh E, Wessels MR, Goldmann D, Lee GM. Burden and economic cost of group A streptococcal pharyngitis. Pediatrics. 2008;121:229-34. |
# 100 Time Series Data Mining Questions (with answers!) - Part 1
#### Posts
I decided to start this series of Time Series Data Mining base on Eamonn’s presentation, so that’s why the title is “100”. That’s the idea, but for now, we only have 19 questions ready to go.
I’ll use the datasets available at https://github.com/matrix-profile-foundation/mpf-datasets so you can try this at home.
The original code (MATLAB) and data are here..
1. Have we ever seen a pattern that looks just like this?
The dataset comes from an accelerometer that records when a person is walking, jogging, or running.
First, let’s load the tsmp library and import our dataset:
# install.packages('tsmp')
library(tsmp)
baseurl <- "https://raw.githubusercontent.com/matrix-profile-foundation/mpf-datasets/a3a3c08a490dd0df29e64cb45dbb355855f4bcb2/"
dataset <- unlist(read.csv(paste0(baseurl, "real/walk-jog-run.txt"), header = FALSE), use.names = FALSE)
And plot it:
plot(dataset, main = "Dataset", type = "l", ylab = "", xlab = "time")
This task is trivial with Mueen’s MASS code…
Here is where tsmp does all for you. All you need is to use the function dist_profile that will return an especial vector called “Distance Profile”. We will talk more about it later in this sequence of posts. This vector is inside the list that is returned by this function:
query <- dataset[5001:5100] # pretend you didn't see this line. This is the query from the first image above.
# our query has a length of 100 units, we can specify this as window_size, but here the
# function will know it.
tictac1 <- Sys.time()
res <- dist_profile(dataset, query)
tictac1 <- Sys.time() - tictac1
cat(paste("dist_profile() finished in ", tictac1, "seconds\n\n"))
## dist_profile() finished in 0.00799798965454102 seconds
str(res)
## List of 3
## $distance_profile: num [1:9902] 188 180 174 170 168 ... ##$ last_product : num [1:9902] 15.4 21.1 25.7 28.5 29.6 ...
## $par :List of 9 ## ..$ window_size: int 100
## ..$data_fft : cplx [1:16384] 5920+0i -1833-2644i 993-317i ... ## ..$ data_size : int 10001
## ..$data_mean : num [1:9902] 0.1029 0.1017 0.101 0.1 0.0994 ... ## ..$ data_sd : num [1:9902] 0.4 0.401 0.401 0.401 0.402 ...
## ..$query_mean : num 0.602 ## ..$ query_sd : num 3.73
## ..$data : num [1:10001] 0.01499 -0.04329 -0.00391 -0.03841 0.00122 ... ## ..$ k : NULL
What this vector represents is the euclidean distance of our query (the pattern that we want to look for) related to the dataset. This means that the minimum value contains the place that is most similar to our query:
first <- which.min(res$distance_profile) first # surprisingly (not) the value is the same as that we used to slice our query... ## [1] 5001 Well, this tells us that at position 5001 there is a pattern that looks like our query. Let’s plot that with a closer look: plot(dataset, main = "Dataset", type = "l", ylab = "", xlab = "time", xlim = c(4001, 6000)) lines(5001:5100, query, col = 2) Yes! There is a match! But there are more similar patterns? Here I just find that a new helper function could exist. As it doesn’t, let’s write a few lines (read the comments!): # This snippet will try to find what we call neighbours, that are patterns that are similar # to your query, but not the best match. We know that 'Trivial Matches' happens close to # the best match, but in this case we are not looking for motifs, but for neighbours. This # will make sense in the future. tictac2 <- Sys.time() st <- sort(res$distance_profile, index.return = TRUE) # this will order the results and give us the position of them
tictac2 <- Sys.time() - tictac2
cat(paste("sort() finished in ", tictac2, "seconds\n\n"))
## sort() finished in 0.0019989013671875 seconds
# the first one we know already is our best match. Let's now plot the results of three more
# 'matches'.
# Remember that our window_size is 100:
w <- 100
plot(dataset, main = "Dataset", type = "l", ylab = "", xlab = "time", xlim = c(4500, 6200))
for (i in 1:5) {
lines(st$ix[i]:(st$ix[i] + w - 1), dataset[st$ix[i]:(st$ix[i] + w - 1)], col = i + 1, lwd = 2)
text(st\$ix[i], -10, label = paste("match", i), adj = 0, col = i + 1, cex = 0.8)
}
So we did it! We found the five best matches of our query, and it took only 0.00999689102172852 seconds to do it!
This ends our first question of one hundred (let’s hope so!).
Until next time.
next post in this series |
# Configuration Files¶
GCHP is controlled using a set of resource configuration files that are included in the GCHP run directory, most of which are denoted by suffix .rc. These files contain all run-time information required by GCHP. Files include:
• CAP.rc
• ExtData.rc
• GCHP.rc
• input.geos
• HEMCO_Config.rc
• HEMCO_Diagn.rc
• input.nml
• HISTORY.rc
Much of the labor of updating the configuration files has been eliminated by run directory shell script runConfig.sh. It is important to remember that sourcing runConfig.sh will overwrite settings in other configuration files, and you therefore should never manually update other configuration files unless you know the specific option is not available in runConfig.sh.
That being said, it is still worth understanding the contents of all configuration files and what all run options include. This page details the settings within all configuration files and what they are used for.
## File descriptions¶
The following table lists the core functions of each of the configuration files in the GCHP run directory. See the individual subsections on each file for additional information.
CAP.rc
Controls parameters used by the highest level gridded component (CAP). This includes simulation run time information, name of the Root gridded component (GCHP), config filenames for Root and History, and toggles for certain MAPL logging utilities (timers, memory, and import/export name printing).
ExtData.rc
Config file for the MAPL ExtData component. Specifies input variable information, including name, regridding method, read frequency, offset, scaling, and file path. All GCHP imports must be specified in this file. Toggles at the top of the file enable MAPL ExtData debug prints and using most recent year if current year of data is unavailable. Default values may be used by specifying file path /dev/null.
GCHP.rc
Controls high-level aspects of the simulation, including grid type and resolution, core distribution, stretched-grid parameters, timesteps, and restart file configuration.
input.geos
Primary config file for GEOS-Chem. Same function as in GEOS-Chem Classic except grid, simulation start/end, met field source, timers, and data directory information are ignored.
HEMCO_Config.rc
Contains emissions information used by HEMCO. Same function as in GEOS-Chem Classic except only HEMCO name, species, scale IDs, category, and hierarchy are used. Diagnostic frequency, file path, read frequency, and units are ignored, and are instead stored in GCHP config file ExtData.rc. All HEMCO variables listed in HEMCO_Config.rc for enabled emissions must also have an entry in ExtData.rc.
HEMCO_Diagn.rc
Contains information mapping HISTORY.rc diagnostic names to HEMCO containers. Same function as in GEOS-Chem Classic except that not all items in HEMCO_Diagn.rc will be output; only emissions listed in HISTORY.rc will be included in diagnostics. All GCHPctm diagnostics listed in HISTORY.rc that start with Emis, Hco, or Inv must have a corresponding entry in HEMCO_Diagn.rc.
input.nml
Namelist used in advection for domain stack size and stretched grid parameters.
HISTORY.rc
Config file for the MAPL History component. Configures diagnostic output from GCHP.
## CAP.rc¶
CAP.rc is the configuration file for the top-level gridded component called CAP. This gridded component can be thought of as the primary driver of GCHP. Its config file handles general runtime settings for GCHP including time parameters, performance profiling routines, and system-wide timestep (hearbeat). Combined with output file cap_restart, CAP.rc configures the exact dates for the next GCHP run.
ROOT_NAME
Sets the name MAPL uses to initialize the ROOT child gridded component component within CAP. CAP uses this name in all operations when querying and interacting with ROOT. It is set to GCHP.
ROOT_CF
Resource configuration file for the ROOT component. It is set to GCHP.rc.
HIST_CF
Resource configuration file for the MAPL HISTORY gridded component (another child gridded component of CAP). It is set to HISTORY.rc.
BEG_DATE
Simulation begin date in format YYYYMMDD hhmmss. This parameter is overrided in the presence of output file cap_restart containing a different start date.
END_DATE
Simulation end date in format YYYYMMDD hhmmss. If BEG_DATE plus duration (JOB_SGMT) is before END_DATE then simulation will end at BEG_DATE + JOB_SGMT. If it is after then simulation will end at END_DATE.
JOB_SGMT
Simulation duration in format YYYYMMDD hhmmss. The duration must be less than or equal to the difference between start and end date or the model will crash.
HEARTBEAT_DT
The timestep of the ESMF/MAPL internal clock, in seconds. All other timesteps in GCHP must be a multiple of HEARTBEAT_DT. ESMF queries all components at each heartbeat to determine if computation is needed. The result is based upon individual component timesteps defined in GCHP.rc.
MAPL_ENABLE_TIMERS
Toggles printed output of runtime MAPL timing profilers. This is set to YES. Timing profiles are output at the end of every GCHP run.
MAPL_ENABLE_MEMUTILS
Enables runtime output of the programs’ memory usage. This is set to YES.
PRINTSPEC
Allows an abbreviated model run limited to initializat and print of Import and Export state variable names. Options include:
• 0 (default): Off
• 1: Imports and Exports only
• 2: Imports only
• 3: Exports only
USE_SHMEM
This setting is deprecated but still has an entry in the file.
REVERSE_TIME
Enables running time backwards in CAP. Default is 0 (off).
## ExtData.rc¶
ExtData.rc contains input variable and file read information for GCHP. Explanatory information about the file is located at the top of the configuration file in all run directories. The file format is the same as that used in the GEOS model, and GMAO/NASA documentation for it can be found at the ExtData component page on the GEOS-5 wiki.
The following two parameters are set at the top of the file:
Ext_AllowExtrat
Logical toggle to use data from nearest year available. This is set to true for GCHP. Note that GEOS-Chem Classic accomplishes the same effect but with more flexibility in HEMCO_Config.rc. That functionality of HEMCO_Config.rc is ignored in GCHP.
DEBUG_LEVEL
Turns MAPL ExtData debug prints on/off. This is set to 0 in GCHP (off), but may be set to 1 to enable. Beware that turning on ExtData debug prints greatly slows down the model, and prints are only done from the root thread. Use this when debugging problems with input files.
The rest of the file contains space-delimited lines, one for each variable imported to the model from an external file. Columns are as follows in order as they appear left to right in the file:
Export Name
Name of imported met field (e.g. ALBD) or HEMCO emissions container name (e.g. GEIA_NH3_ANTH).
Units
Unit string nested within single quotes. ‘1’ indicates there is no unit conversion from the native units in the netCDF file.
Clim
Enter Y if the file is a 12 month climatology, otherwise enter N. If you specify it is a climatology ExtData the data can be on either one file or 12 files if they are templated appropriately with one per month.
Conservative
Enter Y the data should be regridded in a mass conserving fashion through a tile file. F;{VALUE} can also be used for fractional regridding. Otherwise enter N to use the non-conervative bilinear regridding.
Refresh
Time Template Possible values include:
• -: The field will only be updated once the first time ExtData runs
• 0: Update the variable at every step. ExtData will do a linear interpolation to the current time using the available data.
• %y4-%m2-%h2T%h2:%n2:00: Set the recurring time to update the file. The file will be updated when the evaluated template changes. For example, a template in the form %y4-%m2-%d2T12:00:00 will cause the variable to be updated at the start of a new day (i.e. when the clock hits 2007-08-02T00:00:00 it will update the variable but the time it will use for reading and interpolation is 2007-08-02T12:00:00).
Offset Factor
Factor the variable will be shifted by. Use none for no shifting.
Scale Factor
Factor the variable will be scaled by. Use none for no scaling.
External File Variable
The name of the variable in the netCDF data file, e.g. ALBEDO in met fields.
External File Template
Path to the netCDF data file. If not using the data, specify /dev/null to reduce processing time. If there are no tokens in the template name ExtData will assume that all the data is on one file. Note that if the data on file is at a different resolution that the application grid, the underlying I/O library ExtData uses will regrid the data to the application grid.
## GCHP.rc¶
GCHP.rc is the resource configuration file for the ROOT component within GCHP. The ROOT gridded component includes three children gridded components, including one each for GEOS-Chem, FV3 advection, and the data utility environment needed to support them.
NX, NY
Number of grid cells in the two MPI sub-domain dimensions. NX * NY must equal the number of CPUs. NY must be a multiple of 6.
GCHP.GRID_TYPE
Type of grid GCHP will be run at. Should always be Cubed-Sphere.
GCHP.GRIDNAME
Descriptive grid label for the simulation. The default grid name is PE24x144-CF. The grid name includes how the pole is treated, the face side length, the face side length times six, and whether it is a Cubed Sphere Grid or Lat/Lon. The name PE24x144-CF indicates polar edge (PE), 24 cells along one face side, 144 for 24*6, and a cubed-sphere grid (CF). Many options here are defined in MAPL_Generic.
Note
Must be consistent with IM and JM.
GCHP.NF
Number of cubed-sphere faces. This is set to 6.
GCHP.IM_WORLD
Number of grid cells on the side of a single cubed sphere face.
GCHP.IM
Number of grid cells on the side of a single cubed sphere face.
GCHP.JM
Number of grid cells on one side of a cubed sphere face, times 6. This represents a second dimension if all six faces are stacked in a 2-dimensional array. Must be equal to IM*6.
GCHP.LM
Number of vertical grid cells. This must be equal to the vertical resolution of the offline meteorological fields (72) since MAPL cannot regrid vertically.
GCHP.STRETCH_FACTOR
Ratio of configured global resolution to resolution of targeted high resolution region if using stretched grid.
GCHP.TARGET_LON
Target longitude for high resolution region if using stretched grid.
GCHP.TARGET_LAT
Target latitude for high resolution region if using stretched grid.
IM
Same as GCHP.IM and GCHP.IM_WORLD.
JM
Same as GCHP.JM.
LM
Same as GCHP.LM.
GEOChem_CTM
If set to 1, tells FVdycore that it is operating as a transport model rather than a prognostic model.
Toggles offline advection. 0 is off, and 1 is on.
DYCORE
Should either be set to OFF (default) or ON. This value does nothing, but MAPL will crash if it is not declared.
HEARTBEAT_DT
The timestep in seconds that the DYCORE Component should be called. This must be a multiple of HEARTBEAT_DT in CAP.rc.
SOLAR_DT
The timestep in seconds that the SOLAR Component should be called. This must be a multiple of HEARTBEAT_DT in CAP.rc.
The timestep in seconds that the IRRAD Component should be called. ESMF checks this value during its timestep check. This must be a multiple of HEARTBEAT_DT in CAP.rc.
RUN_DT
The timestep in seconds that the RUN Component should be called.
GCHPchem_DT
The timestep in seconds that the GCHPchem Component should be called. This must be a multiple of HEARTBEAT_DT in CAP.rc.
RRTMG_DT
The timestep in seconds that RRTMG should be called. This must be a multiple of HEARTBEAT_DT in CAP.rc.
DYNAMICS_DT
The timestep in seconds that the FV3 advection Component should be called. This must be a multiple of HEARTBEAT_DT in CAP.rc.
Default is 0.
GCHPchem_REFERENCE_TIME
HHMMSS reference time used for GCHPchem MAPL alarms.
PRINTRC
Specifies which resource values to print. Options include 0: non-default values, and 1: all values. Default setting is 0.
Enables or disables parallel I/O processes when writing the restart files. Default value is 0 (disabled).
Number of simultaneous readers. Should divide evenly unto NY. Default value is 1.
BKG_FREQUENCY
Active observer when desired. Default value is 0.
RECORD_FREQUENCY
Frequency of periodic restart file write in format HHMMSS.
RECORD_REF_DATE
Reference date(s) used to determine when to write periodic restart files.
RECORD_REF_TIME
Reference time(s) used to determine when to write periodic restart files.
GCHOchem_INTERNAL_RESTART_FILE
The filename of the internal restart file to be written.
GCHPchem_INTERNAL_RESTART_TYPE
The format of the internal restart file. Valid types include pbinary and pnc4. Only use pnc4 with GCHP.
GCHPchem_INTERNAL_CHECKPOINT_FILE
The filename of the internal checkpoint file to be written.
GCHPchem_INTERNAL_CHECKPOINT_TYPE
The format of the internal checkstart file. Valid types include pbinary and pnc4. Only use pnc4 with GCHP.
Only needed when the file type is set to pbinary. Specifies if a binary file is self-describing.
DYN_INTERNAL_RESTART_FILE
The filename of the DYNAMICS internal restart file to be written. Please note that FV3 is not configured in GCHP to use an internal state and therefore will not have a restart file.
DYN_INTERNAL_RESTART_TYPE
The format of the DYNAMICS internal restart file. Valid types include pbinary and pnc4. Please note that FV3 is not configured in GCHP to use an internal state and therefore will not have a restart file.
DYN_INTERNAL_CHECKPOINT_FILE
The filename of the DYNAMICS internal checkpoint file to be written. Please note that FV3 is not configured in GCHP to use an internal state and therefore will not have a restart file.
DYN_INTERNAL_CHECKPOINT_TYPE
The format of the DYNAMICS internal checkpoint file. Valid types include pbinary and pnc4. Please note that FV3 is not configured in GCHP to use an internal state and therefore will not have a restart file.
Only needed when the file type is set to pbinary. Specifies if a binary file is self-describing.
RUN_PHASES
GCHP uses only one run phase. The GCHP gridded component for chemistry, however, has the capability of two. The two-phase feature is used only in GEOS.
HEMCO_CONFIG
Name of the HEMCO configuration file. Default is HEMCO_Config.rc in GCHP.
STDOUT_LOGFILE
Log filename template. Default is PET%%%%%.GEOSCHEMchem.log. This file is not actually used for primary standard output.
STDOUT_LOGLUN
Logical unit number for stdout. Default value is 700.
MEMORY_DEBUG_LEVEL
Toggle for memory debugging. Default is 0 (off).
WRITE_RESTART_BY_OSERVER
Determines whether MAPL restart write should use o-server. This must be set to YES for high core count (>1000) runs to avoid hanging during file write. It is NO by default.
## input.geos¶
Information about the input.geos file is the same as for GEOS-Chem Classic with a few exceptions. See the input.geos file wiki page for an overview of the file.
The input.geos file used in GCHP is different in the following ways:
• Start/End datetimes are ignored. Set this information in CAP.rc instead.
• Root data directory is ignored. All data paths are specified in ExtData.rc instead with the exception of the FAST-JX data directory which is still listed (and used) in input.geos.
• Met field is ignored. Met field source is described in file paths in ExtData.rc.
• GC classic timers setting is ineffectual. GEOS-Chem Classic timers code is not compiled when building GCHP.
Other parts of the GEOS-Chem Classic input.geos file that are not relevant to GCHP are simply not included in the file that is copied to the GCHP run directory.
## HEMCO_Config.rc¶
Like input.geos, information about the HEMCO_Config.rc file is the same as for GEOS-Chem Classic with a few exceptions. Refer to the HEMCO documentation for an overview of the file.
Some content of the HEMCO_Config.rc file is ignored by GCHP. This is because MAPL ExtData handles file input rather than HEMCO in GCHP.
Items at the top of the file that are ignored include:
• ROOT data directory path
• METDIR path
• DiagnPrefix
• DiagnFreq
• Wildcard
In the BASE EMISSIONS section and beyond, columns that are ignored include:
• sourceFile
• sourceVar
• sourceTime
• C/R/E
• SrcDim
• SrcUnit
All of the above information is specified in file ExtData.rc instead with the exception of diagnostic prefix and frequency. Diagnostic filename and frequency information is specified in HISTORY.rc.
## HEMCO_Diagn.rc¶
Like in GEOS-Chem Classic, the HEMCO_Diagn.rc file is used to map between HEMCO containers and output file diagnostic names. However, while all uncommented diagnostics listed in HEMCO_Diagn.rc are output as HEMCO diagnostics in GEOS-Chem Classic, only the subset also listed in HISTORY.rc are output in GCHP. See the HEMCO documentation for an overview of the file.
## input.nml¶
input.nml controls specific aspects of the FV3 dynamical core used for advection. Entries in input.nml are described below.
&fms_nml
Header for the FMS namelist which includes all variables directly below the header.
print_memory_usage
Toggles memory usage prints to log. However, in practice turning it on or off does not have any effect.
domain_stack_size
Domain stack size in bytes. This is set to 20000000 in GCHP to be large enough to use very few cores in a high resolution run. If the domain size is too small then you will get an “mpp domain stack size overflow error” in advection. If this happens, try increasing the domain stack size in this file.
&fv_core_nml
Header for the finite-volume dynamical core namelist. This is commented out by default unless running on a stretched grid. Due to the way the file is read, commenting out the header declaration requires an additional comment character within the string, e.g. #&fv#_core_nml.
do_schmidt
Logical for whether to use Schmidt advection. Set to .true. if using stretched grid; otherwise this entry is commented out.
stretch_fac
Stretched grid factor, equal to the ratio of grid resolution in targeted high resolution region to the configured run resolution. This is commented out if not using stretched grid.
target_lat
Target latitude of high resolution region if using stretched grid. This is commented out if not using stretched grid.
target_lon
Target longitude of high resolution region if using stretched grid. This is commented out if not using stretched grid.
## HISTORY.rc¶
The HISTORY.rc configuration file controls the diagnostic files output by GCHP. Information is organized into several sections:
1. Single parameters set at the top of the file
2. Grid label declaration list
3. Definition for each grid in grid label list
4. Variable collection declaration list
5. Definition for each collection in collection list.
Single parameters set at the top of HISTORY.rc are as follows and apply to all collections:
EXPID
Filename prefix concatenated with each collection template string to define file path. It is set to OutputDir/GCHP so that all output diagnostic files are output to run subdirectory OutputDir and have filename begin with GCHP.
EXPDSC
Export description included as attribute “Title” in output files
CoresPerNode
Number of CPUs per node for your simulation.
VERSION
Optional parameter included as attribute in output file.
The grid labels section of HISTORY.rc declares a list of descriptive grid strings followed by a definition for each declared grid label. Grids not in the grid label list may have definitions in the file; however, this will prevent them from being used in output collections. See the HISTORY.rc grid label section for syntax on declaring and defining grid labels.
Keywords that may be used for grid label definitions are in the table below. Note that this list is not exhaustive; MAPL may have additional keywords that may be used that have not yet been explored for use with GCHP.
GRID_TYPE
Type of grid. May be Cubed-Sphere or LatLon.
IM_WORLD
Side length of one cubed-sphere face, e.g. 24 if grid resolution is C24, or number of longitudinal grid boxes if lat-lon.
JM_WORLD
Same as IM_WORLD but multiplied by 6 (number of faces), or number of latitudinal grid boxes if lat-lon.
POLE
For lat-lon grids only. PC if latitudes are pole-centered and PE if latitudes are polar edge.
DATELINE
For lat-lon grids only. DC if longitudes are dateline-centered and DE if longitudes are dateline-edge.
LAT_RANGE
For lat-lon grids only. Regional grid latitudinal bounds.
LON_RANGE
For lat-lon grids only. Regional grid longitudinal bounds.
LM
Number of vertical levels.
The collections section of HISTORY.rc declares a list of descriptive strings that define unique collections of output variables and settings. As with grid labels, it is followed by a definition for each declared collection. Collections not in the collection list, or present but commented out, may have definitions in the file; however, this will prevent them from being output. See the HISTORY.rc collection section for syntax on declaring and defining output collections.
Keywords that may be used for collection definitions are in the table below. Note that this list is not exhaustive; MAPL may have additional keywords that may be used that have not yet been explored for use with GCHP.
{COLLECTION}.template
The output filename suffix that is appended to global parameter EXPID to define full output file path. Including a date string, such as ‘%y4%m2%d2, will insert the simulation start day following GrADS conventions. The default template for GCHP is set to %y4%m2%d2_%h2%n2z.nc4.
{COLLECTION}.format
Character string defining the file format. Options include CFIO (default) for netCDF-4 or flat for binary files. Always output as CFIO when using GCHP.
{COLLECTION}.grid_label
Declared grid label for output grid. If excluded the collection will be output on the cubed-sphere grid at native resolution, e.g. C24 if you run GCHP with grid resolution C24.
{COLLECTION}.conservative
For lat-lon grids only. Set to 1 to conservatively regrid from cubed-sphere to lat-lon upon output. Exclude or set to 0 to use bilinear interpolation instead (not recommended).
{COLLECTION}.frequency
The frequency at which output values are computed and archived, in format HHMMSS. For example, 010000 will calculate diagnostics every hour. The method of calculation is determined by the mode keyword. Unlike GEOS-Chem Classic, you cannot specify number of days, months, or years.
{COLLECTION}.duration
The frequency at which files are written, in format HHMMSS. For example, 240000 will output daily files. The number of times in the file are determined by the frequency keyword. Unlike GEOS-Chem Classic, you cannot specify number of days, months, or years.
{COLLECTION}.mode
Method of diagnostic calculation. Options are either instantaneous or time-averaged.
{COLLECTION}.fields
List of character string pairs including diagnostic name and gridded component. All GCHP diagnostics belong to the GCHPchem gridded component.
Diagnostic names have prefixes that determine where MAPL History will look for them. Prefixes Emis, Inv, and Hco are HEMCO diagnostics and must have definitions in config file HEMCO_Diagn.rc. Prefixes Chem and Met are GEOS-Chem state variables stored in objects State_Chm and State_Met respectively. Prefix SPC corresponds to internal state species, meaning the same arrays that are output to the restart file. Prefix GEOS is reserved for use in the GEOS model. All other diagnostic name prefixes are interpreted as variables stored in the GEOS-Chem State_Diag object. |
# exporting graphics from geogebra
I've drawn the following in geogebra:
I am trying to export it to latex, and it generates the following code
\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=5.963052189663429cm,y=6.882465522871498cm]
\clip(3.689076390812617,1.8587708166080559) rectangle (5.3660699306871065,3.3117385019191485);
\fill(4.562096541660087,3.141936112320542) -- (3.864932244907646,2.1201049468877806) -- (5.203961300072035,2.1259431133816373) -- cycle;
\draw (4.562096541660087,3.141936112320542)-- (3.864932244907646,2.1201049468877806);
\draw (3.864932244907646,2.1201049468877806)-- (5.203961300072035,2.1259431133816373);
\draw (5.203961300072035,2.1259431133816373)-- (4.562096541660087,3.141936112320542);
\draw (4.6150499230079465,2.8338166788505954) node[anchor=north west] {$\widetilde{\pi}(t+1)$};
\draw [dash pattern=on 2pt off 2pt] (4.387584856780469,2.6190839429739308)-- (4.604490640656735,2.7694537510805857);
\draw (4.387584856780469,2.6190839429739308)-- (4.555579181100361,2.252693547941523);
\draw (4.555309695124377,2.2790859913603105) node[anchor=north west] {$\mu(t+1)$};
\draw (4.367554693204586,2.40710076539653) node[anchor=north west] {$\pi(t+1)$};
\draw (4.3056808857537465,2.6823325295744023) node[anchor=north west] {$\pi(t)$};
\draw [dash pattern=on 2pt off 2pt] (4.604490640656735,2.7694537510805857)-- (4.489052072597337,2.3977871019259576);
\draw (4.4251613415208855,2.7356720187561603) node[anchor=north west] {drift};
\draw (4.570244752095269,2.588455028614508) node[anchor=north west] {rebalance};
\draw (4.222471282630203,2.505245425490965) node[anchor=north west] {consume };
\draw (4.333417420128261,2.5372491190000197) node[anchor=north west] {$\lambda \gamma^*_\pi(t)$};
\begin{scriptsize}
\draw [fill=black] (4.387584856780469,2.6190839429739308) circle (0.5pt);
\draw [fill=black] (4.555579181100361,2.252693547941523) circle (0.5pt);
\draw [fill=black] (4.604490640656735,2.7694537510805857) circle (0.5pt);
\draw [fill=black] (4.489052072597337,2.3977871019259576) circle (0.5pt);
\end{scriptsize}
\end{tikzpicture}
\end{document}
but it generates:
im not really sure what im doing wrong?
• The second drawing command is \fill. Try changing that to \draw. Oct 24, 2015 at 17:51
Apparently, geogebra does not know how to properly export to tikz. You should in any case submit a bug report to geogebra.
As Loop Space writes, you should replace the first command \fill by \draw. That doesn't really suffice, the output is pretty ugly. As a first fix, you could try to reduce the font size, so that the labels will not meet each other (option font=\scriptsize below). Also, the two labels "consume" and $\lambda \gamma^*_\pi(t)$ are very close. Should this really be one or two labels? Maybe you can fix this one in your geogebra file. Below, I decided to combine the two labels and align them with anchor=north (no west). I am not sure whether this is what you want.
Depending on how many images you want to convert to LaTeX, it would maybe be worth for you to learn more precisely about how to place labels with tikz. Otherwise, you can just play with the precise coordinates of the labels.
\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=5.963052189663429cm,y=6.882465522871498cm,font=\scriptsize]
\clip(3.689076390812617,1.8587708166080559) rectangle (5.3660699306871065,3.3117385019191485);
\draw(4.562096541660087,3.141936112320542) -- (3.864932244907646,2.1201049468877806) -- (5.203961300072035,2.1259431133816373) -- cycle;
\draw (4.562096541660087,3.141936112320542)-- (3.864932244907646,2.1201049468877806);
\draw (3.864932244907646,2.1201049468877806)-- (5.203961300072035,2.1259431133816373);
\draw (5.203961300072035,2.1259431133816373)-- (4.562096541660087,3.141936112320542);
\draw (4.6150499230079465,2.8338166788505954) node[anchor=north west] {$\widetilde{\pi}(t+1)$};
\draw [dash pattern=on 2pt off 2pt] (4.387584856780469,2.6190839429739308)-- (4.604490640656735,2.7694537510805857);
\draw (4.387584856780469,2.6190839429739308)-- (4.555579181100361,2.252693547941523);
\draw (4.555309695124377,2.2790859913603105) node[anchor=north west] {$\mu(t+1)$};
\draw (4.367554693204586,2.40710076539653) node[anchor=north west] {$\pi(t+1)$};
\draw (4.3056808857537465,2.6823325295744023) node[anchor=north west] {$\pi(t)$};
\draw [dash pattern=on 2pt off 2pt] (4.604490640656735,2.7694537510805857)-- (4.489052072597337,2.3977871019259576);
\draw (4.4251613415208855,2.7356720187561603) node[anchor=north west] {drift};
\draw (4.570244752095269,2.588455028614508) node[anchor=north west] {rebalance};
\draw (4.222471282630203,2.505245425490965) node[anchor=north] {consume $\lambda \gamma^*_\pi(t)$};
%\draw (4.333417420128261,2.5372491190000197) node[anchor=north west] {consume $\lambda \gamma^*_\pi(t)$};
\begin{scriptsize}
\draw [fill=black] (4.387584856780469,2.6190839429739308) circle (0.5pt);
\draw [fill=black] (4.555579181100361,2.252693547941523) circle (0.5pt);
\draw [fill=black] (4.604490640656735,2.7694537510805857) circle (0.5pt);
\draw [fill=black] (4.489052072597337,2.3977871019259576) circle (0.5pt);
\end{scriptsize}
\end{tikzpicture}
\end{document}
• thanks for your answer, yes i had a problem combining those two labels in geogebra which only seems to let you write either under an equation environment or none at all, i suppose i shouldve used \text{ } Oct 25, 2015 at 0:27 |
# octahedral compounds hybridization
All the complex ions having a coordination number of central metal atom as six show octahedral geometry. Octahedral complexes. The $\mathrm{4d}$ set, I suppose.. To have the octahedral shape, a molecule must have a central atom and six constituents. Because, all the above said ions contain seven or more electrons in their inner 3d-orbital.Hence, in the formation of octahedral complexes, they can’t attain d 2 sp 3 hybridization. The hybridisation in octahedral complexes are d 2 s p 3 or s p 3 d 2. That is, the metal ions , Co 2+ ,Ni 2+ ,Cu 2+ and Zn 2+ show sp3d 2 hybridization … coordination compounds class 12 is a complex subject and a lot of theory is there in it. But all the $\mathrm{3d}$ orbitals are already populated, so where do the two $\mathrm{d}$ orbitals come from? (b) CO forms more stable complex than CN- because it can form both a as well as n-bond with central metal atom or ion. NOTES: This molecule is made up of 6 equally spaced sp 3 d 2 hybrid orbitals arranged at 90 o angles. The shape of the orbitals is octahedral.Two orbitals contain lone pairs of electrons on opposite sides of the central atom. The shape of the orbitals is octahedral.Since there is an atom at the end of each orbital, the shape of the molecule is also octahedral.. Back to top NOTES: This molecule is made up of 6 equally spaced sp 3 d 2 hybrid orbitals arranged at 90 o angles. Moving on to $\ce{Ni(II)}$ octahedral complexes, like $\ce{[Ni(H2O)6]^2+}$, the typical explanation is that there is $\mathrm{sp^3d^2}$ hybridisation. The octahedral shape looks like two pyramids with four sides each that have been stuck together by their bases. Octahedral - $\ce{d^2sp^3}$ or $\ce{sp^3d^2}$ - the hybridization of one $\ce{s}$, three $\ce{p}$, and two $\ce{d}$ orbitals produce six hybrid orbitals oriented toward the points of … Octahedral geometry arises due to d2sp3 or sp3d2 hybridisation of the central metal atom or ion. Hybridization = What are the approximate bond angles in this substance? A. S 3 : Aqueous H 3 P O 4 is syrupy (i.e more viscous than water). The points raised above for tetrahedral case above still apply here. Hybridization What are the approximate bond angles in this substance Bond angles = B. Octahedral geometry can lead to 2. (ii) [Ni(CO) 4 ] has sp3 hybridization, tetrahedral shape. We can imagine the platinum at the middle with the six fluorines at each of the vertices of the pyramids. What is the hybridization of the central atom in IF? Octahedral complexes in which the central atom is d2sp3 hybridised are called inner- orbital octahedral complexes while the octahedral complexes in which the central atom is sp3d2 hybridised are called outer orbital octahedral. This octahedral geometry arises due to d 2 s p 3 or s p 3 d 2 hybridisation of the central metal atom or ion. (a) (i) [FeF 6]3_ has sp3d2 hybridization, octahedral shape. S 2 : In S F 4 the bond angles, instead of being 9 0 ∘ and 1 8 0 ∘ are 8 9 ∘ a n d 1 7 7 ∘ respectively due to the repulsions between lone pair and bond pairs of electrons. What is the hybridization of the central atom in XeF2? Central metal atom as six show octahedral geometry of 6 octahedral compounds hybridization spaced 3. Is the hybridization of the pyramids angles in This substance a ) ( I ) FeF... I suppose octahedral compounds hybridization above for tetrahedral case above still apply here the middle with the six at. Of electrons on opposite sides of the central atom in IF in.. 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# *Cheap* CYC Wash
#### TupeloTechie
##### Active Member
We do not have any flood/wash/cyc lights for the cyc and we are going to be using it soon. My teacher wanted to buy some of those halogen work lights and gel them, but I wasn't sure if these would work or not. Does anybody know about these, and if they can even be dimmed?
Or does anybody else have any ideas for a wash such as this, we don't really have any money for lighting, we usually spend over the lighting budget just buying gels and new lamps.
#### icewolf08
##### CBMod
CB Mods
Pretty much any incandescent lamp can be dimmed. Are the work lights really any cheaper than single cell cyc lights? Anyway, every now and then we use "work lights" as foot lights, and they work OK, but not great. On your cyc you really want to have a fixture with a J-type reflector as it will give you the best coverage. You can gel the "work lights, you just have to be careful so that the gels don't melt. You also would probably want to use some R113, R104, or G65 with whatever color you choose. These are silks or linear diffusion, it will elongate the light perpendicular to the striations you see in the gel.
#### TupeloTechie
The work lights will cost about $10-15 with the bulb, I havent seen any cyc's for this cheep. #### soundlight ##### Well-Known Member #### Van ##### CBMod CB Mods Premium Member Yes, It is a completely feasible solution. However depending on your budget, which you already said is low, your saturation is going to suck, depending on how many you can buy. Those works are typically 250-500 w thier beams are a bit tighter than you might like and manufacturing a gel holder is going to require finesse < no not the hair conditioner>. Since your going to want them further away they won't have the punch a "real" cyc light would. Manufacturing a gel holder will be a challenge since they burn hot you can't simply install the gel in place of the glass you have to get it further away than that from the lamp. Also double check the glass in the worklight, Many manufacturers install a UV or color correcting coated glass. If you see that remove it, It will increase your total output in the end. Also, if you are going to do this be sure that someone who knows what he's doing wires and mounts the lights onto j boxes. ok ? #### ship ##### Senior Team Emeritus Premium Member I also recommend the American DJ or Used route. But otherwise: On a work light you will fight the hard edge to the beam a lot more than on a cyc light. It’s going to be a really hard edge and the beam spread is comparatively more narrow but it should work to some extent - throw distance will be your friend. Don’t trust the conduit like frames - find a hard point to safety cable the things and pay attention to how you are going to clamp it if hanging it. Also that these things get really hot, much less could be really dangerous if someone were to kick them. If floor mounted, mount them to a floor base or something that will prevent them from being kicked over by accident or someone tripping over the cord. If hanging, the glass is safety glass that while it won’t break in big dangerous chunks will shower in fine sharp particles if it breaks. Removal of the safety glass also is not an option, nor is screening with hardware cloth. Opitcally the hardware cloth shows up like a grid of shadow grid boxes (it is a lighting effect that can be useful). Only real safety glass replacement or cage over it should the lens be removed would be a stainless steel window screening type material such as used on Omni Lights. Such a replacement would work well and allow it to operate fairly cool, but it would cut down on the light to some extent unless a fairly open weave. Theoretically it would be possible to drill some vent/cooling holes In the casting at the top of the fixture to help some with cooling it. No holes larger than 1/4" or you have to do safety screen vents. This all granted that it’s not UL listed for stage lighting... Let me state it again - work lights ar not UL listed for a stage lighting fixture and should not be used. Much less the wiring will with time suffer from heat damage. Lamp bases also will wear out. Try frosted 500w FDN lamps in the fixture instead of the clear 4.11/16" ones that come with the fixture - this will be one step further in getting a wash of light. Years back for stage work lights we used to use outdoor security light fixtures - they were about the same but their yoke/swivel was very fragile once it became standard to be plastic. Halogen work lights usually fail at their stand first followed by the lamp bases burning up. Often you will find such fixtures still in use as work lights. Often a duplex conduit box with cord off the back of it will have been attached to the fixture and a C-Clamp to the other side of the box. This sometimes even with a duplex Edison outlet on the front of the duplex box so that a series of these fixtures could be powered up... yep, them were the days. Mine had ½" schedule 40 water pipe Tee’s attached to both fixture and C-Clamp back than. The other part of the Tee had a cord strain relief on it. A bit more rugged but still not up to code in that water pipe is not NEC compliant. Also did some Bell boxes which were at least a bit more rugged. Still short of doing an all aluminum and really heavy duty security light, the first part to fail on them was always the plastic yoke/swivel part that joined fixture to electrical box - constantly broke. After that the lamp bases would fail. I see lots of work lights show up for repair with bad lamp bases also - if not the above snapped welds or other problems with the stand for the fixture. #### TupeloTechie ##### Active Member We found about 6 worklights under the house, and we are wanting to use them as a ground row mixed with pars from the 4th electric to wash the cyc. We are a school, and the director has broken all kinds of rules, so she will probably just ignore the UL listings. What is the best way to make a gel frame for these? #### gafftaper ##### Senior Team Senior Team Fight Leukemia I have actually done this a few times successfully using a light sort of like this... The key is you need the kind that have a large metal safety basket that protects the lens. Now go to your local auto supply place and purchase Muffler tape. It's a very thin metal backed tape that is perfectly happy at high temperature. Then simply take a big chunk of gel and cover the entire safety basket taping it to the lamp with muffler tape. Do your best to make a small gap between the gel on the basket and the box of the light itself, fill that gap with a strip of muffler tape going all the way around attaching the gel to the instrument and covering your little gap. If the Gel touches the actual instrument it may melt so a gap and the muffler tape is the trick. As you bend the gel around the edges of the basket you can tape the gel TO ITSELF using scotch tape, but no scotch tape to metal. Finally, figure out which way is up and take a small pin and punch a bunch of holes for heat to escape. I haven't had them on for a whole show but I have used them for about a half hour. Wrap one up and see how long it will stay on without melting the gel. Oh yeah and I always used Roscolux... don't know if that matters but that's what I used. YES that's 500 posts!! I'm a real T.D!!! #### dvlasak ##### Active Member Oh man, just because you are a school doesn't mean that you can ignore safety! Make sure that those "work lights" are where no one can touch them or accidently knock them over. As others have said, they burn incredibly hot. I don't know how you could safely fly or hang them. Start saving up money now to get a better alternative. Go the DJ route, cheap cyc wash, or how about scoops? Scoop fixtures are large "floods" that produce a wide, diffused wash of light. Scoop fixtures are often used for lighting drops and/or cycs. Scoops are basically round fixtures that do not use a lens. Scoops have a reflector at the back of the fixture that directs or "pushes" the light out of the fixture. Since scoops do not have any sort of a lens system they are cheaper than most other fixtures. However, because of this you can not focus the light at all - it just provides a fairly wide wash. Depending on how far away you are from the cyc will determine how diffuse the color is and how wide the light thrown is. Not exactly cutting edge technology, but it works. Dennis Last edited: #### BillESC ##### Well-Known Member The first and probably most important question is... how large is the cyc you wish to light? #### dvlasak ##### Active Member BillESC is right. Cyc size is the first thing you need to know to come up with a solution. My cyc is 45' wide. Depending on the color used and how high I fly the electric, I may only need 6 scoops to create an awesome looking cyc. Thanks Bill! Dennis #### gafftapegreenia ##### CBMod CB Mods Last edited: #### gafftaper ##### Senior Team Senior Team Fight Leukemia Oh man, just because you are a school doesn't mean that you can ignore safety! Make sure that those "work lights" are where no one can touch them or accidently knock them over. As others have said, they burn incredibly hot. I don't know how you could safely fly or hang them. They usually have a large handle of some sort that they connect to their frame with. I took it half appart and drilled out the hole wider and put one of those really small C-clamps on the ones I used. I actually bought a set of them and hung them as work lights. Definitely only use them on the ground if the base is substantial and located in a place that no actor is going to get anywhere near them. While I agree a couple of used scoops would be a much better way to go, I've been in this same situation. Sometimes there really isn't$200 to buy 5 used scoops. We did 4 shows a year at my ghetto high school, with a musical every other year. The student government made a $500 donation to my budget each year, other than that I had to rely on ticket sales to keep floating. My tip: Do lot's of Shakespeare, there are no royalties... heck it's legal to print scripts off the net and photocopy them, and you can get middle schools to bring their English classes to see your shows. It's pure profit. If I read this thread correctly they already have the halogen work lights and are trying to make what they have work because the budget is just too limited. So all these other ideas while great, just aren't possible. My concern is the comment about ignoring the UL listing... I'm not sure what you mean by that. But it's never a good idea to ignore UL. Last edited: #### gafftapegreenia ##### CBMod CB Mods My response with the scoops was to the Liberty cyc suggestion. I just think it's better to go with Altman instead of American DJ, but then again I've never used the Liberty Cyc. You could spend$250, get ten scoops, sell off what you don't need and then use that to outfit the scoops. *Mu wa haha master plan*
On another note, I dont see how a 250 watt worklight is hotter tha, say a 1000W fresnel, and we fly those all the time.
Last edited:
#### TupeloTechie
##### Active Member
ok, I found out today that we have 9 worklights that are already mounted to a truss and wired for 3 different channels, but theres no gel frames or anything, and these do not have the metal in front of the lens like the ones on that picture, does anybody have any ideas on how to make a frame, and how to keep the gel from melting
#### DarSax
##### Active Member
Got any pictures?
#### gafftaper
##### Senior Team
Senior Team
Fight Leukemia
Exact dimensions would help too. |
# How to model distributions which are not normally distributed
I would like to model the performance of a rainwater tank, which has a stochastic input (rainfall). The data are the empty volume in the tank at the end of each day. The values are skewed towards the extremes, and I am not sure how to model this or present it statistically. Reviewing various distributions in Wikipedia, I found that it seems like a Beta Distribution - but I am not sure whether it is one. I need to find a statistical method of representing the 'empty volume'.
One friend suggested that I use binomial distribution of getting probability of tank being 25% empty, 50% empty or 75% empty and find confidence intervals associated with those values.
Here is the distribution of my data:
EDIT - 11 July 7:28 GMT (following comments for clarification)
The inflow into the tank occurs randomly due to the rainfall. There is regular abstraction from the tank if there is stored volume.
I would like to estimate the probability of the empty volume in the tank on any random day in future based on the the historic data, and associated confidence of that probability.
I would then like to use that 'empty volume' figure to estimate how much of a large storm rainfall it can a large number of such tanks hold back and reduce the flash flooding volumes. Possibly may need to present combined probabilities with the storm probability.
• What are you actually trying to accomplish. You say you are trying to model it but do you have a model in mind? I.e., are you trying to predict the amount of rainfall for each day? Or make inference about the mean amount of rainfall or....? – user25658 Jul 10 '13 at 21:01
• Also, based on your graphs I am not convinced this strategy would work but you could always try a transformation of the data and see if that helps alleviate the normality assumption you seem to be hoping for. – user25658 Jul 10 '13 at 21:20
• It's certainly not binomial, that's for count data. You might make an argument for a beta as an approximation, but I doubt that it's actually beta. – Glen_b Jul 11 '13 at 2:08
• I meant to mention in my previous comment - the observations are going to have serial dependence, which should also not be ignored. – Glen_b Jul 11 '13 at 5:15
• It seems to be that a time series approach would be most useful. Something like a stochastic process with a trend, a normal distributed rain input and structural breaks for the extraction. I do not think you should model this as some sort of distribution. The book for all this is Hamilton (1994). Serial dependence, trends etc. are all issues here. I would not recommend picking a model which starts with the assumption of random picking as some said below, as this is clearly not the case. One input maybe iid, the actual barrel state is not. – IMA Jul 11 '13 at 8:29
I would recommend a semiparametric model such as the proportional odds model. This nicely handles data clumping. The model will have one intercept per unique $Y$ value, less one. In two days there will be a major update to the R rms package containing a new ordinal regression modeling function orm that uses sparse matrix algebra to efficiently handle continuous $Y$ (thousands of intercepts). Chapter 15 of my latest course notes contains a case study - see http://biostat.mc.vanderbilt.ede/rms and click on Course Notes. orm handles 4 other distribution families besides the logistic.
• This data looks to be nearly continuous (except near the max and min) based on the QQ plot so you'd probably have to group it before fitting the proportional odds model. How would you suggest doing that? – Macro Jul 10 '13 at 23:12
• What makes you think that any grouping is needed? – Frank Harrell Jul 11 '13 at 11:24
• Oops, I did not read your answer carefully enough. I'll be interested to try this when it comes out. – Macro Jul 11 '13 at 12:52
• The update is now on CRAN for linux, windows, and mac. – Frank Harrell Jul 12 '13 at 16:53
@COOLSerdash's comment is right on target (+1). It seems unlikely that your data are actually any of the named distributions, such as beta, and the answer by @Glen_b will provide a nice example of how you might go about exploring your dataset.
The fitdistrplus package in R will provide you with some tools that may be helpful. For example, if you just want to estimate the parameters of the beta distribution that maximize the likelihood of your data, ?fitdist will help.
"The data are the empty volume in the tank at the end of each day."
• The data are time indexed, you have to take this feature into consideration.
• It is likely that the data are dependent. Someone/Something fill up the tank at some time points or when the tank is close to depletion.
I suggest to take a look at Time Series models (e.g. autoregressive models), rather than fitting a distribution to the raw observations, in order to avoid throwing all the features of the data.
The estimation procedures recommended in the other answers do not consider possible dependencies of the data and time indexing.
• Something: the tank is open vertically and there are inputs of rainfall. – Nick Cox Jul 11 '13 at 0:34
• @NickCox Thanks for the clarification. I guess a different something extracts water from the tank. – Kronos Jul 11 '13 at 0:35
• Yes, the input is rain from a catchment surface, and abstraction is for use - e.g. gardening, irrigation or other uses. – surgez Jul 11 '13 at 9:12
I assume you are trying to find some well known distribution to model your data. If this is the case, then you could do a goodness of fit test. This is a well known test and there are several methods. You will be testing many different distributions to see which one best fits. Then just pick the one that best works for you.
Not sure what you are doing this for, but you could use an empirical distribution, which is basically just the sample itself.
These methods are easy to look up online.
• I'd be surprised if the data would follow any well-known distribution at all. @surgez This post might be of interest too. – COOLSerdash Jul 10 '13 at 21:46 |
# High-Yield™ Gross Anatomy (High-Yield Series)
Language: English
Pages: 320
ISBN: 1451190239
Format: PDF / Kindle (mobi) / ePub
# High-Yield™ Gross Anatomy (High-Yield Series)
Language: English
Pages: 320
ISBN: 1451190239
Format: PDF / Kindle (mobi) / ePub
High-Yield Gross Anatomy, Fifth Edition provides a concise review of gross anatomy material tested on course and board exams. The streamlined outline format includes tables, diagrams, clinical photos, and radiographs for a concentrated, efficient review.
In response to student feedback, the Fifth Edition features:
• A new and updated design -- now in full color!
• New clinical considerations, clinical photos, and radiographs
• Concise illustrations and diagrams to clarify important material
• Eye-catching case studies to test your knowledge before course and board exams
Homeostasis and Toxicology of Essential Metals (Fish Physiology, Volume 31A)
A History of Science in World Cultures: Voices of Knowledge
Data Analysis in Molecular Biology and Evolution
Pluralism and the Mind
The Governance of Science: Ideology and the Future of the Open Society (1st Edition) (Issues in Society)
The anterior and posterior spinal arteries supply only the short superior part of the spinal cord. The circulation of the rest of the spinal cord depends on the segmental medullary arteries and radicular arteries. B. ANTERIOR AND POSTERIOR MEDULLARY SEGMENTAL ARTERIES 1. These arteries arise from the spinal branches of the ascending cervical, deep cervical, vertebral, posterior intercostal, and lumbar arteries. 2. The anterior and posterior medullary segmental arteries occur irregularly in place
Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Normal Radiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2 Spinal Cord and Spinal Nerves I. II. III. IV. V. VI. VII. Components of the Spinal Cord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 Meninges and Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . .140 Arterial Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141 Venous Drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 Innervation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 Clinical Considerations of the Kidney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 Ureter . . . .
SUPPLY. The arterial supply of the jejunum is from the vasa rectae (abdominal aorta S superior mesenteric artery S jejunal arteries S one to two arterial arcades S vasa rectae). C. VENOUS DRAINAGE. The venous drainage of the jejunum is to the veins associated with the arcades (veins associated with the arcades S jejunal veins S superior mesenteric vein S portal vein S hepatic sinusoids S central veins S hepatic veins S inferior vena cava). D. INNERVATION. See Chapter 11 VI. VI Innervation of
these are the “traditional” postganglionic parasympathetic neurons that release ACh as a neurotransmitter. 3. The postganglionic axons terminate on mucosal glands and smooth muscle. B. SYMPATHETIC 1. Preganglionic neuronal cell bodies are located in the intermediolateral cell column of the spinal cord (T8–12). Preganglionic axons form the greater splanchnic nerve, lesser splanchnic nerve, and least splanchnic nerve. 2. Postganglionic neuronal cell bodies are located in the celiac ganglion and |
You are currently browsing the tag archive for the ‘incompressible Euler equations’ tag.
Throughout this post, we will work only at the formal level of analysis, ignoring issues of convergence of integrals, justifying differentiation under the integral sign, and so forth. (Rigorous justification of the conservation laws and other identities arising from the formal manipulations below can usually be established in an a posteriori fashion once the identities are in hand, without the need to rigorously justify the manipulations used to come up with these identities).
It is a remarkable fact in the theory of differential equations that many of the ordinary and partial differential equations that are of interest (particularly in geometric PDE, or PDE arising from mathematical physics) admit a variational formulation; thus, a collection ${\Phi: \Omega \rightarrow M}$ of one or more fields on a domain ${\Omega}$ taking values in a space ${M}$ will solve the differential equation of interest if and only if ${\Phi}$ is a critical point to the functional
$\displaystyle J[\Phi] := \int_\Omega L( x, \Phi(x), D\Phi(x) )\ dx \ \ \ \ \ (1)$
involving the fields ${\Phi}$ and their first derivatives ${D\Phi}$, where the Lagrangian ${L: \Sigma \rightarrow {\bf R}}$ is a function on the vector bundle ${\Sigma}$ over ${\Omega \times M}$ consisting of triples ${(x, q, \dot q)}$ with ${x \in \Omega}$, ${q \in M}$, and ${\dot q: T_x \Omega \rightarrow T_q M}$ a linear transformation; we also usually keep the boundary data of ${\Phi}$ fixed in case ${\Omega}$ has a non-trivial boundary, although we will ignore these issues here. (We also ignore the possibility of having additional constraints imposed on ${\Phi}$ and ${D\Phi}$, which require the machinery of Lagrange multipliers to deal with, but which will only serve as a distraction for the current discussion.) It is common to use local coordinates to parameterise ${\Omega}$ as ${{\bf R}^d}$ and ${M}$ as ${{\bf R}^n}$, in which case ${\Sigma}$ can be viewed locally as a function on ${{\bf R}^d \times {\bf R}^n \times {\bf R}^{dn}}$.
Example 1 (Geodesic flow) Take ${\Omega = [0,1]}$ and ${M = (M,g)}$ to be a Riemannian manifold, which we will write locally in coordinates as ${{\bf R}^n}$ with metric ${g_{ij}(q)}$ for ${i,j=1,\dots,n}$. A geodesic ${\gamma: [0,1] \rightarrow M}$ is then a critical point (keeping ${\gamma(0),\gamma(1)}$ fixed) of the energy functional
$\displaystyle J[\gamma] := \frac{1}{2} \int_0^1 g_{\gamma(t)}( D\gamma(t), D\gamma(t) )\ dt$
or in coordinates (ignoring coordinate patch issues, and using the usual summation conventions)
$\displaystyle J[\gamma] = \frac{1}{2} \int_0^1 g_{ij}(\gamma(t)) \dot \gamma^i(t) \dot \gamma^j(t)\ dt.$
As discussed in this previous post, both the Euler equations for rigid body motion, and the Euler equations for incompressible inviscid flow, can be interpreted as geodesic flow (though in the latter case, one has to work really formally, as the manifold ${M}$ is now infinite dimensional).
More generally, if ${\Omega = (\Omega,h)}$ is itself a Riemannian manifold, which we write locally in coordinates as ${{\bf R}^d}$ with metric ${h_{ab}(x)}$ for ${a,b=1,\dots,d}$, then a harmonic map ${\Phi: \Omega \rightarrow M}$ is a critical point of the energy functional
$\displaystyle J[\Phi] := \frac{1}{2} \int_\Omega h(x) \otimes g_{\gamma(x)}( D\gamma(x), D\gamma(x) )\ dh(x)$
or in coordinates (again ignoring coordinate patch issues)
$\displaystyle J[\Phi] = \frac{1}{2} \int_{{\bf R}^d} h_{ab}(x) g_{ij}(\Phi(x)) (\partial_a \Phi^i(x)) (\partial_b \Phi^j(x))\ \sqrt{\det(h(x))}\ dx.$
If we replace the Riemannian manifold ${\Omega}$ by a Lorentzian manifold, such as Minkowski space ${{\bf R}^{1+3}}$, then the notion of a harmonic map is replaced by that of a wave map, which generalises the scalar wave equation (which corresponds to the case ${M={\bf R}}$).
Example 2 (${N}$-particle interactions) Take ${\Omega = {\bf R}}$ and ${M = {\bf R}^3 \otimes {\bf R}^N}$; then a function ${\Phi: \Omega \rightarrow M}$ can be interpreted as a collection of ${N}$ trajectories ${q_1,\dots,q_N: {\bf R} \rightarrow {\bf R}^3}$ in space, which we give a physical interpretation as the trajectories of ${N}$ particles. If we assign each particle a positive mass ${m_1,\dots,m_N > 0}$, and also introduce a potential energy function ${V: M \rightarrow {\bf R}}$, then it turns out that Newton’s laws of motion ${F=ma}$ in this context (with the force ${F_i}$ on the ${i^{th}}$ particle being given by the conservative force ${-\nabla_{q_i} V}$) are equivalent to the trajectories ${q_1,\dots,q_N}$ being a critical point of the action functional
$\displaystyle J[\Phi] := \int_{\bf R} \sum_{i=1}^N \frac{1}{2} m_i |\dot q_i(t)|^2 - V( q_1(t),\dots,q_N(t) )\ dt.$
Formally, if ${\Phi = \Phi_0}$ is a critical point of a functional ${J[\Phi]}$, this means that
$\displaystyle \frac{d}{ds} J[ \Phi[s] ]|_{s=0} = 0$
whenever ${s \mapsto \Phi[s]}$ is a (smooth) deformation with ${\Phi[0]=\Phi_0}$ (and with ${\Phi[s]}$ respecting whatever boundary conditions are appropriate). Interchanging the derivative and integral, we (formally, at least) arrive at
$\displaystyle \int_\Omega \frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0}\ dx = 0. \ \ \ \ \ (2)$
Write ${\delta \Phi := \frac{d}{ds} \Phi[s]|_{s=0}}$ for the infinitesimal deformation of ${\Phi_0}$. By the chain rule, ${\frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0}}$ can be expressed in terms of ${x, \Phi_0(x), \delta \Phi(x), D\Phi_0(x), D \delta \Phi(x)}$. In coordinates, we have
$\displaystyle \frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0} = \delta \Phi^i(x) L_{q^i}(x,\Phi_0(x), D\Phi_0(x)) \ \ \ \ \ (3)$
$\displaystyle + \partial_{x^a} \delta \Phi^i(x) L_{\partial_{x^a} q^i} (x,\Phi_0(x), D\Phi_0(x)),$
where we parameterise ${\Sigma}$ by ${x, (q^i)_{i=1,\dots,n}, (\partial_{x^a} q^i)_{a=1,\dots,d; i=1,\dots,n}}$, and we use subscripts on ${L}$ to denote partial derivatives in the various coefficients. (One can of course work in a coordinate-free manner here if one really wants to, but the notation becomes a little cumbersome due to the need to carefully split up the tangent space of ${\Sigma}$, and we will not do so here.) Thus we can view (2) as an integral identity that asserts the vanishing of a certain integral, whose integrand involves ${x, \Phi_0(x), \delta \Phi(x), D\Phi_0(x), D \delta \Phi(x)}$, where ${\delta \Phi}$ vanishes at the boundary but is otherwise unconstrained.
A general rule of thumb in PDE and calculus of variations is that whenever one has an integral identity of the form ${\int_\Omega F(x)\ dx = 0}$ for some class of functions ${F}$ that vanishes on the boundary, then there must be an associated differential identity ${F = \hbox{div} X}$ that justifies this integral identity through Stokes’ theorem. This rule of thumb helps explain why integration by parts is used so frequently in PDE to justify integral identities. The rule of thumb can fail when one is dealing with “global” or “cohomologically non-trivial” integral identities of a topological nature, such as the Gauss-Bonnet or Kazhdan-Warner identities, but is quite reliable for “local” or “cohomologically trivial” identities, such as those arising from calculus of variations.
In any case, if we apply this rule to (2), we expect that the integrand ${\frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0}}$ should be expressible as a spatial divergence. This is indeed the case:
Proposition 1 (Formal) Let ${\Phi = \Phi_0}$ be a critical point of the functional ${J[\Phi]}$ defined in (1). Then for any deformation ${s \mapsto \Phi[s]}$ with ${\Phi[0] = \Phi_0}$, we have
$\displaystyle \frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0} = \hbox{div} X \ \ \ \ \ (4)$
where ${X}$ is the vector field that is expressible in coordinates as
$\displaystyle X^a := \delta \Phi^i(x) L_{\partial_{x^a} q^i}(x,\Phi_0(x), D\Phi_0(x)). \ \ \ \ \ (5)$
Proof: Comparing (4) with (3), we see that the claim is equivalent to the Euler-Lagrange equation
$\displaystyle L_{q^i}(x,\Phi_0(x), D\Phi_0(x)) - \partial_{x^a} L_{\partial_{x^a} q^i}(x,\Phi_0(x), D\Phi_0(x)) = 0. \ \ \ \ \ (6)$
The same computation, together with an integration by parts, shows that (2) may be rewritten as
$\displaystyle \int_\Omega ( L_{q^i}(x,\Phi_0(x), D\Phi_0(x)) - \partial_{x^a} L_{\partial_{x^a} q^i}(x,\Phi_0(x), D\Phi_0(x)) ) \delta \Phi^i(x)\ dx = 0.$
Since ${\delta \Phi^i(x)}$ is unconstrained on the interior of ${\Omega}$, the claim (6) follows (at a formal level, at least). $\Box$
Many variational problems also enjoy one-parameter continuous symmetries: given any field ${\Phi_0}$ (not necessarily a critical point), one can place that field in a one-parameter family ${s \mapsto \Phi[s]}$ with ${\Phi[0] = \Phi_0}$, such that
$\displaystyle J[ \Phi[s] ] = J[ \Phi[0] ]$
for all ${s}$; in particular,
$\displaystyle \frac{d}{ds} J[ \Phi[s] ]|_{s=0} = 0,$
which can be written as (2) as before. Applying the previous rule of thumb, we thus expect another divergence identity
$\displaystyle \frac{d}{ds} L( x, \Phi[s](x), D\Phi[s](x) )|_{s=0} = \hbox{div} Y \ \ \ \ \ (7)$
whenever ${s \mapsto \Phi[s]}$ arises from a continuous one-parameter symmetry. This expectation is indeed the case in many examples. For instance, if the spatial domain ${\Omega}$ is the Euclidean space ${{\bf R}^d}$, and the Lagrangian (when expressed in coordinates) has no direct dependence on the spatial variable ${x}$, thus
$\displaystyle L( x, \Phi(x), D\Phi(x) ) = L( \Phi(x), D\Phi(x) ), \ \ \ \ \ (8)$
then we obtain ${d}$ translation symmetries
$\displaystyle \Phi[s](x) := \Phi(x - s e^a )$
for ${a=1,\dots,d}$, where ${e^1,\dots,e^d}$ is the standard basis for ${{\bf R}^d}$. For a fixed ${a}$, the left-hand side of (7) then becomes
$\displaystyle \frac{d}{ds} L( \Phi(x-se^a), D\Phi(x-se^a) )|_{s=0} = -\partial_{x^a} [ L( \Phi(x), D\Phi(x) ) ]$
$\displaystyle = \hbox{div} Y$
where ${Y(x) = - L(\Phi(x), D\Phi(x)) e^a}$. Another common type of symmetry is a pointwise symmetry, in which
$\displaystyle L( x, \Phi[s](x), D\Phi[s](x) ) = L( x, \Phi[0](x), D\Phi[0](x) ) \ \ \ \ \ (9)$
for all ${x}$, in which case (7) clearly holds with ${Y=0}$.
If we subtract (4) from (7), we obtain the celebrated theorem of Noether linking symmetries with conservation laws:
Theorem 2 (Noether’s theorem) Suppose that ${\Phi_0}$ is a critical point of the functional (1), and let ${\Phi[s]}$ be a one-parameter continuous symmetry with ${\Phi[0] = \Phi_0}$. Let ${X}$ be the vector field in (5), and let ${Y}$ be the vector field in (7). Then we have the pointwise conservation law
$\displaystyle \hbox{div}(X-Y) = 0.$
In particular, for one-dimensional variational problems, in which ${\Omega \subset {\bf R}}$, we have the conservation law ${(X-Y)(t) = (X-Y)(0)}$ for all ${t \in \Omega}$ (assuming of course that ${\Omega}$ is connected and contains ${0}$).
Noether’s theorem gives a systematic way to locate conservation laws for solutions to variational problems. For instance, if ${\Omega \subset {\bf R}}$ and the Lagrangian has no explicit time dependence, thus
$\displaystyle L(t, \Phi(t), \dot \Phi(t)) = L(\Phi(t), \dot \Phi(t)),$
then by using the time translation symmetry ${\Phi[s](t) := \Phi(t-s)}$, we have
$\displaystyle Y(t) = - L( \Phi(t), \dot\Phi(t) )$
as discussed previously, whereas we have ${\delta \Phi(t) = - \dot \Phi(t)}$, and hence by (5)
$\displaystyle X(t) := - \dot \Phi^i(x) L_{\dot q^i}(\Phi(t), \dot \Phi(t)),$
and so Noether’s theorem gives conservation of the Hamiltonian
$\displaystyle H(t) := \dot \Phi^i(x) L_{\dot q^i}(\Phi(t), \dot \Phi(t))- L(\Phi(t), \dot \Phi(t)). \ \ \ \ \ (10)$
For instance, for geodesic flow, the Hamiltonian works out to be
$\displaystyle H(t) = \frac{1}{2} g_{ij}(\gamma(t)) \dot \gamma^i(t) \dot \gamma^j(t),$
so we see that the speed of the geodesic is conserved over time.
For pointwise symmetries (9), ${Y}$ vanishes, and so Noether’s theorem simplifies to ${\hbox{div} X = 0}$; in the one-dimensional case ${\Omega \subset {\bf R}}$, we thus see from (5) that the quantity
$\displaystyle \delta \Phi^i(t) L_{\dot q^i}(t,\Phi_0(t), \dot \Phi_0(t)) \ \ \ \ \ (11)$
is conserved in time. For instance, for the ${N}$-particle system in Example 2, if we have the translation invariance
$\displaystyle V( q_1 + h, \dots, q_N + h ) = V( q_1, \dots, q_N )$
for all ${q_1,\dots,q_N,h \in {\bf R}^3}$, then we have the pointwise translation symmetry
$\displaystyle q_i[s](t) := q_i(t) + s e^j$
for all ${i=1,\dots,N}$, ${s \in{\bf R}}$ and some ${j=1,\dots,3}$, in which case ${\dot q_i(t) = e^j}$, and the conserved quantity (11) becomes
$\displaystyle \sum_{i=1}^n m_i \dot q_i^j(t);$
as ${j=1,\dots,3}$ was arbitrary, this establishes conservation of the total momentum
$\displaystyle \sum_{i=1}^n m_i \dot q_i(t).$
Similarly, if we have the rotation invariance
$\displaystyle V( R q_1, \dots, Rq_N ) = V( q_1, \dots, q_N )$
for any ${q_1,\dots,q_N \in {\bf R}^3}$ and ${R \in SO(3)}$, then we have the pointwise rotation symmetry
$\displaystyle q_i[s](t) := \exp( s A ) q_i(t)$
for any skew-symmetric real ${3 \times 3}$ matrix ${A}$, in which case ${\dot q_i(t) = A q_i(t)}$, and the conserved quantity (11) becomes
$\displaystyle \sum_{i=1}^n m_i \langle A q_i(t), \dot q_i(t) \rangle;$
since ${A}$ is an arbitrary skew-symmetric matrix, this establishes conservation of the total angular momentum
$\displaystyle \sum_{i=1}^n m_i q_i(t) \wedge \dot q_i(t).$
Below the fold, I will describe how Noether’s theorem can be used to locate all of the conserved quantities for the Euler equations of inviscid fluid flow, discussed in this previous post, by interpreting that flow as geodesic flow in an infinite dimensional manifold.
As we are all now very much aware, tsunamis are water waves that start in the deep ocean, usually because of an underwater earthquake (though tsunamis can also be caused by underwater landslides or volcanoes), and then propagate towards shore. Initially, tsunamis have relatively small amplitude (a metre or so is typical), which would seem to render them as harmless as wind waves. And indeed, tsunamis often pass by ships in deep ocean without anyone on board even noticing.
However, being generated by an event as large as an earthquake, the wavelength of the tsunami is huge – 200 kilometres is typical (in contrast with wind waves, whose wavelengths are typically closer to 100 metres). In particular, the wavelength of the tsunami is far greater than the depth of the ocean (which is typically 2-3 kilometres). As such, even in the deep ocean, the dynamics of tsunamis are essentially governed by the shallow water equations. One consequence of these equations is that the speed of propagation ${v}$ of a tsunami can be approximated by the formula
$\displaystyle v \approx \sqrt{g b} \ \ \ \ \ (1)$
where ${b}$ is the depth of the ocean, and ${g \approx 9.8 ms^{-2}}$ is the force of gravity. As such, tsunamis in deep water move very fast – speeds such as 500 kilometres per hour (300 miles per hour) are quite typical; enough to travel from Japan to the US, for instance, in less than a day. Ultimately, this is due to the incompressibility of water (and conservation of mass); the massive net pressure (or more precisely, spatial variations in this pressure) of a very broad and deep wave of water forces the profile of the wave to move horizontally at vast speeds. (Note though that this is the phase velocity of the tsunami wave, and not the velocity of the water molecues themselves, which are far slower.)
As the tsunami approaches shore, the depth ${b}$ of course decreases, causing the tsunami to slow down, at a rate proportional to the square root of the depth, as per (1). Unfortunately, wave shoaling then forces the amplitude ${A}$ to increase at an inverse rate governed by Green’s law,
$\displaystyle A \propto \frac{1}{b^{1/4}} \ \ \ \ \ (2)$
at least until the amplitude becomes comparable to the water depth (at which point the assumptions that underlie the above approximate results break down; also, in two (horizontal) spatial dimensions there will be some decay of amplitude as the tsunami spreads outwards). If one starts with a tsunami whose initial amplitude was ${A_0}$ at depth ${b_0}$ and computes the point at which the amplitude ${A}$ and depth ${b}$ become comparable using the proportionality relationship (2), some high school algebra then reveals that at this point, amplitude of a tsunami (and the depth of the water) is about ${A_0^{4/5} b_0^{1/5}}$. Thus, for instance, a tsunami with initial amplitude of one metre at a depth of 2 kilometres can end up with a final amplitude of about 5 metres near shore, while still traveling at about ten metres per second (35 kilometres per hour, or 22 miles per hour), and we have all now seen the impact that can have when it hits shore.
While tsunamis are far too massive of an event to be able to control (at least in the deep ocean), we can at least model them mathematically, allowing one to predict their impact at various places along the coast with high accuracy. (For instance, here is a video of the NOAA’s model of the March 11 tsunami, which has matched up very well with subsequent measurements.) The full equations and numerical methods used to perform such models are somewhat sophisticated, but by making a large number of simplifying assumptions, it is relatively easy to come up with a rough model that already predicts the basic features of tsunami propagation, such as the velocity formula (1) and the amplitude proportionality law (2). I give this (standard) derivation below the fold. The argument will largely be heuristic in nature; there are very interesting analytic issues in actually justifying many of the steps below rigorously, but I will not discuss these matters here.
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### Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More
Prabhanjan Ananth, Xiong Fan, and Elaine Shi
##### Abstract
Attribute based encryption (ABE) is an advanced encryption system with a built-in mechanism to generate keys associated with functions which in turn provide restricted access to encrypted data. Most of the known candidates of attribute based encryption model the functions as circuits. This results in significant efficiency bottlenecks, especially in the setting where the function associated with the ABE key is represented by a random access machine (RAM) and a database, with the runtime of the RAM program being sublinear in the database size. In this work we study the notion of attribute based encryption for random access machines (RAMs), introduced in the work of Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (Crypto 2013). We present a construction of attribute based encryption for RAMs satisfying sublinear decryption complexity assuming learning with errors; this is the first construction based on standard assumptions. Previously, Goldwasser et al. achieved this result based on non-falsifiable knowledge assumptions. We also consider a dual notion of ABE for RAMs, where the database is in the ciphertext and we show how to achieve this dual notion, albeit with large attribute keys, also based on learning with errors.
Available format(s)
Category
Public-key cryptography
Publication info
Keywords
attribute-based encryptionRAMsLWE
Contact author(s)
xfan @ cs cornell edu
History
2020-08-04: last of 3 revisions
See all versions
Short URL
https://ia.cr/2018/273
CC BY
BibTeX
@misc{cryptoeprint:2018/273,
author = {Prabhanjan Ananth and Xiong Fan and Elaine Shi},
title = {Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More},
howpublished = {Cryptology ePrint Archive, Paper 2018/273},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/273}},
url = {https://eprint.iacr.org/2018/273}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. |
# 태권도 물리: Lesson 3 – energy and force, part 2
In lesson 1 we started with:
$E=\frac{1}{2}mv^2+mg_y$ and $F_{arm}=ma$
• Let m = mass of the fist and arm of a 45 kg (100 pounds) martial artist, approximately 10 kg (22 pounds).
• Let v = velocity of the fist in the horizontal, or x direction only. Assume $5 \frac{m}{s}$
• Note: In lesson 2 we discovered that the actual $velocity_{arm} = 4 \frac{m}{s}$.
• Inserting values we have $E_{arm}=\frac{1}{2}(10kg)(4\frac{m}{s})^2-(4\frac{m}{s})(9.8\frac{m}{s^2})=80J-39.2J=40.8J$ and $F_{arm}=(10kg)(9.8\frac{m}{s^2})=980N$
This is about 220 pounds of force, if the entire arm is treated as a solid body. In actuality, the entire arm does not travel through the target. Assuming proper extension of the fist through the target zone, at most only 10% of the arm’s force will be delivered to the target.
• Let l = length of fully extended arm, approximately 0.3 m
• Let m = 10 kg, the mass of the fist and arm
• Let v = 4 m/s, as calculated in lesson 2
$F_i=\sum_{i=1}^{10 }m_i\frac{iv}{10t}=478.8N$
Note that by treating the fist as one-tenth of the total arm, we find a more accurate assessment of the force delivered to target. In this case, one-tenth the size yields one-half the force, 108 pounds of force instead of 220 pounds.
Again, this assumes only linear motion. What about rotational motion enacted by twisting the fist during the punch? Let us save that for the next lesson.
Related: |
# Sine Wave Generation
#### kaleanae
Joined Nov 8, 2007
1
Hi!
I was wondering if someone knows how to generate many sine waves at once (I also need to add them), for example, to generate 2 I use:
s_1 = (exp(j*2*pi*f_1*t) - exp(-j*2*pi*f_1*t))/(2*j);
s_2 = imag(exp(j*2*pi*f_2*t));
% plot the 2 and 4 Hz waves together in the same panel
figure
subplot(2,1,1)
plot(t,s_1, 'b-')
hold on
plot(t, s_2, 'r--')
ylabel('Amplitude')
% Plot the sum
subplot(2,1,2)
plot(t, s_1+s_2)
ylabel('Amplitude')
xlabel('Time (s)')
How can I do this without using Hold on.
Thank you
#### cheddy
Joined Oct 19, 2007
87
what language is that?
#### Papabravo
Joined Feb 24, 2006
18,070
The ever popular, but ruinously expensive Matlab.
Go for Scilab as a freeware Matlab clone.
Why are you using the complex exponential? The ordinary sin function isn't good enough for you?
You just load the rows(columns) of a matrix with calls to the sin function where the argument depends on either the row or coulmn index. Heck you could even use a random number generator to pick the frequency of the sin function. When you're done you can use row or column sums as appropriate to add them together.
#### Salgat
Joined Dec 23, 2006
218
I love your brutal honesty Papabravo, I both hate and adore you simultaneously. Anyways, does that clone use identical sytax as Matlab?
#### Papabravo
Joined Feb 24, 2006
18,070
It is identical in many cases. They do have features that were not in Matlab the last time I looked like symbolic polynomial manipulation. For the price it is really hard not to take it for a test drive.
Also you have to know what you are looking for since the help apparently doesn't have a search feature.
I guess brutal honesty works both ways -- Thanks for that.
#### Dave
Joined Nov 17, 2003
6,969
The (free) Matlab clone that most closely resembles Matlab syntax is Octave - it is designed to be that way. There are some very subtle differences, however they are corrections to some of the more illogical Matlab constructs, therefore the experienced programmer should find it *easier* to use. Another one that is worth considering is FreeMat.
Dave
#### Dave
Joined Nov 17, 2003
6,969
Hi!
I was wondering if someone knows how to generate many sine waves at once (I also need to add them), for example, to generate 2 I use:
s_1 = (exp(j*2*pi*f_1*t) - exp(-j*2*pi*f_1*t))/(2*j);
s_2 = imag(exp(j*2*pi*f_2*t));
% plot the 2 and 4 Hz waves together in the same panel
figure
subplot(2,1,1)
plot(t,s_1, 'b-')
hold on
plot(t, s_2, 'r--')
ylabel('Amplitude')
% Plot the sum
subplot(2,1,2)
plot(t, s_1+s_2)
ylabel('Amplitude')
xlabel('Time (s)')
How can I do this without using Hold on.
Thank you
I agree with Papabravo's suggestion - use the sin function.
Declare your time variable t (I have done this arbitrarily below), and the pass that as an argument to your sin function:
Rich (BB code):
t = [1:0.1:100]; % 991 time points at 0.1 resolution
s_1 = sin(2*pi*f_1*t);
s_2 = sin(2*pi*f_2*t);
s_3 = s_1 + s_3
You can have as many, and add as many, sine waves as you want using the above syntax.
You will need to use hold on to plot multiple graphs on the same axis.
Dave |
130 views
Funky Pizzaria was required to supply pizzas to three different parties. The total number of pizzas it had to deliver was $800$, $70\%$ of which were to be delivered to Party $3$ and the rest equally divided between Party $1$ and Party $2$.
Pizzas could be of Thin Crust $(T)$ or Deep Dish $(D)$ variety and come in either Normal Cheese $(NC)$ or Extra Cheese $(EC)$ versions. Hence, there are four types of pizzas: $T-NC$, $T-EC$, $D-NC$ and $D-EC$. Partial information about proportions of $T$ and $NC$ pizzas ordered by the three parties is given below:
$\begin{array}{cccc} & \text{Thin Crust (T)} & \text{Normal Cheese (NC)} \\ \text{Party 1} & 0.6 & - \\ \text{Party 2} & 0.55 & 0.3 \\ \text{Party 3} & - & 0.65 \\ \text{Total }& 0.375 & 0.52 \end{array}$
How many Normal Cheese pizzas were required to be delivered to Party $1$?
1. $104$
2. $84$
3. $16$
4. $196$
1
143 views
2
122 views |
# Using Travis to Deploy My Blog
I’ve been using Travis-CI more and more as a platform from which I can deploy things, due to the fact that we can run any code on it. Today I made it so that this blog is deployed to gh-pages when pushed. I have also set up my personal blog to be pushed this way as well.
Why did I use Travis-CI instead of Shippable or other CI systems for this? Well, its mainly due to the fact that I was already using Travis, and the tools (specifically the Travis gem) are quite mature. Many of the things that are quite troublesome, like generating a key and placing decrypt commands into the .travis.yml, are now covered in simple command line instructions.
My blog uses Jekyll + Octopress, but I don’t like the limitations imposed by github on the templates I can use. So I decided it was better to simply upload the finished product. First of all, I push all my blog sources up to a public repository at https://github.com/davidsiaw/davidsiaw.github.io.source
While the setup is easy, its not obvious that you can do this. Hopefully this will go some way to helping others who want to circumvent the github limitations on their gh-pages content as well.
In this post I will show you how to set it up. First of all, I create a key that will give push access to my blog’s repository at https://github.com/davidsiaw/davidsiaw.github.io by calling up ssh-keygen
I then place the deploy_key.pub in my github repository.
Next, I make use of the Travis gem to encrypt my private key. I add the --add parameter to make it write to my .travis.yml (I am in the directory.)
This gives me a deploy_key.enc that is my encrypted private key.
In order to use this key, I need to add some more lines to .travis.yml to enable it to push to github. First of all, I need to install the key into the .ssh folder so git can use it. I also chmod it so ssh will not complain.
With this, I can now tell Travis to push the generated files. All I do is tell it to generate the site (since this is just Jekyll), and then call my deploy script which simply pushes the right stuff up to github.
With this, my website gets updated everytime I push my changes to https://github.com/davidsiaw/davidsiaw.github.io.source, Travis will automatically update my blog. |
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# Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat
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Math Expert
Joined: 02 Sep 2009
Posts: 50619
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
23 Dec 2014, 08:49
00:00
Difficulty:
5% (low)
Question Stats:
87% (01:35) correct 13% (01:50) wrong based on 114 sessions
### HideShow timer Statistics
Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17
Kudos for a correct solution.
_________________
Manager
Joined: 20 Feb 2013
Posts: 75
Location: India
GMAT 1: 690 Q49 V34
WE: Information Technology (Computer Software)
Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
23 Dec 2014, 09:18
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab
==> a # b = 4 * (a + b)^2
when a # b = 100
==> (a + b) = 5 (ignoring negative solution)
Thus (a + b) + 3 = 8, Answer B
_________________
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Manager
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Posts: 175
Location: United States
GMAT 1: 700 Q49 V35
Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
23 Dec 2014, 20:45
1
Bunuel wrote:
Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17
Kudos for a correct solution.
4a^2 + 4b^2 + 8ab = 100 --->(1)
=>a^2 + b^2 + 2ab = 25 ---> Divide (1) by 4
=> (a + b) ^2 = 25
=> a+b = 5
=>(a + b) + 3 = 8
ANs B
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Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
23 Dec 2014, 23:43
2
Quote:
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17
1) 4a^2 + 4b^2 + 8ab -> (2a+2b)^2 = a # b
2) a # b = 100 = (2a+2b)^2
3) 10 = (2a+2b)
4) 5 = a+b this is the important info for our answer, because we dont need to know the exact values for a or b.
5) (a + b) + 3 = 5 + 3 = 8
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Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
24 Dec 2014, 01:19
2
Given that $$4a^2 + 4b^2 + 8ab = 100$$
$$a^2 + 2ab + b^2 = 25$$
$$(a+b)^2 = 25$$
a+b = 5
a+b+3 = 8
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Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
25 Dec 2014, 03:56
a#b=100=4a*a +4b*b + 8ab
Dividing both sides by 4
a*a+ b*B+ 2ab=25 ==> (a+b)sq=25 ==> a+b=+-5. Taking a+b as -5 gives answer as 2 which is not an option. Taking a=B=5 gives the answer as 8.
hence option b.
Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
08 Jan 2015, 06:56
Bunuel wrote:
Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17
Kudos for a correct solution.
OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 3 = 10/2 + 3 = 8.
_________________
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Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat [#permalink]
### Show Tags
28 Mar 2018, 09:30
Bunuel wrote:
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17
a # b = 100
4a^2 + 4b^2 + 8ab = 100
a^2 + b^2 + 2ab = 25
(a + b)^2 = 25
a + b = 5
So (a + b) + 3 = 5 + 3 = 8.
(Note: a + b can’t be -5 since a # b is defined for non-negative integers only. If a + b = -5, then at least one of a and b has to be negative.)
_________________
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Founder and CEO
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
Re: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat &nbs [#permalink] 28 Mar 2018, 09:30
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# source:anuga_work/publications/boxing_day_validation_2008/patong_validation.tex@7408
Last change on this file since 7408 was 7408, checked in by ole, 14 years ago
Flagged FIXMEs that relate to Richard's work with: Search for RICHARD
File size: 61.8 KB
Line
1\documentclass[a4paper]{article}
2% to be added when submitted to ocean dynamics
3%\documentclass[smallcondensed,draft]{svjour3}
4%\usepackage{mathptmx}
5%\journalname{Ocean Dynamics}
6
7\usepackage{graphicx}
8\usepackage{hyperref}
9\usepackage{amsfonts}
10\usepackage{url} % for URLs and DOIs
11\newcommand{\doi}[1]{\url{http://dx.doi.org/#1}}
12
13
14%----------title-------------%
15\title{Benchmarking Tsunami Models using the December 2004 Indian
16 Ocean Tsunami and its Impact at Patong Bay}
17
18%-------authors-----------
19\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and
20 D. Burbidge \and R. Mleczko \and N. Horspool}
21
22% to be added when submitted to ocean dynamics
23%\institute{J.~D. Jakeman \at
24% The Australian National University, Canberra, \textsc{Australia}\
25% \email{[email protected]}
26% \and
27% O. Nielsen \and R. Mleczko \and D. Burbidge \and K. VanPutten \and N. Horspool \at
28% Geoscience Australia, Canberra, \textsc{Australia}
29%}
30
31
32%================Start of Document================
33\begin{document}
34\maketitle
35%------Abstract--------------
36\begin{abstract}
37This paper proposes a new benchmark for tsunami model validation.
38The benchmark is based upon the 2004 Indian Ocean tsunami,
39which affords a uniquely large amount of observational data for events of this kind.
40Unlike the small number of existing benchmarks, the
41proposed test validates all three stages of tsunami evolution -
42generation (FIXME (Jane): really?), propagation and inundation. Specifically we use geodetic
43measurements of the Sumatra--Andaman earthquake to validate the
44tsunami source, altimetry data from the \textsc{jason} satellite to
45test open ocean propagation, eye-witness accounts to assess near shore
46propagation and a detailed inundation survey of Patong city, Thailand
47to compare model and observed inundation. Furthermore we utilise this
48benchmark to further validate the hydrodynamic modelling tool
49\textsc{anuga} which is used to simulate the tsunami
50inundation. Important buildings and other structures were incorporated
51into the underlying computational mesh and shown to have a large
52influence on inundation extent. Sensitivity analysis also showed that
53the model predictions are comparatively insensitive to large changes
54in friction and small perturbations in wave weight at the 100 m depth
55contour.
56% to be added when submitted to ocean dynamics
57%\keywords{Tsunami \and modelling \and validation and verification \and benchmark}
58\end{abstract}
59
60\tableofcontents
61%================Section===========================
62
63\section{Introduction}
64Tsunami is a potential hazard to coastal communities all over the
65world. A number of recent large events have increased community and
66scientific awareness of the need for effective detection, forecasting,
67and emergency preparedness. Probabilistic, geophysical and hydrodynamic
68models are required to predict the location and
69likelihood of an event, the initial sea floor deformation and
70subsequent propagation and inundation of the tsunami. Engineering, economic and social vulnerability models can then be used to estimate the
71impact of the event as well as the effectiveness of hazard mitigation
72procedures. In this paper, we focus on modelling of
73the physical processes only.
74
75Various approaches are currently used to assess the potential tsunami
76inundation of coastal communities.
77These methods differ in both the formulation used to
78describe the evolution of the tsunami and the numerical methods used
79to solve the governing equations. However any legitimate model must
80address each of the three distinct stages of tsunami evolution---
81generation, propagation and inundation. Models combining observed seismic,
82geodetic and sometimes tsunami data must be used
83to provide estimates of initial sea floor and ocean surface
84deformation. The complexity of these models ranges from empirical to
85non-linear three-dimensional mechanical models. The shallow water wave
86equations, linearised shallow water wave equations, and
87Boussinesq-type equations are frequently used to simulate tsunami
88propagation. These models are typically used to predict quantities
89such as arrival times, wave speeds and heights, and inundation extents
90which are used to develop efficient hazard mitigation plans.
91
92Inaccuracies in model prediction can result in inappropriate
93evacuation plans and town zoning, which may result in loss of life and
94large financial losses. Consequently tsunami models must undergo
95sufficient end-to-end testing to increase scientific and community
96confidence in the model predictions.
97
98Complete confidence in a model of a physical system cannot be
99established. One can only hope to state under what conditions and to what extent the
100model hypothesis holds true. Specifically the utility of a model can
101be assessed through a process of verification and
102validation. Verification assesses the accuracy of the numerical method
103used to solve the governing equations and validation is used to
104investigate whether the model adequately represents the physical
105system~\cite{bates01}. Together these processes can be used to
106establish the likelihood that a model represents a legitimate
107hypothesis.
108
109The sources of data used to validate and verify a model can be
110separated into three main categories: analytical solutions, scale
111experiments and field measurements. Analytical solutions of the
112governing equations of a model, if available, provide the best means
113of verifying any numerical model. However, analytical solutions are
114frequently limited to a small set of idealised examples that do not
115completely capture the more complex behaviour of real' events. Scale
116experiments, typically in the form of wave-tank experiments, provide a
117much more realistic source of data that better captures the complex
118dynamics of flows such as those generated by a tsunami, whilst allowing
119control of the event and much easier and accurate measurement of the
120tsunami properties. Comparison of numerical predictions with field
121data provides the most stringent test. The use of field data increases
122the generality and significance of conclusions made regarding model
123utility. On the other hand, it must be noted that the use of field
124data also significantly increases the uncertainty of the validation
125experiment that may constrain the ability to make unequivocal
126statements~\cite{bates01}.
127FIXME (Jane): Why would that increase the uncertainty?
128FIXME (Phil): references to all of the paragraph above, please
129
130Currently, the extent of tsunami-related field data is limited. The
131cost of tsunami monitoring programs, bathymetry and topography surveys
132prohibits the collection of data in many of the regions in which
133tsunamis pose greatest threat. The resulting lack of data has limited
134the number of field data sets available to validate tsunami
135models.
136
137Synolakis et al~\cite{synolakis07} have developed a set of
138standards, criteria and procedures for evaluating numerical models of
139tsunami. They propose three analytical solutions to help identify the
140validity of a model, and five scale comparisons (wave-tank benchmarks)
141and two field events to assess model veracity.
142
143The first field data benchmark introduced in \cite{synolakis07} compares model
144results against observed data from the Hokkaido-Nansei-Oki tsunami
145that occurred around Okushiri Island, Japan on the 12 July
1461993. This tsunami provides an example of extreme run-up generated from
147reflections and constructive interference resulting from local
148topography and bathymetry. The benchmark consists of two tide gauge
149records and numerous spatially-distributed point sites at which
150modelled maximum run-up elevations can be compared. The second
151benchmark is based upon the Rat Islands tsunami that occurred off the
152coast of Alaska on the 17 November 2003. The Rat Island tsunami
153provides a good test for real-time forecasting models since the tsunami
154was recorded at three tsunameters. The test requires matching the
155tsunami propagation model output with the DART recording to constrain the
156tsunami source model, and then using it to reproduce the tide gauge
157record at Hilo, Hawaii.
158FIXME (Jane): Are the tsunameters and the DART recordings the same thing?
159
160In this paper we develop a field data benchmark to be used in
161conjunction with the other tests proposed by Synolakis et
162al~\cite{synolakis07} to validate and verify tsunami models.
163The benchmark proposed here allows evaluation of
164model structure during all three distinct stages tsunami evolution.
165It consists of geodetic measurements of the
166Sumatra--Andaman earthquake that are used to validate the description
167of the tsunami source, altimetry data from the \textsc{jason} satellite to test
168open ocean propagation, eye-witness accounts to assess near shore
169propagation, and a detailed inundation survey of Patong city, Thailand
170to compare model and observed inundation. A description of the data
171required to construct the benchmark is given in
172Section~\ref{sec:data}.
173
174An associated aim of this paper is to illustrate the use of this new
175benchmark to validate a dedicated inundation model called
176\textsc{anuga} used by Geoscience Australia. A description of
177\textsc{anuga} is given in Section~\ref{sec:models} and the validation
178results are given in Section~\ref{sec:results}.
179
180The numerical models used to simulate tsunami impact
181are computationally intensive and high resolution models of the entire
182evolution process will often take a number of days to
183run. Consequently, the uncertainty in model predictions is difficult to
184quantify as it would require a very large number of runs.
185However, model uncertainty should not be ignored. Section
186~\ref{sec:sensitivity} provides a simple analysis that can
187be used to investigate the sensitivity of model predictions to model
188parameters.
189
190%================Section===========================
191\section{Data}\label{sec:data}
192The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the
193devastation caused by the subsequent tsunami have generated much
194scientific interest. As a result an unusually large amount of post
195seismic data has been collected and documented. Data sets from
196seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses,
197subsequent coastal field surveys of run-up and flooding, and
198measurements of coseismic displacements as well as bathymetry from ship-based
200available. %~\cite{vigny05,amnon05,kawata05,liu05}. FIXME (Ole): Refs?
201
202In this section we present the corresponding data necessary to implement
203the proposed benchmark for each of the three stages of the tsunami's evolution.
204
205\subsection{Generation}\label{sec:gen_data}
206All tsunami are generated from an initial disturbance of the ocean
207which develops into a low frequency wave that propagates outwards from
208the source. The initial deformation of the water surface is most
209commonly caused by coseismic displacement of the sea floor, but
210submarine mass failures, landslides, volcanoes or asteroids can also
211cause tsunami. In this section we detail the information used in
212this study to validate models of the sea floor deformation generated
213by the 2004 Sumatra--Andaman earthquake.
214
215The 2004 Sumatra--Andaman tsunami was generated by a coseismic
216displacement of the sea floor resulting from one of the largest
217earthquakes on record. The mega-thrust earthquake started on the 26
218December 2004 at 0h58'53'' UTC (or just before 8 am local time)
219approximately 70 km offshore of North Sumatra
220(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
221rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
222the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
223minutes~\cite{ammon05}. Estimates of the moment magnitude of this
224event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}.
225
226The unusually large surface deformation caused by this earthquake
227means that there were a range of different geodetic measurements of
228the surface deformation available. These include field measurements of
229uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
230measurements and remote sensing measurements of uplift or subsidence
231(see~\cite{chlieh07} and references therein). Here we use the the near-field
232estimates of vertical deformation in northwestern Sumatra and
233the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate
234that our crustal deformation model of the 2004 Sumatra--Andaman
235earthquake is producing reasonable results. Note that the geodetic
236data used here is a combination of the vertical deformation that
237happened in the $\sim$10 minutes of the earthquake plus the
238deformation that followed in the days following the earthquake before
239each particular measurement was actually made (typically of order
240days). Therefore some of the observations may not contain the purely
241co-seismic deformation but could include some post-seismic deformation
242as well~\cite{chlieh07}.
243
244%DAVID: I commented out the figure since we can combine it with the model result without obscuring it. That will keep the number of figures down.
245
246%\begin{figure}[ht]
247%\begin{center}
248%\includegraphics[width=8.0cm,keepaspectratio=true]{geodeticMeasurements.jpg}
249%\caption{Near field geodetic measurements used to validate tsunami generation. FIXME: Insert appropriate figure here}
250%\label{fig:geodeticMeasurements}
251%\end{center}
252%\end{figure}
253
254\subsection{Propagation}
255\label{sec:propagation data}
256Once generated, a tsunami will propagate outwards from the source until
257it encounters the shallow water bordering coastal regions.
258FIXME (Ole): Need to change this definition. I believe propagation takes place all the way to the shore line and not just up to shallow waters.
259
260This period
261of the tsunami evolution is referred to as the propagation stage. The
262height and velocity of the tsunami is dependent on the local
263bathymetry in the regions through which the wave travels and the size
264of the initial wave. This section details the bathymetry data needed
265to model the tsunami propagation and the satellite altimetry transects
266used here to validate open ocean tsunami models.
267
268\subsubsection{Bathymetry Data}
269The bathymetry data used in this study was derived from the following
270sources:
271\begin{itemize}
272\item a two arc minute grid data set covering the Bay of Bengal,
273 DBDB2, obtained from US Naval Research Labs;
274\item a 3 second arc grid covering the whole of the Andaman Sea based
275 on Thai Navy charts no. 45 and no. 362; and
276\item a one second grid created from the digitised Thai Navy
277 bathymetry chart, no. 358, which covers Patong Bay and the
279 (FIXME (Ole): How was the grid created from these digitised points?) RICHARD
280\end{itemize}
281FIXME (Jane): Refs for all these. RICHARD
282
283%A number of raw data sets were obtained, analysed and checked for
284%quality and subsequently gridded for easier visualisation and input
285%into the tsunami models.
286
287These sets were combined via
288interpolation and resampling to produce four nested grids
289which are relatively coarse in the deeper water and
290progressively finer as the distance to
291Patong Beach decreases as shown in Figure~\ref{fig:nested_grids}
292
293The coarsest
294bathymetry was obtained by interpolating the DBDB2 grid to a 27 second
295arc grid. A subsection of this region was then replaced by nine second
296data which was generated by sub-sampling the three second of arc grid from
297NOAA (FIXME (Jane): This was not mentioned in the dots above). RICHARD
298
299A subset of the nine second grid was replaced by the three second
300data. Finally, the one second grid was used to approximate the
301bathymetry in Patong Bay and the immediately adjacent regions. Any
302points that deviated from the general trend near the boundary were
303deleted as a quality check.
304
305The sub-sampling of larger grids was performed by using {\bf resample},
306a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The
307gridding of data was performed using {\bf Intrepid}, a commercial
308geophysical processing package developed by Intrepid Geophysics. The
309gridding scheme employed the nearest neighbour algorithm followed by
310an application of minimum curvature akima spline smoothing.
311See \url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf}
312for details on the Intrepid model.
313
314
315\begin{figure}[ht]
316\begin{center}
317\includegraphics[width=\textwidth,keepaspectratio=true]{nested_grids}
318\caption{Nested bathymetry grids.}
319\label{fig:nested_grids}
320\end{center}
321\end{figure}
322
323\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
324During the 26 December 2004 event, the \textsc{jason} satellite tracked from
325north to south and over the equator at 02:55 UTC nearly two hours
326after the earthquake \cite{gower05}. The satellite recorded the sea
327level anomaly compared to the average sea level from its previous five
328passes over the same region in the 20-30 days prior. This data was
329used to validate the propagation stage in Section
330\ref{sec:resultsPropagation}.
331FIXME (Ole): See Phil's second point and email with help from David
332
333
334%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
335
336%\begin{figure}[ht]
337%\begin{center}
338%\includegraphics[width=8.0cm,keepaspectratio=true]{sateliteTrack.jpg}
339%\caption{URS wave heights 120 minutes after the initial earthquake with the JASON satellite track and its observed sea level anomalies overlaid. Note the URS data has not been corrected for the flight path time. FIXME: should we just have track and not URS heights.}
340%\label{fig:satelliteTrack}
341%\end{center}
342%\end{figure}
343
344%\begin{figure}[ht]
345%\begin{center}
346%\includegraphics[width=8.0cm,keepaspectratio=true]{jasonAltimetry.jpg}
347%\caption{JASON satellite altimetry seal level anomaly. FIXME: should we include figure here with just JASON altimetry.}
348%\label{fig:jasonAltimetry}
349%\end{center}
350%\end{figure}
351
352%FIXME: Can we compare the urs model against the TOPEX-poseidon satellite as well? DB No (we don't have the data currently).
353
354\subsection{Inundation}
355\label{sec:inundation data}
356FIXME (Ole): Technically propagation covers everything up to
357the coastline and inundation everything on-shore.
358This means that ANUGA covers the final part of the propagation and the inundation part. Should we adopt this distiction throughout the paper?
359
360Inundation refers to the final stages of the evolution of a tsunami and
361covers the propagation of the tsunami in coastal waters and the
362subsequent run-up onto land. This process is typically the most
363difficult of the three stages to model due to thin layers of water
364flowing rapidly over dry land. Aside from requiring robust solvers
365which can simulate such complex flow patterns, this part of the
366modelling process also requires high resolution and quality elevation
367data which is often not available. In the case of model validation
368high quality field measurements are also required. For the proposed
369benchmark a high resolution bathymetry (FIXME (Ole): Bathymetry ? - RICHARD) and
370topography data set and a high quality inundation survey map from the
371Coordinating Committee Co-ordinating Committee for Geoscience Programmes
372in East and Southeast Asia (CCOP) (\cite{szczucinski06}) was obtained
373to validate model inundation. See also acknowledgements at the end of this paper.
374
375In this section we also present eye-witness accounts which can be used
376to qualitatively validate tsunami inundation.
377
378\subsubsection{Topography Data}
379A one second grid was used to approximate the topography in Patong
380Bay. This elevation data was again created from the digitised Thai
381Navy bathymetry chart, no 358.
382FIXME (Ole): I don't think so. The Navy chart is only offshore. RICHARD
383
384 A visualisation of the elevation data
385set used in Patong Bay is shown in
386Figure~\ref{fig:patong_bathymetry}. The continuous topography
387(FIXME(Jane): What is meant by this?) is an
388interpolation of known elevation measured at the coloured dots. FIXME RICHARD
389
390\begin{figure}[ht]
391\begin{center}
392\includegraphics[width=\textwidth,keepaspectratio=true]{patong_bay_data.jpg}
393\caption{3D visualisation of the elevation data set used in Patong Bay showing data points, contours, rivers and roads draped over the final model.}
394\label{fig:patong_bathymetry}
395\end{center}
396\end{figure}
397FIXME (Jane): legend? Were the contours derived from the final dataset?
398This is not the entire model, only the bay and the beach. RICHARD
399
400\subsubsection{Buildings and Other Structures}
401Human-made buildings and structures can significantly affect tsunami
402inundation. The footprint and number of floors of the
403buildings in Patong Bay were extracted from a GIS data set which was also provided by the CCOP (see Section \ref{sec:inundation data} for details).
404The heights of these
405buildings were estimated assuming that each floor has a height of 3 m and they
406were added to the topographic dataset.
407
408\subsubsection{Inundation Survey}
409Tsunami run-up in built-up areas can be the cause of large financial and human
410losses, yet run-up data that can be used to validate model run-up
411predictions is scarce because such events are relatively infrequent.
412Of the two field benchmarks proposed
413in~\cite{synolakis07},
414only the Okushiri benchmark facilitates comparison between
415modelled and observed run-up. One of the major strengths of the
416benchmark proposed here is that modelled run-up can be compared to an
417inundation survey which maps the maximum run-up along an entire coastline
418rather than at a series of discrete sites. The survey map is
419shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
420of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
421al~\cite{szczucinski06} for further details.
422
423\begin{figure}[ht]
424\begin{center}
425%\includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
426\includegraphics[width=\textwidth,keepaspectratio=true]{post_tsunami_survey.jpg}
427\caption{Tsunami survey mapping the maximum observed inundation at
428 Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
429\label{fig:patongescapemap}
430\end{center}
431\end{figure}
432
433
434\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
436report that many people at Patong Beach observed an initial
437retreat (trough or draw down) of
438the shoreline of more than 100 m followed a few minutes later by a
439strong wave (crest). Another less powerful wave arrived another five
440or ten minutes later. Eyewitness statements place the arrival time of
441the first wave between 9:55 am and 10:05 am local time or about 2 hours
442after the source rupture.
443FIXME (Ole): We should add observed arrival time and later relate that to
444the modelled dynamics. Wait for Drew's updated animation.
445
446
447\begin{figure}[ht]
448\begin{center}
449\includegraphics[width=\textwidth,keepaspectratio=true]{gauges.jpg}
450\caption{Location of timeseries extracted from the model output.}
451\label{fig:gauge_locations}
452\end{center}
453\end{figure}
454
455
456
457
458
459Two videos were sourced\footnote{The footage is
460widely available and can for example be obtained from
462(Comfort Hotel) and
464(Novotel)}
465%http://wizbangblog.com/content/2005/01/01/wizbang-tsunami.php
466which include footage of the tsunami in Patong Bay on the day
467of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
468group of buildings. They also show what is to be assumed as the second
469and third waves approaching and further flooding of the buildings and
470street. The first video is in the very north, filmed from what is
471believed to be the roof of the Novotel Hotel marked north'' in Figure
472\ref{fig:gauge_locations}. The second video is in the very south,
473filmed from the second story of a building next door to the Comfort
474Resort near the corner of Ruam Chai St and Thaweewong Road. This
475location is marked `south'' in Figure \ref{fig:gauge_locations}.
476Figure~\ref{fig:video_flow} shows stills from this video. Both videos
477were used to estimate flow speeds and inundation depths over time.
478
479\begin{figure}[ht]
480\begin{center}
481\includegraphics[width=5.0cm,keepaspectratio=true]{flow_rate_south_0_00sec.jpg}
482\includegraphics[width=5.0cm,keepaspectratio=true]{flow_rate_south_5_04sec.jpg}
483\includegraphics[width=5.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg}
484\includegraphics[width=5.0cm,keepaspectratio=true]{flow_rate_south_7_60sec.jpg}
485\caption{Four frames from a video where flow rate could be estimated,
486 circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
487 s, 7.6 s.}
488\label{fig:video_flow}
489\end{center}
490\end{figure}
491
492Flow rates were estimated using landmarks found in both videos and
493were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
494in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south.
495FIXME (Jane): How were these error bounds derived? RICHARD
496Water depths could also
497be estimated from the videos by the level at which water rose up the
498sides of buildings such as shops. Our estimates are in the order of
4991.5 to 2.0 metres (+/- 0.5 m).
500Fritz ~\cite{fritz06} performed a detailed
501analysis of video frames taken around Banda Aceh and arrived at flow
502speeds in the range of 2 to 5 m/s.
503
504
505\subsection{Validation Check-List}
506\label{sec:checkList}
507The data described in this section can be used to construct a
508benchmark to validate all three stages of the evolution of a
509tsunami. In particular we propose that a legitimate tsunami model
510should reproduce the following behaviour:
511\begin{itemize}
512 \item reproduce the vertical deformation observed in north-western
513 Sumatra and along the Nicobar--Andaman islands (see
514 Section~\ref{sec:gen_data}),
515 \item reproduce the \textsc{jason} satellite altimetry sea surface
516 anomalies (see Section~\ref{sec:data_jason}),
517 \item reproduce the inundation survey map in Patong city
518 (Figure~\ref{fig:patongescapemap}),
519 \item simulate a leading depression followed by two distinct crests
520 of decreasing magnitude at the beach, and
521 \item predict the water depths and flow speeds, at the locations of
522 the eye-witness videos, that fall within the bounds obtained from
523 the videos.
524\end{itemize}
525
526Ideally, the model should also be compared to measured timeseries of
527waveheights and velocities but the authors are not aware of the
528availability of such data near Patong Bay.
529
530
531
532%================Section===========================
533\section{Modelling the Event}\label{sec:models}
534Numerous models are currently used to model and predict tsunami
535generation, propagation and run-up~\cite{titov97a,satake95}. Here we
536introduce the three part modelling methodology employed by Geoscience Australia
537to illustrate the utility of the proposed benchmark.
538
539\subsection{Generation}\label{sec:modelGeneration}
540FIXME (Ole and Jane): Does this need to be so long?
541
542There are various approaches to modelling the expected crustal
543deformation from an earthquake. Most approaches model the
544earthquake as a dislocation in a linear elastic medium. Here we use
545the method of Wang et al~\cite{wang03}. One of the main advantages
546of their method is that it allows the dislocation to be located in a
547stratified linear elastic half-space with an arbitrary number of
548layers. Other methods (such as those based on Okada's equations) can
549only model the dislocation in a homogeneous elastic half space, or can
550only include a limited number of layers, and thus cannot model the
551effect of the depth dependence of the elasticity of the
552Earth~\cite{wang03}. The original versions of the codes described here
553are available from \url{http://www.iamg.org/CGEditor/index.htm}. The
554first program, \textsc{edgrn}, calculates elastic Green's function for
555a set of point sources at a regular set of depths out to a specified
556distance. The equations controlling the deformation are solved by
557using a combination of Hankel's transform and Wang et al's
559algorithm~\cite{wang03}. Once the Green's functions are calculated
560a slightly modified version of \textsc{edcmp}\footnote{For this study,
562to \textsc{edcmp} in order for it to provide output in a file format
563compatible with the propagation code in the following section. Otherwise it
564is similar to the original code.} is used to calculate the sea
565floor deformation for a specific subfault. This second code
566discretises the subfault into a set of unit sources and sums the
567elastic Green's functions calculated from \textsc{edgrn} for all the
568unit sources on the fault plane in order to calculate the final static
569deformation caused by a two dimensional dislocation along the
570subfault. This step is possible because of the linearity of the
571governing equations.
572
573In order to calculate the crustal deformation using these codes
574a model that describes the variation in elastic
575properties with depth and a slip model of the earthquake to describe
576the dislocation is required.
577The elastic parameters used for this study are the
578same as those in Table 2 of Burbidge et al~\cite{burbidge08}. For the slip
579model, there are many possible models for the 2004 Andaman--Sumatran
580earthquake to select from
581~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
582determined from various geological surveys of the site. Others solve
583an inverse problem which calibrates the source based upon the tsunami
584wave signal, the seismic signal and/or even the run-up.
585The source
586parameters used here to simulate the 2004 Indian Ocean tsunami were
587taken from the slip model G-M9.15 of Chlieh
588et al~\cite{chlieh07}. This model was created by inversion of wide
589range of geodetic and seismic data. The slip model consists of 686
59020km x 20km subsegments each with a different slip, strike and dip
591angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in
592the south. Refer to Chlieh et al~\cite{chlieh07} for a detailed
593discussion of this model and its derivation. Note that the geodetic
594data used in the validation was also included by~\cite{chlieh07} in
595the inversion used to find G-M9.15. Thus the validation is not
596completely independent. However, a reasonable validation would still
597show that the crustal deformation and elastic properties model used
598here is at least as valid as the one used by Chlieh
599et al~\cite{chlieh07} and can reproduce the observations just as
600accurately.
601
602\subsection{Propagation}\label{sec:modelPropagation}
603The \textsc{ursga} model described below was used to simulate the
604propagation of the 2004 Indian Ocean tsunami across the open ocean, based on a
605discrete representation of the initial deformation of the sea floor, as
606described in Section~\ref{sec:modelGeneration}. For the models shown
607here, the uplift is assumed to be instantaneous and creates a wave of
608the same size and amplitude as the co-seismic sea floor deformation.
609
610\subsubsection{URSGA}
611\textsc{ursga} is a hydrodynamic code that models the propagation of
612the tsunami in deep water using a finite difference method on a staggered grid.
613It solves the depth integrated linear or nonlinear shallow water equations in
614spherical co-ordinates with friction and Coriolis terms. The code is
615based on Satake~\cite{satake95} with significant modifications made by
616the \textsc{urs} corporation, Thio et al~\cite{thio08} and Geoscience
617Australia, Burbidge et al~\cite{burbidge08}.
618The tsunami was propagated via the nested
619grid system described in Section \ref{sec:propagation data} where
620the coarse grids were used in the open ocean and the finest
621resolution grid was employed in the region closest to Patong bay.
622\textsc{Ursga} is not publicly available.
623
624\subsection{Inundation}\label{sec:modelInundation}
625The utility of the \textsc{ursga} model decreases with water depth
626unless an intricate sequence of nested grids is employed. In
627comparison \textsc{anuga}, described below, is designed to produce
628robust and accurate predictions of on-shore inundation, but is less
629suitable for earthquake source modelling and large study areas because
630it is based on projected spatial coordinates. Consequently, the
631Geoscience Australia tsunami modelling methodology is based on a
632hybrid approach using models like \textsc{ursga} for tsunami
633propagation up to an offshore depth contour, typically 100 m.
634%Specifically we use the \textsc{ursga} model to simulate the
635%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
636%on a discrete representation of the initial deformation of the sea
637%floor, described in Section~\ref{sec:modelGeneration}.
638The wave signal and the velocity field is then used as a
639time varying boundary condition for
640the \textsc{anuga} inundation simulation.
641% A description of \textsc{anuga} is the following section.
642
643\subsubsection{ANUGA}
644\textsc{Anuga} is a Free and Open Source hydrodynamic inundation tool that
645solves the conserved form of the depth-integrated nonlinear shallow
646water wave equations using a Finite-Volume scheme on an
647unstructured triangular mesh.
648The scheme, first
649presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
650Godunov-type method that uses the rotational invariance property of
651the shallow water equations to transform the two-dimensional problem
652into local one-dimensional problems. These local Riemann problems are
653then solved using the semi-discrete central-upwind scheme of Kurganov
654et al~\cite{kurganov01} for solving one-dimensional conservation
655equations. The numerical scheme is presented in detail in
656Roberts and Zoppou~\cite{zoppou00,roberts00} and
657Nielsen et al~\cite{nielsen05}. An important capability of the
658finite-volume scheme is that discontinuities in all conserved quantities
659are allowed at every edge in the mesh. This means that the tool is
660well suited to adequately resolving hydraulic jumps, transcritical flows and
661the process of wetting and drying. This means that \textsc{Anuga}
662is suitable for
663simulating water flow onto a beach or dry land and around structures
664such as buildings. \textsc{Anuga} has been validated against
665%a number of analytical solutions and
666%FIXME (Ole): Analytical solutions have not been published. Ask Steve.
667the wave tank simulation of the 1993 Okushiri
668Island tsunami~\cite{nielsen05,roberts06}.
669FIXME (Ole): Add reference to Tom Baldock's Dam Break valiadation of ANUGA.
670
671
672%================Section===========================
673\section{Results}\label{sec:results}
674This section presents a validation of the modelling practice of Geoscience
675Australia against the new proposed benchmarks. The criteria outlined
676in Section~\ref{sec:checkList} are addressed for each of the three stages
677of tsunami evolution.
678
679\subsection{Generation}\label{modelGeneration}
680The location and magnitude of the sea floor displacement associated
681with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15
682model of~\cite{chlieh07} is shown in
683Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor
684displacement ranges from about $-3.0$ to $5.0$ metres. The region near
685the fault is predicted to uplift, while that further away from the
686fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are
687the areas that were observed to uplift (arrows pointing up) or subside
688(arrows point down) during and immediately after the earthquake. Most
689of this data comes from uplifted or subsided coral heads. The length of
690the vector increases with the magnitude of the displacement; the length
691corresponding to 1 m of observed motion is shown in the top right
692corner of the figure. As can be seen, the source model detailed in
693Section~\ref{sec:modelGeneration} produces a crustal deformation that
694matches the vertical displacements in the Nicobar-Andaman islands and
695Sumatra very well. Uplifted regions are close to the fault and
696subsided regions are further away. The crosses on
697Figure~\ref{fig:surface_deformation} show estimates of the pivot line
698from the remote sensing data~\cite{chlieh07} and they follow the
699predicted pivot line quite accurately. The average difference between
700the observed motion and the predicted motion (including the pivot line
701points) is only 0.06 m, well below the typical error of the
702observations of between 0.25 and 1.0 m. However, the occasional point
703has quite a large error (over 1 m); for example a couple of
704uplifted/subsided points appear to be on a wrong
705(FIXME (Jane): This is incorrect) side of the predicted
706pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
707not surprising, since the original slip model was chosen
708by~\cite{chlieh07} to fit this (and the seismic data) well.
709This does demonstrate, however, that \textsc{edgrn} and our modified version of
710\textsc{edstat} (FIXME(Jane): This has never been mentioned before)
711can reproduce the correct pattern of vertical
712deformation very well when the slip distribution is well constrained
713and when reasonable values for the elastic properties are used.
714
715\begin{figure}[ht]
716\begin{center}
717\includegraphics[width=0.8\textwidth,keepaspectratio=true]{surface_deformation.jpg}
718%\includegraphics[totalheight=0.3\textheight,width=0.8\textwidth]{surface_deformation.jpg}
719\caption{Location and magnitude of the vertical component of the sea
720 floor displacement associated with the 2004 Indian Ocean tsunami
721 based on the slip model, G-M9.15. The black arrows which point up
722 show areas observed to uplift during and immediately after the
723 earthquake; those pointing down are locations which subsided. The
724 length of the arrow increases with the magnitude of the deformation. The arrow
725 length corresponding to 1 m of deformation is shown in the top right
726 hand corner of the figure. The cross marks show the location of
727 the pivot line (the region between the uplift and subsided region
728 where the uplift is zero) derived from remote sensing
729 (FIXME(Jane): How was that possible?). All the
730 observational data are from the dataset collated
731 by~\cite{chlieh07}.}
732\label{fig:surface_deformation}
733\end{center}
734\end{figure}
735
736\subsection{Propagation}\label{sec:resultsPropagation}
737The deformation results described in Section~\ref{sec:modelGeneration}
738were used to provide a profile of the initial ocean surface
739displacement. This wave was used as an initial condition for
740\textsc{ursga} and was propagated throughout the Bay of Bengal. The
741rectangular computational domain of the largest grid extended from
74290$^0$ to 100$^0$ East and 0 to 15$^0$ North and contained
7431335$\times$1996 finite difference points. Inside this grid, a nested
744sequence of grids was used. The grid resolution of the nested grids
745went from 27 arc seconds in the coarsest grid, down to nine arc seconds
746in the second grid, three arc seconds in the third grid and finally one arc
747second in the finest grid near Patong. The computational domain is
748shown in Figure~\ref{fig:computational_domain}.
749
750FIXME (Ole): I know that a nested ursga model was trialled for the
751end-to-end modelling. However, for the study done here, where models
752were coupled, I didn't think nested grids were used with URSGA -
753and certainly not down to 1 arc second. Can someone shed some light
755
756\begin{figure}[ht]
757\begin{center}
758\includegraphics[width=0.8\textwidth,keepaspectratio=true]{extent_of_ANUGA_model.jpg}
759\caption{Computational domain of the \textsc{ursga} simulation (inset: white and black squares and main: black square) and the \textsc{anuga} simulation (main and inset: red polygon).}
760\label{fig:computational_domain}
761\end{center}
762\end{figure}
763
764
765Figure \ref{fig:jasonComparison} provides a comparison of the
766\textsc{ursga}-predicted sea surface elevation with the \textsc{jason}
767satellite altimetry data. The \textsc{ursga} model replicates the
768amplitude and timing of the the wave observed at $2.5^0$ South,
769but underestimates the amplitude of the wave further to the south at
770$4^0$ South. In the model, the southern most of these two waves
771appears only as a small bump in the cross section of the model (shown
772in Figure~\ref{fig:jasonComparison}) instead of being a distinct peak
773as can be seen in the satellite data. Also note
774that the \textsc{ursga} model prediction of the ocean surface
775elevation becomes out of phase with the \textsc{jason}
776data at $3^0$ to $7^0$ North
777latitude. Chlieh et al~\cite{chlieh07} also observed these misfits and
778suggest it is caused by a reflected wave from the Aceh Peninsula that
779is not resolved in the model due to insufficient resolution of the
780computational mesh and bathymetry data. This is also a limitation of
781the model presented here which could be improved by nesting
782grids near Aceh.
783
784\begin{figure}[ht]
785\begin{center}
786\includegraphics[width=\textwidth,keepaspectratio=true]{jasonComparison.jpg}
787\caption{Comparison of the \textsc{ursga}-predicted surface elevation
788 with the \textsc{jason} satellite altimetry data. The \textsc{ursga} wave
789 heights have been corrected for the time the satellite passed
790 overhead compared to \textsc{jason} sea level anomaly.}
791\label{fig:jasonComparison}
792\end{center}
793\end{figure}
794FIXME (Jane): This graph does not look nice. The legend URS Model should
795be URSGA model.
796
797\subsection{Inundation}
798After propagating the tsunami in the open ocean using \textsc{ursga},
799the approximated ocean and surface elevation and horisontal flow
800velocities were extracted and used to construct a boundary condition
801for the \textsc{anuga} model. The interface between the \textsc{ursga}
802and \textsc{anuga} models was chosen to roughly follow the 100~m depth
803contour along the west coast of Phuket Island. The computational
804domain is shown in Figure~\ref{fig:computational_domain}.
805
806The domain was discretised into 386,338 triangles. The resolution of
807the grid was increased in regions inside the bay and on-shore to
808efficiently increase the simulation accuracy for the impact area.
809The grid resolution ranged between a
810maximum triangle area of $1\times 10^5$ m$^2$
811(corresponding to approximately 440 m between mesh points)
812near the western ocean
813boundary to $20$ m$^2$ (corresponding to
814approximately 6 m between mesh points)
815in the small regions surrounding the inundation
816region in Patong Bay. The coarse resolution was chosen to be
817commensurate with the model output from the \textsc{ursga} model
818(FIXME - this has to be clearly stated in ursga section) RICHARD
819while the latter was chosen to match the available resolution of topographic
820data and building data in Patong city.
821Due to a lack of available roughness data, friction was
822set to a constant throughout the computational domain. For the
823reference simulation, a Manning's coefficient of 0.01 was chosen to
824represent a small resistance to the water flow. See Section
825\ref{sec:friction sensitivity} for details on model sensitivity to
826this parameter.
827
828
829The boundary condition at each side of the domain towards the south
830and the north where no information about the incident wave or
831its velocity field is available
832was chosen as a transmissive
833boundary condition, effectively replicating the time dependent wave
834height present just inside the computational domain.
835The velocity field on these boundaries was set
836to zero. Other choices include applying the mean tide value as a
837Dirichlet boundary condition. But experiments as well as the
838result of the verification reported here showed that this approach
839tends to underestimate the tsunami impact due to the tempering of the
840wave near the side boundaries, whereas the transmissive boundary
841condition robustly preserves the wave.
842
843During the \textsc{anuga} simulation the tide was kept constant at
844$0.80$ m. This value was chosen to correspond to the tidal height
845specified by the Thai Navy tide charts
846(\url{http://www.navy.mi.th/hydro/}) at the time the tsunami arrived
847at Patong Bay. Although the tsunami propagated for approximately three
848hours before it reach Patong Bay, the period of time during which the
849wave propagated through the \textsc{anuga} domain is much
850smaller. Consequently the assumption of constant tide height is
851reasonable.
852
853Maximum onshore inundation depth was computed from the model
854throughout the entire Patong Bay region and used to generate
855a measure of the inundated area.
856Figure~\ref{fig:inundationcomparison1cm} (left) shows very good
857agreement between the measured and simulated inundation. However
858these results are dependent on the classification used to determine
859whether a region in the numerical simulation was inundated. In
860Figure~\ref{fig:inundationcomparison1cm} (left) a point in the computational
861domain was deemed inundated if at some point in time it was covered by
862at least 1 cm of water. However, the precision of the inundation boundary
863generated by the on-site survey is most likely less than that as it
864was determined by observing water marks and other signs
865left by the receding waters. Consequently the measurement error along
866the inundation boundary of the survey is likely to vary significantly
867and somewhat unpredictably.
868An inundation threshold of 10 cm therefore was selected for inundation
869extents reported in this paper to reflect
870the more likely accuracy of the survey, and subsequently facilitate a more
871appropriate comparison between the modelled and observed inundation
872area.
873Figure~\ref{fig:inundationcomparison1cm} (right) shows the simulated
874inundation using a larger threshold of 10 cm.
875
876
877The datasets necessary for reproducing the results
878of the inundation stage are available on Sourceforge under the \textsc{anuga}
879project (\url{http://sourceforge.net/projects/anuga}).
880At the time of
881writing the direct link is \url{http://tinyurl.com/patong2004-data}.
882%%\url{http://sourceforge.net/project/showfiles.php?group_id=172848&package_id=319323&release_id=677531}.
883The scripts required are part of the \textsc{anuga} distribution also
884available from Sourceforge \url{http://sourceforge.net/projects/anuga} under
885the validation section.
886
887An animation of this simulation is available on the \textsc{anuga} website at \url{https://datamining.anu.edu.au/anuga} or directly from \url{http://tinyurl.com/patong2004}.
888%\url{https://datamining.anu.edu.au/anuga/attachment/wiki/AnugaPublications/patong_2004_indian_ocean_tsunami_ANUGA_animation.mov}.
889
890\begin{figure}[ht]
891\begin{center}
892%\includegraphics[width=6.0cm,keepaspectratio=true]{final_1cm.jpg}
893%\includegraphics[width=6.0cm,keepaspectratio=true]{final_10cm.jpg}
894\includegraphics[width=\textwidth,keepaspectratio=true]{threshold.jpg}
895\caption{Simulated inundation versus observed inundation using an
896inundation threshold of 1cm (left) and 10cm (right).}
897\label{fig:inundationcomparison1cm}
898\end{center}
899\end{figure}
900
901To quantify the agreement between the observed and simulated inundation we
902introduce the measure
903\begin{equation}
904\rho_{in}=\frac{A(I_m\cap I_o)}{A(I_o)}
905\end{equation}
906representing the ratio $\rho_{in}$ of the observed
907inundation region $I_o$ captured by the model $I_m$. Another useful
908measure is the fraction of the modelled inundation area that falls
909outside the observed inundation area given by the formula
910\begin{equation}
911\rho_{out}=\frac{A(I_m\setminus (I_m\cap I_o))}{A(I_o)}
912\end{equation}
913These values for the two aforementioned simulations are given in
914Table~\ref{table:inundationAreas}. High value of both $\rho_{in}$ and $\rho_{out}$ indicate
915that the model overestimates the impact whereas low values of both quantities would indicate
916an underestimation. A high value of $\rho_{in}$ combined with a low value of $\rho_{out}$
917indicates a good model prediction of the survey.
918
919Discrepancies between the survey data and the modelled inundation
920include: unknown distribution of surface roughness, inappropriate
921parameterisation of the source model, effect of humans structures on
922flow, as well as uncertainties in the elevation data, effects of
923erosion and deposition by the tsunami event,
924measurement errors in the GPS survey recordings, and
925missing data in the field survey data itself. The impact of some of
926these sources of uncertainties are is investigated in
927Section~\ref{sec:sensitivity}
928
929\subsection{Eye-witness accounts}
930Figure \ref{fig:gauge_locations} shows four locations where time
931series have been extracted from the model. The two offshore time series
932are shown in Figure \ref{fig:offshore_timeseries} and the two onshore
933timeseries are shown in Figure \ref{fig:onshore_timeseries}. The
934latter coincide with locations where video footage from the event is
935available as described in Section \ref{sec:eyewitness data}.
936
937\begin{figure}[ht]
938\begin{center}
939\includegraphics[width=0.8\textwidth,keepaspectratio=true]{gauge_bay_depth.jpg}
940\includegraphics[width=0.8\textwidth,keepaspectratio=true]{gauge_bay_speed.jpg}
941\caption{Time series obtained from the two offshore gauge locations,
9427C and 10C, shown in Figure \protect \ref{fig:gauge_locations}.}
943\end{center}
944\label{fig:offshore_timeseries}
945\end{figure}
946
947\begin{figure}[ht]
948\begin{center}
949\includegraphics[width=\textwidth,keepaspectratio=true]{gauges_hotels_depths.jpg}
950\includegraphics[width=\textwidth,keepaspectratio=true]{gauges_hotels_speed.jpg}
951\caption{Time series obtained from the two onshore locations, North and South,
952shown in Figure \protect \ref{fig:gauge_locations}.}
953\end{center}
954\label{fig:onshore_timeseries}
955\end{figure}
956
957
958The estimated depths and flow rates given in Section
959\ref{sec:eyewitness data} are shown together with the modelled depths
960and flow rates obtained from the model in
961Table \ref{tab:depth and flow comparisons}.
962The predicted maximum depths and speeds are all of the same order
963of what was observed. However, unlike the real event,
964the model estimates complete withdrawal of the water between waves at the
965chosen locations and shows that the model must be used with caution at this
966level of detail.
967Nonetheless, this comparison serves to check that depths and speeds
968predicted are within the range of what is expected.
969
970
971\begin{table}
972$973 \begin{array}{|l|cc|cc|} 974 \hline 975 & \multicolumn{2}{|c|}{\mbox{Depth [m]}} 976 & \multicolumn{2}{c|}{\mbox{Flow [m/s]}} \\ 977 & \mbox{Observed} & \mbox{Modelled} 978 & \mbox{Observed} & \mbox{Modelled} \\ \cline{2-5} 979 \mbox{North} & 1.5-2 & 1.4 & 5-7 & 0.1 - 3.3 \\ 980 \mbox{South} & 1.5-2 & 1.5 & 0.5-2 & 0.2 - 2.6 \\ \hline 981 \end{array} 982$
983\label{tab:depth and flow comparisons}
984\end{table}
985FIXME (Jane): We should perhaps look at average data in area surrounding these points
986
987%can be estimated with landmarks found in
988%satellite imagery and the use of a GIS and were found to be in the
989%range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to
990%2 metres per second (+/- 1 m/s) in the south.
991
992Given the uncertainties in both model and observations, there is agreement
993between the values obtained from the videos and the simulations.
994
995% Our modelled flow rates show
996%maximum values in the order of 0.2 to 2.6 m/s in the south and 0.1 to
997%3.3 m/s for the north as shown in the figures. Water depths could also
998%be estimated from the videos by the level at which water rose up the
999%sides of buildings such as shops. Our estimates are in the order of
1000%1.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our
1001%modelled maximum depths of 1.4 m in the north and 1.5 m in the south
1002%as seen in the figure.
1003
1004
1005
1006
1007
1008%================Section===========================
1009\section{Sensitivity Analysis}
1010\label{sec:sensitivity}
1011This section investigates the effect of different values of Manning's
1012friction coefficient, changing waveheight at the 100 m depth contour,
1013and the presence and absence of buildings in the elevation dataset on
1014model maximum inundation. The reference model is the one reported in
1015Figure~\ref{fig:inundationcomparison1cm} (right) with a friction coefficient of 0.01,
1016buildings included and the boundary condition produced by the
1017\textsc{ursga} model.
1018
1019%========================Friction==========================%
1020\subsection{Friction}
1021\label{sec:friction sensitivity}
1022The first sensitivity study investigated the impact of surface roughness on the
1023predicted run-up. According to Schoettle~\cite{schoettle2007}
1024appropriate values of Manning's coefficient range from 0.007 to 0.03
1025for tsunami propagation over a sandy sea floor and the reference model
1026uses a value of 0.01. To investigate sensitivity to this parameter,
1027we simulated the maximum onshore inundation using a Manning's
1028coefficient of 0.0003 and 0.03. The resulting inundation maps are
1029shown in Figure~\ref{fig:sensitivity_friction} and the maximum flow
1030speeds in Figure~\ref{fig:sensitivity_friction_speed}. These figures
1031show that the on-shore inundation extent decreases with increasing
1032friction and that small perturbations in the friction cause bounded
1033changes in the output. This is consistent with the conclusions of
1034Synolakis~\cite{synolakis05} et al, who state that the long wavelength of
1035tsunami tends to mean that friction is less important in
1036comparison to the motion of the wave.
1037
1038%========================Wave-Height==========================%
1039\subsection{Input Wave Height}\label{sec:waveheightSA}
1040The effect of the wave height used as input to the inundation model
1041\textsc{anuga} was also investigated.
1042Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
1043severity is directly proportional to the boundary waveheight but small
1044perturbations in the input wave height of 10 cm appear to have little
1045effect on the final inundated area. Obviously larger perturbations
1046will have greater impact. However, wave heights in the open ocean are
1047generally well
1048predicted by the generation and propagation models such as
1049\textsc{ursga} as demonstrated in Section \ref{sec:resultsPropagation}
1050and also in \cite{thomas2009}.
1051
1052
1053
1054%========================Buildings==========================%
1055\subsection{Buildings and Other Structures}
1056The presence or absence of physical buildings in the elevation model was also
1057investigated.
1058Figure~\ref{fig:sensitivity_nobuildings}
1059shows the inundated area and the associated maximum flow speeds
1060in the presence and absence of buildings. It
1061is apparent that densely built-up areas act as
1062dissipators greatly reducing the inundated area. However, flow speeds
1063tend to increase in passages between buildings.
1064
1065
1066\begin{table}
1067\begin{center}
1068\label{table:inundationAreas}
1069\caption{$\rho_{in}$ and $\rho_{out}$ of the reference simulation and all sensitivity studies.}
1070\begin{tabular}{|l|c|c|}
1071\hline
1072 & $\rho_{in}$ & $\rho_{out}$ \\
1073\hline\hline
1074Reference model & 0.79 & 0.20\\
1075Friction = 0.0003 & 0.83 & 0.26 \\
1076Friction = 0.03 & 0.67 & 0.09\\
1077Boundary wave hight minus 10 cm & 0.77 & 0.17 \\
1078Boundary wave hight plus 10 cm & 0.82 & 0.22 \\
1079No Buildings & 0.94 & 0.44 \\
1080\hline
1081\end{tabular}
1082\end{center}
1083\end{table}
1084
1085%================Section===========================
1086
1087\section{Conclusion}
1088This paper proposes an additional field data benchmark for the
1089verification of tsunami inundation models. Currently, there is a
1090scarcity of appropriate validation datasets due to a lack of well-documented
1091historical tsunami impacts. The benchmark proposed here
1092utilises the uniquely large amount of observational data for model
1093comparison obtained during, and immediately following, the
1094Sumatra--Andaman tsunami of 26 December 2004. Unlike the small
1095number of existing benchmarks, the proposed test validates all three
1096stages of tsunami evolution - generation, propagation and
1097inundation. In an attempt to provide higher visibility and easier
1098accessibility for tsunami benchmark problems, the data used to
1099construct the proposed benchmark is documented and freely available at
1100\url{http://tinyurl.com/patong2004-data}.
1101
1102This study also shows that the tsunami impact modelling methodology
1103adopted is credible and able to predict inundation extents with reasonable
1104accuracy. An associated aim of this paper was to further validate the
1105hydrodynamic modelling tool \textsc{anuga} which is used to simulate
1106the tsunami inundation. Model predictions
1107matched well the geodetic measurements of the Sumatra--Andaman earthquake,
1108altimetry data from the \textsc{jason}, eye-witness accounts of wave
1109front arrival times and flow speeds and a detailed inundation survey
1110of Patong Bay, Thailand.
1111
1112A simple sensitivity analysis was performed to assess the influence of
1113small changes in friction, wave height at the 100 m depth contour and
1114the presence of buildings and other structures on the model
1115predictions. Of these three, the presence of buildings was shown to
1116have the greatest influence on
1117the simulated inundation extent. The value of friction and small
1118perturbations in the waveheight at the \textsc{anuga} boundary have
1119comparatively little effect on the model results.
1120
1121%================Acknowledgement===================
1122\section*{Acknowledgements}
1123This project was undertaken at Geoscience Australia and the Department
1124of Mathematics, The Australian National University. The authors would
1125like to thank Niran Chaimanee from the CCOP for providing
1126the post 2004 tsunami survey data, building footprints, aerial
1127photography and the elevation data for Patong city, Prapasri Asawakun
1128from the Suranaree University of Technology and Parida Kuneepong for
1129supporting this work; and Drew Whitehouse from the Australian National
1130University for preparing the animation of the simulated impact.
1131
1132\clearpage
1133\section{Appendix}
1134
1135This appendix present the images used to assess the model
1136sensitivities described in
1137Section~\ref{sec:sensitivity}.
1138
1139\begin{figure}[ht]
1140\begin{center}
1141%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_reference_depth}
1142%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_reference_speed}
1143\includegraphics[width=\textwidth,keepaspectratio=true]{reference}
1144\caption{Results from reference model as reported in Section
1145\protect \ref{sec:results},
1146 i.e.\ including buildings and a friction value of 0.01.
1147 The seaward boundary condition is as
1148 provided by the \textsc{ursga} model. The left image shows the maximum
1149 modelled depth while the right hand image shows the maximum modelled
1150 flow velocities.}
1151\label{fig:reference_model}
1152\end{center}
1153\end{figure}
1154
1155
1156
1157\begin{figure}[ht]
1158\begin{center}
1159%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_minus10cm_depth}
1160%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_plus10cm_depth}
1161\includegraphics[width=\textwidth,keepaspectratio=true]{sensitivity_boundary_wave}
1162\caption{Model results with wave height at \textsc{anuga} boundary artificially
1163 modified to assess sensitivities.
1164 The reference inundation extent is shown in Figure
1165 \protect \ref{fig:reference_model} (left). The left and right images
1166 show the inundation results if the wave at the \textsc{anuga} boundary
1167 is reduced or increased by 10 cm respectively. The inundation
1168 severity varies in proportion to the boundary waveheight, but the
1169 model results are only slightly sensitive to this parameter for the
1170 range of values tested.}
1171\label{fig:sensitivity_boundary}
1172\end{center}
1173\end{figure}
1174FIXME (Jane): How and why was the +/- 10 cm chosen?
1175
1176
1177\begin{figure}[ht]
1178\begin{center}
1179\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_minus10cm_speed}
1180\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_plus10cm_speed}
1181\caption{The maximal flow speeds for the same model parameterisations
1182 found in Figure \protect \ref{fig:sensitivity_boundary}. The
1183 reference flow speeds are shown in Figure \protect
1184 \ref{fig:reference_model} (right).}
1185\label{fig:sensitivity_boundary_speed}
1186\end{center}
1187\end{figure}
1188
1189\begin{figure}[ht]
1190\begin{center}
1191%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_nobuildings_depth}
1192%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_nobuildings_speed}
1193\includegraphics[width=\textwidth,keepaspectratio=true]{sensitivity_buildings}
1194\caption{Model results show the effect of buildings in
1195 the elevation data set.
1196 The left hand image shows the inundation extent as modelled in the reference
1197 model (Figure \protect \ref{fig:reference_model}.})
1198 which includes buildings in the elevation data. The right hand image
1199 shows the result for a bare-earth model i.e. entirely without buildings.
1200 As expected, the absence of
1201 buildings will increase the inundation extent beyond what was
1202 surveyed.
1203
1204 % FIXME (Ole): Include speed picture elsewhere
1205 %The right hand image shows the corresponding flow speeds in the absence of buildings.
1206 %The reference results are as shown in Figure
1207 %\protect \ref{fig:reference_model}.}
1208\label{fig:sensitivity_nobuildings}
1209\end{center}
1210\end{figure}
1211
1212
1213\begin{figure}[ht]
1214\begin{center}
1215%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_f0_0003_depth}
1216%\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_f0_03_depth}
1217\includegraphics[width=\textwidth,keepaspectratio=true]{sensitivity_friction}
1218\caption{Model results for different values of Manning's friction
1219 coefficient shown to assess sensitivities.
1220 The reference inundation extent for a
1221 friction value of 0.01 is shown in Figure
1222 \protect \ref{fig:reference_model} (left). The left and right images
1223 show the inundation results for friction values of 0.0003 and
1224 0.03 respectively. The inundation extent increases for the lower
1225 friction value while the higher slows the flow and decreases the
1226 inundation extent. Ideally, friction should vary across the entire
1227 domain depending on terrain and vegetation, but this is beyond the
1228 scope of this study.}
1229\label{fig:sensitivity_friction}
1230\end{center}
1231\end{figure}
1232
1233\begin{figure}[ht]
1234\begin{center}
1235\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_f0_0003_speed}
1236\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_f0_03_speed}
1237\caption{The maximal flow speeds for the same model parameterisations
1238 found in Figure \protect \ref{fig:sensitivity_friction}. The
1239 reference flow speeds are shown in Figure \protect
1240 \ref{fig:reference_model} (right).}
1241\label{fig:sensitivity_friction_speed}
1242\end{center}
1243\end{figure}
1244
1245\clearpage
1246
1247%====================Bibliography==================
1248\bibliographystyle{spmpsci}
1249\bibliography{tsunami07}
1250\end{document}
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# How do you convert (-7pi)/4 radians into degrees?
convert $\frac{- 7 \pi}{4}$ to deg
$\left(\frac{180}{\pi}\right) \left(- \frac{7 \pi}{4}\right) =$ - 315 deg |
Completing the Square Test
We can solve any quadratic equation using a process known as completing the square. This process creates a perfect square trinomial on one side of the equation, with a constant on the other. We then factor using our special factoring formulas and solve the equation using the square root property.
Test Objectives:
•Demonstrate the ability to form a perfect square trinomial by completing the square
•Demonstrate the ability to factor a perfect square trinomial into the square of a binomial
•Demonstrate the ability to solve a quadratic equation of the form: (x + a)2 = k
Completing the Square Test:
#1:
Instructions: Solve each equation by completing the square.
a) $$4p^2 - 16 = 6p$$
Watch the Step by Step Video Solution
|
View the Written Solution
#2:
Instructions: Solve each equation by completing the square.
a) $$-k^2-15k = 14$$
Watch the Step by Step Video Solution
|
View the Written Solution
#3:
Instructions: Solve each equation by completing the square.
a) $$8m^2 + 9m - 72 = 5m$$
Watch the Step by Step Video Solution
|
View the Written Solution
#4:
Instructions: Solve each equation by completing the square.
a) $$19a = -4a^2 + 93$$
Watch the Step by Step Video Solution
|
View the Written Solution
#5:
Instructions: Solve each equation by completing the square.
a) $$7p^2 + 21p = -9$$
Watch the Step by Step Video Solution
|
View the Written Solution
Written Solutions:
#1:
Solution:
a) $$p = \frac{\pm\sqrt{73} + 3}{4}$$
Watch the Step by Step Video Solution
#2:
Solution:
a) $$k = -1$$ or $$k = -14$$
Watch the Step by Step Video Solution
#3:
Solution:
a) $$m = \frac{\pm \sqrt{145} - 1}{4}$$
Watch the Step by Step Video Solution
#4:
Solution:
a) $$a = 3$$ or $$a = -\frac{31}{4}$$
Watch the Step by Step Video Solution
#5:
Solution:
a) $$p = \frac{\pm 3\sqrt{21} - 21}{14}$$
Watch the Step by Step Video Solution |
# Sum of independent Gaussians via change-of-variables formula
Let $X \sim N(\mu_1, \sigma_1^2)$ and $Y \sim N(\mu_2, \sigma_2^2)$ be independent. It can easily be shown via moment generating functions that $Z=X+Y$ is also normally distributed with $Z\sim N(\mu_1+\mu_2, \sigma_1^2+\sigma_2^2)$.
I was wondering if one could instead use the change-of-variables formula to derive the distribution of $Z$. The obvious way seems to be to go from the vector $(X,Y)$ to the vector $(Z,Y) = (X+Y, Y)$. The Jacobian of this is 1 and the result seems at first to be straightforward.
However the result of course is the joint distribution of $Z$ and $Y$, so to get the distribution of $Z$ one has to then marginalise out $y$ by integration.
It is easy to see from the result that in the general case, i.e. Gaussian or not, the sum of independent random variables is distributed as the convolution (see also Wikipedia). In the Gaussian case, how would one go about computing the required integral? That is, the integral
$$\int \frac{1}{\sqrt{2\pi}} \frac{1}{\sigma_1} \exp(-\frac{1}{2} \frac{((z-y)-\mu_1)^2}{\sigma_1^2} ) \frac{1}{\sqrt{2\pi}} \frac{1}{\sigma_2} \exp(-\frac{1}{2} \frac{(y-\mu_2)^2}{\sigma_2^2} d y \,?$$
Or, instead of $(X,Y) \rightarrow (X+Y,Y)$, is there another change or variables that would result in an easier integral?
• By inspection, it's clear that any linear combination of $X$ and $Y$ will have some normal distribution. At that point it becomes unnecessary to compute any integrals, because basic properties of expectation and variance tell you immediately what the expectation and variance of the linear combination is--and those two parameters completely determine any Normal distribution.
– whuber
Mar 19 '17 at 17:16
The technique used to evaluate that integral is called completing the square in the exponent which is pretty close to what you learned (and undoubtedly soon forgot) in high school when you derived the formula for the roots of a quadratic polynomial. Multiply the exponential functions that are in the integrand by using the identity $\exp(a+b) = \exp(a)\exp(b)$ bass ackwards to get $\exp\left(-\frac{1}{2\alpha} (y^2 - 2\beta y +\gamma)\right)$ where $\beta$ is a linear function of $z$, $\gamma$ is a quadratic function of $z$ and $\alpha$ does not depend on $z$ at all. Then, massage the argument of the exponent to write it as \begin{align} y^2 - 2\beta y +\gamma &= y^2 - 2\beta y + \beta^2 + \gamma - \beta^2\\ &= (y-\beta)^2 + (\gamma - \beta^2) \end{align} Consequently, the integral becomes of the form $$\frac{1}{2\pi \sigma_1\sigma_2} \exp\left(-\frac{1}{2\alpha} (\gamma-\beta^2)\right) \int_{-\infty}^\infty \exp\left(-\frac{1}{2\alpha} (y-\beta^2)\right) \, \mathrm dy$$ where the integrand needs to be recognized as almost the density function of a $N(\beta, \alpha)$ random variable giving $$f_Z(z) = A \exp\left(-\frac{1}{2\alpha} (\gamma-\beta^2)\right)$$ for specific value of $A$ that I will leave it for you to work out. Notice that the argument of the exponential is a quadratic function of $z$ and so $Z$ has a Gaussian density. As Huber remarks in a comment, somewhere along such a calculation it might dawn on you that the density of $Z$ is going to end up being a Gaussian density at which point you can save yourself a lot of algebra by working out the mean and variance of $Z$ and plugging in results into the Gaussian density formula. And no, I don't mean plugging in $E[Z]$ etc into the integrand of the convolution integral; the integrand of the convolution integral has nothing to do with $Z$.
If one is not all set on using the convolution integral formula and nothing else must be used, the easiest way of directly determining the pdf of $Z=X+Y$ where $X$ and $Y$ are independent Gaussian random variables is to find the CDF first, recognize it as a Gaussian CDF and hence write down the density of $Z$. The argument is as follows.
Consider independent random variables $A, B \sim N(0,1)$ and set $$Z = (\sigma_1 A + \mu_1) + (\sigma_2 B + \mu_2) = X + Y$$ where $X\sim N(\mu_1, \sigma_1^2), Y \sim N(\mu_2, \sigma_2^2)$ are independent random variables. Then, $$F_Z(z) = P\{\sigma_1 A + \sigma_2 B + \mu_1 + \mu_2)\leq z\} =\iint_{\sigma_1a + \sigma_2b + (\mu_1 + \mu_2)\leq z} \phi(a)\phi(b) \,\mathrm da \mathrm db$$ where $\phi(\cdot)$ is the standard Gaussian density. But the integral has circular symmetry and so the probability depends only on the distance of the line $\sigma_1 a + \sigma_2 b + (\mu_1 + \mu_2) = z$. Indeed, by a rotation of coordinates we can make this line vertical (say), and if it crosses the $a$ axis at $d$, then $$F_Z(z) = P\{A \leq d\} = \Phi(d)$$ showing that $Z$ is a Gaussian random variable. At this point, as whuber says, we can compute $$E[Z] = E[X+Y] = \mu_1 + \mu_2, \operatorname{var}(Z) =\operatorname{var}(X+Y) = \operatorname{var}(X) + \operatorname{var}(Y) = \sigma_1^2+\sigma_2^2$$ and write down the density of $Z$. Or, we can bull ahead and note that standard results in analytical geometry tell us that $$d = \left(\frac{z - (\mu_1+\mu_2)}{\sqrt{\sigma_1^2 + \sigma_2^2}}\right)$$ and so \begin{align} F_Z(z) &= \Phi\left(\frac{z - (\mu_1+\mu_2)}{\sqrt{\sigma_1^2 + \sigma_2^2}}\right)\\ f_Z(z) &= \frac{1}{\sqrt{\sigma_1^2 + \sigma_2^2}}\phi\left(\frac{z - (\mu_1+\mu_2)}{\sqrt{\sigma_1^2 + \sigma_2^2}}\right) \end{align} where we can recognize this last expression as the density of a $N(\mu_1+\mu_2,\sigma_1^2+\sigma_2^2)$ random variable. |
# i can't detect what wrong have i done in a kinematics problem [closed]
a question was given to us in assignment which was as follows
A person moves 20 metres towards north then 30 metres towards east and then moves 30 x 1.414 metres towards south west. The whole trip takes 5 seconds. What is the person's average velocity for this whole journey?
i just squared every magnitude of velocity in all the three directions and then I took square root of that sum
doing so what i got is this number 55.735267112 so this will be the total displacement of that person and dividing this with the given time [5in this case] we get the answer as 11.1 but the answer is 2 m/s
can any one suggest me where is my concept going wrong
-
## closed as off-topic by John Rennie, BMS, Ali, Brandon Enright, David Z♦Jul 6 at 22:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – John Rennie, BMS, Ali, Brandon Enright, David Z
If this question can be reworded to fit the rules in the help center, please edit the question.
The problem as written isn't very clear. You just gives directions and distance and no time so no velocities can be found. – jkeuhlen Jul 6 at 16:18
but this is the only information given in the question – agha rehan abbas Jul 6 at 16:20
@jkeuhlen i think distances and time would be enough for us to calculate the average velocity – agha rehan abbas Jul 6 at 16:21
You have distance and then you have a time to stop. That time would be used to find acceleration. You would need time to cover the distance to get a speed. – jkeuhlen Jul 6 at 16:23
@jkeuhlen yes time is given and it is 5secs in this case – agha rehan abbas Jul 6 at 16:24 |
# Extracting the natural numbers from the infinite set. [closed]
In this wikipedia article, natural numbers are extracted from the infinite set which includes all the natural numbers as $\forall n(n\in N \Leftrightarrow ([n=\emptyset \lor \exists k(n=k\cup \{k\})]\land \forall m\in n[m=\emptyset \lor \exists k\in n (m=k\cup \{k\})]))$.
Let the extracted set be $N'$ and $n_1\in N'$.
1. If $n_1\neq \emptyset$, $\exists n_2(n_1=n_2\cup \{n_2\}).$
2. If $n_2\neq \emptyset, \exists n_3\in n_1(n_2 = n_3\cup \{n_3\}).$
3. If $n_3\neq \emptyset, \exists n_4\in n_1(n_3= n_4\cup \{n_4\}).$
4. ...
How to prove that this can't continue infinitely?
## closed as unclear what you're asking by Andrés E. Caicedo, José Carlos Santos, Namaste, The Phenotype, GNUSupporter 8964民主女神 地下教會Jan 25 '18 at 0:36
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
• Not clear... What are you trying ? The starting point is the def of Inductive set, i.e. a set that contains $0$ and, for very element $a$, contains also $a \cup \{ a \}$. The issue is that e.g. the set $I'$ that "starts" with $0$ and $\phi$ and is closed with respect to the operation $x \cup \{ x \}$ also satisfy the def. – Mauro ALLEGRANZA May 8 '17 at 7:58
• The proposal is to carve out exactly the set $\mathbb N$; how to do this ? With a new def that says: $\mathbb N$ is the inductive set (and the only one, by extensionality) that contains only $0$ and it is closed with respect to the successor operation. In this way, unwanted elements (as $\phi$ above) cannot "crop in". – Mauro ALLEGRANZA May 8 '17 at 8:00
• You cannot prove it, unless ZF is inconsistent, because otherwise there are models with "infinite" natural numbers, ones where the given process would keep on going indefinitely (you can prove it using the compactness theorem if you know ir). But you would still be able to do induction and so on. – Max May 8 '17 at 8:26
The def'n in the article, and the "more formal" def'n immediately following it, are flawed. Without the axiom of Foundation (a.k.a Regularity) it is consistent that there exists $x$ with $x=\{x\}.$ It is even consistent that there is an uncountable non-empty set $S$ such that $\forall x\in S\;(x=\{x\}).$ But according to the def'ns in the article, any such $x$ belongs to $N.$ |
Cryptology ePrint Archive: Report 2018/702
Tight Proofs of Space and Replication
Ben Fisch
Abstract: We construct a concretely practical proof-of-space (PoS) with arbitrarily tight security based on stacked depth robust graphs and constant-degree expander graphs. A proof-of-space (PoS) is an interactive proof system where a prover demonstrates that it is persistently using space to store information. A PoS is arbitrarily tight if the honest prover uses exactly N space and for any $\epsilon > 0$ the construction can be tuned such that no adversary can pass verification using less than $1-\epsilon N$ space. Most notably, the degree of the graphs in our construction are independent of $\epsilon$, and the number of layers is only $O(\log(1/\epsilon))$. The proof size is $O(d/\epsilon)$. The degree $d$ depends on the depth robust graphs, which are only required to maintain $\Omega(N)$ depth in subgraphs on 80% of the nodes. Our tight PoS is also secure against parallel attacks.
Tight proofs of space are necessary for proof-of-replication (PoRep), which is a publicly verifiable proof that the prover is dedicating unique resources to storing one or more retrievable replicas of a file. Our main PoS construction can be used as a PoRep, but data extraction is as inefficient as replica generation. We present a second variant of our construction called ZigZag PoRep that has fast/parallelizable data extraction compared to replica generation and maintains the same space tightness while only increasing the number of levels by roughly a factor two.
Category / Keywords: proof of space, proof of replication, tight security
Date: received 24 Jul 2018, last revised 16 Aug 2018
Contact author: benafisch at gmail com
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2018/702
[ Cryptology ePrint archive ] |
# How to find the general solution 5 sin(x)+2 cos(x)=3?
May 10, 2018
$\rightarrow x = n \pi + {\left(- 1\right)}^{n} \cdot \left({\sin}^{- 1} \left(\frac{3}{\sqrt{29}}\right)\right) - {\sin}^{- 1} \left(\frac{2}{\sqrt{29}}\right)$ $n \in \mathbb{Z}$
#### Explanation:
$\rightarrow 5 \sin x + 2 \cos x = 3$
rarr(5sinx+2cosx)/(sqrt(5^2+2^2))=3/(sqrt(5^2+2^2)
$\rightarrow \sin x \cdot \left(\frac{5}{\sqrt{29}}\right) + \cos x \cdot \left(\frac{2}{\sqrt{29}}\right) = \frac{3}{\sqrt{29}}$
Let $\cos \alpha = \frac{5}{\sqrt{29}}$ then $\sin \alpha = \sqrt{1 - {\cos}^{2} \alpha} = \sqrt{1 - {\left(\frac{5}{\sqrt{29}}\right)}^{2}} = \frac{2}{\sqrt{29}}$
Also, $\alpha = {\cos}^{- 1} \left(\frac{5}{\sqrt{29}}\right) = {\sin}^{- 1} \left(\frac{2}{\sqrt{29}}\right)$
Now, given equation transforms to
$\rightarrow \sin x \cdot \cos \alpha + \cos x \cdot \sin \alpha = \frac{3}{\sqrt{29}}$
$\rightarrow \sin \left(x + \alpha\right) = \sin \left({\sin}^{- 1} \left(\frac{3}{\sqrt{29}}\right)\right)$
$\rightarrow x + {\sin}^{- 1} \left(\frac{2}{\sqrt{29}}\right) = n \pi + {\left(- 1\right)}^{n} \cdot \left({\sin}^{- 1} \left(\frac{3}{\sqrt{29}}\right)\right)$
$\rightarrow x = n \pi + {\left(- 1\right)}^{n} \cdot \left({\sin}^{- 1} \left(\frac{3}{\sqrt{29}}\right)\right) - {\sin}^{- 1} \left(\frac{2}{\sqrt{29}}\right)$ $n \in \mathbb{Z}$
May 11, 2018
$x = {12}^{\circ} 12 + k {360}^{\circ}$
$x = {124}^{\circ} 28 + k {360}^{\circ}$
#### Explanation:
5sin x + 2cos x = 3.
Divide both sides by 5.
$\sin x + \frac{2}{5} \cos x = \frac{3}{5} = 0.6$ (1)
Call $\tan t = \sin \frac{t}{\cos t} = \frac{2}{5}$ --> $t = {21}^{\circ} 80$ --> cos t = 0.93.
The equation (1) becomes:
$\sin x . \cos t + \sin t . \cos x = 0.6 \left(0.93\right)$
$\sin \left(x + t\right) = \sin \left(x + 21.80\right) = 0.56$
Calculator and unit circle give 2 solutions for (x + t) -->
a. x + 21.80 = 33.92
$x = 33.92 - 21.80 = {12}^{\circ} 12$
b. x + 21.80 = 180 - 33.92 = 146.08
$x = 146.08 - 21.80 = {124}^{\circ} 28$
$x = {12}^{\circ} 12 + k {360}^{\circ}$
$x = {124}^{\circ} 28 + k {360}^{\circ}$
$x = {12}^{\circ} 12$ --> 5sin x = 1.05 --> 2cos x = 1.95
$x = {124}^{\circ} 28$ --> 5sin x = 4.13 --> 2cos x = -1.13 |
# Law of Cosines
Law of cosines and sines are the Trigonometric laws, which are used to find the angles of a triangle. Once we are given all the three sides of the triangle(SSS), we can easily compute the angles. Similarly, these laws can be used to calculate the sides of the triangle, where the values of angles will be given already.
Here you will learn the definition, formula, proof of the law of cosines with solved questions. Student’s can also reach us to learn about the law of sines. Keep reading the article below for further knowledge and to understand the concepts of cosine rule.
## Law of Cosines Definition
Law of Cosines, also known as Cosine Rule or Cosine Formula, basically relates the length of the triangle to the cosines of one its angles, in Trigonometry.
### Law of Cosine Formula
As per the law of cosines formula, to find the length of sides of triangle say △ABC, we can write as;
a2 = b2 + c22 – 2bc cos(x)
b2 = a2 + c2 – 2ac cos(y)
c2 = a2 + b2 – 2bc cos(z)
And if we want to find the angles of △ABC, then the cosine rule is applied as;
cos x = b2 + c2 – a2/2bc
cos y = a2 + c2– b2/2ac
cos z = a2 + b2– c2/2ab
### Proof of Law of Cosines
Now let us learn the law of cosines proof here;
In the right triangle BCD, by the definition of cosine:
cos C = CD/a
or
CD=a cos C
Subtracting above equation from side b, we get
DA = b − acosC ……(1)
In the triangle BCD, according to Sine definition
sin C=$\frac{BD}{a}$
or
BD=asinC ……(2)
In the triangle ADB, if we apply the Pythagorean Theorem, then
c2 = BD2 + DA2
Substituting for BD and DA from equations (1) and (2)
c2 = (a sin C)2 + (b-acosC)2
By Cross Multiplication we get:
c2 = a2 sin2C + b2 – 2abcosC + a2 cos2C
Rearranging the above equation:
c2 = a2 sin2C + a2 cos2C + b2 – 2ab cosC
Taking out aas a common factor, we get;
c2 = a2(sin2C + cos2C) + b2 – 2ab cosC
Now from the above equation, you know that,
sin2θ + cos2θ = 1
∴ c2 = a2 + b2 – 2ab cosC
Hence, the Cosine rule proved.
### Law of Cosine Problems and Solutions
Let us understand the concept by solving one of the law of cosines problems;
Problem: A triangle ABC has sides a=10cm, b=7cm and c=5cm. Now, find its angle ‘x’.
Solution: Consider the below triangle as triangle ABC, where,
a=10cm
b=7cm
&c=5cm
By using cosines law or the law of cosines,
a2 = b2 + c2 – 2bc cos(x)
Or
cos x = (b2 + c2 – a2)/2bc
Substituting the value of the sides of the triangle, a,b and c, we get
cos(x) = (72 + 52 – 102)/(2 × 7 × 5)
cos(x)=(49 + 25 -100)/70 |
# PyQt5 validator for decimal numbers
This class is similar to QDoubleValidator, but it improves slightly on the editing comfort. The comments mention "comma" but it's actually the decimal point of your locale (comma for me).
class DecimalValidator(QDoubleValidator):
def __init__(self, *args):
QDoubleValidator.__init__(self, *args)
self.setNotation(QDoubleValidator.StandardNotation)
def validate(self, input, pos):
sep = self.locale().decimalPoint()
if pos and (input[pos-1]==sep) and (sep in input[pos:]):
# When we're left of the comma, and comma is pressed,
# remove the inserted comma and move right of the old comma.
input = input[:pos-1] + input[pos:]
pos = input.find(sep)+1
elif sep in input[:pos] and (len(input.split(sep)[1]) > self.decimals()):
# When we're right of the comma, and all decimal places are used already,
# go into overwrite mode (by removing the old digit)
input = input[:pos] + input[pos+1:]
return QDoubleValidator.validate(self, input, pos)
I noticed your commenting style and decided it's worthy of it's own answer.
You admit the comma is not always a comma. So don't call it a comma. I went for separator, which is as neutral as it gets. If you think of something better, go for it.
class DecimalValidator(QDoubleValidator):
def __init__(self, *args):
QDoubleValidator.__init__(self, *args)
self.setNotation(QDoubleValidator.StandardNotation)
def validate(self, input, pos):
'''
When we're left of the separator, and separator is pressed,
remove the inserted separator and move right of the old separator.
When we're right of the separator, and all decimal places are used already,
go into overwrite mode (by removing the old digit)
'''
sep = self.locale().decimalPoint()
if pos and (input[pos-1]==sep) and (sep in input[pos:]):
input = input[:pos-1] + input[pos:]
pos = input.find(sep)+1
elif sep in input[:pos] and (len(input.split(sep)[1]) > self.decimals()):
input = input[:pos] + input[pos+1:]
return QDoubleValidator.validate(self, input, pos)
• You're right about the "comma" topic (I noticed that myself. Just wasn't happy calling it a "decimal point" as called in the QLocale class), Docstring at the beginning of the function isn't what I wanted. I wanted the comments to explain the code that they preceed. – Sebastian Nov 10 '15 at 0:49 |
# Exponential topology
The weakest topology on the set $\mathop{\rm exp} X = 2 ^ {X}$ of all closed subsets of a topological space $X$ in which the sets $\mathop{\rm exp} A$ are open (in $\mathop{\rm exp} X$) if $A$ is open, and closed (in $\mathop{\rm exp} X$) if $A$ is closed. If $A \subseteq X$, then $\mathop{\rm exp} A$ denotes the set of all subsets of $A$ that are closed in $X$.
Example. The topology of the metric space of closed bounded subsets of a metric space endowed with the Hausdorff metric. The general definition is: Let $U _ {1} \dots U _ {n}$ be an arbitrary finite collection of non-empty open sets in $X$; a basis for the exponential topology consists of sets of the form
$$\langle U _ {1} \dots U _ {n} \rangle =$$
$$= \ \left \{ \widehat{F} \in \mathop{\rm exp} X : F \subseteq \cup _ { 1 } ^ { n } U _ {i} \& F \cap U _ {i} \neq \emptyset , i = 1 \dots n \right \} ,$$
where $\widehat{F}$ denotes the point of $\mathop{\rm exp} X$ corresponding to a given closed set $F \subseteq X$. The space $\mathop{\rm exp} X$ endowed with the exponential topology is called the exponent of the space $X$. If $X$ is a $T _ {1}$- space, then so is $\mathop{\rm exp} X$. If $X$ is regular, then $\mathop{\rm exp} X$ is a Hausdorff space. If $X$ is normal, then $\mathop{\rm exp} X$ is completely regular. For the exponential topology normality is equivalent to compactness. If the space $X$ is compact, then so is $\mathop{\rm exp} X$. If $X$ is a dyadic compactum and the weight of $X$ does not exceed $\aleph _ {1}$, then $\mathop{\rm exp} X$ is also a dyadic compactum. On the other hand, the exponent of any compactum of weight greater than or equal to $\aleph _ {2}$ is not a dyadic compactum. The exponent of a Peano continuum is an absolute retract in the class of metric compacta and, consequently, it is a continuous image of an interval. However, an exponent of uncountable weight is not a continuous image of the Tikhonov cube $I ^ \tau$. Let $f : X \rightarrow Y$ be a closed mapping of a space $X$ onto a space $T$. The mapping $\mathop{\rm exp} f : \mathop{\rm exp} X \rightarrow \mathop{\rm exp} Y$ defined by $( \mathop{\rm exp} f ) ( \widehat{F} ) = ( f ( F) ) \widehat{ {}}$ is called the exponential mapping. If $f : X \rightarrow Y$ is a continuous mapping of a compactum $X$ onto a compactum $Y$, then it is open if and only if the mapping $\mathop{\rm exp} f$ is open. The functor $\mathop{\rm exp} X$ acting from the category of compacta and continuous mappings into the same category is a covariant functor of exponential type. Here to a morphism $f$ there corresponds its exponent $\mathop{\rm exp} f$.
#### References
[1] K. Kuratowski, "Topology" , 1–2 , Acad. Press (1966–1968) (Translated from French) |
# Hamming code
Binary Hamming Codes
The Hamming(7,4)-code (with r = 3)
Named after Richard W. Hamming
Classification
Type Linear block code
Block length 2r − 1 where r ≥ 2
Message length 2rr − 1
Rate 1 − r/(2r − 1)
Distance 3
Alphabet size 2
Notation [2r − 1, 2rr − 1, 3]2-code
Properties
perfect code
In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code, and were invented by Richard Hamming in 1950. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.[1]
In mathematical terms, Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2r − 1 and message length k = 2rr − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2r − 1. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the punctured Hadamard code. The parity-check matrix has the property that any two columns are pairwise linearly independent.
Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory (ECC memory), where bit errors are extremely rare and Hamming codes are widely used. In this context, an extended Hamming code having one extra parity bit is often used. Extended Hamming codes achieve a Hamming distance of four, which allows the decoder to distinguish between when at most one one-bit error occurs and when any two-bit errors occur. In this sense, extended Hamming codes are single-error correcting and double-error detecting, abbreviated as SECDED.
## History
Richard Hamming, the inventor of Hamming codes, worked at Bell Labs in the 1940s on the Bell Model V computer, an electromechanical relay-based machine with cycle times in seconds. Input was fed in on punched cards, which would invariably have read errors. During weekdays, special code would find errors and flash lights so the operators could correct the problem. During after-hours periods and on weekends, when there were no operators, the machine simply moved on to the next job.
Hamming worked on weekends, and grew increasingly frustrated with having to restart his programs from scratch due to the unreliability of the card reader. Over the next few years, he worked on the problem of error-correction, developing an increasingly powerful array of algorithms. In 1950, he published what is now known as Hamming Code, which remains in use today in applications such as ECC memory.
### Codes predating Hamming
A number of simple error-detecting codes were used before Hamming codes, but none were as effective as Hamming codes in the same overhead of space.
#### Parity
Main article: Parity bit
Parity adds a single bit that indicates whether the number of ones (bit-positions with values of one) in the preceding data was even or odd. If an odd number of bits is changed in transmission, the message will change parity and the error can be detected at this point; however, the bit that changed may have been the parity bit itself. The most common convention is that a parity value of one indicates that there is an odd number of ones in the data, and a parity value of zero indicates that there is an even number of ones. If the number of bits changed is even, the check bit will be valid and the error will not be detected.
Moreover, parity does not indicate which bit contained the error, even when it can detect it. The data must be discarded entirely and re-transmitted from scratch. On a noisy transmission medium, a successful transmission could take a long time or may never occur. However, while the quality of parity checking is poor, since it uses only a single bit, this method results in the least overhead.
#### Two-out-of-five code
Main article: Two-out-of-five code
A two-out-of-five code is an encoding scheme which uses five bits consisting of exactly three 0s and two 1s. This provides ten possible combinations, enough to represent the digits 0–9. This scheme can detect all single bit-errors, all odd numbered bit-errors and some even numbered bit-errors (for example the flipping of both 1-bits). However it still cannot correct for any of these errors.
#### Repetition
Another code in use at the time repeated every data bit multiple times in order to ensure that it was sent correctly. For instance, if the data bit to be sent is a 1, an n = 3 repetition code will send 111. If the three bits received are not identical, an error occurred during transmission. If the channel is clean enough, most of the time only one bit will change in each triple. Therefore, 001, 010, and 100 each correspond to a 0 bit, while 110, 101, and 011 correspond to a 1 bit, as though the bits count as "votes" towards what the intended bit is. A code with this ability to reconstruct the original message in the presence of errors is known as an error-correcting code. This triple repetition code is a Hamming code with m = 2, since there are two parity bits, and 22 − 2 − 1 = 1 data bit.
Such codes cannot correctly repair all errors, however. In our example, if the channel flips two bits and the receiver gets 001, the system will detect the error, but conclude that the original bit is 0, which is incorrect. If we increase the number of times we duplicate each bit to four, we can detect all two-bit errors but cannot correct them (the votes "tie"); at five repetitions, we can correct all two-bit errors, but not all three-bit errors.
Moreover, the repetition code is extremely inefficient, reducing throughput by three times in our original case, and the efficiency drops drastically as we increase the number of times each bit is duplicated in order to detect and correct more errors.
## Hamming codes
If more error-correcting bits are included with a message, and if those bits can be arranged such that different incorrect bits produce different error results, then bad bits could be identified. In a seven-bit message, there are seven possible single bit errors, so three error control bits could potentially specify not only that an error occurred but also which bit caused the error.
Hamming studied the existing coding schemes, including two-of-five, and generalized their concepts. To start with, he developed a nomenclature to describe the system, including the number of data bits and error-correction bits in a block. For instance, parity includes a single bit for any data word, so assuming ASCII words with seven bits, Hamming described this as an (8,7) code, with eight bits in total, of which seven are data. The repetition example would be (3,1), following the same logic. The code rate is the second number divided by the first, for our repetition example, 1/3.
Hamming also noticed the problems with flipping two or more bits, and described this as the "distance" (it is now called the Hamming distance, after him). Parity has a distance of 2, so one bit flip can be detected, but not corrected and any two bit flips will be invisible. The (3,1) repetition has a distance of 3, as three bits need to be flipped in the same triple to obtain another code word with no visible errors. It can correct one-bit errors or detect but not correct two-bit errors. A (4,1) repetition (each bit is repeated four times) has a distance of 4, so flipping three bits can be detected, but not corrected. When three bits flip in the same group there can be situations where attempting to correct will produce the wrong code word. In general, a code with distance k can detect but not correct k − 1 errors.
Hamming was interested in two problems at once: increasing the distance as much as possible, while at the same time increasing the code rate as much as possible. During the 1940s he developed several encoding schemes that were dramatic improvements on existing codes. The key to all of his systems was to have the parity bits overlap, such that they managed to check each other as well as the data.
### General algorithm
The following general algorithm generates a single-error correcting (SEC) code for any number of bits.
1. Number the bits starting from 1: bit 1, 2, 3, 4, 5, etc.
2. Write the bit numbers in binary: 1, 10, 11, 100, 101, etc.
3. All bit positions that are powers of two (have only one 1 bit in the binary form of their position) are parity bits: 1, 2, 4, 8, etc. (1, 10, 100, 1000)
4. All other bit positions, with two or more 1 bits in the binary form of their position, are data bits.
5. Each data bit is included in a unique set of 2 or more parity bits, as determined by the binary form of its bit position.
1. Parity bit 1 covers all bit positions which have the least significant bit set: bit 1 (the parity bit itself), 3, 5, 7, 9, etc.
2. Parity bit 2 covers all bit positions which have the second least significant bit set: bit 2 (the parity bit itself), 3, 6, 7, 10, 11, etc.
3. Parity bit 4 covers all bit positions which have the third least significant bit set: bits 4–7, 12–15, 20–23, etc.
4. Parity bit 8 covers all bit positions which have the fourth least significant bit set: bits 8–15, 24–31, 40–47, etc.
5. In general each parity bit covers all bits where the bitwise AND of the parity position and the bit position is non-zero.
The form of the parity is irrelevant. Even parity is simpler from the perspective of theoretical mathematics, but there is no difference in practice.
This general rule can be shown visually:
Bit position 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
Shown are only 20 encoded bits (5 parity, 15 data) but the pattern continues indefinitely. The key thing about Hamming Codes that can be seen from visual inspection is that any given bit is included in a unique set of parity bits. To check for errors, check all of the parity bits. The pattern of errors, called the error syndrome, identifies the bit in error. If all parity bits are correct, there is no error. Otherwise, the sum of the positions of the erroneous parity bits identifies the erroneous bit. For example, if the parity bits in positions 1, 2 and 8 indicate an error, then bit 1+2+8=11 is in error. If only one parity bit indicates an error, the parity bit itself is in error.
As you can see, if you have ${\displaystyle m}$ parity bits, it can cover bits from 1 up to ${\displaystyle 2^{m}-1}$. If we subtract out the parity bits, we are left with ${\displaystyle 2^{m}-m-1}$ bits we can use for the data. As ${\displaystyle m}$ varies, we get all the possible Hamming codes:
Parity bits Total bits Data bits Name Rate
2 3 1 Hamming(3,1) (Triple repetition code) 1/3 ≈ 0.333
3 7 4 Hamming(7,4) 4/7 ≈ 0.571
4 15 11 Hamming(15,11) 11/15 ≈ 0.733
5 31 26 Hamming(31,26) 26/31 ≈ 0.839
...
${\displaystyle m}$ ${\displaystyle 2^{m}-1}$ ${\displaystyle 2^{m}-m-1}$ Hamming${\displaystyle (2^{m}-1,2^{m}-m-1)}$ ${\displaystyle (2^{m}-m-1)/(2^{m}-1)}$
If, in addition, an overall parity bit (bit 0) is included, the code can detect (but not correct) any two-bit error, making a SECDED code. The overall parity indicates whether the total number of errors is even or odd. If the basic Hamming code detects an error, but the overall parity says that there are an even number of errors, an uncorrectable 2-bit error has occurred.
## Hamming codes with additional parity (SECDED)
Hamming codes have a minimum distance of 3, which means that the decoder can detect and correct a single error, but it cannot distinguish a double bit error of some codeword from a single bit error of a different codeword. Thus, they can detect double-bit errors only if correction is not attempted.
To remedy this shortcoming, Hamming codes can be extended by an extra parity bit. This way, it is possible to increase the minimum distance of the Hamming code to 4, which allows the decoder to distinguish between single bit errors and two-bit errors. Thus the decoder can detect and correct a single error and at the same time detect (but not correct) a double error. If the decoder does not attempt to correct errors, it can detect up to three errors.
This extended Hamming code is popular in computer memory systems, where it is known as SECDED (abbreviated from single error correction, double error detection). Particularly popular is the (72,64) code, a truncated (127,120) Hamming code plus an additional parity bit, which has the same space overhead as a (9,8) parity code.
## [7,4] Hamming code
Graphical depiction of the four data bits and three parity bits and which parity bits apply to which data bits
Main article: Hamming(7,4)
In 1950, Hamming introduced the [7,4] Hamming code. It encodes four data bits into seven bits by adding three parity bits. It can detect and correct single-bit errors. With the addition of an overall parity bit, it can also detect (but not correct) double-bit errors.
### Construction of G and H
The matrix ${\displaystyle \mathbf {G} :={\begin{pmatrix}{\begin{array}{c|c}I_{k}&-A^{\text{T}}\\\end{array}}\end{pmatrix}}}$ is called a (canonical) generator matrix of a linear (n,k) code,
and ${\displaystyle \mathbf {H} :={\begin{pmatrix}{\begin{array}{c|c}A&I_{n-k}\\\end{array}}\end{pmatrix}}}$ is called a parity-check matrix.
This is the construction of G and H in standard (or systematic) form. Regardless of form, G and H for linear block codes must satisfy
${\displaystyle \mathbf {H} \,\mathbf {G} ^{\text{T}}=\mathbf {0} }$, an all-zeros matrix.[2]
Since [7, 4, 3] = [n, k, d] = [2m − 1, 2m−1−m, m]. The parity-check matrix H of a Hamming code is constructed by listing all columns of length m that are pair-wise independent.
Thus H is a matrix whose left side is all of the nonzero n-tuples where order of the n-tuples in the columns of matrix does not matter. The right hand side is just the (nk)-identity matrix.
So G can be obtained from H by taking the transpose of the left hand side of H with the identity k-identity matrix on the left hand side of G.
The code generator matrix ${\displaystyle \mathbf {G} }$ and the parity-check matrix ${\displaystyle \mathbf {H} }$ are:
${\displaystyle \mathbf {G} :={\begin{pmatrix}1&0&0&0&1&1&0\\0&1&0&0&1&0&1\\0&0&1&0&0&1&1\\0&0&0&1&1&1&1\\\end{pmatrix}}_{4,7}}$
and
${\displaystyle \mathbf {H} :={\begin{pmatrix}1&1&0&1&1&0&0\\1&0&1&1&0&1&0\\0&1&1&1&0&0&1\\\end{pmatrix}}_{3,7}.}$
Finally, these matrices can be mutated into equivalent non-systematic codes by the following operations:[2]
• Column permutations (swapping columns)
• Elementary row operations (replacing a row with a linear combination of rows)
### Encoding
Example
From the above matrix we have 2k = 24 = 16 codewords. The codewords ${\displaystyle {\vec {x}}}$ of this binary code can be obtained from ${\displaystyle {\vec {x}}={\vec {a}}G}$. With ${\displaystyle {\vec {a}}=a_{1}a_{2}a_{3}a_{4}}$ with ${\displaystyle a_{i}}$ exist in ${\displaystyle F_{2}}$ (A field with two elements namely 0 and 1).
Thus the codewords are all the 4-tuples (k-tuples).
Therefore,
(1,0,1,1) gets encoded as (1,0,1,1,0,1,0).
### [7,4] Hamming code with an additional parity bit
The same [7,4] example from above with an extra parity bit. This diagram is not meant to correspond to the matrix H for this example.
The [7,4] Hamming code can easily be extended to an [8,4] code by adding an extra parity bit on top of the (7,4) encoded word (see Hamming(7,4)). This can be summed up with the revised matrices:
${\displaystyle \mathbf {G} :={\begin{pmatrix}1&1&1&0&0&0&0&1\\1&0&0&1&1&0&0&1\\0&1&0&1&0&1&0&1\\1&1&0&1&0&0&1&0\end{pmatrix}}_{4,8}}$
and
${\displaystyle \mathbf {H} :={\begin{pmatrix}1&0&1&0&1&0&1&0\\0&1&1&0&0&1&1&0\\0&0&0&1&1&1&1&0\\1&1&1&1&1&1&1&1\end{pmatrix}}_{4,8}.}$
Note that H is not in standard form. To obtain G, elementary row operations can be used to obtain an equivalent matrix to H in systematic form:
${\displaystyle \mathbf {H} =\left({\begin{array}{cccc|cccc}0&1&1&1&1&0&0&0\\1&0&1&1&0&1&0&0\\1&1&0&1&0&0&1&0\\1&1&1&0&0&0&0&1\end{array}}\right)_{4,8}.}$
For example, the first row in this matrix is the sum of the second and third rows of H in non-systematic form. Using the systematic construction for Hamming codes from above, the matrix A is apparent and the systematic form of G is written as
${\displaystyle \mathbf {G} =\left({\begin{array}{cccc|cccc}1&0&0&0&0&1&1&1\\0&1&0&0&1&0&1&1\\0&0&1&0&1&1&0&1\\0&0&0&1&1&1&1&0\end{array}}\right)_{4,8}.}$
The non-systematic form of G can be row reduced (using elementary row operations) to match this matrix.
The addition of the fourth row effectively computes the sum of all the codeword bits (data and parity) as the fourth parity bit.
For example, 1011 is encoded (using the non-systematic form of G at the start of this section) into 01100110 where blue digits are data; red digits are parity bits from the [7,4] Hamming code; and the green digit is the parity bit added by the [8,4] code. The green digit makes the parity of the [7,4] codewords even.
Finally, it can be shown that the minimum distance has increased from 3, in the [7,4] code, to 4 in the [8,4] code. Therefore, the code can be defined as [8,4] Hamming code. |
# plugging in terms of a sequence
I am having some trouble understanding how to plug terms into the following sequence. I was given the following,
$$a_1=1, a_{n+1}=\frac{a_n}{\sqrt{n}}$$ for all n greater or equal to 1.
Plugging in terms we get the following,
$$a_1=1$$ $$a_2=a_1=1$$ $$a_3=\frac{a_2}{\sqrt{2}}=\frac{1}{\sqrt{2}}$$ $$a_4=\frac{a_3}{\sqrt{3}}=\frac{1}{\sqrt{6}}$$
How are they getting these terms $a_2,a_3,a_4$?
Notice that
$$a_2=\frac{a_1}{\sqrt1}=1$$
$$a_3=\frac{a_2}{\sqrt2}=\frac1{\sqrt2}$$
$$a_4=\frac{a_3}{\sqrt3}=\frac1{\sqrt6}$$
Try to prove by induction that
$$a_{n+1}=\frac1{\sqrt{1\cdot2\cdot3\cdots n}}=\frac1{\sqrt{n!}}$$
• why are the $a_1,a_2,a_3$ terms disappearing in the numerator? – jh123 Feb 14 '17 at 15:32
• @jh123 Let's start with $a_2$. Do you understand that $a_2=\frac{a_1}{\sqrt1}$? From there, what is $a_1$? (check definition?) – Simply Beautiful Art Feb 14 '17 at 15:33
• why would $a_2$ be equal to that? I thought $a_2=a_1+a_2$? – jh123 Feb 14 '17 at 15:34
• Because $a_2$ was defined to be equal to that. Plug $n=1$ into the definition of the sequence. Why would $a_2=a_1+a_2$, which would require $a_1=0$? – Ross Millikan Feb 14 '17 at 15:37
• @jh123 But don't forget to take a peak at the second part of my answer:$$a_{n+1}=\frac1{\sqrt{n!}}$$ – Simply Beautiful Art Feb 14 '17 at 15:55
They are using the definition. If you plug in $n=1$ you get $a_2=\frac {a_1}{\sqrt 1}=\frac 11=1.$ Then plug in $n=2$ to get $a_3=\frac {a_2}{\sqrt 2}=\frac 1{\sqrt 2}$ and so on.
• why are the $a_1,a_2,a_3$ terms disappearing in the numerator? – jh123 Feb 14 '17 at 15:33
• Because we plug in the value we know for them based on the earlier calculation. – Ross Millikan Feb 14 '17 at 15:36
• so if $a_1=1$ then shouldn't $a_2 = \frac{a_1}{\sqrt{2}}= \frac{1}{\sqrt{2}}$ – jh123 Feb 14 '17 at 15:38
• No, because we were taking $n=1$ and the denominator is $\sqrt n$, not $\sqrt {n+1}$ – Ross Millikan Feb 14 '17 at 15:56
We have that for $n \in \mathbb Z^+$, $$a_{n+1} = \frac {a _n}{\sqrt {n}} \tag {1}$$
Thus, using the relation $(1)$ successively, we get, $$a_2 = a_{1+1} = \frac {a_1}{\sqrt {1}} = \frac {1}{1} =1$$ $$a_3 = a_{2+1} = \frac {a_2}{\sqrt {2}} = \frac {1}{\sqrt {2}}$$ $$a_4 = a_{3+1 } = \frac {a_3}{\sqrt {3}} = \frac {1}{\sqrt {2}\times \sqrt {3}} = \frac {1}{\sqrt {6}}$$
Hope it helps.
• why is the $a_1$. $a_2$ $a_3$ terms disappearing in the numerator? – jh123 Feb 14 '17 at 15:31 |
# ProblemSolving_RunChart
## Run Chart
• Definition: A Run Chart is a statistical tool to assess, monitor, and maintain process stability. The main purpose is to monitor a particular activity or continuous process in order to discover any deviation or variation of this activity or process so we can prevent defects, avoid waste of time, reduce costs, etc.
Example 1) Draw a run chart and interpret it for the costs of operations over 20 months in the launching area.
Step 1: Calculate the average cost $\bar X$
$\bar X = ( 128 + 48 + 211 + 45 + ... + 87 + 48 + 75) / 20$
$\bar X = 75.3$
Step 2: Draw a simple line graph
Step 3: Interpretation
1) Look for patterns such as cycles, trends or changes.
2) Observe if the average value line represents the desired behavior level.
3) Not all the changes or variations are important.
Following the change of an activity or process statistically where the activities are repeated, which is also one of the principles of this tool, we can find two types of variation:
• Common or random: are variations inherent to the process and usually comes from various sources of minor variations. Eliminating the Common Causes is more difficult because it requires knowledge and analysis of the entire change process: procedures, people, patterns, etc ..
• Special or exclusive events: are variations that occasionally arise in the process and the elimination of this variation is generally related to execution of the activities of that process. Once identified the Special Cause Variation, it must to be eliminated and prevent recurrence of the same cause with a preventive action is required. |
We investigate high-Reynolds number gravity currents (GC) in a horizontal channel of circular cross-section. We focus on GC sustained by constant or time varying inflow (volume of injected fluid $\propto\;t^{\alpha}$, with $\alpha=1$ and $\alpha>1$). The novelty of our work is in the type of the gravity currents: produced by influx/outflux boundary conditions, and propagation in circular (or semi-circular) channel. The objective is to elucidate the main propagation features and correlate them to the governing dimensionless parameters; to this end, we use experimental observations guided by shallow-water (SW) theoretical models. The system is of Boussinesq type with the denser fluid (salt water) injected into the ambient fluid (tap water) at one end section of a circular tube of 19 cm diameter and 605 cm long. The ambient fluid fills the channel of radius $r*$ up to a given height $H^* = \beta r^*$ ($0<\beta<2$) where it is open to the atmosphere. This fluid is displaced by the intruding current and outflows either at the same or at the opposite end-side of the channel. The two different configurations (with return and no-return flow) allow to analyse the impact of the motion of the ambient fluid on the front speed of the intruding current. For $Q$ larger than some threshold value, the current is expected theoretically to undergo a choking process which limits the speed/thickness of propagation. Two series of experiments were conducted with constant and time varying inflow. The choking effect was observed, qualitatively, in both series. The theory correctly predicts the qualitative behavior, but systematically overestimates the front speed of the current (consistent with previously-published data concerning rectangular and non-rectangular cross-sections), with larger discrepancies for the no-return flow case. These discrepancies are mainly due to: i) the variations of the free-surface of the ambient fluid with respect to its nominal value (the theoretical model assumes a rigid wall at the upper limit of the ambient fluid), and ii) mixing/entrainment effects, as shown by specific measurements of the open interface level and velocity profiles.
Gravity currents produced by constant and time varying inflow in a circular cross-section channel: experiments and theory / Longo, Sandro; Ungarish, Marius; Di Federico, Vittorio; Chiapponi, Luca; Addona, Fabio;. - In: ADVANCES IN WATER RESOURCES. - ISSN 0309-1708. - 90(2016), pp. 10-23. [10.1016/j.advwatres.2016.01.011]
### Gravity currents produced by constant and time varying inflow in a circular cross-section channel: experiments and theory
#### Abstract
We investigate high-Reynolds number gravity currents (GC) in a horizontal channel of circular cross-section. We focus on GC sustained by constant or time varying inflow (volume of injected fluid $\propto\;t^{\alpha}$, with $\alpha=1$ and $\alpha>1$). The novelty of our work is in the type of the gravity currents: produced by influx/outflux boundary conditions, and propagation in circular (or semi-circular) channel. The objective is to elucidate the main propagation features and correlate them to the governing dimensionless parameters; to this end, we use experimental observations guided by shallow-water (SW) theoretical models. The system is of Boussinesq type with the denser fluid (salt water) injected into the ambient fluid (tap water) at one end section of a circular tube of 19 cm diameter and 605 cm long. The ambient fluid fills the channel of radius $r*$ up to a given height $H^* = \beta r^*$ ($0<\beta<2$) where it is open to the atmosphere. This fluid is displaced by the intruding current and outflows either at the same or at the opposite end-side of the channel. The two different configurations (with return and no-return flow) allow to analyse the impact of the motion of the ambient fluid on the front speed of the intruding current. For $Q$ larger than some threshold value, the current is expected theoretically to undergo a choking process which limits the speed/thickness of propagation. Two series of experiments were conducted with constant and time varying inflow. The choking effect was observed, qualitatively, in both series. The theory correctly predicts the qualitative behavior, but systematically overestimates the front speed of the current (consistent with previously-published data concerning rectangular and non-rectangular cross-sections), with larger discrepancies for the no-return flow case. These discrepancies are mainly due to: i) the variations of the free-surface of the ambient fluid with respect to its nominal value (the theoretical model assumes a rigid wall at the upper limit of the ambient fluid), and ii) mixing/entrainment effects, as shown by specific measurements of the open interface level and velocity profiles.
##### Scheda breve Scheda completa Scheda completa (DC)
Gravity currents produced by constant and time varying inflow in a circular cross-section channel: experiments and theory / Longo, Sandro; Ungarish, Marius; Di Federico, Vittorio; Chiapponi, Luca; Addona, Fabio;. - In: ADVANCES IN WATER RESOURCES. - ISSN 0309-1708. - 90(2016), pp. 10-23. [10.1016/j.advwatres.2016.01.011]
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Preface
# On the Advancements in Boiling, Two-Phase Flow Heat Transfer, and Interfacial PhenomenaOPEN ACCESS
[+] Author and Article Information
Raj M. Manglik
Thermal-Fluids and Thermal Processing Laboratory, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, Cincinnati, OH [email protected]
J. Heat Transfer 128(12), 1237-1242 (Dec 01, 2006) (6 pages) doi:10.1115/1.2374897 History:
## Introduction
Phase change by boiling or evaporation is a highly efficient heat transport mechanism, which accommodates large heat fluxes with relatively small driving temperature differences. This mode of heat transfer is in fact encountered in a wide spectrum of engineering systems that include, among others, energy conversion, refrigeration and air-conditioning, chemical thermal processing, heat treatment and manufacturing, microelectronic cooling, and numerous microscale devices (microelectromechanical systems (MEMS), MTMS, $μ$-TAS, sensors, microheat pipes, biochips or lab-on-chips, etc.) that are emerging in the current wave of new developments and changing applications. The consequent research interest, spanning more than two centuries of work with an ever-increasing literature database, is therefore not surprising (1-10). The energy crunch with attendant needs for higher thermal efficiencies and demands for mitigation of environmental degradation in recent years have further led to efforts to enhance boiling heat transfer (11-15).
The explosive growth in research and its technical literature generation in the last six decades or so (8-10,14,16-17) has considered a variety of fundamental and applied aspects of this intrinsically complex heat transport process in order to advance our basic understanding as well as provide design tools. The continued interest in the field is further articulated in the set of papers appearing in this special issue of the Journal of Heat Transfer, and they address the many technical challenges that are still presented by the intricacies of heat transfer by means of boiling and forced-convective two-phase flow, and the concomitant interfacial phenomena. In its evolutionary essence, this field of scientific and engineering engagement is at once quite ancient in its simplicity and elegance of application, and yet complexly modern in its experimental investigations, theoretical modeling, and computational simulations (16,18-20).
## Historical Antecedents
Given the present-day advancements in our understanding of boiling, two-phase flow heat transfer, and interfacial phenomena, and the many yet to be resolved issues with the fundamental physics and optimal applications, it is instructive to reflect briefly upon the historical antecedents of the field. An excellent and insightful review of the work up to 1981, with exhaustive annotations that characterize both fundamental and applications-driven developments in the multifacetted unfolding of phase-change heat transfer, has been provided by Bergles (16). This is further supplemented by the 1987 review by Nishikawa (18), providing a good commentary to link the evolution of basic understanding of boiling with engineering practice as well as the development of enhancement techniques.
The quest to develop mechanical devices based on two-phase processes in ancient western traditions, and as recounted by Bergles (16), can be traced to Archimedes ($∼287–212$ B.C.E.) (21) and the whirling aeolipile of Heron of Alexandria ($∼60$ C.E.) (22). It was more than $1650years$ later that phase-change machines became the prime movers of the Industrial Revolution ($∼1750–1850$), epitomized by the development of a single-acting steam engine by Watt and the subsequent steam-engine-powered locomotives (16,23). An understanding of the phase-change process represented by film boiling also appeared in this period, when in 1756 the German medical doctor Leidenfrost recorded the evaporation behavior of distilled water droplets on a hot iron spoon and the application of this phenomena (distillation or separation by boiling) to determine the quality or proof of wine or brandy (24). An advanced and elaborate knowledge of distillation and its practical applications, however, predate this in the ancient eastern traditions (19,25-27). The classical Indian text Rasarnavam Rastantram ($∼500$ B.C.E.), and subsequently Nagarjuna’s Rasratnakar and Rasaratna Samuchchaya ($∼2nd$ century C.E.) describe the attendant boiling and condensation processes, and a rather intricately refined distillation technology and apparatus were used in ancient India for the distillation of water, wine, mercury, and zinc, among others (26,28). Also, quite remarkably, a sophisticated understanding of liquid wetting, surface-tension-driven liquid motion, and capillary forces was available in ancient India (25,27). In the present-day context, these phenomena form an essential part of the interfacial behavior associated with phase-change heat transfer, and are a basis for developing techniques for enhancing boiling and two-phase flow as well as newer microchannel heat exchangers and microfluidic devices (7,13,29-30).
The beginnings of modern day advancements can perhaps be ascribed to the pioneering work in the 1930s by Jakob and Fritz (31-32), and Nukiyama (33). Jakob and Fritz (31-32) explored effects of boiling history (or nonreproducibility), heater surface roughness, bubble dynamics, and increase in nucleation sites with heat flux. Nukiyama (33) essentially established the complete boiling curve (as measured by heat transfer from an electrically heated platinum wire) and which has become the cornerstone of representing virtually all nucleate boiling results. In the subsequent decade, McAdams (34) reported the subcooled fully developed nucleate boiling curve, and Lockhart and Martinelli (35) considered separated two-phase flow pressure drop to develop the classical multiplier function. With rapid developments in nuclear power and aerospace industries in the 1950s, there was an exponential growth in the research literature (16,18). Notable advancements included the classical nucleate pool boiling correlation proposed by Rohsenow (36), which endures to this day (1-6). Theoretical models for various mechanistic aspects of the phase-change process (bubble dynamics, microlayer evaporation, nucleation site density and stability, burnout, etc.) were attempted, and they continue to provide the framework for current research. The growing demands for energy and improved process heat transfer efficiencies in the 1960s brought efforts to augment or enhance heat transfer to the fore (12-13,37). This exploded as a major field of study in the 1970s, driven in part by the space and energy programs and later by the Mid-Eastern countries’ “oil embargo.” The present-day energy crisis, which is compounded by pressures for mitigating environmental degradation due to excessive energy consumption and imperatives for sustainable development, warrants a generational growth in enhancement science and technology (13-14,38).
In this unfolding, there has been ever growing interest over the last two decades in addressing the problems of two-phase flow and boiling heat transfer, and the concomitant interfacial phenomena. Some of the issues that baffled early research still engage continued activity, as more refined experiments are conducted and theoretical models developed to advance our fundamental as well as applications-oriented understanding (7,12,39-42). The primary determinants of the general nucleate boiling problem in pure or additive-laden liquids, which has been referred to as a conjugate problem (40,43) that can be essentially classified under three broad categories (heater, fluid, and heater-fluid interface), and the associated potential mechanisms are depicted in Fig. 1. This broad description includes two more prominently employed passive enhancement techniques, by either structuring the heater surface or adding reagents, electrolytes, and/or nanoparticles to the liquid (13-14,44-46). A direct correlation of the heat transfer with suitable descriptive parameters for all possible phenomenological effects, however, remains elusive because of the intricate nature of the problem.
## Current Research
While the complex phase-change heat transfer process in nucleate and/or flow boiling has many parametric determinants, a major part can be considered to be associated with the local heat transfer and hydrodynamics phenomena in the vicinity of ebullience and governed by the solid-liquid-vapor interfacial activity. Schematic illustrations of the primary flow-boiling and CHF regime map, and the interfacial mechanisms that affect liquid-vapor bubble dynamics are given in Fig. 2. In essence, liquid-solid interface wetting and the consequent “film” behavior, along with the transient liquid-vapor interface dynamics and the attendant bubbling characteristics significantly influence boiling performance. The set of papers in this special issue of Journal of Heat Transfer address some basic aspects of these processes, as well as issues of heat transfer enhancement and applications of surface-tension driven flow phenomenon.
An extended review of both empirical correlations and mechanistic heat transfer models for predicting the wall heat flux in subcooled flow nucleate boiling is given by Warrier and Dhir (47). Recognizing the importance of interfacial and microscale effects to the basic boiling and phase-change processes, Fuchs et al. (48), Panchamgam et al. (49), Carey and Wemhoff (50), and Mukherjee and Kandlikar (51) have considered different aspects of thin-film evaporation. Computational simulation, theoretical modeling, and microscale experimentation results are presented to inform the mechanisms that fundamentally govern heat and mass transfer in nucleate pool boiling of pure liquids, binary mixture evaporation, and thin-film phase-change in micropassages. As would be expected in current research (13-14,52), enhancement of heat transfer is the focus of papers by Schneider et al. (53), Ghiu and Joshi (54), and Ahn et al. (55), which explore microchannel flows, performance characteristics of structured surfaces, and novel techniques. Li et al. (56-57) and Cai et al. (58), respectively, have investigated evaporation and CHF in thin capillary wicks, and thermal characteristics of a pulsating heat pipe. Finally, in the best traditions of technical debate and scientific dissemination that bodes well for the vibrancy of heat transfer research, a discussion and its response consider some aspects of the motion of bubbles emanating from a microwire heater.
In his eloquent recounting of the early modern history of boiling and two-phase flow heat transfer, Bergles (16) had predicted that “Looking into the future, there will be much more emphasis on computer solutions of two-phase phenomena.” There was also a caveat (“We must remember, however, that the computer codes are only as good as the basic thermal-hydraulic input”) with a reminder that experimentation, along with mechanistic modeling, would continue to occupy center stage in scientific and technological discoveries. This foresight is indeed reflected in the ensuing articles, and they represent critical efforts in ameliorating imperfections in our understanding of many areas of boiling, two-phase flow heat transfer, and interfacial phenomena, as well as extending the exploitation of these processes to novel and emerging applications.
## Future Prospects and Directions
One can safely surmise a vibrant and challenging future of this field of study, which can perhaps be predicted to be marked by many more fundamental studies (both experimental and theoretical computational) that resolve the gaps in our phenomenological understanding, as well as expand the development of application-oriented performance evaluation and design tools. For the latter, as an example, the scrutiny of diminishing length and time scales (mili-, micro-, and nanoscale) has generated various novel devices (MEMS, MTMS, $μ$-TAS, microsensors, and lab-on-chips, among others) that in many cases exploit boiling and interfacial phenomena. This has attracted considerable attention to issues relating to microchannel flows (7,59-60), particularly for sustaining very high heat fluxes and thermal management of microelectronic devices, and some enterprising sensor and actuator development. Regardless of the scales of applications, nevertheless, the problems in ebullient phase change and interfacial heat and mass transfer abound (16,18,20,38,40) to provide opportunities for exploring hitherto uncharted dimensions as well as advancing our basic understanding.
An especially vital component of future research, given the growing problems of diminishing energy availability, environmental damage, and thermal management in new technologies, is enhancement of boiling heat transfer. A variety of techniques and schemes have been proposed, developed, and transferred into every-day use (13,15,38). Prominent among these is to either structure the heated surface to provide pre-existing nucleation sites that tend to be active and stable, or to treat the surface so as to change wetting. A few novel passive and/or active schemes have been proposed in some recent studies (29-30,45,61-62) that exploit surface adsorption and electrokinetics of surface-active molecular additives in solvents in different ways, along with some external stimulus in some cases, to produce self-assembled monolayers or micellar layers on the surface and thereby doctoring interfacial properties and wetting.
In a recent set of studies (43-46,63), it has been shown that by adding small quantities of surface-active soluble agents (polymers and surfactants, for example) the liquid-vapor interfacial tension (surface tension) and liquid-solid interfacial tension (wetting) can be altered and decoupled. The additives have a unique long-chain molecular structure composed of a hydrophilic head and a hydrophobic tail, with a natural tendency to adsorb at surfaces and interfaces when added in low concentrations in water. The interfacial changes are caused by their molecular mobility at interfaces, which manifests in a dynamic surface tension behavior (adsorption-desportion at the liquid-vapor interface) and varying surface wetting (physisorption and electrokinetics at the solid-liquid interface). A conceptualization of the molecular dynamics and altered surface tension and wetting is depicted in Fig. 3. These molecular-scale phenomena, modulated by the monomer and/or micellar structure of reagent, distinguishably alter the boiling bubble dynamics, as seen in the typical boiling signatures in three different reagent solutions given in Fig. 4(45), thereby providing an attractive passive technique for changing (enhancing or degrading, and controlling) “on demand” the nucleate boiling behavior.
A similar theme of controlling surface wettability by using self-assembled monolayers of polymers, or other long-chain molecules that have a hydrophilic head and a hydrophobic tail, but coupling it with the application of an electric potential to tune the surface charge is documented by Lahann et al. (62). By altering its charge, a surface can be “reversibly” switched from a hydrophobic to hydrophilic state, and vice versa, as schematically depicted in Fig. 5. Another method (30) considers the application of an electrical field to a nanostructured superhydrophobic surface to alter the contact angle of pure liquids. A typical set of surfaces used in this study (30), produced by etching arrays of cylindrical nanosized pins or posts on a silicon wafer, and the changed droplet contact angle when an electrical potential is applied between the droplet and substrate are shown, respectively, in Figs. 66. In yet another scheme, light-induced modification of liquid wetting on a photoresponsive surface (produced by a photoirradiated cover of photoisomerizable monolayer), shown by the droplet motion in Fig. 7, has been reported by Ichimura et al. (61). All of these techniques, it may be noted, represent what would be termed as compound techniques and require external input of active energy (electric charge or light) along with some form of passive surface modification, and they are a part of growing trend in the enhancement literature (13,38).
In closing, it is perhaps appropriate to reiterate that the challenges of advancing the science and engineering of boiling and two-phase flow heat transfer, and the concomitant interfacial phenomena would expand considerably in the foreseeable future. These would undoubtedly be driven by both large-scale (given our globe’s ever increasing energy needs for domestic, commercial, and industrial consumption) and small-scale (emerging applications in sensors, microactuators, and electromechanical-thermal machines, among others) applications and their design needs. This special issue of the Journal of Heat Transfer and its collection of technical contributions certainly reflect this direction.
## References
View article in PDF format.
## Figures
Figure 1
Schematic statement of the conjugate problem in modeling nucleate boiling heat transfer and attendant interfacial processes (Ref. 43 adapted from Ref. 40)
Figure 2
Flow boiling regimes and CHF in a vertical tube, and the influence of interfacial properties on the nucleation and dynamics of a boiling bubble
Figure 3
Representation of the modification of interfacial phenomena in nucleate boiling in aqueous surfactant solutions (not to scale) Ref. 45
Figure 4
Boiling behavior in distilled water, and aqueous surfactant (SDS, CTAB, and Triton X-305) solutions in their respective half-micellar concentrations (or C=0.5CMC) and at a heater wall heat flux of qw″=20kW∕m2
Figure 5
Conceptual representation of a “reversibly switching surface” by applying an electrical charge to dynamically tune the orientation of self-assembled molecular monolayers and render the surface hydrophilic or hydrophobic Ref. 62
Figure 6
Dynamic tuning of surface wetting on a nanostructured hydrophobic surface with application of electrical potential Ref. 30 (a) surface structure produced on a silicon substrate and (b) change in droplet contact angle when an electrical potential is applied
Figure 7
Light-driven droplet motion on a surface that is photoirradiated with a coating of a photoisomerizable monolayer Ref. 61
## Discussions
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# A long spring is stretched by 3cm and its potential energy is U.If spring is stretched by 12cm,its potential energy will be
$\begin{array}{1 1}(A)\;U/4\\(B)\;U/16\\(C)\;4U\\(D)\;16U\end{array}$
## 1 Answer
$U \propto (strain)^2$
So $\large\frac{U_2}{U_1}=(\frac{12}{3})^2$
$\Rightarrow 16$
$U_2=16U$
Hence (D) is the correct answer.
answered May 8, 2014
1 answer
1 answer
1 answer
1 answer
1 answer
1 answer
1 answer |
Differential equation
Solve the differential equation: $$x \frac{dy}{dx} = y(3-y)$$ where x=2 when y=2, giving y as a function of x.
Can someone solve this and then explain what the second line about $x=2$, $y=2$ means?
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Solutions of differential equations generally depend on a specified initial value. (Compare to the case of taking antiderivatives of a function: you have to write $+C$ because there is a free constant in the expression. By specifying the value of the antiderivative you want at a point, you fix that constant uniquely.) – Willie Wong Mar 25 '11 at 22:19
The second line just tells you that $y(2) = 2$. – Arturo Magidin Mar 26 '11 at 3:14
So you want to "solve" the initial value problem:
$\begin{cases} x y^\prime (x) = y(x)\ (3-y(x)) \\ y(2)=2 \end{cases}$.
Your ODE has a singular point in $x=0$ (for the coefficient of the $y^\prime (x)$ term vanishes), hence if the IVP has a solution it will have not to be defined in $x=0$.
Put the ODE in normal form, i.e. rewrite:
$\displaystyle y^\prime (x) =\frac{y(x)\ (3-y(x))}{x}$;
the function $f(x,y):= \frac{y (3-y)}{x}$ is of class $C^\infty$ in $(x,y)\in \Big(]-\infty ,0[\cup ]0,+\infty[\Big)\times \mathbb{R}$, hence the existence and uniqueness theorem applies and your IVP has unique local solution $y(x)$ whose graph passes through the point $(2,2)$.
The solution $y(x)$ is continuous in a neighbourhood $I_1$ of $x=2$ (because it has to be differentiable to satisfy the ODE), hence the composite function $f(x,y(x))$ is continuous in $I_1$; as $y^\prime (x)=f(x,y(x))$, then $y^\prime (x)$ is continuous in $I_1$, therefore $y(x)$ is a $C^1$ function in $I_1$. But then $y^\prime (x)$ is of class $C^1$ in $I_1$, for the composite function $f(x,y(x))$ is of class $C^1$ (apply the chain rule); therefore $y(x)$ is of class $C^2$... Bootstrapping, you see that $y(x)$ is of class $C^\infty$ in the neighbourhood $I_1$ of the initial point $2$.
Moreover, the solution $y(x)$ is also strictly increasing in a neighbourhood of $2$: in fact, $y(2)=2>0$ hence by continuity you can find a neighbourhood $I_2\subseteq I_1$ of $2$ in which $0<y(x)<3$, so:
$\displaystyle y^\prime (x)=\frac{y(x)\ (3-y(x))}{x} >0$,
thus $y(x)$ increases strictly.
Now you have all the ingredients to properly solve your problem: in fact, in $I_2$ you can divide both sides of the ODE by $y(x)\ (3-y(x))$ and rewrite:
$\displaystyle \frac{y^\prime (x)}{y(x)\ (3-y(x))} =\frac{1}{x}$;
now fix a point $x \in I_2$ and integrate both sides from $2$ to $x$:
$\displaystyle \int_2^x \frac{y^\prime (t)}{y(t)\ (3-y(t))}\ \text{d} t =\int_2^x \frac{1}{t}\ \text{d} t$
(I've introduced a dummy variable in the integrals); now the RHside gives you $\ln x -\ln 2$, hence you have to work on the LHside. Keeping in mind that $y(t)$ is strictly monotone hence invertible in $I_2$, we can make the change of variable $\theta =y(t)$: as $y(2)=2$ and $\text{d} \theta = y^\prime (t)\ \text{d} t$, you get:
$\displaystyle \begin{split}\int_2^x \frac{y^\prime (t)}{y(t)\ (3-y(t))}\ \text{d} t &= \int_2^{y(x)} \frac{1}{\theta (3-\theta)}\ \text{d} \theta \\ &=\frac{1}{3} \ln \theta - \frac{1}{3} \ln (3-\theta) \Big|_2^{y(x)} \\ &=\frac{1}{3} \left(\ln y(x) -\ln (3-y(x)) -\ln 2\right)\end{split}$.
Therefore the solution to your problem is implicitly determined by the equation:
$\displaystyle \ln \left( \frac{y(x)}{3-y(x)}\right) = \ln \frac{x^3}{4}$,
i.e.:
$\displaystyle \frac{4y(x)}{3-y(x)}=x^3$.
The latter equation is a rational algebraic equation w.r.t. $y(x)$ and can be solved with the usual tools, which yield:
$\displaystyle y(x)=\frac{3x^3}{4+x^3}$.
There is more that can be said, e.g. how the local solution $y(x)$ can be extended to a maximal solution... But that's another story.
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another story indeed! Despite the overkill, I am grateful for a formal discussion and solution. +1 – The Chaz 2.0 Mar 26 '11 at 13:40
@The Chaz: My two cents: I don't think it's an overkill... It is just the correct way of doing the exercise. – Pacciu Mar 26 '11 at 15:53
This belief is evident by the nature of your answer! I'll continue to appreciate your rigor while "monkeying around" in my own way ;) – The Chaz 2.0 Mar 26 '11 at 16:07
@The Chaz: Thank you! And watch your steps while "monkeying around" ;D – Pacciu Mar 26 '11 at 16:25
This is easy because it's separable variables. So solve $dy/(y(3-y))=dx/x$.
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... by integrating both sides, and then use the initial value to determine the constant of integration – Henry Mar 25 '11 at 22:45
The method you adopted for separating variables is usually called urang-utang© method by some funny mathematicians. They mock: "People using this method whitout knowing its fomal justification (if any!) resemble Orangutans using thing to make rudimental tools and messing with them"; in fact, the method is based on a totally unformal algebraic manipulation of differentials which is hard to formalize (hence it's almost meaningless). – Pacciu Mar 25 '11 at 23:56
@Pacciu: See this question, and in particular, Mike Spivey's answer there. – Rahul Mar 26 '11 at 2:29
@pac its not meaningless, just leave $y'$ alone, two functions (of $x$) are equal, so are their integrals (wrt $x$). – yoyo Mar 26 '11 at 14:31
@Rahul: Thanks for the reference, but I already know the story ;D @yoyo: There are people believing that, say, one can pass from $\frac{\text{d} y}{\text{d} x} =f(y)$ to $\text{d} y=f(x)\ \text{d} x$ by multiplying both sides by $\text{d} x$... But what's the meaning of this? How can a differential be considered as a number when it is not a number (for, it is just a symbol or a linear map)? This is what I was referring to when I wrote unformal algebraic manipulation of differentials which is [...] almost meaningless. – Pacciu Mar 26 '11 at 15:46
This is just an Initial Value Problem. You use the techniques you know to solve for the general solution. Here is a good resource: http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx. More specifically, you should look at "Separable Equations"
The general solution in this case will have one arbitrary constant. You use the I.V.P to solve for this constant.
- |
# Math Help - help me check the answer
1. ## help me check the answer
question
here is my answer, tell me whether i did it right?
if u have a better, don't hesitate to share
2. Originally Posted by IamLittle
question
here is my answer, tell me whether i did it right?
if u have a better, don't hesitate to share
Well, Correct me if I'm wrong, but haven't you only contradicted the 2nd assumption, i.e. "assume there exists a point b..." Does the solution follow from that?
3. Originally Posted by southprkfan1
Well, Correct me if I'm wrong, but haven't you only contradicted the 2nd assumption, i.e. "assume there exists a point b..." Does the solution follow from that?
thank you for reading
yes i have proved that the 2nd assumption is wrong
and the last contradiction is to contradict the question which claims f(x) is bounded |
## Zip Introduction
### Introduction
In this chapter of our Python tutorial we deal with the wonderful and extremely useful functionality 'zip'. Unfortunately, beginners of Python are quite often unnecessarily confused and frightened by zip. First of all the name is confusing. Lots of people confuse the zip of Python with the well-known archive file format ZIP, which is used for lossless data compression. Since this data compression not only keeps the required storage space very small, but is also carried out very quickly, the name 'zip' was chosen. In this context, "zip" means "to act quickly or move quickly".
The 'zip' of Python has absolutely nothing to do with it. The functionality 'zip' in Python is based on another meaning of the English word 'zip', "closing something with a zipper".
We will see that zip can be very easy to understand. However, this does not apply if you come up with the idea of using the Python help function. The help text is certainly partly responsible for this and frightens the novices away:
Return a zip object whose .next() method returns a tuple where the i-th element comes from the i-th iterable argument. The .next() method continues until the shortest iterable in the argument sequence is exhausted and then it raises StopIteration.
This text is correct but it is hard to understand. Let us start with simple examples before we try to simplify the theory behind zip.
We will start with two lists and apply zip to those two lists:
a_couple_of_letters = ["a", "b", "c", "d", "e", "f"]
some_numbers = [5, 3, 7, 9, 11, 2]
print(zip(a_couple_of_letters, some_numbers))
<zip object at 0x7efc8724f9b0>
The result is a zip object and you are not wiser than before, if you don't know zip. The application of zip returns an iterator, which is capable of producing tuples. It is combining the first items of each iterable (in our example lists) into a tuple, after this it combines the second items and so on. It stops when one of them is exhausted, i.e. there are no more items available.
The best way to see what it creates is to use it in a for loop.
for t in zip(a_couple_of_letters, some_numbers):
print(t)
('a', 5)
('b', 3)
('c', 7)
('d', 9)
('e', 11)
('f', 2)
If you look closely at the output above and the following picture, you will hopefully understand why zip has something to do with a zipper and why they had chosen the name.
zip can have an arbitrary number of iterable arguments as we can see in the following example:
location = ["Helgoland", "Kiel",
"Berlin-Tegel", "Konstanz",
"Hohenpeißenberg"]
air_pressure = [1021.2, 1019.9, 1023.7, 1023.1, 1027.7]
temperatures = [6.0, 4.3, 2.7, -1.4, -4.4]
altitude = [4, 27, 37, 443, 977]
for t in zip(location, air_pressure, temperatures, altitude):
print(t)
('Helgoland', 1021.2, 6.0, 4)
('Kiel', 1019.9, 4.3, 27)
('Berlin-Tegel', 1023.7, 2.7, 37)
('Konstanz', 1023.1, -1.4, 443)
('Hohenpeißenberg', 1027.7, -4.4, 977)
The use of zip is not restricted to lists and tuples. It can be applied to all iterable objects like lists, tuples, strings, dictionaries, sets, range and many more of course.
food = ["ham", "spam", "cheese"]
for item in zip(range(1000, 1003), food):
print(item)
(1000, 'ham')
(1001, 'spam')
(1002, 'cheese')
### Calling zip with no Argument
Let us have a look at what happens, if we call zip without any parameter:
for i in zip():
print("This will not be printed")
The body of the loop was not being executed!
### Calling zip with One Iterable
What happens if we call zip with just one argument, e.g. a string:
s = "Python"
for t in zip(s):
print(t)
('P',)
('y',)
('t',)
('h',)
('o',)
('n',)
So this call creates an iterator which produces tuples with one single element, in our case the characters of the string.
### Parameters with Different Lengths
As we have seen, zip can be called with an arbitrary number of iterable objects as arguments. So far the number of elements or the length of these iterables had been the same. This is not necessary. If the Lengths are different, zip will stop producing an output as soon as one of the argument sequences is exhausted. "stop producing an output" actually means it will raise a StopIteration exception like all other iterators do. This exception is caught by the for loop. You will find more about this way of working in the chapter "Iterators and Iterables" of our Python tutorial.
The following example is a zip call with two list with different lenghts:
colors = ["green", "red", "blue"]
cars = ["BMW", "Alfa Romeo"]
for car, color in zip(cars, colors):
print(car, color)
BMW green
Alfa Romeo red
### Advanced Usages of zip
We have a list with the six largest cities in Switzerland. It consists of tuples with the pairs, city and population number:
cities_and_population = [("Zurich", 415367),
("Geneva", 201818),
("Basel", 177654),
("Lausanne", 139111),
("Bern", 133883),
("Winterthur", 111851)]
The task consists of creating two lists: One with the city names and one with the population numbers. zip is the solution to this problem, but we also have to use the star operator to unpack the list:
cities, populations = list(zip(*cities_and_population))
print(cities)
print(populations)
('Zurich', 'Geneva', 'Basel', 'Lausanne', 'Bern', 'Winterthur')
(415367, 201818, 177654, 139111, 133883, 111851)
This is needed e.g., if we want to plot these data. The following example is just used for illustrating purposes. It is not necessary to understand it completely. You have to be familiar with Pandas. In the following program, we assume that only the combined list is available at the beginning:
import pandas as pd
cities_and_population = [("Zurich", 415367),
("Geneva", 201818),
("Basel", 177654),
("Lausanne", 139111),
("Bern", 133883),
("Winterthur", 111851)]
cities, populations = list(zip(*cities_and_population))
s = pd.Series(populations, index=cities)
s.plot(kind="bar")
Output:
<matplotlib.axes._subplots.AxesSubplot at 0x7fdd6494e490>
### Converting two Iterables into a Dictionary
zip also offers us an excellent opportunity to convert two iterables into a dictionary. Of course, only if these iterables meet certain requirements. The iterable, which should be used as keys, must be unique and can only consist of immutables. We demonstrate this with the following morse code example. The full morse code alphabet can be found in our chapter on dictionaries:
abc = "abcdef"
morse_chars = [".-", "-...", "-.-.", "-..", ".", "..-."]
text2morse = dict(zip(abc, morse_chars))
print(text2morse)
{'a': '.-', 'b': '-...', 'c': '-.-.', 'd': '-..', 'e': '.', 'f': '..-.'}
### Footnotes
1 The data are from the 1st of April 2020, no joke. The locations are chosen arbitrarily. Yet, there is a special reason, why I had chosen Hohenpeißenberg. On the Hohenpeißenberg I was invited to give two unforgettable Python courses for the German weather service: Great people and a fantastic view! |
# Find the span of a set of vectors
In general, what is the most straightforward way to find the span of a set of vectors? I'm trying to find the span of these three vectors:
[1, 3, 3]
[0, 0, 1]
[1, 3, 1]
-
I would probably start by writing the set of vectors as a system of linear equations, then writing the system as an augmented matrix, and then converting to reduced row echelon form - is this the correct procedure? – Anderson Green Dec 7 '12 at 20:14
Do you know the definition of span? – Math_Illiterate Dec 7 '12 at 20:19
@Ockham Yes - the span of a set of vectors is the set of all linear combinations of a set of vectors. How can I find the set of all linear combinations of a set of vectors? – Anderson Green Dec 7 '12 at 20:20
I think I understand it now (at least partially). The span would be a[1, 3, 3] + b[0, 0, 1] + c[1, 3, 1], which would be [a + c, 3a + 3c, 3a + b + c], where a, b, and c are arbitrary constants. But how can I use this information to determine whether the set of vectors spans R^3? – Anderson Green Dec 7 '12 at 20:23
Once you have the echelon form, the rows that are not identically zero (interpreted as vectors) will form the basis. – David Mitra Dec 7 '12 at 21:00
If by finding the span you mean finding a set of linearly independent equations who define the subspace spanned by the given vectors, you can go like this. Suppose you are given $v_1,\ldots, v_k\in \mathbb{R}^n$; construct the matrix $$A=\begin{pmatrix}\phantom{hhh}v_1^t\phantom{hhh}\\\hline\vdots\\\\\hline\phantom{hhh}v_k^t\phantom{hhh}\end{pmatrix}$$ then find a basis for $\ker A$, say $\{w_1,\ldots, w_h\}$. The subspace spanned by your vectors is described by the equations $$w_j^tx=0\qquad j=1,\ldots, h$$ where $x=\begin{pmatrix}x_1\\\vdots\\x_n\end{pmatrix}$.
-
${\text{Span}}\{{\vec v_1}, {\vec v_2}, {\vec v_3}\}$ is the set of all vectors $(x, y, z) \in {{\mathbb R}^3}$ s.t. $(x, y, z) = {c_1}{\vec v_1} + {c_2}{\vec v_2} + {c_3}{\vec v_3}$. We need to find the values of $\vec x = (x, y, z)$ so that our system of equations has solutions for ${c_1}$, ${c_2}$ and ${c_3}$. We need to solve $$\left[{\begin{array}{ccc|c} {\vec v_1}&{\vec v_2}&{\vec v_3}&{\vec x} \end{array}}\right].$$ In your case $$\left[{\begin{array}{ccc|c} 1&0&1&x\\ 3&0&3&y\\ 3&1&1&z \end{array}}\right].$$
-
Does [v1, v2, v3, x] represent a set of vectors, or does it represent a system of equations? – Anderson Green Dec 7 '12 at 20:33
It is not a set. It is just a compact way of writing matrices. – glebovg Dec 7 '12 at 20:39
You're quite right that the span would be all vectors of the form $$[a+c,3a+3c,3a+b+c],$$ where $a,b,c$ are real. The question becomes how we can describe this using as few parameters as possible. The idea is to reduce your spanning set to a basis--that is, a spanning set that is linearly independent--by discarding superfluous vectors.
Let's suppose that $[a+c,3a+3c,3a+b+c]=[0,0,0]$ and see what we can determine about $a,b,c$. Well, since $a+c=0$, then we certainly have $c=-a$, and making the substitution $c=-a$ gives us $$[0,0,2a+b]=[0,0,0].$$ This holds exactly when $b=-2a$. Thus, $$a[1,3,1]-2a[0,0,1]-a[1,3,1]=[0,0,0],$$ regardless of what value of $a$ we choose, so your given spanning set is linearly dependent. Indeed, setting $a=1$, this means that $$[1,3,3]=2[0,0,1]+[1,3,1],$$ so the first vector is unnecessary to span the whole space, since it's a linear combination of the other two vectors. In particular, $$[a+c,3a+3c,3a+b+c]=(2a+b)[0,0,1]+(a+c)[1,3,1].$$
Thus, every vector in the generated space can be written in the form $$u[0,0,1]+v[1,3,1]=[v,3v,u+v]$$ for some real $u,v$. All that's left to do is confirm that $[0,0,1]$ and $[1,3,1]$ are linearly independent, which we can do by setting $[v,3v,u+v]=0$, and showing that this implies $u=v=0$.
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First you should investigate what is a linear independent set in your span. Then your set will be the linear combination of this set. For example, I will do your example
$$\left| \begin{array}{ccc} 1 & 3 & 3 \\ 1 & 3 & 1 \\ 0 & 0 & 1\\ \end{array} \right| = 0$$ So they are not linearly independent. In fact, $(1,3,3) = (1,3,1) +2(0,0,1)$. But as $$\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 3 & 1 \\ 0 & 0 & 1\\ \end{array} \right| = 2 \neq 0$$ $(1,3,1),(0,0,1)$ are linearly independent. Then, \begin{eqnarray} \langle (1,3,3),(1,3,1),(0,0,1) \rangle &=& \langle (1,3,1),(0,0,1) \rangle \\ &=& \{ \alpha (1,3,1) + \beta (0,0,1) : \alpha , \beta \in \mathbb{R}\} \\ &=& \{ (\alpha ,3 \alpha , \alpha +\beta) : \alpha , \beta \in \mathbb{R}\} \end{eqnarray}
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# Included pdf (wallpaper, or includegraphics) has different colors [duplicate]
Edit: Duplicate-clickers, please read on - I believe this case is different, for the following reasons:
a) As I said in original post, I am not printing with Acrobat, but using Skim and Mac OSX preview. In fact, Acrobat prints the colors correctly!
b) If it were the said problem, then the suggested solution by Martin Heller (pdf page attributes / transparency) should cure it. But it does not.
c) I did further tests, because I found that OpenOffice also uses cairo (the PDF engine used by Inkscape). So, to really rule out Inkscape/cairo, I created the included PDF file from printing a HTML file into pdf (on OSX), that included both a single-colored png image and a plain colored area (style="background:#67b737"). I additionally included the png directly in LaTeX (includegraphics), besides the pdf.
Result:
1) The plain HTML color prints correctly and matches the LaTeX color.
2) The png in the included pdf file prints in the wrong color (too light).
3) Also the directly included png prints in the wrong color!!
4) As before, Acrobat Reader prints the colors correctly.
From 3) I conclude that it is not specifically a problem of including PDFs.
I found the long answer in PDF color model and LaTeX very informative, and I tried the pdfx package to create a PDF/A (a-1b), but it did not seem to help in my case, or maybe I missed something...
My test pages are piling up, and I am still clueless.
Any ideas?
I have a feeling that maybe things behave differently on Mac OSX, because color management seems to be implemented differently. But does this explain my findings? Still, printing my PDF on a Linux PC (using okular) produces the same color mismatch.
Possible Duplicate:
\includegraphics PDF, color problem
I use Inkscape to design a cover page (rgb colors), and save the file as pdf.
In LaTeX (pdflatex), I include the pdf using the wallpaper package, and write some title text on that same page (reason: title should be editable in LaTeX code without using inkscape, and wallpaper because I need the title running across the graphics, not below it).
For the title text in LaTeX, I use exactly the same rgb color as for my graphics in inkscape.
On screen, all looks ok (using Skim or Mac OSX Preview).
When I print the PDF, the title text has a clearly different color than the graphics from inkscape!
The resulting pdf is here
Printout:
Minimal working example:
\documentclass[11pt]{amsart}
\usepackage{wallpaper}
\usepackage{graphicx}
\definecolor{mygreen}{rgb}{0.404, 0.718, 0.216} %% equivalent to 103,183,55
% \pdfpageattr {/Group << /S /Transparency /I true /CS /DeviceRGB>>} (Martin Heller) does not solve the problem
\begin{document}
\ThisULCornerWallPaper{1}{Colortest-OO}
\textbf{\Huge{\color{mygreen}LaTeX - 103,183,55}}\\
\textbf{\Huge{\color{mygreen}LaTeX - 103,183,55}}
\end{document}
I believe it is not this and not directly this problem.
A funny thing is: When I take the output pdf (from LaTeX) and include it in a second LaTeX file (again with wallpaper or with includegraphics), the final pdf has matching colors.
How weird is that!?
To summarize my problem:
I dont need exact color reproduction.
But I want my PDF document to have consistent colors for the same rgb values.
What I tried so far:
1. Fiddle with CMYK and color profiles in Inkscape. I came to the conclusion that it should not matter as long as I stay with plain RGB in both InkScape and LaTeX.
2. Fiddle with color model in the PDF by converting color space with Acobat Pro before including it in LaTeX... a lot of possibilities, no clear success.
3. Rule out Inkscape. I created a PDF with NeoOffice (OpenOffice) and included it in LaTeX. Problem remains.
4. I tried specifying the rgb option in \usepackage[rgb]{xcolor}. No difference.
5. Updated my MacTeX to 2012. No difference.
Any ideas what is going on here?
It would be greatly appreciated.
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## marked as duplicate by Martin Schröder, Kurt, Andrew Swann, Paul Gaborit, ThorstenOct 29 '12 at 6:38
You don't have to sign with your name since it automatically appears in the lower right corner of your post. – Kurt Oct 28 '12 at 15:16
Thanks, Kurt - I will try to avoid such redundancy in the future :-) – Philippp Oct 28 '12 at 16:51
@Philippp: It's probably better to post a question to TeX - LaTeX Meta about the reopening of your question, you'll have a better chance of people seeing it there. – doncherry Oct 31 '12 at 23:16
@doncherry, Thank you very much! I will do so, when I deal with the problem again (currently, I just dont have the time, and I think it would be inappropriate to ask for help when I dont have the time to go and try the suggested solutions). – Philippp Jan 6 '13 at 12:46
The exact values found in the PDF file are:
\definecolor{mygreen}{rgb}{0.40392,0.71764,0.21568}
Found by
pdftk test.pdf cat output t.pdf uncompress
and looking for the operator rg or RG with three numbers as arguments in front of the operator.
Perhaps it helps a little.
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Thanks Heiko! We looked into the PDF, and found that the numbers are slightly different, so we thought it could be a rounding problem between 8-bit integer in Inkscape vs. decimal rgb in LaTeX, and replaced the values in a crafted PS file - problem remains. In fact it is very weird - see my next edit... – Philippp Oct 31 '12 at 21:21
I had the same problem when I exported Inkscape graphics to .png. You have to avoid transparency.
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Well, good to know, but does not mean "3. Rule out Inkscape. I created a PDF with NeoOffice (OpenOffice) and included it in LaTeX. Problem remains." that the problem is not caused by Inkscape? – Stephen Oct 28 '12 at 16:15
Thanks - Yes, exactly. The same thing happens with OpenOffice instead of Inkscape. And, my text is 100% opaque, so I would not expect transparency to be an issue... – Philippp Oct 28 '12 at 16:45
Jonas: I remember having that effect, too. I found it helps to just add a white, 100% opaque rectangle in Inkscape to give the png a solid background (or, I believe there is an option somewhere). But this case is different (I just verified it to be sure). – Philippp Oct 28 '12 at 17:00 |
# The existence of an elliptic curve with a specific Galois representation induced by a character
In Kevin Buzzard's survey article on potential modularity Buzzard writes:
Let us say that we have an elliptic curve $E$ over a totally real field $F$, and we want to prove that $E$ is potentially modular (that is, that $E$ becomes modular over a finite extension field $F^{′}$ of $F$, also assumed totally real). Here is a strategy. Say $p$ is a large prime such that $E[p]$ is irreducible. Let us write down a random odd $2$-dimensional mod $ℓ$ Galois representation $\rho_{ℓ} : > Gal(\overline{F}/F) → GL(2,\mathbf{F}_ℓ )$ which is induced from a character; because this representation is induced it is known to be modular. Now let us consider the moduli space parametrising elliptic curves $A$ equipped with
1. An isomorphism $A[p] \cong E[p]$
2. An isomorphism $A[ℓ]\cong ρ_ℓ$
This moduli problem will be represented by some modular curve, whose connected components will be twists of $X(pℓ)$ and hence, if $p$ and $ℓ$ are large, will typically have large genus. However, such a curve may well still have lots of rational points, as long as I am allowed to look for such things over an arbitrary finite extension $F^{′}$ of $F$ !
It's not immediately obvious to me that there's an elliptic curve $A$ over some $F^{′}$ satisfying the second condition alone (never mind satisfying both conditions simultaneously). Is there a simple explanation for why there should be such an $A$? Did Professor Buzzard mean "consider the set of A such that $A[ℓ]\cong ρ_ℓ$ for some representation induced by a character" (as opposed to a particular one)?
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In this context, if $\rho$ is a mod $\ell$ representation of $Gal(\overline{F} / F)$, and $A$ is an elliptic curve over an extension $F' / F$, then the statement "$A[\ell] \cong \rho$" needs a little bit of interpretation, because the two sides are representations of different things: $A[\ell]$ is a mod $\ell$ representation of the subgroup $Gal(\overline{F} / F') \subset Gal(\overline{F} / F)$. So the statement is to be read as "$A[\ell]$ is isomorphic as a $Gal(\overline{F} / F')$-representation to the restriction of $\rho$". Now, the bigger $F'$ is, the weaker this condition becomes: in particular, if we take any elliptic curve $A$ over $F$ and define $F'$ to be the extension of $F$ generated by the $\ell$-torsion points of $A$ and the splitting field of $\rho$, then the statement is automatic (both sides are the trivial representation).
David, the $A[\rho]$ in the third line should be $A[l]$. – Chandan Singh Dalawat Oct 28 '12 at 10:34
If that doesn't address your question, I'm not entirely sure what your question is. Certainly not every mod $\ell$ representation of $Gal(\overline{F} / F)$ can be realized in the $\ell$-torsion of an elliptic curve over $F$; but the restriction of any such representation to $Gal(\overline{F} / F')$ can be realized by an elliptic curve over some big enough $F'$, simply because that restriction can be made trivial. – David Loeffler Oct 28 '12 at 21:18
PS: Don't be tempted to read "$A[\ell] \cong \rho$" as "the image of $\Gal(\overline{F} / F)$ acting on $\rho$ and of $\Gal(\overline{F} / F')$ acting on $A[\ell]$ coincide as subgroups of $GL_2(\mathbb{F}_\ell)$". Although plausible, this reading isn't what's meant here at all. – David Loeffler Oct 28 '12 at 21:21 |
## Algebra 1: Common Core (15th Edition)
Multiplying these two numbers would give us $5x^{2}+32x-21$. This answer can be solved by finding the factors of -21 and testing which pair adds to 32. |
# List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians
20 Nov 2017Ilias DiakonikolasDaniel M. KaneAlistair Stewart
We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved guarantees for these problems... (read more)
PDF Abstract |
Article | Open
# Laminar differences in decision-related neural activity in dorsal premotor cortex
• Nature Communicationsvolume 8, Article number: 614 (2017)
• doi:10.1038/s41467-017-00715-0
Accepted:
Published:
## Abstract
Dorsal premotor cortex is implicated in somatomotor decisions. However, we do not understand the temporal patterns and laminar organization of decision-related firing rates in dorsal premotor cortex. We recorded neurons from dorsal premotor cortex of monkeys performing a visual discrimination task with reaches as the behavioral report. We show that these neurons can be organized along a bidirectional visuomotor continuum based on task-related firing rates. “Increased” neurons at one end of the continuum increased their firing rates ~150 ms after stimulus onset and these firing rates covaried systematically with choice, stimulus difficulty, and reaction time—characteristics of a candidate decision variable. “Decreased” neurons at the other end of the continuum reduced their firing rate after stimulus onset, while “perimovement” neurons at the center of the continuum responded only ~150 ms before movement initiation. These neurons did not show decision variable-like characteristics. “Increased” neurons were more prevalent in superficial layers of dorsal premotor cortex; deeper layers contained more “decreased” and “perimovement” neurons. These results suggest a laminar organization for decision-related responses in dorsal premotor cortex.
## Introduction
Imagine coming to a stoplight in your car. The sight of the stoplight results in patterns of neural activity that lead you to press the brakes to stop the car. This process of choosing and performing appropriate actions based on sensory inputs is termed perceptual decision-making and in this scenario involves the somatomotor system of the brain1,2,3,4,5. Lesion experiments in monkeys6, clinical case studies of human patients7, and physiological studies in monkeys using reach-target selection8, 9 and perceptual decision-making tasks10, 11 all suggest that somatomotor decision-related signals are present in dorsal premotor cortex (PMd)1. Despite these important studies, many questions about neural circuit dynamics in PMd during somatomotor decisions remain unresolved. In this study, we address two of these questions.
First, we lack a detailed description of the temporal patterns of firing rates (FRs) in PMd during perceptual decisions. An understanding of the temporal patterns of FRs is an important first step for building mechanistic models of decision-making12,13,14,15. Classical examinations of motor structures including PMd using task designs that involve instructed delays16,17,18,19,20,21 and recent studies focused on establishing a role for PMd in reach target selection8 or perceptual decision-making10, 11 have established that FR patterns demonstrate substantial temporal variation or “complexity”22, consistent with other reports of heterogeneous, temporally complex FRs in several brain regions during perceptual decision-making tasks14, 23,24,25,26,27. By temporal variation, we mean that PMd FRs exhibit mixed responses to the visual stimulus and movement onset that can involve both increases and decreases in FRs8, 28. One hypothesis proposed in studies of the frontal eye field is that these types of FRs can be viewed as organized along a visuomotor continuum29,30,31,32,33,34,35. Here, our first goal was to further investigate the temporal variation in PMd FRs during perceptual decisions and examine if they are also well described by a visuomotor continuum29. In particular, we wanted to examine how FR patterns of cells in different parts of the continuum covary with sensory parameters (e.g., stimulus difficulty), behavioral markers of task performance (e.g., reaction time (RT), choice), and temporal events (e.g., stimulus onset, movement onset) and thereby delineate putative decision-related neurons. To elicit a broad range of decision-related FR patterns that we wished to investigate, we used a variant of a recently reported RT static visual checkerboard discrimination task11.
Our second goal was to ask whether putative decision-related neurons tend to be anatomically localized, such that anatomically informed neural network models can be created13,14,15, 30, 36,37,38. Anatomical studies suggest that superficial layers of PMd receive substantial corticocortical input from frontal association areas39, and connectivity studies in the rodent motor cortex suggest a prominent descending projection from superficial to deep layers40. Therefore, we investigated the hypothesis that there are differences in the FR dynamics in the superficial layers compared to the deeper layers of PMd during the process of decision formation. To study this question, we used multi-contact electrodes that provide recordings across the different layers of the cortex.
We found that FR patterns in PMd demonstrated substantial temporal variation during the decision-formation process. This variation could be readily viewed along a systematic visuomotor continuum9, 29, 33. This conclusion was supported by a variety of analyses ranging from simple indices computed on a single neuron basis to methods such as principal components and K-means clustering that exploit covariance structure in the neural population26. The activity of PMd neurons that increased their FRs after visual stimulus onset had the strongest and earliest covariation with stimulus difficulty, choice, and RT—consistent with the characteristics of a candidate decision variable predicted by decision-making models41,42,43,44. Finally, using relative depth information we found that there are more putative decision-related neurons in superficial layers of PMd, thus providing a constraint for anatomically informed neural network models14, 30, 37.
## Results
### Monkeys discriminate visual checkerboard cues
Two trained monkeys (T and O) discriminated the dominant color of a central, static checkerboard cue composed of mixtures of red and green squares and used an arm movement to report the decision (Fig. 1a 11). The use of a static checkerboard cue meant that the sensory stimulus itself had no temporal dynamics, and all sensory evidence was provided at the onset of the stimulus and did not vary over time. Figure 1b depicts a trial timeline. The trial began when the monkey touched the center target and fixated on the cross. After a variable target viewing period, the red-green checkerboard cue appeared. The task of the monkey was to make an arm movement to the target (red vs. green) that matched the dominant color of the checkerboard cue. We parameterized difficulty of the discrimination (Fig. 1c) by a color coherence measure (C) defined as the absolute difference in the number of red and green squares normalized by the total number of squares in the checkerboard (100×|R − G|/(R + G)). A corresponding signed color coherence measure (SC) is defined as 100×(R − G)/(R + G).
We first examined the effects of changes in color coherence on the behavior of the monkeys. On average across sessions, decreases in color coherence (example stimuli shown in Fig. 1c) resulted in more errors (Fig. 1d, fitting the proportion correct as a function of coherence (C) using a psychometric function; average R 2, T: 0.99 (over 75 sessions), O: 0.99 (over 66 sessions), slope (β), M ± SD over sessions, T: 1.30 ± 0.16, O: 1.22 ± 0.16). In Fig. 1d, the measured data points (mean across sessions) are shown as gray circles with 2 × SEM. Black lines are drawn in between these data points to guide the eye. Monkey T was more sensitive than monkey O (thresholds (α) are computed on a per session basis at 81.6% correct (M ± SD): T, 10.77 ± 1.26%, O: 15.42 ± 1.87%, unpaired t 140 = −17.65, p = 2.67e−37, two-tailed test, Wilcoxon rank sum comparing median thresholds, p = 2.91e−23).
Decreases in color coherence also resulted in slower RTs (Fig. 1e, using a regression to test if mean RT increases as loge coherence decreases (harder stimulus difficulties) as in ref. 45; average R 2, T: 0.94, O: 0.65; slope of regression: M ± SD over sessions, T: −42.1 ± 8.1 ms/loge coherence (%), O: −8.6 ± 4.5 ms/loge coherence (%)). Again in Fig. 1e, the measured data points (mean across sessions) are shown in gray circles with 2 × SEM and to guide the eye, black lines are drawn in between the points. Monkey T had a larger range of RTs compared to monkey O (comparing the RT range between easiest and hardest difficulties (M ± SD) estimated over sessions; T: 143 ± 32 ms and O: 52 ± 17 ms, Wilcoxon ranksum comparing median ranges of RT, p = 4.85e−24).
We also investigated the behavior of the monkeys by fitting the RT distributions and accuracy using the drift diffusion (DDM) and urgency gating models (UGM) developed to explain behavior in two alternative forced choice tasks46,47,48 (Supplementary Note 1, Supplementary Figs. 1, 2 and Supplementary Tables 14). We performed this model-fitting analysis to identify if these candidate computational frameworks could help us interpret decision-related responses in PMd, and if the behavior was better explained by the DDM, estimate decision times for the monkeys. Quantitative modeling of how monkeys perform discrimination of static stimuli such as the checkerboard used here is lacking47. Both the UGM and the DDM provided reasonable fits. However, neither model was completely sufficient to describe the RT and accuracy of the monkeys (Supplementary Figs. 1, 2 and Supplementary Note 1). The UGM with an intercept and slope term provided the best fit of all three models considered here10. Our results here further highlight the increasing realization that differentiating between these models of decision-making behavior using purely statistical techniques is currently very difficult47,48,49—explicit stimulus manipulations are necessary. Additional elaboration of these models is likely needed to better describe the behavior of these monkeys in this and likely other discrimination tasks.
### PMd neurons are organized along a visuomotor continuum
Having observed that the behavior of the monkeys in this task is similar to other reports of monkeys performing decision-making tasks3, 11, 45, 50, we next examined the temporal patterns of FRs of neurons in caudal PMd during the period of decision formation to delineate putative decision-related neurons (Fig. 1f, 546 units in T, 450 units in O; single neurons and multi-units that responded during any epoch in the task). Of the 996, 801 PMd units reported here are single neurons (384 from O, 417 from T, mean ISI violation (<=2ms) = 0.43%, ~0.13 additional spikes per trial) and the remaining 195 units reported here are classified as multi-units (129 from T, 66 from O, mean ISI violation = 3.36%, ~1.4 additional spikes per trial). We did not exclude multi-units because they were often robustly modulated during the task and we wanted all the power we could get for analysis of laminar differences. Conclusions did not change when restricting the analyses to just the isolated single neurons. The number of neurons/units reported here is substantially larger than other recent studies of neuronal responses in PMd during decision-making tasks10, 11. We leverage this large physiological data set recorded in PMd to attempt to address the two goals we proposed in the introduction.
Qualitatively, electrophysiological characteristics and effects reported here were similar in both monkeys. The main figures report data pooled across both monkeys and also single and multi-units for more clarity. Analyses are also shown in Supplementary Figures for each monkey where appropriate to emphasize the generality of our results.
Caudal PMd units did not typically modulate their FRs to target onset in this task. Modest changes in FRs in response to target onset might be either a result of the targets always being shown at predictable spatial locations. Suppressive effects on FRs may also occur when there is movement uncertainty due to the presence of multiple targets9. Unlike the modest modulations observed to target onset, visual checkerboard cue onset resulted in a robust modulation of FRs of some PMd units. For example, the unit in Fig. 2a (782 trials) increased its FR ~150–200 ms after checkerboard cue onset. Moreover, for this unit, higher color coherence stimuli were associated with a faster rate of divergence of FRs as a function of choice and lower color coherence stimuli resulted in a slower rate of divergence of FRs as a function of choice. In contrast, the unit in Fig. 2b (1454 trials) decreased its FR after checkerboard cue onset. The FRs of this unit only modestly changed with coherence; FRs ultimately covaried with the animal’s choice for this unit, but only for the last ~100 ms before movement onset.
In contrast to FR modulation time-locked to checkerboard cue onset for the units shown in Fig. 2a, b, FR modulations in “perimovement” units appeared in the last ~150 ms before movement onset and were clearly time-locked to the movement (Fig. 2c, 655 trials). The response pattern of the “perimovement” unit shown in Fig. 2c only modestly changed with color coherence. These examples shown in Fig. 2a–c suggest that some units increase or decrease in FR in response to the visual stimulus and identification of the choice, whereas others are more tightly associated with the movement initiation process. The single examples suggest that FR patterns in PMd during the process of decision formation span a bidirectional visuomotor continuum9, 29, with increased and decreased activity in response to visual stimuli at opposite poles and perimovement activity in the middle.
This proposal that PMd FRs lie along a bidirectional continuum was again apparent when the FRs of units in Fig. 2a–c were re-sorted and re-averaged as a function of RT (Fig. 2d–f). Figure 2d shows the FR of the unit shown in Fig. 2a now organized by RT. FRs of this unit when organized by RT again exhibited choice-dependent modulation ~150–200 ms after checkerboard cue onset. The longest RTs (500–1000 ms) are associated with FR modulations up to 350–400 ms before the onset of movement (Fig. 2d, bottom panel, see arrow 45). Similarly, Fig. 2e shows the FRs of the unit in Fig. 2b now sorted by RT. FR of this unit again decreased after checkerboard cue onset; the duration of this decrease covaries with RT. The unit only recovered its FRs and selectivity for choice just before (~100 ms) movement onset. Finally, Fig. 2f shows the FRs of the perimovement unit in Fig. 2c now organized by RT. FR modulations for this unit again appeared only ~150 ms before movement initiation and regardless of RT they are tightly locked to movement initiation (bottom panel of Fig. 2f, see arrow). We exploited this organization by RT when aligned to movement onset to broadly categorize the units.
### Increased PMd neurons show stronger decision-related activity
To summarize the activity of the population of units distributed along this continuum, we first developed an index to broadly separate the units into “increased”, “decreased”, and “perimovement” categories (Fig. 3a). The index was defined as the trial-by-trial correlation coefficient between RT and time-averaged FR in the −600 to −200 ms epoch before movement onset, after subtraction of the baseline FR during the holding period (measured in the 200 ms epoch before checkerboard cue onset). For computing the correlation coefficient, both left and right reach directions are included, and choice is not included as a factor. For trials with RT less than 600 ms, we truncated the start of the measurement window to coincide with the start of checkerboard cue presentation when measured relative to movement onset. We correlated the modified time-averaged FR to the RT across all trials to estimate the index.
We labeled units with significantly positive indices as “increased” (e.g., Fig. 2a, d, index (M ± CI): 0.37 ± 0.08), significantly negative indices as “decreased” (e.g., Fig. 2b, e, index:−0.4 ± 0.12), and units with indices not significantly different from zero as perimovement (e.g., Fig. 2c, f, index: 0.04 ± 0.2). The distribution of the index from negative to positive values reflects the continuum of responses from decreased to increased responses to checkerboard cue onset (Fig. 3a, Supplementary Fig. 3a). The median visuomotor index is positive and significantly different from zero, suggesting a slightly greater presence of increased compared to decreased and perimovement units (median = 0.065, two-tailed Wilcoxon signrank vs. 0, p = 1.13e−57, Fig. 3a). As per the index and the criteria we used, 514/996 units (51.6%) were categorized as increased, 141/996 (14.15%) as decreased, and the remaining 341/996 (34.25%) as perimovement. Increased, decreased, and perimovement units were observed in both monkeys (Supplementary Fig. 3c, d, median index for monkey T = 0.099, Wilcoxon signrank p = 2.12e−22; median for monkey O = 0.045, Wilcoxon signrank p = 1.56e−37).
We next used the visuomotor index to selectively average FRs of PMd units and show that the population responses of the increased units covary the strongest with color coherence, choice, and RT. We also correlated this visuomotor index to various metrics of interest such as the timing of choice selectivity and to other metrics proposed in recent studies of visuomotor continuums26, 33. Using these results, we contend that the FRs of increased, but not decreased and perimovement units are consistent with a candidate decision variable.
The first neural prediction made by computational models of decision-making for neurons that covary with an evolving decision is that on average the build-up of neural activity in favor of a choice, as measured in plots of trial-averaged FR vs. time, is faster for easier compared to harder color coherences45. The FRs of increased units were the most consistent with this prediction. For increased units, increases in color coherence were accompanied by an increase in the rate at which the average choice selective signal (defined as |left—right| averaged over units) developed (Fig. 3b–c, Supplementary Fig. 3e, slope of FR curve from 150–350 ms, M ± SE: 50.16 ± 3.33 spks/s2/100% color coherence, comparison to shuffled, sign test p = 1.22e−27). This 200 ms range over which we computed slopes is within the range of decision times estimated in Supplementary Fig. 1d for both monkeys, assuming that the DDM is the correct model to describe the behavior.
The rate of the build-up of neural activity in favor of a choice for the decreased and perimovement units also increased modestly as a function of color coherence, suggesting that they still contained vestiges of the decision-formation process (Fig. 3c, M ± SE, decreased: 24.73 ± 3.30 spks/s2/100% color coherence, comparison to shuffled, sign test p = 2.72e−08; perimovement: 19.71 ± 1.86 spks/s2/100% color coherence, comparison to shuffled, sign test p = 3.72e−15).
The dependence on color coherence was stronger for increased units compared to the other two broad categories of units (positive correlation between the visuomotor index and the dependence of slopes on color coherence, Spearman’s r = 0.25, p = 6.35e−16; comparison of slopes of lines in Fig. 3c, bar plots shown in Supplementary Fig. 3f, g, Wilcoxon ranksum p = 3.505e−04, increased vs. perimovement: Wilcoxon ranksum p = 1.43e−09, decreased vs. perimovement: Wilcoxon ranksum p = 0.36; permutation tests, 10,000 repeats: increased vs. decreased and increased vs. perimovement: p = 2e−4; decreased vs. perimovement: p = 0.21). Thus, increased units demonstrate the strongest modulation of FRs with the stimulus color coherence and choice. The order of these effects (increased > decreased ~ perimovement) and the positive correlation between the dependence on color coherence and the visuomotor index was again present in both monkeys (Supplementary Fig. 3g, monkey T: r = 0.36, p = 3.2e−18; monkey O: r = 0.23, p = 1.02e−6).
### Choice selective signals emerge earlier in increased neurons
We next examined the latency of the population level choice selectivity signal for each of the broad unit categories. This latency which is termed 'discrimination time' was defined as the first time at which the choice selective signal significantly departed from the FR in the hold period before the onset of the checkerboard cue as estimated using a paired t-test that corrected for multiple comparisons34. Error bars on discrimination time were obtained through bootstrapping. Population level choice selectivity in increased units appeared ~100–150 ms after checkerboard cue onset, and this discrimination time increased only modestly with RT (mean slope of regression M ± SE: 0.2 ± 0.06 ms/1 ms of RT, Fig. 3d–e, Supplementary Fig. 4a–c). Furthermore, discrimination times were earlier for the increased compared to decreased and perimovement units (bootstrapped time estimates do not overlap). Decreased and perimovement units also exhibited a more pronounced increase in discrimination time with RT (decreased: M ± SE = 0.53 ± 0.15 ms/1 ms of RT, perimovement: 0.4 ± 0.11 ms/1 ms of RT, Fig. 3e, Supplementary Fig. 4a–c). These trends were observed separately in each monkey (Supplementary Fig. 4a, c) and also when the analysis was performed on a neuron-by-neuron basis (Supplementary Note 2, Supplementary Fig. 4d–f).
The differences between FR patterns for long vs. short RTs in Fig. 3d could emerge entirely due to mixing responses to different levels of visual stimulus difficulty. Long RTs are more likely to come from harder color coherences and short RTs from easier color coherences. Differences as a function of RT could just be an artifact of this separation. However, this explanation did not hold for our results. For increased units and for every color coherence level, the slope of the choice selective signal increased faster for short compared to long RTs (Fig. 3f, sign rank test comparing the slope of the choice selective signal for fast vs. slow RTs; maximum p-value = 9.21e−31; monkey T: 1.65e−19; monkey O:5.29e−13) arguing against explanations which posit that observed effects of RT are due to the spurious mixing of visual (i.e., sensory) responses to different color coherences.
### Choice selectivity does not depend on coherence at movement onset
We next examined how FRs at the time of movement initiation depended on coherence and RT. At the time of movement onset, regardless of broad unit category, the magnitude of the average choice selective signal in the −100 ms to movement epoch was only weakly modulated by color coherence/RT (for instance in the PMTHs shown in Fig. 2d–f; M ± SE, sign-test to compare median slopes for the average FR in −100 ms to move as a function of color coherence and the slopes for a shuffled curve, increased: 0.30 ± 0.24 spks/s2/100% color coherence, p < 0.1; decreased: 0.49 ± 0.33 spks/s2/100% color coherence, p < .16; perimovement: 0.54 ± 0.25 spks/s2/100% color coherence, p < 0.09; Fig. 3g, h, Supplementary Fig. 4g). These results were again observed in both monkeys (Supplementary Fig. 4j, sign test, monkey T: increased, p < .07, decreased: p < .14, perimovement: 0.59; monkey O: increased, p < 0.51, decreased: p < 0.67, perimovement: p < 0.37).
This observation that the magnitude of the choice selective signal at the time of movement onset only changes weakly with color coherence or RT is consistent with proposals of a commitment state in the network prior to the initiation of the choice10, 45, 51. In some contexts, additional analysis has been used to argue for a threshold implemented by single neurons45, perhaps mimicking the thresholds used in behavioral models. Our analysis showing a lack of correlation between the magnitude of the choice selective signal (which is the difference in FRs for different reach directions) and coherence cannot be considered as evidence for the rise-to-threshold mechanism in PMd for decisions. Previous studies suggest that a rise-to-threshold mechanism provides a poor explanation of FRs of PMd neurons even in simple delayed-reach tasks that do not involve perceptual decisions52.
Choice selectivity is distributed in a continuum in this PMd neural population and is not well described as clusters of high and low choice selectivity (Supplementary Note 3, Supplementary Fig. 4h). One concern is that the visuomotor index we use to partition and understand our large data set of neurons is too simplistic and collapses over many key features of the data. To ensure that increased, decreased, and perimovement units were not a spurious artifact specific to the index that we developed here, we also tested if our results were consistent when applying other methods for describing a visuomotor continuum9, 33 as well as a novel technique reported by Erlich and collaborators53 for estimating a correlation between RT and neural responses (Supplementary Note 4, Supplementary Figs. 59). These results were also not explained as an effect of differences in the kinematics of the eventual arm movement (e.g., speed) or eye position (Supplementary Note 5, Supplementary Fig. 10). Finally, the conclusions did not change even when we excluded the multi-units and only analyzed the single neuron responses (Supplementary Note 6, Supplementary Fig. 13).
### PMd superficial layers show earlier choice selectivity
We next addressed the second goal of the study. We asked the following question. Are there differences between the FR dynamics of the superficial layers of PMd and the deep layers during the process of decision formation? Specifically, are the increased, decreased, and perimovement units systematically or randomly distributed as a function of cortical depth in PMd54, 55? Identifying how decision-related response properties of neurons vary as a function of anatomical and physiological properties (e.g., layer) is an important first step for building and testing cortical circuit models of decision-making14, 56, 57.
The laminar multi-contact electrodes allowed us to record simultaneously from small populations of neurons and identify their cortical depth. We used this technique and examined PSTHS/PMTHs from single sessions to identify if there was any rough organization as a function of cortical depth. Figure 4a and Supplementary Fig. 11a show units from example sessions from monkey T during this task. In both single session examples, increased units were more prevalent in the superficial electrodes, whereas the decreased and perimovement-related units were more common in the deeper electrodes. For instance, in Fig. 4a, for the units recorded from electrodes 1, 4, and 6, the index (shown with confidence intervals in the figure) is significantly positive and different from zero. In contrast, the units recorded from electrodes 10 and 11 have significantly negative indices. Finally, electrode 15 recorded a unit with an insignificant index, suggesting a perimovement unit. Figure 4b shows the visuomotor index for this session as a function of cortical depth. A similar trend is observed for the examples in Supplementary Fig. 11. Units recorded from superficial electrodes (1, 3, and 5) have positive and significant indices, whereas the units recorded from deeper electrodes (8, 11, 13, and 14) either have insignificant perimovement indices or negative indices. This separation was not perfect. Occasionally deeper electrodes recorded from units that demonstrated increases in FR before movement onset. For example, electrode 16 recorded from an increased unit. Supplementary Fig. 11b plots the visuomotor index as a function of the depth for this session. As the depth increases the visuomotor index also appears to decrease for this session.
The single session examples indicate that units at different cortical depths can have different FR modulations during decision-making and thus a laminar organization. This indication of differences in response profiles as a function of cortical depth held in the population of recordings. As one moves from superficial to deep electrodes, the index decreased as a function of depth (Fig. 4c, a cubic regression between the index averaged over 68 sessions (24 in T, 44 in O) vs. cortical depth, r 2 = 0.87, p < .001). At least, on average across both monkeys, the increased units are more likely in superficial parts of PMd, whereas decreased and perimovement units are found at relatively deeper depths in PMd. Effects of cortical depth on the visuomotor index were observed in both monkeys (Supplementary Fig. 11c). In monkey O, the decrease in the visuomotor index as a function of depth was somewhat less pronounced albeit still significant (cubic fit, monkey T: r 2 = 0.86, p < .001; monkey O: r 2 = 0.67, p < .003) and when pooled over both monkeys this effect remained significant. The same results were observed even when we used the more sophisticated correlation method developed in ref. 53 (correlation between the sign corrected correlation coefficient estimated in ref. 53 and cortical depth, Spearman’s pooled r = −0.83, p = 5.24e−5, monkey T: r = −0.45, p = 0.08, monkey O: r = −0.81, p = 3.5e−4).
Given that the FRs of the increased units have the strongest relationship to a decision variable, the preponderance of increased units in superficial electrodes of PMd naturally resulted in differences in discrimination time as a function of cortical depth. Figure 4d shows the average time of significant choice selectivity (computed over all RTs from 300–1000 ms when aligned to checkerboard cue onset) as a function of cortical depth. As cortical depth increases, the discrimination time also increases (Spearman’s r = 0.77, p = 6.3e−04, T: r = 0.67, p = 0.005, O: r = 0.64, p = 0.012, Supplementary Fig. 11d). These trends for visuomotor index and discrimination time were not observed in the posterior locations of our recording chamber (likely M1, Supplementary Note 7, Supplementary Fig. 12a).
We finally used the simultaneously recorded neurons from the U-probe recordings in PMd and performed a decoding analysis to identify if single-trial population level choice selectivity emerged earlier in the superficial compared to the deeper layers. We separated the units into two groups, superficial (electrodes 1–8) and deep (electrodes 9–16). We ensured that we restricted the classification analysis to the same trials and also equalized the number of units for both superficial and deep electrodes. We only included sessions where we had more than 10 neurons/multi-units recorded for this classification analysis to give us sufficient power and be confident in the classification results. This criterion left us with 19 sessions in monkey T and 12 sessions in monkey O. When pooled over all these sessions, average and median classification accuracy increased earlier for the superficial compared to the deep electrodes (Fig. 4e, latency for 55% accuracy, ~15.57±4.8 ms earlier, p < 8e−4, bootstrap test vs. 0, 10,000 iterations). When examined individually in each monkey, classification accuracy showed trends similar to the pooled average although it was only significant in monkey T (superficial vs. deep, Supplementary Fig. 12b, c, T: ~14.41 ms earlier, p = 3e−4, O: ~15.23 ms earlier, p = 0.15).
## Discussion
The motivation for our study was to address key unresolved questions regarding the neural circuit dynamics in PMd underlying somatomotor decisions. We had two concrete goals: (1) to investigate the temporal pattern of FRs in PMd during decisions and use various parameters and predictions of computational models of decision-making to identify putative decision-related neurons, and (2) to investigate if these putative decision-related neurons were anatomically localized as a function of cortical depth. To achieve these goals, we used a visual RT discrimination task and multi-electrode recordings to demonstrate that FR dynamics of a diverse population of PMd units covary with decision formation and movement initiation. At the highest level, our results provide additional support for observations from lesion and physiological studies in monkeys performing target selection and perceptual decision-making tasks5, 6, 8,9,10,11 and clinical examinations of stroke patients that suggested a role for PMd in selecting appropriate actions based on sensory cues7.
We found that FR dynamics in PMd exhibit substantial variation within the population during decision formation8,9,10,11. Our first result shows that this variation can be summarized by viewing neural responses as organized along a bidirectional visuomotor continuum9, 29, 31, 33, 34, 58. We emphasize that we are not just showing that PMd units can increase or decrease their FR during somatomotor decision-making. By correlating response profiles to behavioral parameters such as choice, RT, and stimulus difficulty, our second result shows that a broad class of neurons within this continuum exhibits properties consistent with a role in the decision formation process. Specifically, increased units signal choice earlier than the decreased and perimovement units and are the most consistent with the predictions of computational models such as the DDM29, 30, 45, 46, 59, 60 and the UGM10, 43, 44.
In contrast to the increased units, the perimovement units we report only modulated their FRs in an all-or-none manner starting approximately 150 ms before the initiation of movement. These FR modulations appeared after decision-related modulations in the increased units. This temporal order and differences in degree of covariation with the decision-formation process is reminiscent of FR profiles in multi-module neural network models that can simulate both the temporal integration of sensory inputs and threshold detection aspects of an RT task30, 36, 56. In one such influential multi-module neural network model36, neurons in the first module accumulate sensory evidence and show FR profiles similar to those observed for the increased units in our task. In contrast, the second module, which receives connections from the first accumulation module, demonstrates all-or-nothing changes in FR just prior to the initiation of the movement. All-or-nothing changes in this module implement the threshold for the initiation of the movement and the FRs of this second all-or-nothing module resembles the FRs of the perimovement units we find in PMd. In the original study36, these modules were considered as implemented in different brain areas with lateral intraparietal area (LIP) acting as an accumulator and the superior colliculus, which contains burst neurons that demonstrate perimovement discharges, as the threshold detection mechanism. Based on this neural network model36, one interpretation of our results is that there are multiple computational modules even within a single area, PMd, during decision-making30, 56. How decreased units fit into this framework is currently unclear. Training randomly connected recurrent neural networks and then perturbing them may help provide additional insight into the role of these different types of FR dynamics in PMd during somatomotor decisions23, 37.
The decreased neurons had tonic levels of FRs that began to reduce after the checkerboard cue onset and showed minimal choice selectivity. FRs of these neurons were similar for left and for right reaches and only diverged as a function of choice just before movement onset. These FR characteristics share some characteristics with fixation neurons documented in the frontal eye fields35 and the superior colliculus61. Fixation neurons, like the decreased neurons described here, reduce their activity before the initiation of a saccade35. They also form a small proportion of neurons described in FEF—an observation consistent with the result that decreased neurons were the least common of the broad categories (~15% of the neural population). Finally, fixation neurons are thought to be colocalized with movement-related neurons in layer 5 of the FEF—a result consistent with our report here of finding these decreased and perimovement neurons largely in the deeper electrodes of the U-probes and thus the deeper layers of PMd35.
Our primary analysis using indices that exploit features of the FRs and showing that PMd neurons are organized along a visuomotor continuum might be construed as supporting the standard practice in neuroscience which uses either preselection criteria45 or indices and metrics to divide neurons into subcategories9, 29, 62. This is not our intention. Like others25, 27, we recognize and indeed show that in an almost randomly sampled population of PMd neurons there is considerable variation in the signals carried by single neurons during decision-making. For instance, even within the broad category of increased units, there are interesting temporal features in the neuronal FR patterns (as seen in the clustering analysis shown in Supplementary Fig. 9). Said differently, the FR of every increased neuron is not easily described as a scaled version of a prototypical integrator (e.g., Fig. 4 and Supplementary Fig. 11). Across the entire PMd population, the FRs of some units are tightly associated with the visual stimulus, others more associated with movement, while yet others occupy the continuum between these extremes9, 29, 33. The visuomotor continuum we show here is one effort to provide some organizational principles for this temporal variation in PMd during a somatomotor decision.
How might one understand this variation and heterogeneity in the PMd population? The initial approach that we (and others) have used is to treat population activity in a brain region as a dynamical system23, 25, 63. In this view, the focus is on a population-level description using either supervised or unsupervised dimensionality reduction techniques. These techniques allow visualization and description of FR variance in lower dimensions23, 25, 63. This dynamical systems view is a largely agnostic approach, by which we mean that there are minimal assumptions and ad hoc sorting of neurons into subcategories is not performed. In a broad sense, the visuomotor continuum that we used here is a handcrafted dimensionality reduction technique that organizes FR variance along one axis. As we showed in the results, this handcrafted axis was tightly related to the first principal component, which explained nearly 50% of the variance. We also explored other recent methods of characterizing this neural population including the normalized latency and covariance metrics adopted in other studies of visuomotor continuums33.
Future work that analyzes trial-averaged and single-trial trajectories of these PMd FRs may provide additional insights into the underlying computational mechanisms, and additional organizing principles to subsume this temporal variation23. In parallel, we also expect that additional understanding of FR variation in PMd (and other structures) will emerge from systematic reverse engineering of the cortical circuit using techniques such as optical imaging64, laminar recordings57, 64, cell-type identification9, 57, optogenetic perturbation65, and the use of both conventional66, as well as novel anatomical techniques67. This combined computational and experimental approach will hopefully provide an understanding of perceptual decisions at multiple levels of abstraction ranging from the single-neuron to the underlying dynamical system in PMd.
We recognize that our and other demonstrations of decision-related activity in PMd are correlational and cannot be used to identify whether the decision computation itself emerges in PMd10, 11. Additional causal experiments that involve inactivation or perturbation of PMd during a decision-making task are necessary to resolve this question68 (Supplementary Note 8).
The second advance from our study was the observation that FR dynamics of PMd units are roughly organized as a function of cortical depth during perceptual decisions. The increased units, which show the strongest decision variable characteristics, were more likely in the superficial layers of PMd. The decreased and perimovement units were more likely in the deeper layers in PMd. Differences in FR dynamics in PMd as a function of cortical depth are consistent with reports of cognitive signals appearing in the superficial layers of PFC in monkeys performing visual54 and working memory tasks55. The laminar separation of these broad unit categories was not absolute. For instance, increased units were also occasionally present in the deeper layers in PMd, a result observed in other studies of primate and rodent motor cortex. FR modulations are observed during the delay period of an instructed delay task in layer 5 motor cortical neurons that project to the spinal cord20, and neurons in layer 5 of the rat motor cortex modulate their FRs during the hold, pre-movement, movement, and post-movement phases of a delayed motor task57.
Our observation of an organization as a function of cortical depth in PMd complements descriptions of a functional gradient of responses parallel to the cortical surface8. In a reach target selection task, neurons in the more rostral parts of PMd (pre-PMd/rostral PMd, closer to the arcuate sulcus) appear to have stronger covariation with the target selection process compared to the most caudal portions of PMd that appear to have more movement-related signals (closer to primary motor cortex)8. This prior suggestion of a rostrocaudal organization in PMd along with our results, which show a depth dependent organization, provides additional evidence for an anatomically organized circuit in PMd that contains signals related to somatomotor decisions. Combining magnetic resonance imaging with dense electrode recordings is a promising strategy to recover an “electroanatomical” map of this circuit in PMd and M169.
Differences in timing of choice selectivity observed in PMd as a function of cortical depth may arise from differences in connectivity between PMd and other cortical areas and connectivity within PMd itself. Reciprocal connections are present between PMd and prefrontal, parietal as well as premotor areas70 and these projections from prefrontal and pre-arcuate areas are thought to terminate in superficial layers of PMd39. Deeper layers of PMd are also thought to be connected to subcortical structures such as the spinal cord and striatal circuits71. Examinations of laminar connectivity in rodent motor cortex40 also suggest a prominent descending projection from L2/3→L5. Based on these anatomical studies, our results, and insights from multi-module computational models of decision-making36, 56, we propose a summary schematic for decision-related dynamics in PMd (Fig. 5). The framework we propose is that decision-related activity will initially appear in the increased units either as a result of anatomical inputs from other brain regions or as a result of the circuit in premotor cortex. Activity in these increased units, which are more likely in the superficial layers or other brain areas, may in turn influence the dynamics in the decreased and perimovement units, which are more likely in the deeper layers and perhaps involved in the decision threshold mechanism36. We view this schematic as a starting point for further investigations into circuit dynamics underlying decision-making13,14,15, 30, and perhaps guide the design of the next generation of anatomically guided recurrent neural network models36, 37, 56.
## Methods
### Subjects
Our experiments were conducted using two adult male macaque monkeys (Macaca mulatta; monkey T, 7 years, 14 kg; O, 11 years, 15.5 kg) trained to reach to visual targets for a juice reward. Monkeys were housed in a social vivarium with a normal day/night cycle. The protocols for our experiments were approved by the Stanford University Institutional Animal Care and Use Committee. We initially trained monkeys to come out of the cage and sit comfortably in a chair. After initial training, we performed sterile surgeries during which monkeys were implanted with head restraint holders (Crist Instruments, cylindrical head holder) and standard recording cylinders (Crist Instruments, Hagerstown, MD). Cylinders were centered over caudal PMd (+16, 15 stereotaxic coordinates) and placed surface normal to the cortex. We covered the skull within the cylinder with a thin layer of dental acrylic/palacos.
### Apparatus
Monkeys sat in a customized chair (Crist Instruments, Snyder Chair) with the head restrained via the surgical implant. The arm not used for reaching was gently restrained using a tube and a cloth sling. Experiments were controlled and data were collected under a custom computer control system (xPC target and Psychophysics Toolbox). Stimuli were displayed on an Acer HN2741 computer screen placed approximately 30 cm from the monkey. A photodetector (Thorlabs PD360A) was used to record the onset of the visual stimulus at a 1 ms resolution. Every session, we taped a small reflective hemispheral bead (11.5 mm, NDI Digital passive spheres) to the middle digit of the right hand (left hand, monkey O). The bead was taped 1 cm from the tips of the fingers, and the position of this bead was tracked optically in the infrared (60 Hz, 0.35 mm root mean square accuracy; Polaris system; Northern Digital). Eye position was tracked with an overhead infrared camera (estimated accuracy of 1°, Iscan, Burlington, MA). To get a stable eye image for the overhead infrared camera that acquires the eye image, an infrared mirror transparent to visible light was positioned at a 45° angle (facing upward) immediately in front of the nose. This mirror reflected the image of the eye in the infrared range while letting visible light pass through. A visor placed around the chair prevented the monkey from touching the infrared mirror, the juice tube or bringing the bead to his mouth.
Experiments consisted of a sequence of trials, each of which lasted a few seconds; successful trials resulted in a juice reward, unsuccessful trials in a time-out from 2–4 s. Monkeys used their unrestrained arm (monkey T used his right arm, monkey O his left arm) to reach to touch either red or green targets based on the dominant color in a central, static checkerboard cue composed of isoluminant red and green squares. For every trial, the monkey placed its unrestrained arm on a central target (diameter = 24 mm) and fixated on a small white cross (diameter = 6 mm). After ~350–400 ms had elapsed, two isoluminant colored targets appeared 100 mm to the right and left of the central target. The target configuration was randomized so that colors were not always tied to reach directions. On some trials, the target configuration was red on the left and green on the right; other trials had the opposite configuration. This manipulation allows us to examine if PMd FRs also covary with the color of the target chosen. After an additional hold period (varying from 400–900 ms), a static checkerboard cue (15 × 15 grid of squares; 225 squares in total; each square 2.5 mm × 2.5 mm) composed of isoluminant red and green squares appeared on the screen around the fixation cross (example stimuli are shown in Fig. 1d). The monkeys reached to the target whose color matched the dominant color in the central checkerboard cue. For example, when there was more green than red in the central checkerboard cue, the monkey had to choose the green target. To “choose” a target, the animals moved their hand from the central hold point and stably held a target for a short duration (minimum of 200 ms). The task was an RT paradigm, and thus the monkeys were free to initiate their reach whenever they felt there was sufficient evidence accrued to inform their choices. We did not impose a delayed feedback procedure in this task. That is, if the correct target was chosen, a juice reward was provided to the monkey immediately after the monkeys chose the target45.
We parameterized the checkerboard cue at several different levels from almost fully red to almost fully green. We used 14 levels of red (ranging from 11 red squares to 214 red squares) in the central checkerboard cue. Each level of red had a complementary green level (e.g., 214 R, 11 G; and 214 G, 11 R squares). We defined seven levels of color coherence (defined as C = 100×|R − G|/(R + G), 4–90%). The corresponding signed coherence (SC) was estimated without taking the absolute value of the difference (SC = 100×(R − G)/(R + G)). For monkey T, we used a uniform distribution of hold period durations between the onset of the targets and the onset of the checkerboard cue. Monkey O attempted to anticipate the checkerboard cue onset. To minimize this anticipation we used an exponential hold period duration (400–800 ms) between the onset of the targets and the onset of the checkerboard cue to reduce predictability.
### Training
We used the following operant conditioning protocol to train our animals. First, the animal was rewarded for arm movements toward the screen and learnt to take pieces of fruit on the screen. Once the animal acquired the association between reaching and reward, the animal was conditioned to touch a central target for a juice reward. The position, as well as the color of this target, was then randomized as the monkey learned to touch targets at different locations on the screen. We then adopted a design in which the monkey first held the central hold for a brief period, and then a checkerboard cue, which was nearly 100% red or 100% green, appeared for 400–600 ms and finally the two targets appeared. The monkey received a reward for making a reach to the color of the target that matched the checkerboard cue. Two-target “Decision” blocks were interleaved with single target blocks to reinforce the association between checkerboard color and the correct target. After a couple of weeks of training with this interleaved paradigm, the animal reliably reached to the target matching the color of the central checkerboard cue. We then switched the paradigm around by adopting a design in which the targets appeared before the checkerboard cue onset. We initially trained on holding periods (where the monkeys view targets) from 300 to 1800 ms. We trained the animal to maintain the hold on the center until the checkerboard cue appeared by providing small amounts of juice. When the animal reliably avoided breaking central hold during the holding period, we stopped providing small amounts of juice. In subsequent weeks, we introduced more difficult checkerboard cues to the animal while reducing the maximal holding period to 900 ms. We then encouraged the animal to perform this discrimination as accurately and as fast as possible while discouraging impulsivity by adopting timeouts.
### Electrophysiological recordings
Stereotactic coordinates, known response properties of PMd and M1, and neural responses to muscle palpation served as our guides for electrophysiological recordings. We placed the chambers surface normal to the cortex to align with the skull of the monkey and recordings were performed perpendicular to the surface of the brain. Recordings were made anterior to the central sulcus, lateral to the spur of the arcuate sulcus, and lateral to the precentral dimple. For both monkeys, we confirmed our estimate of the upper and lower arm representation by repeated palpation at a large number of sites to identify muscle groups associated with the sites. Monkey T used his right arm (O used his left arm) to perform tasks. Recordings were performed in PMd and M1 contralateral to the arm used by the monkey.
A subset of the electrophysiological recording was performed using traditional single electrode recording techniques. Briefly, we made small burr holes in the skull using handheld drills. We then used a Narishige drive with a blunt guide tube placed in firm contact with the dura. Recordings were obtained using FHC electrodes to penetrate the overlying dura. Every effort was made to isolate single units during the recordings with FHC electrodes.
We performed linear multi-contact electrode (U-probe) recordings in the same manner as single electrode recordings with some minor modifications. We used a slightly sharpened guide tube to provide more purchase on the dura. We also periodically scraped away under anesthesia any overlying tissue on the Dura. Sharp guide tubes and scraping away dura greatly facilitated penetration of the U-probe. We typically penetrated the brain at very slow rates (~2–5 μm/s). Once we felt we had a reasonable sample population of neurons, potentially spanning different cortical layers, we stopped and waited for 45–60 min for the neuronal responses to stabilize. The experiments then progressed as usual. We used 180-μm thick 16-electrode U-probes with an inter-electrode spacing of 150 μm; electrode contacts were ~100 Kohm in impedance.
We attempted to minimize the variability in U-probe placement on a session-by-session basis so that we could average across sessions for the analyses in Fig. 4. Our approach was to place the U-probe so that the most superficial electrodes (electrodes 1, 2 on the 16 channel probe) were able to record multi-unit spiking activity. Any further movement of the electrode upwards resulted in the spiking activity disappearing and a change in the overall activity pattern of the electrode (suppression of overall LFP amplitudes). Similarly, driving the electrodes deeper resulted in multiphasic extracellular waveforms and also a change in auditory markers which were characterized by decreases in overall signal intensity and frequency content. Both markers suggested that the electrode entered white matter. Recording yields and this careful electrode placement were in general better in monkey T (average of ~16 units per session) than monkey O (average of ~9 units per session). We utilized these physiological markers as a guide to place electrodes and thus minimize variability in electrode placement on a session-by-session basis. Importantly, the variability in placement would act against our findings of depth-related differences in activity (Fig. 4). Random placement of U-probes on a day-to-day basis would flatten out the average visuomotor index and dilute or entirely remove significant differences in the discrimination time differences between superficial and deep electrodes.
The technique necessitated a careful watch over the electrode while lowering to ensure that it did not bend, break at the tip or excessively dimple the dura. We, therefore, were unable to use a grid system to precisely localize the location of the U-probes on different days and to provide a map of how laminar profiles change in the rostrocaudal direction. However, we recorded a small subset of units in a more posterior location in the recording chamber (putatively M1, n = 12 sessions, 95 units) that we also report in Supplementary Fig. 12a in this manuscript.
### Description of neural populations included in our database
We report here the activity of 996 units recorded in PMd of two monkeys while they performed the task (546 units in T, 450 units in O; single neurons and multi-units which responded during any epoch in the task). The majority of the units in the database were well-isolated single neurons, and as per convention, we term them single neurons. Some of these single neurons were collected using high impedance (i.e., small electrode contact area, >6 MΩ) sharp FHC electrodes. When using these electrodes, every attempt was made to isolate and track single neurons and to stably record from them.
We also had excellent success recording from isolated single neurons from the U-probes. The U-probes are low impedance electrodes (~100 kΩ) with a small contact area and were thus excellent for isolation of single units. We used a conservative threshold to maximize the number of clearly defined waveforms and minimize contamination from spurious non-neuronal events. Online, we used the hoops provided by the software client for our Cerebus system (BlackRock MicroSystems) to delineate single neurons after the electrodes had been placed in the cortex for at least half an hour to 45 min. Every time a spike was detected by the threshold method, a 1.6 ms snippet was stored and used for subsequent evaluation of the clusters as well as adjustments needed for spike sorting. Recordings from some electrodes in the U-probes consisted of mixtures of 2 or more neurons well separated from the noise and from one another. In a majority of these cases, the waveforms were clearly separated, and these were labeled as single units. We verified these separations visually by viewing the waveforms in a principal component space using custom code written in MATLAB and adjusted the clusters that were isolated online using the MatClust MATLAB-based clustering tool that allows the drawing of polygons to label clusters or the Plexon Offline Sorter. Finally, we had two other types of recordings that we labeled as multi-units. The first category consisted of the multi neuron mixtures that were not separable using a principal components method. The second rarer class consisted of recordings with waveforms only weakly separated from the noise. Both of these types of units were classed as multi-units. We included all of these different units in our analysis here.
To reduce the subjectivity in our assessments we used the number of ISI violations (after clustering and sorting) to distinguish between single and multi-units. We labeled a unit as a single neuron if the percentage of ISI violations (refractory period of <=2 ms) was less than 1.5% and a unit with ISI violations exceeding 1.5% as a multi-unit. Using this criterion, 801 of the 996 PMd units reported here are identified as single neurons (384 from O, 417 from T, mean ISI violation = 0.43%, ~0.13 additional spikes per trial). Similarly, 195 out of 996 are classified as multi-units (129 from T, 66 from O, mean ISI violation = 3.36%, ~1.4 additional spikes per trial).
All main claims made in the paper were unchanged when only restricting the analysis to single neurons (Supplementary Note 6, Supplementary Fig. 13).
### General notes on physiological analyses
Electrophysiological characteristics were similar in both monkeys, so we pooled data from both monkeys for more power as well as clarity. PMd units were tuned to different reach directions even when recordings were performed in the hemisphere contralateral to the arm. For example, some units recorded in the left hemisphere would be tuned for reaches to left targets; other units were tuned for reaches to right targets. We developed a tuning measure by testing if the FR in the −150 ms to move onset +50 ms time window was significantly different for left vs. right reaches. According to this metric (555/996 units (55.72%) were tuned to reaches to the left, 441/996 (44.28%) were tuned to reaches to the right). Thus, even within the same hemisphere, units were almost equally likely to be tuned to left reach or right reaches (although there is a slight tendency to be more tuned for left reaches overall). Tuning to both left and right reaches was often present within the same U-probe penetration. We, therefore, did not seek to place reach targets for each unit in the preferred and anti-preferred directions. Instead, we fixed the spatial locations of the two targets to the left and right of the central hand target and randomized the target color.
PMd units often switched their tuning preference across time within a trial. In such conditions, as suggested previously26, we computed the mean absolute difference between FR for left vs. right reaches and plotted it as a function of time. This subtraction provided a “choice selectivity” signal that depends on color coherence (or RT). This is the signal plotted in Fig. 3b, d, g when aligned to checkerboard cue and movement onset. The FR in the hold period is subtracted from the choice selectivity signal for each unit before averaging.
We also occasionally observed in some PMd units a covariation between the hold period FR and overall RT. These effects will be the subject of another study and will not be discussed in this manuscript.
### Trials used in single and population unit PSTHs
For averaging, we included both correct and incorrect trials and sorted them by the choice of the monkey. However, we excluded a small proportion of change of mind trials (~2–3% of trials) from averages. We chose to do this because, for the change of mind trials, the monkey would initiate in one direction and then change the direction mid-reach. The reaches were thus multiphasic in nature and did not possess a clear initial reach direction making choice attribution for these trials ambiguous. Including them in the averages inflated the variance of FR around movement onset. So we excluded this small proportion of explicit change of mind trials from the averages reported in the Figs. 2, 3, and 4 and the Supplementary Figures. We expect to report the behavioral and neural correlates of explicit change of mind trials elsewhere.
On average across all units, PSTHs/PMTHs rates were estimated using 1194 trials per unit (comprising all conditions and choices) for monkey T (5th and 95th percentiles: 242, 2182 trials) and using 928 trials per unit for monkey O (5th and 95th percentiles: 400, 1644 trials).
For PSTH plots and the analyses shown in Figs. 24, trials were separated according to color coherences (seven different color coherences) or by RT (using different overlapping bins 325–425 ms, 350–450 ms … 500–1000 ms). The use of these overlapping bins allows us to better visualize organization with RT. This gave us several curves for each of the plots when sorted by RT.
### General analysis notes
For PSTHs, we used large numbers of trials as well as several units to compute our statistical tests (>100 units typically for comparisons) and assumed normality because of the central limit theorem. To be confident that potential non-Gaussian nature of the data did not impact our results, we compared medians of these distributions and where appropriate used shuffling and permutation to perform comparisons. No blinding or randomization of animals was performed in this study. All tests were two-tailed unless noted.
### Effects of coherence on accuracy and RT
We analyzed the behavior using two different methods. Our first approach was to fit psychometric curves, which describe how discrimination accuracy changed as a function of coherence. In the same approach, to test if RT changed with coherence, we used a regression between RT and log coherence as in ref. 45. Our second approach was to jointly fit both accuracy and RT using a DDM, which provides descriptions of choice and RT distributions42.
For the analysis of the behavior, we used the same 75 sessions for monkey T (128,989 trials) and 66 sessions for monkey O (108,344 trials) from which we report electrophysiological data. Fits to psychometric curves and RT regressions were performed on a per-session basis and then averaged over sessions. The behavior for an average session was estimated from ~1500 trials. RT was estimated for each session by including both correct and incorrect trials for each SC.
### Psychometric curves for accuracy
For every experiment, we estimated the monkey’s sensitivity to the checkerboard cue by estimating the probability (p) of a correct choice as a function of the color coherence of the checkerboard cue (C). We fit this accuracy function using a Weibull cumulative distribution function:
$p ( c ) =1-0.5 e - c α γ .$
The discrimination threshold α is the color coherence level at which the monkey would make 81.6% correct choices. The second parameter, γ, describes the slope of the psychometric function. The mean alpha parameter across sessions is used as the threshold. We fit threshold and slope parameters on a session-by-session basis and averaged the estimates. The mean and standard deviation of the threshold estimates are reported in Fig. 1d. R 2 values from the fit are provided in the text.
### RT vs. coherence
To examine if RT changed with coherence, we adopted the procedure from ref. 45 and used a linear regression between RT and log coherence.
$RT c =Intercept+ a c log e ( c ) .$
We fit this regression model and report the slope as well as the R 2 values from the fit. a c is the slope of the regression. We complemented this simple characterization of how RT changed with coherence and fit both choice behavior and RT using a DDM or UGM, which we describe in the following section (Supplementary Note 1, Supplementary Figs. 12).
### Fitting behavior using a DDM
We first fit the behavioral observations of discrimination accuracy and RT with a DDM that proposes the integration of momentary evidence (e.g., noisy spike trains in sensory areas in response to the red squares of the checkerboard cue) to one of two predefined bounds (Supplementary Fig. 1a). Even though our stimulus is a static checkerboard cue, the spike trains in response to static stimuli are time varying in nature and DDMs have been used in other tasks with static stimuli and shown to capture key features of the discrimination behavior42.
A succinct modeling description is provided here; detailed descriptions of the model are available elsewhere42. The DDM is mathematically equivalent to the one-dimensional movement of a particle undergoing Brownian motion to one of two absorbing boundaries. The model provides a quantitative account of both the choice (which boundary was reached) and the decision time (when the boundary was reached) on each trial. The DDM model uses the formulation of a putative decision variable (V) that depends on the SC of the checkerboard cue according to the stochastic differential equation:
$dV=μdt+dW.$
A decision occurs when V reaches a decision bound (A or 0, corresponding to a red choice or a green choice). The quantity μdt is the momentary evidence (termed drift rate) and is distributed as a random variable with a Gaussian distribution (N (μ, 1)). The mean of this momentary evidence distribution (μ) is different for each condition. dW refers to Gaussian noise which is added at each time step.
We did not want to make assumptions about how stimulus strength mapped to the mean of the momentary evidence. Moreover, we wanted to fit full RT distributions and not just the mean RTs because very different models can predict the same mean RT42. For these reasons, we chose to use the formulation of the DDM for the decision time with the following parameters: slope of the diffusion process for each color coherence level (v), threshold separation (A), and starting point (z)60. We also included variability in the drift rate (s v) but not the starting point. Overall both monkeys showed very little red-green bias.
The diffusion model only provides an estimate of the decision time and does not incorporate non-decision times, such as other sensory encoding and motor preparation latencies. The common approach is to consider decision time and other residual times as independent additive contributions to the total RT. Therefore, mean RT for every condition is the sum of the mean decision time and the non-decision time (t 0). We also assumed trial-to-trial variability in this non-decision time parameter (s t0). This improved overall RT fits but tended to increase the mean non-decision time (fits with this parameter often led to a 40–60 ms increase in the mean non-decision time, and we report this number in the main text). Our decision times are therefore better understood as a lower bound. We chose to report fits with this parameter included in the main text because they provided the best fits to the overall RT distribution as measured by the χ 2 goodness of fit. The goodness of fits for other comparison models that excluded these parameters are shown in Supplementary Table 1. The parameters from the best fit DDM are shown in Supplementary Tables 2 and 3.
Finally, non-decision times are often assumed to be equal for both choices. However, this assumption may not apply if other cognitive factors are involved. For example, if one of the response types occurs more frequently, or is perceived to be more likely in a given situation, it might result in a faster motor response42. Overall, the fits to the RT data shown in Supplementary Fig. 1b–c were better when including the static parameter (d) which shifts the non-decision time for one choice by this amount. This use of variable non-decision times for different responses is often used in decision-making studies to explain RT.
Model fits were performed using the fast-dm toolbox with minimization of the χ 2 criterion which is robust with large numbers of trials42. For input to the model, we included all trials pooled over all sessions (correct as well as incorrect) and labeled it with the choice the monkey made as well as RT (128,989 trials for T and 108,344 trials for O). The χ 2 goodness of fit for the DDM from this best fit model can be found in Supplementary Table 1. The parameters from this best fit model are provided in Supplementary Table 2.
Plots of decision times in Supplementary Fig. 1d were generated by subtracting the estimates of non-decision times from the mean and 95th percentiles of the RT distributions. The 95th percentile of the RT distribution provides an upper bound on the decision times used by the monkey and facilitates comparison to the data from variable duration tasks. For our monkeys, approximately 35–40% of trials lie between the mean and the 95th percentile of RTs.
### Comparing fits from the UGM and the DDM
We also compared fits between a DDM and an UGM44, 48, 49. For this comparison, we used a toolbox developed as part of a recent study that investigated the differences between these two models47. This toolbox is available on request from Dr. Guy Hawkins. The models being compared here are a DDM with variability in drift rate44, 47 and an UGM that incorporates variability in drift rate and an urgency signal44. The time constant for the UGM was chosen to be 100 ms44. An extensive description of these models is provided in ref. 47 and here we only briefly describe the models.
We used the same basic framework from refs. 44, 47 to implement our DDMs and UGMs. The first variant of the UGM was implemented by an urgency function that was linear in time (U(t) = b × t, b = 1) and included a low pass filter with a time constant of 100 ms44, 47. Further details of model implementation are provided in ref. 47. We assumed variability in the drift rate for both the DDM and the UGM. Both models have equal numbers of estimated parameters, and thus goodness of fit can be compared without any penalization for model complexity. The parameters estimated for the UGM (DDM) and the parameters kept constant are reported in the Supplementary Table 4 and replicated from ref. 47. We also explored a second variant of the UGM that included an additional intercept term (U(t) = a + b × t, with b = 1). The inclusion of this additional intercept parameter allows the UGM to model fast RTs observed in discrimination tasks.
The models were implemented in a combination of R and C++. To ensure that we were correctly performing the model fitting, we first fit the behavior of the monkeys from Roitman and Shadlen45 and verified that the QMPE statistics72 were near identical (small variations occur due to the random number generators in different iterations) to the statistics reported for this data set in ref. 47. We then applied this analysis to the behavioral data collected in this study.
### Peristimulus/perimovement time histograms (PSTH/PMTH)
For each unit, we calculated mean FR over trials to define a PSTH/PMTH over time. Trials were aligned to several events such as checkerboard cue onset, target onset, and movement. Spike trains for each trial were binned in 1 ms bins, convolved with a causal boxcar and averaged over trials depending on condition identities. For single examples shown in Figs. 2, 4 and Supplementary Fig. 4, we used a 75 ms causal boxcar. For population data, we convolved the spike trains with a 50 ms causal boxcar. When aligned to checkerboard cue onset, for both single examples as well as population FR plots, we removed spikes starting 100 ms before movement onset until the end of the trial and assigned them to not a number (NaN). Similarly, when aligned to movement onset, we used the RT and set all spikes before the onset of the checkerboard to NaN. We then averaged across the trials and reported the mean and standard error across trials (for single examples) and neurons (population level).
### Visuomotor index for separation into unit classes
We partitioned our unit database into a continuum of unit classes by developing a visuomotor index based on the observation that before movement onset there are systematic FR modulations in some units that covary with RT. We exploited the existence/absence as well as the direction (increases or decreases) of this main effect of RT to define the index.
The index is estimated as the trial-by-trial correlation between the RT and time averaged FR in the −600 to −200 ms epoch before movement onset. We only included FR until 200 ms before movement based on two observations. First, most perimovement units often began modulating their responses around that time. Second, when using the regression analysis, the number of units with RT as a significant predictor at −150 to −200 ms before movement onset began to approach chance levels (Supplementary Fig. 10a).
Before computing this correlation coefficient, we first subtracted the hold period FR (from the 200 ms epoch before checkerboard cue onset). Then for each trial, to ensure that FRs before checkerboard cue onset do not bias the index, we set spikes before the onset of the checkerboard relative to movement onset to be NaN. We then averaged the FR (across time) from −600 to −200 ms for each trial and then correlated this quantity to the RT. For n trials of one unit, we had n RTs and n time-averaged FRs. Both the left and right choices were included in the computation of the correlation. The correlation coefficient was significant if the 90% confidence intervals (p < .05, for each tail) estimated by bootstrapping did not overlap with zero. Changing confidence intervals to 95% did not result in a qualitative change in the results.
The perimovement units were defined as the ones with insignificant indices. We were concerned that some of the decreased units, which had smaller values of the index, could be mistakenly classified as perimovement units and vice versa. To address this concern, we used the Bayes Factor method that provides the ratio of the likelihood of two competing hypotheses or models73 and is typically interpreted as evidence for one model over the other. In our case the ratio is between classifying a unit as decreased (or increased, H1) vs. perimovement (H0)73. A large value of Bayes Factor suggests that model H1 is more likely than the model H0 and in our case would provide strong support that the unit is correctly classified as increased or decreased. In contrast, a low Bayes Factor would suggest strong evidence for H0 and support the classification of the unit as perimovement in nature. We examined the Bayes Factors computed for the different broad unit categories and found that the Bayes Factors for the units classified as perimovement based on the visuomotor index were very low suggesting that they were correctly classified (Supplementary Fig. 3b). The Bayes Factors computed for perimovement units also had very little overlap with Bayes Factors for both the decreased and increased units (Supplementary Fig. 3b)73. This suggests that there was minimal contamination of the perimovement group by the decreased units and vice versa.
### Slope analyses
For every level of color coherence, we regressed the 150–350 ms epoch of the boxcar smoothed choice selectivity signal (e.g., Fig. 3b) to time to estimate the rate at which the choice selectivity increased in this epoch (plotted in Fig. 3c for each color coherence level). Using 150–250 ms after checkerboard cue onset (which would suggest an even shorter average decision time of 100 ms) did not change our conclusions.
### Population timing analyses
We identified the time at which the population activity significantly changed as a function of the choice of the monkey by using a paired t-test comparing responses during the epoch after checkerboard cue onset to the responses of the same neurons during the hold period (−500 ms to 0 before checkerboard cue onset). This latency for choice selectivity is termed discrimination time and is plotted in Fig. 3e. We chose a paired t-test for this analysis because the decreased neurons did not have a significant choice latency with more stringent measures. The discrimination time was identified as the first time point after checkerboard cue onset for which at least 50 ms was significantly different from hold period FR (paired t-test vs. hold period FR, p < .05 false discovery rate corrected). When aligned to checkerboard cue onset FR from 100 ms before movement onset onward were set to NaN. To derive error bars around this estimate of the time at which significant choice selectivity emerged, we bootstrapped trials for each unit to come up with 50 surrogate distributions of FRs for each unit. We then reran the timing analyses and used the standard deviation of the bootstrap distribution to estimate the error in our estimate of the discrimination time. Alternative methods by bootstrapping over units yielded similar results.
### Estimate of the discrimination time for each single neuron
We also performed the same analysis identifying the discrimination time on a neuron-by-neuron basis. We used the 95th percentile of the bootstrap estimates of baseline FRs for each neuron to identify the time at which the neuron demonstrated significant choice selectivity. The FRs should be significantly different as a function of choice for at least 50 ms after this first identified time to be included as an estimate of a time of significant choice selectivity. The analysis was performed aligned to both checkerboard cue onset and movement onset. Data are shown aligned to checkerboard cue onset in Supplementary Fig. 4g–i.
We computed the slope of this discrimination latency vs. RT when aligned to both checkerboard cue onset and movement onset and used this to perform the analysis described in ref. 9 and in Supplementary Fig. 7b. The mean slopes aligned to checkerboard cue onset and aligned to movement onset are shown in Supplementary Fig. 7c, d, respectively.
### Neural response latency (λ) and covariation with RT (β)
We also used the method developed in DiCarlo and Maunsell33 to characterize our neural population. This method helps determine the response onset (termed Neuronal Latency or NL, λ) and is thought to estimate where in the “processing chain” the neurons might operate. Smaller values of λ suggest that the neuron is more sensory (visual in our case) and larger values of λ signify that the neuron is closer to the motor output.
The method also provides an estimate of the covariance between the neuronal latency and the RT (β). β is unitless and ranges from near zero for neurons whose FRs have no correlation with RT (neurons involved in the early stage of information processing) to near unity for neurons with activity closely correlated with the timing of the behavioral response (the RT). Note that λ and β do not distinguish whether the neuron increased or decreased it FR after checkerboard cue onset. Code and a Jupyter notebook explaining this technique are available at https://github.com/mailchand/ephysutils.
### Unsupervised clustering of PMd FRs
Another analysis we performed was inspired by a recent study that used a clustering technique to suggest the presence of diversity in neural responses in LIP during a perceptual decision-making task26. Using the tuning metric measured around movement onset (described above), we first identified for each neuron a FR averaged over all trials in the preferred direction and a FR over all trials for the non-preferred direction aligned to the checkerboard cue onset. We included 100 ms before checkerboard cue onset and 600 ms after checkerboard cue onset in our averages. We then concatenated these FRs and then performed a k-means clustering analysis.
To decide on k, the number of clusters to show, we used the gap statistic method74. The gap statistic quantifies the change in within-cluster dispersion with that expected under an appropriate reference null distribution74. The number of clusters is chosen to be the minimal value of k that involves the largest separation between the true distribution and the reference distribution. With very small numbers of clusters, the difference between the within group dispersion and the reference distribution is low. At some point, this difference increases and roughly saturates. The first such value is a good indication of a reasonable clustering solution for the data74.
### Principal component analysis (PCA) of PMd FRs
We also used an alternative unsupervised method, PCA to examine the FR variance recorded in our neural population. The FRs of all units were first “softmax” normalized by dividing the FR for each unit across all conditions by the range of the FR for the neuron across all conditions for the unit. Softmax normalization reduced the bias induced by high FR units. This ensures that each unit has roughly the same overall variability across conditions. Dimensionality reduction was performed on a FR matrix of dimension (units (n) × ∑t i), where n is the number of recorded units, and t i denotes the number of time points for the ith condition over time. We performed PCA on this space to reduce these dimensions to k × ∑c i × t i, where k represents the dimensions across which the most neural variance was explained.
PCA makes few assumptions about the underlying structure of the data, simply revealing dimensions that explain a large percentage of the variance. PCA does not guarantee that the dimensions extracted are meaningful. However, often they can align quite well with behavioral variables of interest as seen in Supplementary Fig. 8. Other methods such as factor analysis can be used. However, they often require additional assumptions about the data. Several studies have employed PCA as a dimensionality reduction technique for trial-averaged data63. The RT nature of the task precluded us from using techniques such as targeted dimensionality reduction23.
Analysis of the loading matrices from PCA provided us with additional credence to the claim that there are broad unit populations in PMd that demonstrate a specific relationship to the decision formation process. We tested if the distribution of loadings in this two-dimensional space was consistent with a uniform random distribution by using a χ 2 test that assumes an equal number of neurons in each octant or by using the more sophisticated PAIRS (Projection Angle Index of Response Similarity) test developed in a recent study27.
The PAIRS test compares each neurons loading on the first two (or more) principal components with its “nearest neighbors” in the principal component space by computing the angle between the vectors. If there is a nonuniformity in the loading in this space, then the distribution of angles would not be uniform, and a median of this distribution is compared to the median from 10,000 simulated data sets from a two-dimensional Gaussian distribution. The simulated data sets are used to estimate a p-value for this statistic.
### Estimating correlation between RT and neuronal responses
We also adopted an analysis method developed for heterogeneous neural populations by Erlich and collaborators53. This method measures the correlations between RT and neuronal responses by using an alignment algorithm to find a temporal offset for each trial that would best align that trial’s FR with the average over all the other trials.
The algorithm first computes a trial-averaged FR aligned to a marker of interest (in our case movement onset). The FR of every trial is then cross-correlated with the trial-averaged signal, and the location of the peak of the cross-correlation is measured as the offset needed to align the trial to the average. The trial was then shifted accordingly, and the trial-averaged FR was recomputed. This process was then repeated until the variance of the trial-average signal converged, typically within less than 10 iterations for a criterion of 1% variance. The final output of this alignment procedure was an offset that was then correlated to RT.
When aligned to movement onset, the expectation is that the perimovement units would require minimal shifts and would thus show the lowest correlation between the offset time and RT. In contrast, the increased and decreased units would show a larger degree of shift, and this would emerge as a significant correlation. Because the analysis was performed aligned to movement onset, longer RT trials would require a positive shift (to match the average). The shorter RT trials would need a negative shift resulting in a significant positive correlation between RT and offsets estimated from the algorithm.
One limitation of this metric is that it does not provide any indication of whether the neuron was decreasing its FR during the decision-formation process or increasing its FR. To estimate the direction of FR change, we examined the FR in the 100 ms epoch before movement onset and compared it to the FR in a reference epoch (−800 to −700 ms before movement onset). If the perimovement period FR was lower than the reference epoch FR, we multiplied the sign of the correlation coefficient estimate from the offset method by −1. We then correlated this modified coefficient to the visuomotor index we proposed.
### Classification analysis
We also examined if the superficial layers (electrodes 1–8) of PMd signaled choice earlier than the deeper layers (electrodes 9–16) by using linear classifiers. A separate naïve Bayes classifier (from classify in MATLAB) with 10-fold cross-validation (over trials) was used for the superficial and the deep layers. For classification analysis, we only included sessions where we had more than 10 units recorded for this classification analysis to give us sufficient power and be confident in the classification results. This criterion left us with 19 sessions in monkey T and 12 sessions in monkey O. To reduce the bias in the classification results we equalized the number of units for each classifier to be the same. When either the superficial or deep had more units, we randomly selected from the greater of the two pools, a number of units that was equal to the number of units in the other pool. We repeated this selection 10 times and then averaged over both folds (10 folds) and selections. All RTs from 300 to 1000 ms were included in this analysis. Input to the classifier was 50 ms boxcar spike counts and retrained on each time point. We chose a 2 ms spacing between adjacent time points for the classifier.
To estimate the reduction in discrimination time for the superficial compared to the deep layers, we used a threshold of 55% accuracy and estimated the first time at which the accuracy increased above this value for the superficial and deep layers. We then defined the benefit as t Deept Superficial and used it as our estimate of the discrimination time delay between the superficial vs. deep layers. We also estimated through bootstrapping (10,000 repeats) by randomly drawing with replacement from this population of sessions and obtained a distribution of these delays. We report the mean of this randomly sampled distribution as our estimate of the reduction in discrimination time. To estimate if this reduction in discrimination time was significant, we used the bootstrapped distribution and estimated the fraction of delays that were lower than 0 and report this as the p-value for the reduction in discrimination time.
### Control: regression analysis
We assumed that FR at each time point is a linear combination of several predictors such as RT, reach direction choice, the color of the target chosen, color coherence, interaction terms between these predictors, as well as several potential nuisance variables related to the arm and eye movements. The regression equation for the ith trial when aligned to movement onset was as follows:
$r i t = β 0 + β coh × coh i + β choice × choice i + β color × Chosen Color i + β R T × R T i + β handX × X handX,i t + β handY × X handY,i t + β EyeX × E y e X i t + β EyeY × EyeY i t + β s p e e d × H a n d S p e e d i + β R T × c o h e r e n c e × R T i × c o h i + β R T × c h o i c e × R T i × C h o i c e i .$
The different predictors were first Z-scored and then input into the regression. The predictor variables are defined as follows:
$β 0 - I n t e r c e p t t e r m c o h i - C o h e r e n c e o n t h e i t h t r i a l C h o i c e i - C h o i c e o f t h e m o n k e y o n t h e i t h t r i a l L , R ( - 1 , 1 ) C h o s e n C o l o r i - T h e c o l o r o f t h e t a r g e t t o u c h e d b y t h e m o n k e y o n t h e i t h t r i a l ( - 1 , 1 ) R T i - R e a c t i o n t i m e f o r t h e t r i a l X H a n d X , i t - H a n d p o s i t i o n i n X f o r i t h t r i a l a n d a s a f u n c t i o n o f t i m e X H a n d Y , i t - H a n d p o s i t i o n i n Y f o r i t h t r i a l a n d a s a f u n c t i o n o f t i m e X E y e X , i t - E y e p o s i t i o n i n X f o r i t h t r i a l a n d a s a f u n c t i o n o f t i m e X E y e Y , i t - E y e p o s i t i o n i n Y f o r i t h t r i a l a n d a s a f u n c t i o n o f t i m e H a n d S p e e d i - S p e e d o f t h e r e a c h o n t h e i t h t r i a l$
We used 95% confidence intervals at each time point to estimate if the betas for predictor variables were significantly different from chance. We used this to generate plots of the number of significant units as a function of time aligned to movement onset (Supplementary Fig. 10a, b).
### Code availability
All analyses were performed using custom code written in MATLAB to process spike trains and perform statistical analyses. Code used in this paper is available on request. Some of this code is already available in github repositories for which links are provided in the paper.
### Data availability
All data examined in the paper are available from us on request.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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## Acknowledgements
We would like to thank Dr. Guy Hawkins for guidance and R code for fitting Urgency Gating and Drift Diffusion Models and Prof. Jeffrey Erlich for assistance and code for implementing analyses examining correlations between RT and FRs53 (code available at https://github.com/erlichlab/elutils). We would also like to thank Ms. Megan Wang and other members of the Shenoy Lab for helpful discussions and comments on earlier versions of this paper. The views and comments from three anonymous reviewers greatly improved the paper. C.C. was supported by an NIH/NINDS K99/R00 grant NS092972. D.P. was supported by the Champalimaud Foundation, Portugal, and Howard Hughes Medical Institute. B.N. was supported by the Howard Hughes Medical Institute. K.V.S. was supported by the following: Christopher and Dana Reeve Paralysis Foundation, Burroughs Welcome Fund Career Awards in the Biomedical Sciences, Defense Advanced Research Projects Agency Reorganization and Plasticity to Accelerate Injury Recovery N66001-10-C-2010, US National Institutes of Health Institute of Neurological Disorders and Stroke Transformative Research Award R01NS076460, US National Institutes of Health Director’s Pioneer Award 8DP1HD075623-04, US National Institutes of Health Director’s Transformative Research Award (TR01) from the NIMH #5R01MH09964703, Defense Advanced Research Projects Agency NeuroFAST award from BTO #W911NF-14-2-0013, the Simons Foundation, and the Howard Hughes Medical Institute.
## Author information
### Affiliations
1. #### Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
• Chandramouli Chandrasekaran
• & Krishna V. Shenoy
2. #### Department of Neurobiology, Stanford University, Stanford, CA, 94305, USA
• Diogo Peixoto
• , William T. Newsome
• & Krishna V. Shenoy
3. #### Champalimaud Neuroscience Programme, Avenida Brasília, Lisbon, 1400-038, Portugal
• Diogo Peixoto
4. #### Howard Hughes Medical Institute, Stanford University, Stanford, CA, 94305, USA
• William T. Newsome
• & Krishna V. Shenoy
5. #### Stanford Neurosciences Institute, Stanford University, Stanford, CA, 94305, USA
• William T. Newsome
• & Krishna V. Shenoy
6. #### Department of Bioengineering, Stanford University, Stanford, CA, 94305, USA
• Krishna V. Shenoy
7. #### Bio-X Program, Stanford University, Stanford, CA, 94305, USA
• Krishna V. Shenoy
### Contributions
All authors contributed extensively to the experimental design and analyses presented in this study. C.C. trained animals, performed all electrophysiological experiments, analyses, and wrote initial drafts of the paper. All authors contributed analytical insights and commented on statistical tests, discussed the results and implications, participated in interpretation, responded to criticisms, and helped finalize the drafts of the paper.
### Competing interests
The authors declare no competing financial interests.
### Corresponding authors
Correspondence to Chandramouli Chandrasekaran or Krishna V. Shenoy. |
# How to this solve this differential equation?
$y'=\dfrac{1}{x^2+y^2}$ where $y=f(x)$ and $x$ lies in $[1,\infty)$ and $f(1)=1$ and it is is differentiable in that interval
I don't know how to even proceed in this problem.
Even the range of $y$ is sufficient
• A cheap observation: $f(x)$ is an increasing concave down function. – iamvegan Aug 21 '16 at 15:08
• @iamvegan Since when vegan people are smart? – Von Neumann Aug 21 '16 at 15:47
• @MathMan: Certainly you are not asked to solve the ODE. Read carefully the wording of the problem. It is not necessary to solve the ODE to answer. By the way, the analytical solving is possible but of height level: The $x(y)$ ODE is a Riccati equation involving Bessel functions in the solution. But you don't need it. – JJacquelin Aug 21 '16 at 15:52
• @JJacquelin can i get its maximum value.Even that can be sufficient – MathMan Aug 21 '16 at 16:41
• @iamvegan can u giveits maximum value? – MathMan Aug 21 '16 at 16:41
What is wanted isn't clear. May be this :
$y'=\frac{1}{x^2+y^2}>0$ implies that $y(x)$ is increasing.
$y(1)=1$ hence $y(x)>1$ . As a consequence :
$$y'=\frac{1}{x^2+y^2}<\frac{1}{x^2+1}$$
$$y(x)<y(1)+\int_1^x \frac{dt}{t^2+1}=1+\tan^{-1}(x)-\tan^{-1}(1)$$ $$y(x)<1+\frac{\pi}{2}-\frac{\pi}{4}=1+\frac{\pi}{4}$$
• Yes perhaps this is sufficient.actually it is. Thanks – MathMan Aug 22 '16 at 2:03
• @MathMan The provided answer is not what the title suggests. I wouldn't mind if you would share the actual answer from your textbook – imranfat Aug 22 '16 at 21:13
• @imranfat Well the answer what jacquelin gave .Even solving it is fine.But i am afraid i dont have the solution of this DE – MathMan Aug 23 '16 at 11:43
• @Mathman : Nobody has the solution $y(x)$ of this ODE on explicit form. The analytical solving is possible but of height level : The related x(y) ODE is a Riccati equation involving Bessel functions in a complicated formula. In fact, with a formula involving Bessel functions, it is possible to express the solution on the inverse form $x(y)$ but not on the form $y(x)$. Obviously, the original wording of this problem was deliberately given with an ODE that students cannot solve, in order to oblige them to answer without having an explicit solution of the ODE. – JJacquelin Aug 23 '16 at 13:07 |
Conference paper Open Access
# Continuous Wavelet Vocoder-Based Decomposition of Parametric Speech Waveform Synthesis
Al-Radhi, Mohammed Salah; Csapó, Tamás Gábor; Németh, Géza
### DataCite XML Export
<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="URL">https://zenodo.org/record/5730361</identifier>
<creators>
<creator>
<givenName>Mohammed Salah</givenName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0003-3094-6916</nameIdentifier>
<affiliation>Budapest University of Technology and Economics</affiliation>
</creator>
<creator>
<creatorName>Csapó, Tamás Gábor</creatorName>
<givenName>Tamás Gábor</givenName>
<familyName>Csapó</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0003-4375-7524</nameIdentifier>
<affiliation>Budapest University of Technology and Economics</affiliation>
</creator>
<creator>
<creatorName>Németh, Géza</creatorName>
<givenName>Géza</givenName>
<familyName>Németh</familyName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-2311-4858</nameIdentifier>
<affiliation>Budapest University of Technology and Economics</affiliation>
</creator>
</creators>
<titles>
<title>Continuous Wavelet Vocoder-Based Decomposition of Parametric Speech Waveform Synthesis</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2021</publicationYear>
<subjects>
<subject>wavelet model</subject>
<subject>speech synthesis</subject>
<subject>statistical features</subject>
<subject>continuous vocoder</subject>
</subjects>
<dates>
<date dateType="Issued">2021-09-03</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="ConferencePaper"/>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/5730361</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.21437/Interspeech.2021-1600</relatedIdentifier>
<relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/ai4eu</relatedIdentifier>
</relatedIdentifiers>
<version>1</version>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract"><p>To date, various speech technology systems have adopted the vocoder approach, a method for synthesizing speech waveform that shows a major role in the performance of statistical parametric speech synthesis. However, conventional sourcefilter systems (i.e., STRAIGHT) and sinusoidal models (i.e., MagPhase) tend to produce over-smoothed spectra, which often result in muffled and buzzy synthesized text-to-speech (TTS). WaveNet, one of the best models that nearly resembles the human voice, has to generate a waveform in a time-consuming sequential manner with an extremely complex structure of its neural networks. WaveNet needs large quantities of voice data before accurate predictions can be obtained. In order to motivate a new, alternative approach to these issues, we present an updated synthesizer, which is a simple signal model to train and easy to generate waveforms, using Continuous Wavelet Transform (CWT) to characterize and decompose speech features. CWT provides time and frequency resolutions different from those of the short-time Fourier transform. It can also retain the fine spectral envelope and achieve high controllability of the structure closer to human auditory scales. We confirmed through experiments that our speech synthesis system was able to provide natural-sounding synthetic speech and outperformed the state-of-the-art WaveNet vocoder.</p></description>
</descriptions>
<fundingReferences>
<fundingReference>
<funderName>European Commission</funderName>
<funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/100010661</funderIdentifier>
<awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/825619/">825619</awardNumber>
<awardTitle>A European AI On Demand Platform and Ecosystem</awardTitle>
</fundingReference>
</fundingReferences>
</resource>
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# basic arithmetic of matrices
## +
To add two matrices, use the + operator.
i1 : ff = matrix{{1,2,3},{4,5,6}} o1 = | 1 2 3 | | 4 5 6 | 2 3 o1 : Matrix ZZ <--- ZZ i2 : gg = matrix{{4,5,6},{1,2,3}} o2 = | 4 5 6 | | 1 2 3 | 2 3 o2 : Matrix ZZ <--- ZZ i3 : ff+gg o3 = | 5 7 9 | | 5 7 9 | 2 3 o3 : Matrix ZZ <--- ZZ
The matrices in question must have the same number of rows and columns and also must have the same ring.
## -
To subtract two matrices, use the - operator.
i4 : ff-gg o4 = | -3 -3 -3 | | 3 3 3 | 2 3 o4 : Matrix ZZ <--- ZZ
The matrices in question must have the same number of rows and columns and also must have the same ring.
## *
To multiply two matrices use the * operator.
i5 : R = ZZ/17[a..l]; i6 : ff = matrix {{a,b,c},{d,e,f}} o6 = | a b c | | d e f | 2 3 o6 : Matrix R <--- R i7 : gg = matrix {{g,h},{i,j},{k,l}} o7 = | g h | | i j | | k l | 3 2 o7 : Matrix R <--- R i8 : ff * gg o8 = | ag+bi+ck ah+bj+cl | | dg+ei+fk dh+ej+fl | 2 2 o8 : Matrix R <--- R
## ^
To raise a square matrix to a power, use the ^ operator.
i9 : ff = matrix{{1,2,3},{4,5,6},{7,8,9}} o9 = | 1 2 3 | | 4 5 6 | | 7 8 9 | 3 3 o9 : Matrix ZZ <--- ZZ i10 : ff^4 o10 = | 7560 9288 11016 | | 17118 21033 24948 | | 26676 32778 38880 | 3 3 o10 : Matrix ZZ <--- ZZ
## inverse of a matrix
If a matrix f is invertible, then f^-1 will work.
## ==
To check whether two matrices are equal, one can use ==.
i11 : ff == gg o11 = false i12 : ff == ff o12 = true
However, given two matrices ff and gg, it can be the case that ff - gg == 0 returns true but ff == gg returns false.
i13 : M = R^{1,2,3} 3 o13 = R o13 : R-module, free, degrees {-1, -2, -3} i14 : N = R^3 3 o14 = R o14 : R-module, free i15 : ff = id_M o15 = {-1} | 1 0 0 | {-2} | 0 1 0 | {-3} | 0 0 1 | 3 3 o15 : Matrix R <--- R i16 : gg = id_N o16 = | 1 0 0 | | 0 1 0 | | 0 0 1 | 3 3 o16 : Matrix R <--- R i17 : ff - gg == 0 o17 = true i18 : ff == gg o18 = false
Since the degrees attached to the matrices were different, == returned the value false.
## !=
To check whether two matrices are not equal, one can use !=:
i19 : ff != gg o19 = true
From the definition above of ff and gg we see that != will return a value of true if the degrees attached the the matrices are different, even if the entries are the same.
## **
Since tensor product (also known as Kronecker product and outer product) is a functor of two variables, we may compute the tensor product of two matrices. Recalling that a matrix is a map between modules, we may write:
ff : K ---> L
gg : M ---> N
ff ** gg : K ** M ---> L ** N
i20 : ff = matrix {{a,b,c},{d,e,f}} o20 = | a b c | | d e f | 2 3 o20 : Matrix R <--- R i21 : gg = matrix {{g,h},{i,j},{k,l}} o21 = | g h | | i j | | k l | 3 2 o21 : Matrix R <--- R i22 : ff ** gg o22 = | ag ah bg bh cg ch | | ai aj bi bj ci cj | | ak al bk bl ck cl | | dg dh eg eh fg fh | | di dj ei ej fi fj | | dk dl ek el fk fl | 6 6 o22 : Matrix R <--- R |
# The sum of rational terms in the expansion of $(2^{\large\frac{1}{5}}$$+\sqrt 3)^{20} is ## 1 Answer General term T_{r+1} in the expansion of (2^{\large\frac{1}{5}}$$+\sqrt 3)^{20}$ is
$^{20}C_r.(2^{\large\frac{1}{5}}$$)^{20-r}.\sqrt 3^r =^{20}C_r.2^{4-\large\frac{r}{5}}$$.3^{\large\frac{r}{5}}$
Since $2$ and $3$ are relatively prime, |
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# Properties
Label 1200.2.v.b Level $1200$ Weight $2$ Character orbit 1200.v Analytic conductor $9.582$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1200.v (of order $$4$$, degree $$2$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$9.58204824255$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 30) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{8}$$. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + ( -1 - \zeta_{8}^{2} + \zeta_{8}^{3} ) q^{3} + ( -1 + \zeta_{8}^{2} ) q^{7} + ( 2 \zeta_{8} + \zeta_{8}^{2} - 2 \zeta_{8}^{3} ) q^{9} +O(q^{10})$$ $$q + ( -1 - \zeta_{8}^{2} + \zeta_{8}^{3} ) q^{3} + ( -1 + \zeta_{8}^{2} ) q^{7} + ( 2 \zeta_{8} + \zeta_{8}^{2} - 2 \zeta_{8}^{3} ) q^{9} + ( -\zeta_{8} - \zeta_{8}^{3} ) q^{11} -2 \zeta_{8} q^{17} + 4 \zeta_{8}^{2} q^{19} + ( 2 - \zeta_{8} - \zeta_{8}^{3} ) q^{21} -4 \zeta_{8}^{3} q^{23} + ( -1 - 5 \zeta_{8} + \zeta_{8}^{2} ) q^{27} + ( -5 \zeta_{8} + 5 \zeta_{8}^{3} ) q^{29} + 2 q^{31} + ( 1 + \zeta_{8}^{2} + 2 \zeta_{8}^{3} ) q^{33} + ( -6 + 6 \zeta_{8}^{2} ) q^{37} + ( 4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{41} + ( 6 + 6 \zeta_{8}^{2} ) q^{43} + 5 \zeta_{8}^{2} q^{49} + ( 2 + 2 \zeta_{8} + 2 \zeta_{8}^{3} ) q^{51} -4 \zeta_{8}^{3} q^{53} + ( 4 - 4 \zeta_{8} - 4 \zeta_{8}^{2} ) q^{57} + ( -7 \zeta_{8} + 7 \zeta_{8}^{3} ) q^{59} -6 q^{61} + ( -1 - \zeta_{8}^{2} + 4 \zeta_{8}^{3} ) q^{63} + ( -4 + 4 \zeta_{8}^{2} ) q^{67} + ( -4 \zeta_{8} + 4 \zeta_{8}^{2} + 4 \zeta_{8}^{3} ) q^{69} + ( 10 \zeta_{8} + 10 \zeta_{8}^{3} ) q^{71} + ( 5 + 5 \zeta_{8}^{2} ) q^{73} + 2 \zeta_{8} q^{77} + 6 \zeta_{8}^{2} q^{79} + ( 7 + 4 \zeta_{8} + 4 \zeta_{8}^{3} ) q^{81} + 12 \zeta_{8}^{3} q^{83} + ( 5 + 10 \zeta_{8} - 5 \zeta_{8}^{2} ) q^{87} + ( 2 \zeta_{8} - 2 \zeta_{8}^{3} ) q^{89} + ( -2 - 2 \zeta_{8}^{2} + 2 \zeta_{8}^{3} ) q^{93} + ( -3 + 3 \zeta_{8}^{2} ) q^{97} + ( \zeta_{8} - 4 \zeta_{8}^{2} - \zeta_{8}^{3} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{3} - 4q^{7} + O(q^{10})$$ $$4q - 4q^{3} - 4q^{7} + 8q^{21} - 4q^{27} + 8q^{31} + 4q^{33} - 24q^{37} + 24q^{43} + 8q^{51} + 16q^{57} - 24q^{61} - 4q^{63} - 16q^{67} + 20q^{73} + 28q^{81} + 20q^{87} - 8q^{93} - 12q^{97} + O(q^{100})$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.
$$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$-\zeta_{8}^{2}$$ $$1$$ $$1$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
257.1
0.707107 − 0.707107i −0.707107 + 0.707107i 0.707107 + 0.707107i −0.707107 − 0.707107i
0 −1.70711 + 0.292893i 0 0 0 −1.00000 1.00000i 0 2.82843 1.00000i 0
257.2 0 −0.292893 + 1.70711i 0 0 0 −1.00000 1.00000i 0 −2.82843 1.00000i 0
593.1 0 −1.70711 0.292893i 0 0 0 −1.00000 + 1.00000i 0 2.82843 + 1.00000i 0
593.2 0 −0.292893 1.70711i 0 0 0 −1.00000 + 1.00000i 0 −2.82843 + 1.00000i 0
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
15.e even 4 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1200.2.v.b 4
3.b odd 2 1 inner 1200.2.v.b 4
4.b odd 2 1 150.2.e.a 4
5.b even 2 1 240.2.v.e 4
5.c odd 4 1 240.2.v.e 4
5.c odd 4 1 inner 1200.2.v.b 4
12.b even 2 1 150.2.e.a 4
15.d odd 2 1 240.2.v.e 4
15.e even 4 1 240.2.v.e 4
15.e even 4 1 inner 1200.2.v.b 4
20.d odd 2 1 30.2.e.a 4
20.e even 4 1 30.2.e.a 4
20.e even 4 1 150.2.e.a 4
40.e odd 2 1 960.2.v.k 4
40.f even 2 1 960.2.v.c 4
40.i odd 4 1 960.2.v.c 4
40.k even 4 1 960.2.v.k 4
60.h even 2 1 30.2.e.a 4
60.l odd 4 1 30.2.e.a 4
60.l odd 4 1 150.2.e.a 4
120.i odd 2 1 960.2.v.c 4
120.m even 2 1 960.2.v.k 4
120.q odd 4 1 960.2.v.k 4
120.w even 4 1 960.2.v.c 4
180.n even 6 2 810.2.m.f 8
180.p odd 6 2 810.2.m.f 8
180.v odd 12 2 810.2.m.f 8
180.x even 12 2 810.2.m.f 8
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
30.2.e.a 4 20.d odd 2 1
30.2.e.a 4 20.e even 4 1
30.2.e.a 4 60.h even 2 1
30.2.e.a 4 60.l odd 4 1
150.2.e.a 4 4.b odd 2 1
150.2.e.a 4 12.b even 2 1
150.2.e.a 4 20.e even 4 1
150.2.e.a 4 60.l odd 4 1
240.2.v.e 4 5.b even 2 1
240.2.v.e 4 5.c odd 4 1
240.2.v.e 4 15.d odd 2 1
240.2.v.e 4 15.e even 4 1
810.2.m.f 8 180.n even 6 2
810.2.m.f 8 180.p odd 6 2
810.2.m.f 8 180.v odd 12 2
810.2.m.f 8 180.x even 12 2
960.2.v.c 4 40.f even 2 1
960.2.v.c 4 40.i odd 4 1
960.2.v.c 4 120.i odd 2 1
960.2.v.c 4 120.w even 4 1
960.2.v.k 4 40.e odd 2 1
960.2.v.k 4 40.k even 4 1
960.2.v.k 4 120.m even 2 1
960.2.v.k 4 120.q odd 4 1
1200.2.v.b 4 1.a even 1 1 trivial
1200.2.v.b 4 3.b odd 2 1 inner
1200.2.v.b 4 5.c odd 4 1 inner
1200.2.v.b 4 15.e even 4 1 inner
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(1200, [\chi])$$:
$$T_{7}^{2} + 2 T_{7} + 2$$ $$T_{11}^{2} + 2$$ $$T_{17}^{4} + 16$$
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T^{4}$$
$3$ $$9 + 12 T + 8 T^{2} + 4 T^{3} + T^{4}$$
$5$ $$T^{4}$$
$7$ $$( 2 + 2 T + T^{2} )^{2}$$
$11$ $$( 2 + T^{2} )^{2}$$
$13$ $$T^{4}$$
$17$ $$16 + T^{4}$$
$19$ $$( 16 + T^{2} )^{2}$$
$23$ $$256 + T^{4}$$
$29$ $$( -50 + T^{2} )^{2}$$
$31$ $$( -2 + T )^{4}$$
$37$ $$( 72 + 12 T + T^{2} )^{2}$$
$41$ $$( 32 + T^{2} )^{2}$$
$43$ $$( 72 - 12 T + T^{2} )^{2}$$
$47$ $$T^{4}$$
$53$ $$256 + T^{4}$$
$59$ $$( -98 + T^{2} )^{2}$$
$61$ $$( 6 + T )^{4}$$
$67$ $$( 32 + 8 T + T^{2} )^{2}$$
$71$ $$( 200 + T^{2} )^{2}$$
$73$ $$( 50 - 10 T + T^{2} )^{2}$$
$79$ $$( 36 + T^{2} )^{2}$$
$83$ $$20736 + T^{4}$$
$89$ $$( -8 + T^{2} )^{2}$$
$97$ $$( 18 + 6 T + T^{2} )^{2}$$ |
# Thread: solving cosine ratio equations
1. ## solving cosine ratio equations
I have an identily of the form:
cos(a1 – b)/cos(a2 – b) =(x1/x2)*cos(a1)/cos(a2)
Given a1,a2,x1 and x2, how can I solve it for b?
Thanks in advance for any help
2. Hello jrr
Welcome to Math Help Forum!
Originally Posted by jrr
I have an identily of the form:
cos(a1 – b)/cos(a2 – b) =(x1/x2)*cos(a1)/cos(a2)
Given a1,a2,x1 and x2, how can I solve it for b?
Thanks in advance for any help
It's not clear what the symbols are between the $\cos$ and the brackets, so I shall ignore them for now. (If it turns out to be a power, like $\cos^2(a_1-b)$ the same method applies.)
Expand each of the cosine expressions on the LHS using $\cos(A-B) = \cos A \cos B + \sin A\sin B$, and then divide top and bottom by $\cos b$. Then solve the resulting equation for $\tan b$.
Here's the start:
$\frac{\cos(a_1-b)}{\cos(a_2-b)}=\frac{x_1}{x_2}\cdot\frac{\cos a_1}{\cos a_2}$
$\Rightarrow\frac{\cos a_1\cos b+\sin a_1\sin b}{\cos a_2\cos b+\sin a_2\sin b}=\frac{x_1}{x_2}\cdot\frac{\cos a_1}{\cos a_2}$
$\Rightarrow\frac{\cos a_1+\sin a_1\tan b}{\cos a_2+\sin a_2\tan b}=\frac{x_1}{x_2}\cdot\frac{\cos a_1}{\cos a_2}$
Can you now make $\tan b$ the subject of this equation, and hence find $b$?
3. ## Thanks
That makes it starightforward now
jrr
4. I re-arranged to get
tan(b)= (x1-x2).cos(a1).cos(a2)/(x2.cos(a2).sin(a1)-x1.cos(a1).sin(a2))
but I was wondering if this could be simplified any further?
5. Hello jrr
Originally Posted by jrr
I re-arranged to get
tan(b)= (x1-x2).cos(a1).cos(a2)/(x2.cos(a2).sin(a1)-x1.cos(a1).sin(a2))
but I was wondering if this could be simplified any further?
Yes, you can divide top-and-bottom by $\cos a_1\cos a_2$ to get:
$\tan b = \frac{x_1-x_2}{x_2\tan a_1 - x_1\tan a_2}$ |
# Finding good pants for winter biking
Winter is soon upon us here, and I'm gearing up for the season. I currently have a pair of rain over-pants which I use during the other 3 seasons, but honestly I really dislike them. They're baggy, requiring the use of an ankle band, and not entirely warm. They do a decent job of keeping out water, but I don't know how they will perform with snow.
Can someone recommend a type of pants which are more form-fitting and will do well in both rain and snow?
-
<rant>Why does everyone assume we all live in the northern hemisphere? I am looking forward to summer!</rant> – Anthony K Oct 15 '10 at 12:09
@Anthony The joys of a more global community. He did say "upon us here". But I do see your point. At the same time, I'm not going to constantly convert from miles to km, northern to southern hemisphere, left side of road to right side of road etc. as I type questions and answers. I am, however, going to greatly enjoy the fact that pants = underwear in parts of the world and how that influenced my first read of the title of this question. – Mike Two Oct 15 '10 at 12:15
@Mike, I took the "us" to mean the bicycles.se community. I don't think there is a need to convert units, though I have no idea about Fahrenheit. And when I say summer I am being a little facetious since today was pouring rain & only 8 degrees C where I am ;-) – Anthony K Oct 15 '10 at 12:24
@Anthony - Good point about the "us". I was really just using that as a lead in to the pants joke. I can do C or F but I have to think the C through. a bit. – Mike Two Oct 15 '10 at 12:33
I was using "us" poetically, because it would sound weird to say "me". No intention of discriminating against Southern Hemisphere, folks. ;) But just think -- for anyone reading this question next June, the opposite will be true! – Nik Reiman Oct 15 '10 at 12:44
It really depends on your budget, but you should check this out (or anything similar), from Gore bike wear :
They aren't the tightest pants out there, but "real" tight pants are very rarely (trying not to say never) waterproof because of the type of fabric used to make them.
An alternative idea would be a nylon pant (waterproof, windproof, but absulutely not warm) that's relatively tight with a warm baselayer.
-
I own em. They are very nice and I do endorse them. But, to me, the ideal is a pair of those for rain and a pair of insulated tights for snow. – tplunket Oct 15 '10 at 12:25
Foxwear makes great rain pants and jackets. They're a little baggy, but they close at the ankle -- no ankle clip required. They're also good layered over tights for winter riding. I have two pair, and will use them until they fall apart (which may take some time).
-
The trick to staying warm for your winter rides is layers. Keep in mind your overpants aren't there to keep you warn, per se, just to keep you dry. You can wear under them pants, long johns, long warm spandex, whatever floats your boat. That's part of why they would be baggy too.
When I used to commute in Boston through the winter, I wore thick long spandex pants under my snow pants, and that, combined with the heat generated by riding, was enough to keep me warm through -5F blizzards :)
-
I have a pair of Sugoi long tights for commuting in the winter. I add or subtract a base layer depending on conditions.
I don't really care if it's Sugoi or not; other companies make bike-tights compatible with base layers.
Maybe I choose a different brand next year? Depends on what's on sale...
-
I changed the link. Manufacturers constantly change product lines and websites. Just go to the Sugoi site and look for what you want. – user313 Dec 21 '11 at 6:26
REI has a Novara brand rain pant that isn't too expensive. I use mine all year round, rain or snow. I don't wear them when it is warm, as they tend to keep moisture in as well as out, which leads to soaked clothing. However, I believe that is a problem with most rain gear.
I got my pants on sale for around $30 a few years ago. When I go to the website now, I see that the men's version is around$100 in the catalog. I'm not sure why the price difference.
www.rei.com
-
Don't forget about the REI 100% satisfaction guarantee! Though, I've found the Novara brand products run on the long and large side and it's extraordinarily rare for me to find something that I would consider "form fitting". YMMV. – James Schek Dec 25 '11 at 8:05
They aren't form fitting per-say, but I have long legs, so they work well for me. I don't have to worry about the leg ends getting stuck in the gears, as they taper and have elastic and zippers/velcrow for ease of removal over shoes. – ananka Jan 4 '12 at 19:49
After shopping around quite a bit, I picked up a pair of the Novaras from REI (\$120 USD) last week, and I'm quite happy with them. Thanks! – Matt Ball Jan 17 '12 at 1:27
I have a pair of Polartec tights from Col d'Lizard that are the cat's pajamas (or some such metaphor). Definitely not baggy (when you see them you'll understand -- "I'm going to fit into THOSE???"), and plenty warm down to maybe 5-10F, but they breathe well -- never get clammy.
I no longer do winter cycling, but I often use the tights when I run the snow blower. The snow doesn't stick to them and they keep me warm in the wind without overheating.
-
I wear my Craft Storm Tights for my winter commuting and even some recreational longer rides (I get too hot when I wear them for an interval type of workout).
http://shop.craftsports.us/sports/bike/mens-pxc-storm-tights.html
They have a thermal liner and keep me nice and warm. I also like them for the ease of use, I just slip them over my underwear and off I go. Not skin tight but not loose around the lower legs.
-
I got the MEC Roubaix Tights this year and I have found them surprisingly warm, despite that they are quite thin. I wore them down to -15 Celsius and had no problems with my legs getting cold. Depending on where you live, and what you consider "winter" something like this might be just fine.
- |
Chemistry Quick revision of Basic concepts of chemistry
Click for Only Video
Significant figures
Precision : It is the closeness of various measurements for the same quantity .
Accuracy : It is the agreement of a particular value to the true value of the result.
Law of conservation of mass
Statement : Matter can neither be created nor destroyed.
Law of multiple proportions
Statement : If two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element, are in the ratio of small whole numbers. This law was given by Dalton in 1803.
e.g Hydrogen +oxygen → water
\ \ \ \ \ \ \ 2g \ \ \ \ \ \ \ 16g \ \ \ \ \ \ \18g
Hydrogen + Oxygen → Hydrogen peroxide
2g \ \ \ \ \ \ \ \ \ 32 g \ \ \ \ \ \ \ \ \ \ \ \ 34g
Here, the ratio of masses of oxygen (i.e. 16 g and 32 g) which combine with a fixed mass of hydrogen (2 g) is 1 : 2.
Gay Lussac's law of gaseous volume
Statement : When gases combine or are produced in a chemical reaction they do so in a simple ratio by volume provided all gases are at
same temperature and pressure.
Hydrogen + Oxygen → Water
\ \ \ \ 100 \ mL \ \ \ \ \ \ \ 50 \ mL \ \ \ \ \ \ \100 \ mL
Here, ratio of volumes of hydrogen and oxygen is 2:1.
This law is also known as the law of definite proportions by volume.
Statement : Equal volumes of gases at the same temperature and pressure should contain equal number of molecules.
Percentage composition
Percentage composition gives the idea about the purity of a given sample by analyzing the given data.
Mass % of an element = text(mass of that element in the compound)/text(molar mass of the compound)
e.g. For H_2O
Molar mass of water = 18.02g
Mass % of H = (2xx1.008)/18.02 xx100
Mass % of O = 16.00/18.02 xx100= 88.79 |
# Exponential and Power Function Together?
Calculus Level 4
$$x^2=2^x$$ has integral solutions $$x=2 \text{ or } 4$$, but it also has one other negative, real solution. If $$P$$ is this solution, what is the absolute value of $$\lfloor 10^7 \times P \rfloor$$?
You may use a calculator only for indirect calculations (i.e., not directly finding $$P$$).
× |
109 views
In each question, you are given certain data followed by two statements. For answering the questions:
Mark a, if both the statements together are insufficient to answer the question.
Mark b, if any one of the two statements is sufficient to answer the question.
Mark c, if each statement alone is sufficient to answer the question.
Mark d, if both the statements together are sufficient to answer the question, but neither statement alone is sufficient.
What is the Cost Price of the article?
1. After selling the article, a loss of $25$% on Cost Price incurred.
2. The Selling Price is three-fourths of the Cost Price.
1. if both the statements together are insufficient to answer the question.
2. if any one of the two statements is sufficient to answer the question.
3. if each statement alone is sufficient to answer the question.
4. if both the statements together are sufficient to answer the question, but neither statement alone is sufficient.
recategorized | 109 views
+1 vote
Selling Price = Cost Price + Profit
or Selling Price = Cost Price – Loss
1 : “After selling the article, a loss of 25% on Cost Price incurred.”
SP = CP – 25 % of CP = CP – 0.25 * CP => SP = 0.75 * CP
2 : “The Selling Price is three-fourths of the Cost Price.”
SP = ¾ * CP => SP = 0.75 * CP
Equations from both the statements are the same. You need two different linear equations with the same variables to find a solution.
by (142 points) 1 3 |
Thesis Open Access
# DEVELOPING BACTERIAL WILT DETECTION MODEL ON ENSET CROP USING A DEEP LEARNING APPROACH
YIDNEKACHEW KIBRU AFEWORK
### DataCite XML Export
<?xml version='1.0' encoding='utf-8'?>
<creators>
<creator>
<creatorName>YIDNEKACHEW KIBRU AFEWORK</creatorName>
<affiliation>ADDIS ABABA SCIENCE AND TECHNOLOGY UNIVERSITY</affiliation>
</creator>
</creators>
<titles>
<title>DEVELOPING BACTERIAL WILT DETECTION MODEL ON ENSET CROP USING A DEEP LEARNING APPROACH</title>
</titles>
<publisher>National Academic Digital Repository of Ethiopia</publisher>
<publicationYear>2019</publicationYear>
<subjects>
<subject>Convolutional Neural Network, Deep Learning, Image Classification, Disease detection, Enset Bacterial Wilt.</subject>
</subjects>
<contributors>
<contributor contributorType="Supervisor">
<contributorName>Vuda Sreenivasa Rao (PhD)</contributorName>
<affiliation>ADDIS ABABA SCIENCE AND TECHNOLOGY UNIVERSITY</affiliation>
</contributor>
<contributor contributorType="Supervisor">
<contributorName>Taye Girma (MSc)</contributorName>
<affiliation>ADDIS ABABA SCIENCE AND TECHNOLOGY UNIVERSITY</affiliation>
</contributor>
</contributors>
<dates>
<date dateType="Issued">2019-10-25</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="Text">Thesis</resourceType>
<alternateIdentifiers>
</alternateIdentifiers>
<relatedIdentifiers>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract"><p>Ethiopia is one of the countries in Africa which have a huge potential for the development of different varieties of crops. There are many cultivated crops which are used as a staple food in different regions of the country. From those crops Enset is the one and which is used by around 15 million peoples as a staple food in central, south, and southwestern regions of Ethiopia. Enset crop is affected by disease caused by bacteria, fungi, and virus. From these, bacterial wilt of Enset is the most determinant constraint to Enset production. Identification of the disease needs special attention from experienced experts in the area and it is not possible for the plant pathologists to reach each and every Enset crop to observe the disease, because the crop is physically big. Thus, developing a computer vision model that can be deployed in drones that automatically identify the disease can help to support the community which cultivates Enset crop. To this end, a deep learning approach for automatic identification of Enset bacterial wilt disease is proposed. The proposed approach has three main phases. The first phase is the collection of healthy and diseased Enset images with the help of agricultural experts from different farms to create a dataset. Then the design of a convolutional neural network that can classify the given image in to healthy and diseased is done. Finally, the designed model is trained and tested by using the collected dataset and compared the designed model with different pre-trained convolutional neural network models namely VGG16 and InceptionV3. The dataset contains 4896 healthy and diseased Enset images. From this, 80% of the images are used for training and the rest for testing the model. During training, data augmentation technique is used to generate more images to fit the proposed model. The experimental result demonstrates that the proposed technique is effective for the identification of Enset bacterial wilt disease. The proposed model can successfully classify the given image with a mean accuracy of 98.5% even though images are captured under challenging conditions such as illumination, complex background, different resolution, and orientation of real scene images.<br>
&nbsp;</p></description>
</descriptions>
</resource>
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## Tuesday, August 16, 2011
### Finding Files with PowerShell
I miss the UNIX find command in Windows. I could get it with Cygwin or GNUWin32, but that requires littering my machine with extra stuff. So, PowerShell to the rescue: |
# Givens rotation vs 2x2 Householder reflection
The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $$e_1$$, while Givens is better if you want to map a 2-vector to $$e_1$$. However, I can't find a reference which explains why Givens is better in the 2-vector case. Can anyone explain?
Typically you don't apply these matrices to a single vector; you apply them to a $$m\times n$$ matrix, where $$n$$ is large, so you can amortize the cost of computing the various coefficients. Applying a Householder reflector to a vector costs $$4m-1$$. Applying a Givens rotation works only for $$m=2$$, and costs $$6$$ operations, which is cheaper.
• @gTcV Good point -- I was referring to Householder reflectors when applied in the usual form $I-vv^T$; if you convert them to a $2\times 2$ matrix and apply them directly then the cost becomes the same. – Federico Poloni Aug 21 at 14:13 |
# Synopsis: Protons in the Fast Lane
A proposed graphene-based material could offer speedy transport of protons without the need for water.
Membranes that conduct protons form the basis of fuel cells in hydrogen-powered cars and buses. But they only conduct well in the presence of water and at temperatures below about $80{\phantom{\rule{0.3em}{0ex}}}^{\circ }\text{C}$—hotter than that, and they become dehydrated. Operating such membrane-based fuel cells at higher temperatures would come with several perks, including decreased carbon monoxide poisoning of the cells’ anodes. Karl Johnson from the University of Pittsburgh and colleagues now predict that if you add hydroxyl (OH) groups to a variant of graphene known as graphane, you’ll end up with a material that conducts protons fast, even in the absence of water and at increased temperatures.
Graphane (with two a’s) is graphene with a layer of hydrogen atoms bonded to each side of it. Using density-functional-theory calculations and molecular-dynamics simulations, Johnson and co-workers found that OH groups covalently attached to graphane can form a continuous hydrogen-bonded network. This network works like a bucket brigade, allowing protons to be handed over from one OH group to another, very fast and at a wide range of temperatures. This fast motion is in contrast with that of other materials that have been shown to conduct protons in the absence of water but lack an unbroken transport pathway, such as polymers with OH groups tacked on and ionic crystals. The researchers reckon that hydroxylated graphane could be produced with electron-beam-generated plasmas, which have been used to attach fluorine, hydrogen, and oxygen atoms to graphene.
This research is published in Physical Review Letters.
–Ana Lopes
Ana Lopes is a Senior Editor of Physics.
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### Viewpoint: Crystalline Metals Effortlessly Fit the Mold
Molding crystalline metals like silver into nanopillar structures is both possible and easier to achieve for narrower pillars, in contrast with other materials. Read More »
Condensed Matter Physics
### Viewpoint: Pushing Towards Room-Temperature Superconductivity
Two independent studies report superconductivity at record high temperatures in hydrogen-rich materials under extreme pressure. Read More » |
atan2
Version:
Computes the arctangent of y/x.
Syntax
c = atan2(z)
c = atan2(y, x)
z
Real or complex scalar or array of any dimension. atan2(z) is equivalent to atan2(real(z), imag(z)).
y
Real or complex scalar or array of any dimension.
x
Real or complex scalar or array of any dimension.
c
Arctangent, in radians, of the elements in x and y. c is a scalar or an array of the same size as x and y.
atan2 versus atan
The atan2 function can compute the arctangent for angles in any of the four quadrants of the x-y plane, whereas the atan function computes the arctangent in only two quadrants.
C = atan2(3, 4)
C = atan2(3+4i)
Where This Node Can Run:
Desktop OS: Windows
FPGA: DAQExpress does not support FPGA devices |
Skip to main content
# Instrument Profile Format
## Introduction
This document describes an open format to represent and exchange basic profile information about market instruments or set of field values that define corresponding attributes of the instrument. It covers all types of tradable and indicative instruments, including stocks, funds, bonds, indices, futures, options, and others. The format provides a common framework to represent necessary information, defines the data model, and describes file formats for data distribution and exchange.
## Data model
Every market instrument is represented by a single profile record as a set of field values that define corresponding attributes of the instrument. The set of defined fields and interpretations of their values form the abstraction layer of the format. Each field is characterized by its name, meaning, applicability to specific instrument types, interpretation rules, and data format. For the purpose of readability and interoperability, all values are represented in textual form even if their primary use is non-textual (e.g. numbers and dates). All values must use a Unicode standard for representation of their textual form.
## Data availability
Except for a few identification fields, many fields are either optional or simply not applicable for a given instrument type. Inapplicable fields shall be ignored if present and they shall be left empty when exported. Also, in many cases, the value of certain fields is not known by the data source. Such fields are considered to have an empty value and they are usually represented by a text of length 0. Empty or missing fields shall be interpreted as undefined or unknown.
## Field types
• Text – value is textual information, such as a company name or exchange code.
• Formatted text – complex fields use proprietary formats, such as a list of exchanges.
• Number – value is a number, such as a contract size or strike price; value can be either integer or floating point; floating point values must use the . character as a decimal point; a numeric value of 0 is often considered an empty value.
• Date – value is a date, such as the last trading day or expiration date; value must be formatted using YYYY-MM-DD; date 1970-01-01 is often considered an empty value.
## Format extensibility
The format can be extended by the addition of new fields and new literals (enumerated values) for existing fields. All parties working with this format shall be prepared to deal with such extensions. Standard method is to ignore unknown fields as if they were not there. If some known and important field uses an unknown literal then the application can either ignore the profile altogether, replace the unknown literal with some default one or show an error to an operator and ask him to resolve the situation.
## Symbology
This format assumes that instrument profiles use symbology as defined on corresponding exchanges and national markets. Extensions and augmentations of native symbology are formally beyond the scope of this format. However, there are several common notations that are currently in use:
• Future symbols use the prefix "/" for convenience, e.g. "/ESZ22:XCME"
• Option symbols use the prefix "." for convenience, e.g. ".GOOG220527C1500"
• Future Option symbols use the prefix "./", e.g. "./ESM22P4300:XCME"
• Spread symbols use the prefix "=", e.g. "=/AFRJ19:IFEU-/AFRM19:IFEU"
## List of fields
In order to simplify interoperability, the syntax of field names is restricted: names may use only capital Latin letters, decimal digits and underscore character, and they shall start with a Latin letter.
• TYPE, text – type of instrument; takes precedence in conflict cases with other fields; mandatory field; may not be empty; example: STOCK, FUTURE, OPTION
• SYMBOL, text – identifier of instrument; preferable to an international one in the Latin alphabet; mandatory field; may not be empty; example: GOOG, /YGM9, .ZYEAD
• DESCRIPTION, text – description of instrument; preferable to an international one in the Latin alphabet; example: Google Inc., Mini Gold Futures,Jun-2009,ETH
• LOCAL_SYMBOL, text – identifier of instrument in national language; shall be empty if it is the same as the SYMBOL field
• LOCAL_DESCRIPTION, text – description of instrument in national language; shall be empty if it is the same as the DESCRIPTION field
• COUNTRY, text – country of origin (incorporation) of corresponding company or parent entity; shall use a two-letter country code from ISO 3166-1 standard; see ISO 3166-1 on Wikipedia; example: US, RU
• OPOL, text – Official Place Of Listing, the organization that has listed this instrument; instruments with multiple listings shall use separate profiles for each listing; shall use Market Identifier Code (MIC) from ISO 10383 standard (see ISO 10383 on Wikipedia or MIC homepage) or custom dxFeed values (see Custom OPOL values chapter); example: XNAS, RTSX
• EXCHANGE_DATA, text – exchange-specific data required to properly identify an instrument when communicating with an exchange; uses exchange-specific format
• EXCHANGES, formatted text – list of exchanges where instrument is quoted or traded; shall use the following format:
<VALUE> ::= <empty> | <LIST>
<LIST> ::= <MIC> | <MIC> <semicolon> <LIST>
The list shall be sorted by MIC; example: ARCX;CBSX;XNAS;XNYS
• CURRENCY, text – currency of quotation, pricing and trading. For Forex data, mainly shall use a three-letter currency code from ISO 4217 standard; see ISO 4217 on Wikipedia; example: USD, RUB; exclusions: MUKO, M5P, etc. For cryptocurrencies, shall use the format transferred by exchange.
• BASE_CURRENCY, text – base currency of currency pair. For Forex data, shall use a three-letter currency code with some exclusions (see CURRENCY field). For cryptocurrencies, shall use the format transferred by exchange.
• CFI, text – Classification of Financial Instruments code; mandatory field for OPTION instruments as it is the only way to distinguish Call/Put type, American/European exercise, Cash/Physical delivery; shall use a six-letter CFI code from ISO 10962 standard; allowed to use 'X' extensively and to omit trailing letters (assumed to be 'X'); see ISO 10962 on Wikipedia; example: ESNTPB, ESXXXX, ES , OPASPS
• ISIN, text – International Securities Identifying Number; shall use a twelve-letter code from ISO 6166 standard; see ISO 6166 on Wikipedia or ISIN on Wikipedia; example: DE0007100000, US38259P5089
• SEDOL, text – Stock Exchange Daily Official List; shall use a seven-letter code assigned by the London Stock Exchange; see SEDOL on Wikipedia or SEDOL on LSE; example: 2310967, 5766857
• CUSIP, text – Committee on Uniform Security Identification Procedures code; shall use a nine-letter code assigned by CUSIP Services Bureau; see CUSIP on Wikipedia; example: 38259P508
• ICB, number – Industry Classification Benchmark; shall use a four-digit number from ICB catalog; see ICB on Wikipedia or ICB homepage; example: 9535
• SIC, number – Standard Industrial Classification; shall use a four-digit number from SIC catalog; see SIC on Wikipedia or SIC structure; example: 7371
• MULTIPLIER, number – market value multiplier; the weight that is multiplied by the contracted price when calculating the contracted value. E.g., for HSI and H-Shares Index futures, the contract multiplier is $50 per index point, whereas in a mini-HSI futures contract, it is$10 per index point. For HKEx stock futures contracts, this is one board lot of the underlying stock; example: 100, 33.2
• PRODUCT, text – an instrument which represents the series of futures contracts with the same parameters (underlying, settlement style, expiration period); example: /YG
• UNDERLYING, text – primary underlying symbol for options; example: C, /YGM9
• SPC, number – shares per contract for options; example: 1, 100
• ADDITIONAL_UNDERLYINGS, formatted text – additional underlyings for options, including additional cash; shall use the following format:
<VALUE> ::= <empty> | <LIST>
<LIST> ::= <AU> | <AU> <semicolon> <space> <LIST>
<AU> ::= <UNDERLYING> <space> <SPC>
the list shall be sorted by UNDERLYING; example: SE 50, FIS 53; US\$ 45.46
• MMY, text – maturity month-year as provided for corresponding FIX tag (200); can use several different formats depending on the data source:
YYYYMM – if only year and month are specified
YYYYMMDD – if full date is specified
YYYYMMwN – if week number (within a month) is specified
• EXPIRATION, date – date of expiration; example: 2009-01-17
• LAST_TRADE, date – date of last trading day; example: 2009-01-16
• STRIKE, number – strike price for options; example: 80, 22.5
• OPTION_TYPE, text – type of option; shall use one of the following values:
STAN = Standard Options
LEAP = Long-term Equity AnticiPation Securities
SDO = Special Dated Options
BINY = Binary Options
FLEX = FLexible EXchange Options
VSO = Variable Start Options
RNGE = Range
• EXPIRATION_STYLE, text – expiration cycle style. Possible values are Daily, Weeklys, EOM, Quarterlys, SemiAnnualys, Yearlys
• SETTLEMENT_STYLE, text – settlement price determination style such as Open, Close
• PRICE_INCREMENTS, formatted text – minimum allowed price increments with corresponding price ranges; shall use the following format:
<VALUE> ::= <empty> | <LIST>
<LIST> ::= <INCREMENT> | <RANGE> <semicolon> <space> <LIST>
<RANGE> ::= <INCREMENT> <space> <UPPER_LIMIT>
the list shall be sorted by UPPER_LIMIT; example: 0.01 3; 0.05
• TRADING_HOURS, formatted text – trading schedule; example: NewYorkUS(rt=0300;0=p04000930r09301600a16002000)
• FIRST_INTEREST_DATE, date – for fixed coupon rate bonds: the periodic interest payment that the issuer makes during the life of the bond; example: 2009-01-17
• INTEREST_RATE, number – the periodic interest payment that the issuer makes during the life of the bond, denominated in %; example: 2.68
• ISSUE_DATE, date – the date on which an instrument is issued and begins to accrue interest; example: 2009-01-27
• ANNOUNCEMENT_DATE, date – date of announcement; example: 2010-01-16
• AUCTION_DATE, date – date of auction; example: 2009-01-16
• PRICE_TYPE, formatted text. Possible values are PerUnit, Yield, YieldSpread
• ISSUED_AS_BENCHMARK, number – <number><period: Y or M>; example: 30Y, 20Y, 12M, 1M
• BENCHMARK_STATUS, formatted text. Possible values are WhenIssued, Benchmark, OffTheRun
### Note
ISSUED_AS_BENCHMARK and BENCHMARK_STATUS fields shall be both filled or both empty.
## List of types
• BOND – debt instruments, excluding money market funds; see Bond on Wikipedia
• ETF – exchange-traded fund; see ETF on Wikipedia
• FOREX – foreign exchange market or cryptocurrency; see Forex on Wikipedia and Cryptocurrency on Wikipedia
• FUTURE – futures contract, derivative instrument; see Futures on Wikipedia
• INDEX – non-tradable market performance indicators
• MONEY_MARKET_FUND – funds that invest in short-term debt instruments; see Money market fund on Wikipedia
• MUTUAL_FUND – investment funds, excluding ETFs and money market funds; see Mutual fund on Wikipedia
• OPTION – option contract, derivative instrument; see Option on Wikipedia
• PRODUCT – grouping instrument for futures, aka futures product
• STOCK – tradable equities, excluding ETFs and mutual funds; see Stock on Wikipedia
• SPREAD – composite virtual instrument consisting of two or several individual instruments that represent multileg order. Learn more about spread instrument format
• WARRANT – derivative that gives the right, but not the obligation, to buy or sell a security at a certain price before expiration
• CFD – contract for differences, an arrangement where the differences in the settlement between the open and closing trade prices are cash-settled; see CFD on Wikipedia
• CATEGORY:FRED – economic data time series from Federal Reserve Economic Data
• OTHER – non-tradable miscellaneous instruments
• REMOVED – special instrument type indicating instrument removal (see below)
## Field applicability
FOREX
BOND
INDEX
STOCK
ETF
MUTUAL_FUND
MONEY_MARKET_FUND
PRODUCT
FUTURE
OPTION
SPREAD
OTHER
WARRANT
CFD
CATEGORY:FRED
TYPE
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
SYMBOL
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
DESCRIPTION
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
LOCAL_SYMBOL
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
LOCAL_DESCRIPTION
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
COUNTRY
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
OPOL
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
EXCHANGE_DATA
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
EXCHANGES
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
CURRENCY
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
BASE_CURRENCY
M
-
-
-
-
--
-
-
-
-
-
+
-
-
-
CFI
+
+
+
+
+
+
+
+
+
M
+
+
+
-
-
ISIN*
+
+
+
+
+
+
+
-
+
+
+
+
-
-
-
SEDOL*
-
+
-
+
+
+
+
-
-
-
-
+
-
-
-
CUSIP*
-
+
-
+
+
+
+
-
-
-
-
+
-
-
-
ICB
-
+
+
+
+
+
+
+
+
+
-
+
+
-
-
SIC
-
+
+
+
+
+
+
+
+
+
-
+
+
-
-
MULTIPLIER
+
-
-
-
-
-
-
-
M
M
M
+
+
-
-
PRODUCT
-
-
-
-
-
-
-
-
M
+
+
+
-
-
-
UNDERLYING
-
-
-
-
-
-
-
-
-
M
-
+
M
-
-
SPC
-
-
-
-
-
-
-
-
-
M
-
+
+
-
-
ADDITIONAL_UNDERLYINGS
-
-
-
-
-
-
-
-
-
+
-
+
-
-
-
MMY
-
+
-
-
-
-
-
-
+
+
+
+
+
-
-
EXPIRATION
-
+
-
-
-
-
-
-
M
M
+
+
+
-
-
LAST_TRADE
-
+
-
-
-
-
-
-
M
M
+
+
+
-
+
STRIKE
-
-
-
-
-
-
-
-
-
M
-
+
+
-
-
OPTION_TYPE
-
-
-
-
-
-
-
-
-
+
-
+
-
-
-
EXPIRATION_STYLE
-
-
-
-
-
-
-
-
-
+
-
+
-
-
-
SETTLEMENT_STYLE
-
-
-
-
-
-
-
-
-
+
-
+
+
-
-
PRICE_INCREMENTS
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
TRADING_HOURS
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
FIRST_INTEREST_DATE
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
INTEREST_RATE
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
ISSUE_DATE
-
+
-
-
-
-
-
-
-
+
-
+
-
-
-
ANNOUNCEMENT_DATE
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
AUCTION_DATE
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
PRICE_TYPE
-
M
-
-
-
-
-
-
-
-
-
+
-
-
-
ISSUED_AS_BENCHMARK
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
BENCHMARK_STATUS
-
+
-
-
-
-
-
-
-
-
-
+
-
-
-
Check values for the table above:
Value
Description
M
Mandatory field
+
Optional field is specified if available
-
Inapplicable field is empty
*
For some markets, ISIN, CUSIP and SEDOL fields are available only with the corresponding license
## Snapshot and live updates model
Instrument profiles are usually received as a "snapshot" of all available instruments. Yet, profiles may change, new market instruments may appear at any time (even during trading hours), and existing ones may be removed (after their expiration or maturity). So another streaming (live updates) mode can be used. You can receive an initial snapshot followed by a stream of live updates of changed instrument profiles and additional signals.
To work with the live updates model, do the following:
• Maintain the set of instrument profiles identified by the unique SYMBOL.
• Consider a set of instruments as incomplete until the initial snapshot is fully received. This is indicated by the special signal marking Snapshot Complete state.
• Consider all other profiles as live updates after receiving the initial snapshot.
• Add the profile to the set (add action) after you receive it for the unknown symbol.
• Override the previous profile (update action) after you receive it for an existing symbol.
• Remove the profile from the set (delete action) after you receive it with the special REMOVED instrument type.
• Send a Heartbeat signal to keep the stream alive, depending on the implementation.
For consistency reasons, a static snapshot must also contain the Snapshot Complete signal for integrity. Depending on the implementation, update and remove actions can appear in any part of a snapshot or live updates stream. Simply process them by the rules above. More than one Snapshot Complete signal can occur in a snapshot or live updates stream.
## File format
Instrument profiles can be written to a file in the format, which is based on a CSV (Comma-Separated Values) format as defined in RFC 4180 - see CSV on Wikipedia or RFC 4180 homepage. The basic CSV format is extended to support several alternating record formats which formally violates CSV restrictions. To avoid possible confusion files in this format shall use an IPF extension.
The similarities and differences are:
• Each record is located on a separate line. Each line ends with a line break (CRLF). The last line with a record also ends with a line break. Empty lines (parsing artifacts) shall be ignored.
• Records contain fields, separated by commas. The last field must not be followed by a comma.
• Header line is not used. Instead, records can be of 2 variants: metadata and profile.
• Metadata records start with # (hash) character and can be either type records or commands (tags) or comments
• Metadata type records define a list of fields used by profile records for a given instrument type.
• Metadata commands represent signalling (e.g. Snapshot Complete) in the file format.
• All other metadata records are considered comments.
• Fields use standard CSV quotation rules by enclosing them in double-quotes.
• UTF-8 encoding is used throughout the entire file.
A metadata type record can be distinguished by the special format of its first field: it starts with #character and ends with ::=TYPE text, and the text in the middle specifies the instrument type. The rest of the metadata type record defines a list of fields (in addition to TYPE) that are used by subsequent profile records for a specified instrument type. Thus, a metadata type record looks like the BNF definition of a profile record. Note that the TYPE field must be the first field for each profile record and it determines what format is used by this record.
The ##COMPLETE metadata command represents the Snapshot Complete signal. Note that at least one ##COMPLETE must be present in the file: usually it is located at the end of the file, but can occur in some other place separating the "initial snapshot" part from the live update part of the file. The ## metadata command represents the Heartbeat signal.
If some line starts with a hash character but does not form a correct metadata record, as described above then this line is considered a comment line and can be safely ignored. Note that a comment line must follow the CSV format in regard to the correct field separation and quotation. In this regard, commenting valid but unused CSV lines works perfectly, but plain comments shall avoid double quote characters or they can easily violate CSV specification. These extensions allow for a single IPF file to contain profiles for different instrument types with different record formats. They also allow a user to merge several files with different record formats for the same instrument types into a single one because each new metadata record redefines the record format.
## Sample IPF file
#STOCK::=TYPE,SYMBOL,DESCRIPTION,CURRENCY
STOCK,GOOG,"Alphabet Inc. - Class C Capital Stock",USD
#FUTURE::=TYPE,SYMBOL,DESCRIPTION,CURRENCY,MULTIPLIER,PRODUCT,LAST_TRADE
FUTURE,/YGM23:IFUS,"Mini Gold Futures - ICUS - Jun23",USD,32.15,/YG:IFUS,2023-06-28
##COMPLETE
## Sample IPF from live updates stream
# Comment (comments here and below are added for documentation purposes only)
# Metadata type records
#STOCK::=TYPE,SYMBOL,DESCRIPTION,CURRENCY
#FUTURE::=TYPE,SYMBOL,DESCRIPTION,CURRENCY,MULTIPLIER,PRODUCT,LAST_TRADE
# Instrument profile records
STOCK,GOOG,"Alphabet Inc. - Class C Capital Stock",USD
FUTURE,/YGM23:IFUS,"Mini Gold Futures - ICUS - Jun23",USD,32.15,/YG:IFUS,2023-06-28
# Initial snapshot is complete
##COMPLETE
# Profile update: changed description
FUTURE,/YGM23:IFUS,"Mini Gold Futures ICUS, June 2023",USD,32.15,/YG:IFUS,2023-06-28
# Heartbeat command
##
# FUTURE type is updated: new field CFI is added
#FUTURE::=TYPE,SYMBOL,DESCRIPTION,CURRENCY,CFI,MULTIPLIER,PRODUCT,LAST_TRADE
# Profile update: new value for CFI field is added
FUTURE,/YGM23:IFUS,"Mini Gold Futures ICUS, June 2023",USD,FXXPSX,32.15,/YG:IFUS,2023-06-28
# Profile removal: profile for /YGM23:IFUS symbol must be removed
REMOVED,/YGM23:IFUS
##
# etc. |
# How to blur part of the screen in the game engine?
I'm making an FPS game, and for some of my guns, i want to be able to zoom in so that i can see farther. This isn't the problem. What i really want is to make the rest of the screen (The part not looking through the scope) blurry so that it looks like the character is focusing through the scope.
I want everything that is not seen directly through the scope to be blurred, for example, refer to the scopes of Crysis 3.
• You can use a 2Dfilter to accomplish this. Probably also with a few custom uniforms so you can pass the information to the shader about when and where to blur. – Mike Pan Aug 5 '14 at 18:34
• Are you looking to simulate DOF (Depth of Field), or do you specifically want to blur everything not in scope, by the same factor, regardless of distance from focus point? – Goran Milovanovic Oct 12 '14 at 4:07
• Does this help at all? – VRM Jan 10 '15 at 2:54
• @GoranMilovanovic I want to blur everything not in the scope – christai Jan 27 '15 at 9:40
How it works: the shader gets the rendered image as a texture its x/y coordinates range from 0 to 1.0
The distance from center is calculated by sqrt(x*x+y*y) > .3 to exclude a circular region from blur.
uniform sampler2D bgl_RenderedTexture;
void main(void)
{
vec4 texcolor = texture2D(bgl_RenderedTexture, gl_TexCoord[0].st);
float x = gl_TexCoord[0].st.x - .5;
float y = gl_TexCoord[0].st.y - .5;
if ( sqrt(x*x+y*y) > .3 ) {
float value = 0.0015;
vec4 color = texture2D(bgl_RenderedTexture, vec2(gl_TexCoord[0].st.x + value, gl_TexCoord[0].st.y + value)); // Sample area around current pixel
color += texture2D(bgl_RenderedTexture, vec2(gl_TexCoord[0].st.x - value, gl_TexCoord[0].st.y - value));
color += texture2D(bgl_RenderedTexture, vec2(gl_TexCoord[0].st.x + value, gl_TexCoord[0].st.y - value));
color += texture2D(bgl_RenderedTexture, vec2(gl_TexCoord[0].st.x - value, gl_TexCoord[0].st.y + value));
color /= 4.0;
gl_FragColor = color;
}
else {
gl_FragColor =texcolor;
}
}
Node setup: Add a Filter 2D configure it as Custom Shader and select the above script.
Sample render
Disclaimer: A decent blur needs to incorporate values from a 3x3, 5x5 or bigger matrix, the sample code only uses the left and right neighbor.
• Gosh this was a while back, sorry for not confirming your answer yet :/ Is the float value the blur amount? And how would I incorporate a matrix? – christai Feb 24 '17 at 9:51 |
# What is the slope intercept form of the line passing through (7,2) with a slope of 3/2 ?
Jul 27, 2016
$y = \frac{3}{2} x - \frac{17}{2}$
#### Explanation:
Slope-intercept form is $y = m x + b$. Substitute the values for the variables and solve for b:
$2 = \frac{3}{2} \left(7\right) + b$
$2 = \frac{21}{2} + b$
$- \frac{17}{2} = b$
$y = \frac{3}{2} x - \frac{17}{2}$ |
This site's `404 not found` image is not unique. It's shared with Cross Validated.
It's entirely possible that this is intentional, but since most sites don't have the same image, I thought it was reasonable to suspect that it was a bug.
Sister bug report:
on Meta Cross Validated
• Interestingly creating a CrossValidated account (to tell them that this isn't a bug) gave me 100 free rep on the TeX site (saying that I associated my Area 51 account). Nov 30 '10 at 23:36
• not all sites' 404/captcha/error images are unique, although I'd like them to be. I re-use those that I think are appropriate. For now, I think the Stats ones work OK with the Tex site. Also see @Stefan's answer below.
– Jin
Dec 2 '10 at 6:11
• @Caramdir, yeah, the associations can be a bit wonky, there's been discussion on MSO about that.
– Pops
Dec 2 '10 at 19:41
• @Jin, okay, I didn't know if it was by design. I saw one dupe, and thought it might just have been an oversight, but then I found more....
– Pops
Dec 2 '10 at 19:41 |
## Live Video Streaming with Apache and Nginx
You have set up a video processing pipeline or simply have a camera attached to a Raspberry Pi and want to be able to watch the video from a browser?
Streaming live video can be done using several protocols, among the most popular we have HTTP, RTMP and RTSP.
HTTP is the most widely used protocol to serve static video but can also be used for live content.
RTMP was initially developed by Macromedia (Adobe) to enable streaming of audio and video between a server and a Flash player and is a TCP-based protocol.
RTSP (Real Time Streaming Protocol) was developed by RealNetworks, Netscape, and Columbia University and is not supported natively by most browsers.
Ideally the solution would enable anyone with a working browser, including smartphones and tablets, to be able to consume the video. A good option is to use HTTP Live Streaming (HLS). HLS was developed by Apple Inc. and according to Wikipedia:
“works by breaking the overall stream into a sequence of small HTTP-based file downloads, each download loading one short chunk of an overall potentially unbounded transport stream. A list of available streams, encoded at different bit rates, is sent to the client using an extended M3U playlist.”
By being based on standard HTTP, it is not being blocked by firewalls or proxys that let standard HTTP traffic go through. The drawback is the relatively high latency compared to other protocols.
The solution proposed here is to use the RTMP protocol to send the stream form the camera to the cloud and then convert it to HLS using NGINX. If you want to use Apache or another web server to serve the stream this can be done easily.
NGINX has a very nice rtmp module that is perfectly suited for the task. In order to use it we are going to build NGINX with support for it.
$sudo apt-get install build-essential libpcre3 libpcre3-dev libssl-dev$ git clone git://github.com/arut/nginx-rtmp-module.git
$wget http://nginx.org/download/nginx-1.12.0.tar.gz$ tar xzf nginx-1.12.0.tar.gz
$cd nginx-1.12.0$ ./configure --with-http_ssl_module --add-module=../nginx-rtmp-module
$make$ sudo make install
This will install NGINX in /usr/local.
To start the service
$sudo /usr/local/nginx/sbin/nginx while to stop it: $ sudo /usr/local/nginx/sbin/nginx -s stop
If you are using already a web server, it’s better to modify the nginx configuration file before starting it.
Open the file “/usr/local/nginx/conf/nginx.conf” with an editor and enable RTMP and HLS following the example below (note that i used the user www-data since I have apache installed that uses www-data as user):
user www-data;
worker_processes 1;
error_log logs/error.log debug;
events {
worker_connections 1024;
}
http {
sendfile off;
tcp_nopush on;
directio 512;
default_type application/octet-stream;
server {
listen localhost:2222;
server_name $hostname; location / { root /var/nginx_www; index index.html; } location /hls { # Disable cache add_header Cache-Control no-cache; # CORS setup add_header 'Access-Control-Allow-Origin' '*' always; add_header 'Access-Control-Expose-Headers' 'Content-Length'; # allow CORS preflight requests if ($request_method = 'OPTIONS') {
return 204;
}
types {
application/vnd.apple.mpegurl m3u8;
video/mp2t ts;
}
root /tmp/hls;
}
# rtmp stat
location /stat {
rtmp_stat all;
rtmp_stat_stylesheet stat.xsl;
}
location /stat.xsl {
# you can move stat.xsl to a different location
root /usr/build/nginx-rtmp-module;
}
# rtmp control
location /control {
rtmp_control all;
}
error_page 500 502 503 504 /50x.html;
location = /50x.html {
root html;
}
}
}
rtmp {
server {
listen localhost:1935;
ping 30s;
notify_method get;
application live {
live on;
# sample HLS
hls on;
hls_path /tmp/hls;
hls_sync 100ms;
hls_fragment 3;
hls_playlist_length 60;
allow play all;
}
}
}
With this configuration both the http server and the rtmp servers will listen on localhost with the http on port 2222 and rtmp on the standard 1935.
The HLS files and playlist will be generated and put in “/tmp/hls” (specified by hls_path /tmp/hls;)
To push the stream to the server from a device we can use an ssh tunnel on the port 1935 and map the device-local port 1935 to the remote server port 1935
\$ ssh -L1935:remoteserver:1935
To make the stream accessible by a browser there is a javascript video player video.js that can be embedded in a normal html page.
<!DOCTYPE html>
<html lang="en">
<script src="https://vjs.zencdn.net/7.1/video.min.js"></script>
<body>
<video id="player" class="video-js vjs-default-skin" controls >
<source src="http://remoteserver.com/hls/mystream.m3u8" type="application/x-mpegURL" />
</video>
<script>
var options, video;
options = {
autoplay: true,
muted: true
};
video = videojs('player', options);
</script>
</body>
</html>
the line with
<source src="http://remoteserver.com/hls/mystream.m3u8" type="application/x-mpegURL" />
tells the player where the stream source is located.
In NGINX the rtmp application is called live and the name of the .m3u8 file is mystream.m3u8.
This must match the published rtmp stream url
rtmp://localhost/live/mystream
Since the stream is composed by regular files that are video fragments, it’s sufficient to expose the directory that contains them to the outside world. For example by creating an alias with apache2, inside the virtualhost conf put
Alias /hls "/tmp/hls"
<Directory "/tmp/hls">
AllowOverride All
Order allow,deny
Allow from all
Require all granted
</Directory>
and ensure that the directory /tmp/hls is accessible by the user with which apache executes.
The example working with apache and the opencv + ffmpeg + rtmp streaming example program to generate the stream
Happy streaming!!!
## RTMP streaming using OpenCV and FFMPEG libraries
Do you have a project using OpenCV to process video?
At some point, after your proof-of-concept works, you want to send the result of the processing in real time to some other device. For example to a VM in the cloud with a web server that can push the stream to a browser. You need to use streaming!
When googling for examples of streaming, the option of using ffmpeg libraries becomes appealing but…
FFmpeg examples are mostly about using the FFmpeg command line tool to produce a stream from a video file, while you want to stream on the fly the cv::Mat frames produced by your code.
Using libavcodec libavformat libavutil libswscale libavfilter and libavdevice is not straightforward. It is fairly easy to have crashes and memory leaks that are extremely time consuming to discover and fix.
After spending some time walking through the FFmpeg code, docs and examples, I decided to implement a little example with basic rtmp streaming functionality and share it in the hope it can save some pain to people wanting to implement streaming from OpenCV based applications.
Here is the github repo with the example.
Feel free to contact me for questions, help or suggestions on how to improve it!
## How to alleviate the memory bottleneck in batch normalization
Batch normalization is an important component of Convolutional Neural Networks (CNN). The various improvements it brings, in particular speed and easiness of training, have made the technique widespread. In contrast with convolution operations, that have a high arithmetic intensity (ratio between number of arithmetic operations and data required), batch normalization has a pretty low arithmetic intensity.
This makes batch normalization appear as a non-negligible fraction of the time spent in CNN inference despite the relatively low arithmetic operation count.
It is well known to people concerned with performance in particular in the computer hardware and high performance computing (HPC) communities that memory bandwidth and latency are an important bottleneck in existing computing system (the memory wall). The 3 or 4 level cache hierarchy and associated hardware complexity and power requirements in current processors would have no reason to exist if the main memory could achieve the same level of performance of the caches. It’s interesting to look at the typical latency of operations that are thought to be expensive and compare those with memory accesses that miss the cache.
In the subconscious mind of many programmers floating point operations have high cost while memory operations are virtually free. Nothing is more far from reality. As an example we can look at the latency in clock cycles needed to compute a square root, an operation for which very clever and famous approximate implementations have been produced for game engines. Let’s look at this amazing document : For example SQRTSS on an AMD Bulldozer takes 14-15 clock cycles, while latency to access memory is of the order of ~100 ns or more which at 3GHz translates to ~300 cycles. This is a whopping 20 times the cost of a costly square root.
This observation should immediately make us think about how our program moves and uses data. Writing fast code is primarily about maximizing the amount of useful work done with the data we have loaded into the caches.
In order to manipulate arrays it is common practice to use high level functions that execute very simple operations like element-wise sum, multiply or multiply an array by a scalar, instead of using loops. While this is a good approach in interpreted languages like python (in which a loop can be expensive and it’s preferred to call a function implemented in native code) it might not be always the best option at the C/C++ level.
As an example let’s take a simple sequence of operations we want to do on a few arrays. I will assume the vectors are big and do not fit into the small cache available.
$$A \leftarrow A+B\times d + C\times e$$
where $$A, B$$ and $$C$$ are arrays and $$d, e$$ are scalars.
in pseudo-code a typical implementation might look like:
tmp1 = array_scale(B, d)
tmp2 = array_scale(C, e)
tmp3 = array_sum(tmp1, tmp2)
A = array_sum(A, tmp3)
“Not too bad!” you would think, since array_scale and array_sum are highly optimized functions written by experts. While it is certainly true that array_sum and array_scale are well optimized, and very likely reach the maximum performance obtainable on the system, this alone does not guarantee that the implementation above cannot be improved. Actually it can be greatly improved.
At line 1 we read 1 array and we write out 1 array, for a total of 2 arrays moved. At line 2 the same happens while at line 3 we have 2 array reads and 1 array write, at line 4 we have 2 array reads and 1 array write. If we sum all the movements we get a grand total of 10 array moves between main memory and the execution units. We have also 3 temporary arrays. This is a bit strange isn’t it? In our expression we only have 3 arrays on the right and 1 on the left, which gives 4. How can we get a more efficient implementation? The answer is simple! Let’s use a good old-fashioned loop!
for(i=0;i<n;i++) {
A[i] = A[i] + B[i]*d + C[i]*e;
}
What have we gained? Now the computation is on 1 line, it’s clear to read, no temporary arrays are needed and we have moved 4 arrays, as necessary for our expression, not more.
It’s extremely likely that this implementation is faster than the previous one even if we have not used carefully tuned functions. This is because our computation is memory-bandwidth bound on all modern architectures. The simple loop implementation above is likely to reach the maximum bandwidth available to a core on an typical out-of-order processor with a good hardware prefetcher. The compiler is also likely to optimize well the loop if we are careful enough to make clear that the arrays A, B and C are disjoint. The same maximum bandwidth will be reached by the highly optimized functions called in the first implementation but in that case we have moved 10 arrays! So the speedup $$s$$ of the “loop” implementation compared to the “function call” is approximately:
$$s \approx \frac{10}{4} = 2.5 .$$
Let’s have a look at batch normalization now! From the original paper, we look at the expression defining batch norm:
$$\hat{x}_i = \frac{x_i – \mu_B}{\sqrt{\sigma^2_B + \epsilon}}$$
where $$\mu_B$$ is the mean and $$\sigma^2_B$$ is the variance of the inputs.
They also add a scale and shift operation:
$$y_i = \gamma \cdot \hat{x}_i + \beta$$
The authors, to shine more light on the math, clearly express in the paper that:
Since the means and variances are fixed during inference,
the normalization is simply a linear transform applied to
each activation. It may further be composed with the scaling
by γ and shift by β, to yield a single linear transform
Let’s now “compress” the entire batch norm to a very simple linear transform as claimed and derive the parameters:
$$y_i = \gamma \cdot \frac{x_i – \mu_B}{\sqrt{\sigma^2_B + \epsilon}} + \beta$$
Since $$\gamma$$, $$\mu_B$$, $$\sigma^2_B$$, and $$\epsilon$$ are constants known ahead of running inference, we can simplify the expression and get:
$$y_i = \eta x_i + \omega$$
With $$\eta = \frac{\gamma}{\sqrt{\sigma^2_B + \epsilon}}$$ and $$\omega = – \frac{\gamma\mu_B}{\sqrt{\sigma^2_B + \epsilon}} + \beta$$.
How do we implement batch normalization for inference then?
A loop can do the job very well. In this case also a BLAS function called AXPY together with a couple of other calls might do the job. Since AXPY will destroy the input data replacing it with the output it is not a perfect fit for our operation. We can quickly code the straightforward loop:
for(i=0;i<n;i++) {
output[i] = input[i]*eta + omega;
}
I had a look at the batch norm implementation in a couple of frameworks, Caffe and clDNN from Intel. Caffe does not distinguish well between training and inference time so it does not take real advantage of the situation. While clDNN does a great job, it still does calculations and data movements that can be avoided at inference time.
$$\eta$$ and $$\omega$$ can be computed at model loading ahead of time so the only calculation that needs to be done at every inference is the simple loop above.
In my simple inference engine the batch norm implementation (Caffe-compatible) is merged with ReLU activation to further reduce memory traffic. The unoptimized, but already well performing kernel looks like:
static inline void bn_arrays(float * __restrict__ data_in, float * __restrict__ data_out, size_t n, float nrm, float mn_nrm, bool relu)
{
if(relu) {
for(size_t k=0;k<n;k++) {
data_out[k] = max(data_in[k]*nrm - mn_nrm, 0.0f);
}
} else {
for(size_t k=0;k<n;k++) {
data_out[k] = data_in[k]*nrm - mn_nrm;
}
}
}
We see that in order to reduce memory traffic, we have to give up some code modularity and group operations while looping on data. We might not find in a library the function that does exactly what we need such that we can avoid having a naked loop in our code. Even if we could find it, if the performance is an important factor, the right approach is to measure the performance of different approaches and choose the best one. The way to come up with efficient code is to think in terms of data movement and remember that there is a memory bottleneck.
Code generality and aiming at code reuse are very good principles, but when performance is an important requirement it is not always obvious how to satisfy these often incompatible constraints.
My preference goes to performance, in this case the function is very simple, the logic is straightforward, and I find it more clear than the function-call based implementations. |
# Some Trys related to Von Mangoldt function, What is $\Lambda * \Lambda$
Given Mangoldt function: $$\Lambda(x)=\begin{cases}\ln p,&\text{if x=p^k}\\0,&\text{otherwise}\end{cases}$$
I wonder what about $$\Lambda* \Lambda$$ where $$*$$ denotes the dirichlet multiplication of two arithmetic function.
From my try I think that $$\Lambda(n)=\Lambda(p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3} \dots p_k^{\alpha_k})=\sum_{d|{p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3} \dots p_k^{\alpha_k}}}\Lambda(d)\Lambda(\frac{n}{d})=\begin{cases} 0,&\text{if k=0}\\ (\alpha_1-1)(\log p_1)^2,&\text{if k=1}\\ 2(\log p_1)(\log p_2),&\text{if k=2}\\ 0,&\text{otherwise}\end{cases}$$ Is it correct?
What about $$(\Lambda)*(\Lambda)*(\Lambda) * \dots * (\Lambda)$$
I just started Analytic Number Theory and I am following Tom Apostol
I wanted to know this because of curiousity, It looks like $$\Lambda$$ is necessary function in Analytic Number Theory.
If there is some use of studying $$\Lambda* \Lambda$$
Can you please give me some elementary properties of Mangoldt Function which are usually not written in the books
• Your try on $\Lambda\ast\Lambda$ is correct (fix the LHS). For the $m$-fold Dirichlet convolution of $\Lambda$ with itself - call it $\Lambda_m$ - a formula like yours can be derived; another way to see it is from $\sum_{n>0}\Lambda_m(n)/n^s=(-\zeta'(s)/\zeta(s))^m$. Your last question is somewhat confusing ("elementary" but "not usually in the books"). Start with something like this and follow the links - what else could be recommended?.. – metamorphy Dec 23 '18 at 20:18
• (I should have added "... and the expression for $-\zeta'(s)/\zeta(s)$ from the Euler product".) – metamorphy Dec 23 '18 at 20:29 |
I provided water bottle to my opponent, he drank it then lost on time due to the need of using bathroom. When used, there is a special hash function, which is applied in addition to the main one. Power of two sized tables are often used in practice (for instance in Java). If the arguments range from $0$ to $2^{16}-1$ then the key can only be unique if it can reach $2^{32}-1$. Why are those hash functions considered a bad choice? Thanks for contributing an answer to Stack Overflow! Is this unethical? That works for points in positive plane. To learn more, see our tips on writing great answers. Your function looks interesting, unfortunately I do not understand what the ones help here? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Understanding the zero current in a simple circuit. does calculating the arithmetic mean of a serie of standar deviation measures make sense? your coworkers to find and share information. So, each of $x$ and $y$ can occupy 15 bits. Writing thesis that rebuts advisor's theory. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. The inverse function is described at the wiki page. of int and its size is unknown before setting points in there. But this is slightly wasteful. A solution many people use in practice is to, instead of a simple ad-hoc hash function like h (x) = x \bmod m h(x) = x mod m, use a much more complicated ad-hoc function, with a lot of arbitrary arithmetic instructions thrown together: shift bits around, … This is the reason for the limit of 2,147,483,647, I suppose. How can I write a bigoted narrator while making it clear he is wrong? Use MathJax to format equations. Best prime numbers to choose for a double hashed hash table size? This process can be divided into two steps: Map the key to an integer. So it makes your answer being 2^8*x+y : is this the better solution ? Thanks for contributing an answer to Mathematics Stack Exchange! unordered_map can takes upto 5 arguments: Key : Type of key values. :-). There are 2^32 (about 4 billion) values for x, and 2^32 values of y. The input items can be anything: strings, compiled shader programs, files, even directories. So, for example, we selected hash function corresponding to a = 34 and b = 2, so this hash function h is h index by p, 34, and 2. The resultant of hash function is termed as a hash value or simply hash. Examples: Input : arr[] = {1, 5, 7, -1}, sum = 6 Output : 2 Pairs with sum 6 are (1, 5) and (7, -1) Input : arr[] = {1, 5, 7, -1, 5}, sum = 6 Output : 3 Pairs with sum 6 are (1, 5), (7, … Using hash() on a Custom Object. Since the default Python hash() implementation works by overriding the __hash__() method, we can create our own hash() method for our custom objects, by overriding __hash__(), provided that the relevant attributes are immutable.. Let’s create a class Student now.. We’ll be overriding the __hash__() method to call hash() on the relevant attributes. The hash table in a Python dictionary grows in size as the number of entries increases in order to reduce the number of collisions within the cell. The condition regarding $2^{31}-1$ is perplexing. That is, if $\max(x,y)\lt2^n$, then $\mathrm{key}(x,y)\lt2^{2n}$. Generate a Hash from string in Javascript, Formula for Unique Hash from Integer Pair, Notation from some text about Universal Hashing. @IggY: I was just about to post this same answer. Can one build a "mechanical" universal Turing machine? H(.) I can write the code, if you don't know how. To do that I needed a custom hash function. • A hash function should be consistent with the equality testing function • If two keys are equal, the hash function should map them to the same table location • Otherwise, the fundamental hash table operations will not work correctly • A good choice of hash function can depend on the type of keys, the But there are only 2^32 possible values in a … You may use built-in hashing values as a building block and add your "hashing flavor" in to the mix. No idea about how many collisions this causes for larger integers, though. I have a pair of positive integers $(x, y)$, with $(x, y)$ being different from $(y, x)$, and I'd like to calculate an integer "key" representing them in order that for a unique $(x, y)$ there is an unique key and no other pair $(w, z)$ could generate the same key. Also, for "differ" defined by +, -, ^, or ^~, for nearly-zero or random bases, inputs that differ in any bit or pair of input bits will change Table allows only integers as values. The probability of collision depends of the hash's resolution: if two objects are closer than the intrinsic resolution, the calculated hash will be identical. consecutive integers into an n-bucket hash table, for n being the powers of 2 21.. 220, starting at 0, incremented by odd numbers 1..15, and it did OK for all of them. So hash(x, y) has 2^64 (about 16 million trillion) possible results. this is the same as Jason's solution for the given question, hash function providing unique uint from an integer coordinate pair, http://en.wikipedia.org/wiki/Counting_argument, Mapping two integers to one, in a unique and deterministic way, https://aws.amazon.com/fr/blogs/mobile/geo-library-for-amazon-dynamodb-part-1-table-structure/, Podcast Episode 299: It’s hard to get hacked worse than this. The problem in general: In Section 4 we show how we can efficiently produce hash values in arbitrary integer ranges. Hash function to be used is the remainder of division by 128. It sounds like you are using a 32-bit integer variable in some programming language to represent the key. Why do different substances containing saturated hydrocarbons burns with different flame? Ideal: How to decide whether to optimize model hyperparameters on a development set or by cross-validation? Allow bash script to be run as root, but not sudo. Generally, you should always design your data structures to deal with collisions. https://en.wikipedia.org/wiki/Geohash Hash Table: Should I increase the element count on collisions? Inertial and non-inertial frames in classical mechanics. It only takes a minute to sign up. If you want to hash two uint32's into one uint32, do not use things like Y & 0xFFFF because that discards half of the bits. Some ingeneous encoding trick, or something. Typical example. I had a program which used many lists of integers and I needed to track them in a hash table. Then searching for a key takes expected time at most 1+α. If your coordinates can be in negative axis too, then you will have to do: But to restrict the output to uint you will have to keep an upper bound for your inputs. Can a planet have asymmetrical weather seasons? Let me be more specific. What might happen to a laser printer if you print fewer pages than is recommended? How can I write a bigoted narrator while making it clear he is wrong? In addition, similar hash keys should be hashed to very different hash results. You could use something like $\text{key}(x,y) = 2^{15}x + y$, where $x$ and $y$ are both restricted to the range $[0, 2^{15}]$. by a 16 bit shift and OR. (it may even change), That way you get a random-looking result rather than high bits from one dimension and low bits from the other. Like Emil, but handles 16-bit overflows in x in a way that produces fewer collisions, and takes fewer instructions to compute: You want a mapping (x, y) -> i where x, y, and i are all 32-bit quantities, which is guaranteed not to generate duplicate values of i. ), "hash function to my knowledge only has to provide a surjective mapping from a larger space to a smaller (hash) space". The auxiliary space used by the program is O(1).. 2. Note. A hash function that provides keys with a very low probability of collision. The job of the hash function is to take a key and convert it into a number, which will be the index at which the key-value pair will be stored. But there are only 2^32 possible values in a 32-bit int, so the result of hash() won't fit in a 32-bit int. You can recursively divide your XY plane into cells, then divide these cells into sub-cells, etc. with uint32" into "able to count the dots on the canvas (or the number of coordinate pairs to store" by uint32. Value : Type of value … Anyway, you get the idea -- stuff two 2-byte unsigned integers into a 4-byte word. If a disembodied mind/soul can think, what does the brain do? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Well $2147483647 = 2^{31} - 1$, so we have 31 bits to use, I guess. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Extend unallocated space to my C: drive? There are 2^32 (about 4 billion) values for x, and 2^32 values of y. Properties of good hash function: Should be a one-way algorithm. A hash table is a data structure that is used to store keys/value pairs. Emil's solution is great, in C#: See Mapping two integers to one, in a unique and deterministic way for a plethora of options.. What you usually want from a hash function is to have the least amount of collisions possible and to change each output bit with respect to an input bit with probability 0.5 without discernible patterns. https://github.com/awslabs/dynamodb-geo. Proof. Are these positive or non-negative integers?? Deterministic, you will always get the same hash for a specific input. Yeah thx. the Fibonacci hash works very well for integer pairs, other word sizes 1/phi = (sqrt(5)-1)/2 * 2^w round to odd, this will give very different values for close together pairs, I do not know about the result with all pairs. Connection between SNR and the dynamic range of the human ear. This implies when the hash result is used to calculate hash bucket address, all buckets are equally likely to be picked. Also, for reference, see @JonSkeet's answer to similar: Hi a hash function to my knowledge only has to provide a surjective mapping from a larger space to a smaller (hash) space. I am aware of that. Here's why: suppose there is a function hash() so that hash(x, y) gives different integer values. Making statements based on opinion; back them up with references or personal experience. A hash function maps keys to small integers (buckets). So this is a family of hash functions which contains p multiplied by p-1, different hash functions for different bayers ab. I don't mind if we can/can't guess the pair values based on the key. What happens when all players land on licorice in Candy Land? Unordered Map does not contain a hash function for a pair like it has for int, string, etc, So if we want to hash a pair then we have to explicitly provide it with a hash function that can hash a pair. Like: And also having test cases like "predefined million point set" running against each possible hash generating algorithm comparison for different aspects like, computation time, memory required, key collision count, and edge cases (too big or too small values) may be handy. is true for (3^k - 2^k) / 4^k pairs, ie. IMPORTANT: It is impossible to know the size of the canvas beforehand It uses a hash function to compute an index into an array in which an element will be inserted or searched. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. + min (a,b)) c will be unique and reversible for all interchangeable combinations of a and b. so for example, myhash (124,24) = 124.24 myhash (24,124) = 124.24 myhash (11231,26611) = 26611.11231. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. However, the statement about the key being less than $2^{31}-1$ was a bit perplexing. You can then use 16 bits for $x$, and 16 bits for $y$. For a hash function, the distribution should be uniform. The values returned by a hash function are … Split a number in every way possible way within a threshold, Animated TV show about a vampire with extra long teeth. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. If you're already using languages or platforms that all objects (even primitive ones like integers) has built-in hash functions implemented (Java platform Languages like Java, .NET platform languages like C#. This is not a programming forum, but still, remember that. A hash function is a function or algorithm that is used to generate the encrypted or shortened value to any given key. Split a number in every way possible way within a threshold. Assume that we hash n keys to a table of size m, n ≤ m, using a hash function h chosen at random from a universal family of hash functions, and we resolve collisions by chaining. High Speed Hashing for Integers and Strings Mikkel Thorup July 15, 2014 1 Hash functions The concept of truly independent hash functions is extremely useful in the design of randomized algorithms. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Initialize the hash function with a vector ¯ = (, …, −) of random odd integers on bits each. See also http://en.wikipedia.org/wiki/Counting_argument. Representing a String of n characters, as a unique integer. @tohecz: I had no idea that in someplaces "positive integers" included $0$. Ih(x) = x mod N is a hash function for integer keys. What is a minimal hash function for a pair of ints that has low chance of collisions? The time complexity of the above solution O(n 2), where n is the size of the input array. I changed the assumption "able to count the number of points of the canvas Under reasonable assumptions, the average time required to search for an element in a hash table is O(1). It is actually a sparse representation for points and will need a custom Quadtree structure that extends the canvas by adding branches when you add points off the canvas but it avoids collisions and you'll have benefits like quick nearest neighbor searches. My Problem is, though, that the number of dots on the canvas is very low compared to the canvas size, so I thought, there should be some way to stay collision free. I have a big 2d point space, sparsely populated with dots. Can the plane be covered by open disjoint one dimensional intervals? The problem is that when you take it modulo some number to find out the real index in the hashmap, the upper bits are just discarded and you get a lot of collisions. For every pair of distinct keys k … So maybe I should have said $k(x,y) = 2^{15}x + y$. How is HTTPS protected against MITM attacks by other countries? We have a large universe Uof keys, e.g., 64-bit numbers, that we wish to map ran-domly to a range [m] = f0;:::;m 1gof hash values. Asking for help, clarification, or responding to other answers. It looks like it runs at least 8 bit of x into the wall (? Discreet bounding/mapping function with convergence/uniformity. The following hash family is universal: [14] h a ¯ ( x ¯ ) = ( ( ∑ i = 0 ⌈ k / 2 ⌉ ( x 2 i + a 2 i ) ⋅ ( x 2 i + 1 + a 2 i + 1 ) ) mod 2 2 w ) d i v 2 2 w − M {\displaystyle h_{\bar {a}}({\bar {x}})=\left({\Big (}\sum _{i=0}^{\lceil k/2\rceil }(x_{2i}+a_{2i})\cdot (x_{2i+1}+a_{2i+1}){\Big )}{\bmod {~}}2^{2w}\right)\,\,\mathrm {div} \,\,2^{2w-M}} . I have to iterate over and search through these dots a lot. The advantage is that when $x,y= 0). By using a good hash function, hashing can work well. +1. Calculate unique Integer representing a pair of integers. My original question didn't make much sense, because I would have had a sqrt(max(uint32))xsqrt(max(uint32)) sized canvas, which is uniquely representable This is nicely reversible if you know the original x and y are 16 bit. The hash value of an array of positive integers will always be between 0 and$2n$where$n$is the largest value in the array. The Canvas (point space) can be huge, bordering on the limits The same input always generates the same hash value, and a good hash function tends to generate different hash values when given different inputs. The only catch is that since the sign bit is treated specially, you have to be a little careful when a negative x is a possibility. Is the Gloom Stalker's Umbral Sight cancelled out by Devil's Sight? So the formula for the hash function is on the side, and parameters a and b are from one to p-1 and from zero to p-1, respectively. Generally, hash functions calculate an integer value from the key. Think of it like a fingerprint of any given input data. Why should hash functions use a prime number modulus? If you still want to use an int variable for the key (k), then the code (in C#) is: With this approach, we require$x \le 65535$(16 bits) and$y \le 32767$(15 bits), and k will be at most 2,147,483,647, so it can be held in a 32-bit int variable. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. It is reasonable to make p a prime number roughly equal to the number of characters in the input alphabet.For example, if the input is composed of only lowercase letters of English alphabet, p=31 is a good choice.If the input may contain … Do something like, (you need to transform one of the variables first to make sure the hash function is not commutative). You can assume that the number of Is it safe to use a receptacle with wires broken off in the backstab connectors? x * 0x1f1f1f1f does not run any bits of x into wall, multiplying by an odd number modulo 2**32 is a bijective mapping! Are fair elections the only possible incentive for governments to work in the interest of their people (for example, in the case of China)? Thanks, this hash has the advantage that it works much better in practice than (y<<16)^x. Hash functions. This covers squares first, so should meet your conditions as well as not being limited to a given argument maximum. Is the Gloom Stalker's Umbral Sight cancelled out by Devil's Sight? If you want output to be strictly uint for unknown range of inputs, then there will be reasonable amount of collisions depending upon that range. Hash Function. The question says nothing about the numbers being restricted to a given range. Both right - for proof, see. Using this sort of approach, recovering$x$and$y$from a given key is easy to code and extremely fast -- you just grab the relevant bits from the key variable. There are many applications where there keys will be a large number of arrays with a small range and for those applications there will be many collisions, so worse than$O(1)$expected time for operations on the hash table. In the view of implementation, this hash function can be encoded using remainder operator or using bitwise AND with 127. rev 2020.12.18.38240, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide. This past week I ran into an interesting problem. A hash function takes an item of a given type and generates an integer hash value within a given range. and if so, then it turns out that you know the bounds. Checking whether a mutable set contains an object with identical properties. (in my example, k) which should be small (ie. https://aws.amazon.com/fr/blogs/mobile/geo-library-for-amazon-dynamodb-part-1-table-structure/ Is it safe to use a receptacle with wires broken off in the backstab connectors? Like 3 months for summer, fall and spring each and 6 months of winter? must fit in an integer or long). I don't mind if we can/can't guess the pair … The resulting Geohash value is a 63 bit number. A hash functionis any functionthat can be used to map dataof arbitrary size to fixed-size values. In other words in programming its impractical to write a function without having an idea on the integer type your inputs and output can be and if so there definitely will be a lower bound and upper bound for every integer type. 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## Escaping from the police: a brute-force solver
Posted by Diego Assencio on 2013.10.27 under Computer science (Algorithms)
A group of $N$ fugitives is running away from the police. They reach a very narrow bridge. Since it's dark and they have a single flashlight, they can only cross the bridge in pairs. The $i^{th}$ fugitive takes $T_i$ minutes to cross the bridge. When a pair of fugitives crosses the bridge, they must go at the speed of the slowest fugitive. In other words, the crossing time for the pair of fugitives $(i,j)$ is $\max\{T_i,T_j\}$.
After a pair of fugitives crosses the bridge, one of those who already crossed must return with the flashlight so that another pair of fugitives can go too (this new pair can include the fugitive who just brought back the flashlight). The process goes on until everyone has crossed the bridge.
If the police is $T_p$ minutes behind the prisoners, and assuming they can no longer safely escape unless all of them have crossed the bridge by the time the police gets to it, can they make it? If yes, how?
I was asked this question during a job interview and found it very interesting, so I decided to write a brute-force solver for this problem and discuss it here.
The problem only becomes interesting if $N \ge 3$. Indeed, if $N = 2$ the two fugitives will make it as long as $\max\{T_1,T_2\} \le T_p$, meaning if the slower fugitive needs longer than $T_p$ to cross the bridge, the police will arrive before they can safely flee. The case $N = 1$ is excluded as we would have a single fugitive crossing the bridge, but the statement of the problem says they should cross it (to the safe side) in pairs (so $N \ge 2$).
NOTE: readers who just wish to play with the brute-force solver should go directly to the end of this post. If you are interested in the discussion of the problem, read on!
Let's first compute the number of steps $S_N$ which must happen until all $N$ fugitives have crossed the bridge. A step can be either a pair of fugitives crossing the bridge or one fugitive returning. We will prove that: $$\boxed{ S_N = 2N - 3 }$$
To see this, notice first that for $N = 2$ we have only one step (the two fugitives cross the bridge), so the equation above applies since $S_2 = 1$. Now assume the formula formula is valid for $N-1$ fugitives. Then, for $N$ fugitives, after the first two cross and one returns with the flashlight (in other words, after two steps), we have $N-1$ fugitives left to cross the bridge. From there on, there are $S_{N-1}$ steps until all fugitives have crossed. So: $$S_N = S_{N-1} + 2 = \left[2(N-1) - 3\right] + 2 = 2N-3$$ as we wanted to prove.
Now let's compute the theoretical maximum number of possibilities that one has to try when using brute force to solve the problem. First notice that if $N$ fugitives have not yet crossed the bridge, the number of possible pairs for crossing it is: $$\left(\matrix{N \\ 2}\right) = \frac{N(N-1)}{2}$$
When a fugitive must return with the flashlight, and if $M$ fugitives have already crossed the bridge, then the number of choices is, well... $M$.
We will therefore have the scheme shown below. I have marked the side which has the flashlight in green; "crossed" refers to the number of fugitives which have already crossed the bridge while "must still cross" refers to the fugitives which must still cross it:
CrossedMust still crossPossibilities
$0$$N$$\frac{N(N-1)}{2}$
$2$$N-2$$2$
$1$$N-1$$\frac{(N-1)(N-2)}{2}$
$3$$N-3$$3$
$\vdots$$\vdots$$\vdots$
$N-5$$5$$\frac{5\cdot 4}{2} = 10$
$N-3$$3$$N-3$
$N-4$$4$$\frac{4\cdot 3}{2} = 6$
$N-2$$2$$N-2$
$N-3$$3$$\frac{3\cdot 2}{2} = 3$
$N-1$$1$$N-1$
$N-2$$2$$\frac{2 \cdot 1}{2} = 1$
$N$$0$$0$ (done)
The maximum number of moves $P_N$ which a brute-force solver must simulate is then: $$\begin{eqnarray} P_N & = & \displaystyle\frac{N(N-1)}{2}\cdot 2\cdot \frac{(N-1)(N-2)}{2} \ldots (N-2) \frac{3\cdot 2}{2} (N-1) \frac{2 \cdot 1}{2} \nonumber \\[5pt] & = & \left[2 \ldots (N-2)(N-1)\right]\left[\displaystyle\frac{N(N-1)}{2}\frac{(N-1)(N-2)}{2} \ldots \frac{3\cdot 2}{2} \frac{2 \cdot 1}{2}\right] \nonumber \\[5pt] & = & (N-1)! \displaystyle \frac{N(N-1)^2(N-2)^2 \ldots 3^2 \cdot 2^2 \cdot 1}{2^{N-1}} \nonumber \\[5pt] & = & (N-1)! \displaystyle \frac{N^2(N-1)^2(N-2)^2 \ldots 3^2 \cdot 2^2}{2^{N-1}N} \nonumber \\[5pt] & = & \displaystyle\frac{(N-1)!}{2^{N-1}N} (N!)^2 \end{eqnarray}$$ and therefore: $$\boxed{ P_N = \displaystyle\frac{N!^3}{2^{N-1}N^2} }\label{post_eeb0a9ec9ceed243221955dad220b478_num_possibilities}$$
The table below shows the values of $P_N$ for some values of $N$:
$N$$P_N 2$$1$
$3$$6 4$$108$
$5$$4320 6$$324000$
$7$$40824000 8$$8001504000$
From the numbers above and from equation \eqref{post_eeb0a9ec9ceed243221955dad220b478_num_possibilities}, it is clear that the computational work required to simulate all possibilities grows extremely fast ($N!$ grows much faster than both $2^{N-1}$ and $N$). This will impose a limitation on how many fugitives ($N$) we can have when trying to solve the problem using brute force. The solver can be made more efficient, however, if it uses recursion and only keeps on going down a given branch of possibilities as long as the total crossing time has not yet exceeded the police time on that branch (for the picky reader: recursion will not be a problem here as the number of fugitives will hardly exceed a dozen). Also, the solver can be made more efficient by not distinguishing between fugitives which take the same time to cross the bridge.
Now, to the brute-force solver! On the text fields below, enter the times taken by each fugitive to cross the bridge and the time the police will take to reach it. The values must be separated by commas (the values already entered are the ones I received on my job interview). If two or more fugitives take the same amount of time to cross the bridge, the solver will not output solutions with the same numbers twice.
Fugitive times: 1,2,5,10 Police time:
Find all solutions |
# Proving Cantelli's inequality
I'm assuming that the random variable $X$ has mean $0$ and finite variance ${\sigma}^2$. It is immediate from Chebyshev's inequality that $$P(X\geq x)\leq \frac{{\sigma}^2}{x^2},$$ but I'm still trying to show that $$P(X\geq x)\leq \frac{{\sigma}^2}{{\sigma}^2+x^2}$$ for $x>0$. Any hints would be appreciated.
(I've shown that $$P(X\geq x)\leq \frac{E[(X+a)^2]}{(a+x)^2}$$ for $a\geq 0$.)
• this is known as the Cantelli inequality. – mookid Feb 9 '15 at 20:53
• @mookid Thanks! – Aubrey Feb 9 '15 at 21:02
• @mookid Your comment helped me look up a hint and find the answer. I guess I could now delete the question since I don't need an answer anymore? – Aubrey Feb 9 '15 at 21:08
• It could help someone. Maybe try to answer yourself! – mookid Feb 9 '15 at 21:09
Note that $t=E(t-X) \leq\sum_{i:x_i<t}(t-x_i)p_i$
Now, $t^2\leq (\sum_{i:x_i<t}(t-x_i)p_i)^2=(\sum_{i:x_i<t}(t-x_i)\sqrt{p_i} \sqrt{p_i})^2\\\le E(t-X)^2 P[X<t],$
having used the Cauchy-Schwarz inequality.
So, $P[X<t]\ge \frac{t^2}{t^2+\sigma^2}$ as $E(t-X)^2=t^2+\sigma^2$
So, $P[X\ge t] \le \frac{\sigma^2}{t^2+\sigma^2}$
• How would this argument work if the probability space is not discrete? Aubrey's hint is one without any assumption on the space. – Batominovski Jul 24 '15 at 20:42
After showing that $$P(X\geq x)\leq \frac{E[(X+a)^2]}{(a+x)^2}$$ for $a\geq 0$, we only need to minimize over $a$ and we obtain the result. |
# Is it true that $\mathbb{Z}[\sqrt{-3}] + \mathbb{Z}[\sqrt{-5}]$ not a ring?
Question: Is it true that $$\mathbb{Z}[\sqrt{-3}] + \mathbb{Z}[\sqrt{-5}]$$ not a ring?
I think it is not because it is not closed under multiplication. More precisely, if $$a_1+b_1\sqrt{-3}, a_2+b_2\sqrt{-3}\in \mathbb{Z}[\sqrt{-3}]$$ and $$c_1+d_1\sqrt{-5},c_2+d_2\sqrt{-5}\in \mathbb{Z}[\sqrt{-5}],$$ then $$(a_1+b_1\sqrt{-3} + c_1+d_1\sqrt{-5}) \cdot (a_2+b_2\sqrt{-3} + c_2+d_2\sqrt{-5})$$ is not an element of $$\mathbb{Z}[\sqrt{-3}] + \mathbb{Z}[\sqrt{-5}].$$
• That would be correct. – Parcly Taxel Nov 17 '18 at 4:50
• That can be an element of $\Bbb Z[\sqrt{-3}]+\Bbb Z[\sqrt{-5}]$ for some values of the variables. To show it's not closed under multiplication, all one has to do is give an example. The easy example is $\sqrt{-3}\times\sqrt{-5}$. – Lord Shark the Unknown Nov 17 '18 at 5:28
For instance, $$\sqrt{-3}$$ and $$\sqrt{-5}$$ are both in your set, but their product (whether that's $$-\sqrt{15}$$ or $$\sqrt{15}$$) isn't.
However, $$\Bbb Z[\sqrt{-3}]+\Bbb Z[\sqrt{-5}]+\Bbb Z[\sqrt{15}]$$ is a ring. |
• Linear regression is one of the simplest supervised learning algorithms.
• Consider the example of autonomous driving which is a supervised learning problem. The term supervised learning implies that you’re given inputs $$X$$ and the algorithm maps that to an output $$Y$$.
• In case of autonomous driving, $$X$$ is a picture of what’s in front of the car, $$Y$$ is the steering direction.
• Particularly, that was a regression problem because the output $$Y$$ is a continuous value; as opposed to a classification problem, where $$Y$$ is the speed.
• supervised learning regression. So I think the simplest, maybe the simplest possible learning algorithm, a supervised learning regression problem, is linear regression. And to motivate that, rather than using a self-driving car example which is quite complicated, we’ll- we’ll build up a supervised learning algorithm using a simpler example. so let’s say you want to predict or estimate the prices of houses. So the way you build a learning algorithm is start by collecting a data-set of houses, and their prices. so this is a data-set that we collected off Craigslist a little bit back. This is data from Portland, Oregon. But so there’s the size of a house in square feet, um, and there’s the price of a house in thousands of dollars. And so there’s a house that is 2,104 square feet whose asking price was \(400,000. house with, uh, that size, with that price, and so on. Okay? and maybe more conventionally if you plot this data, there’s a size, there’s a price. So you have some dataset like that. And what we’ll end up doing today is fit a straight line to this data. And go through how to do that. So in supervised learning, um, the process of supervised learning is that you have a training set such as the data-set that I drew on the left, and you feed this to a learning algorithm. And the job of the learning algorithm is to output a function, to make predictions about housing prices. And by convention, um, I’m gonna call this a function that it outputs a hypothesis. And the job of the hypothesis is, you know, it will- it can input the size of a new house, or the size of a different house that you haven’t seen yet, and will output the estimated price. Okay? so the job of the learning algorithm is to input a training set, and output a hypothesis. The job of the hypothesis is to take as input, any size of a house, and try to tell you what it thinks should be the price of that house. Now, when designing a learning algorithm, and- and, you know, even though linear regression. You may have seen it in a linear algebra class before, or some other class before, um, the way you go about structuring a machine learning algorithm is important. And design choices of, you know, what is the workflow? What is the data-set? What is the hypothesis? How does this represent the hypothesis? These are the key decisions you have to make in pretty much every supervised learning, every machine learning algorithm’s design. So, as we go through linear regression, I will try to describe the concepts clearly as well because they’ll lay the foundation for the rest of the algorithms. Sometimes it’s much more complicated with the algorithms you’ll see later this quarter. So when designing a learning algorithm the first thing we need to ask is, um, how- how do you represent the hypothesis, H. And in linear regression, for the purpose of this lecture, we’re going to say that, um, the hypothesis is going to be that. Right? That the input, size X, and output a number as a- as a linear function, of the size X, okay? And then, the mathematicians in the room, you’ll say technically this is an affine function. It was a linear function, there’s no theta 0, technically, you know, but- but the machine learning sometimes just calls this a linear function, but technically it’s an affine function. Doesn’t- doesn’t matter. so more generally in- in this example we have just one input feature X. More generally, if you have multiple input features, so if you have more data, more information about these houses, such as number of bedrooms Excuse me, my handwriting is not big. That’s the word bedrooms. Then, I guess- All right. Yeah. Cool. My- my- my father-in-law lives a little bit outside Portland, and he’s actually really into real estate. So this is actually a real data-set from Portland. [LAUGHTER] so more generally, if you know the size, as well as the number of bedrooms in these houses, then you may have two input features where X1 is the size, and X2 is the number of bedrooms. I’m using the pound sign bedrooms to denote number of bedrooms, and you might say that you estimate the size of a house as, h of x equals, theta 0 plus theta 1, X1, plus theta 2, X2, where X1 is the size of the house, and X2 is- is the number of bedrooms. Okay? so in order to- so in order to simplify the notation, in order to make that notation a little bit more compact, I’m also gonna introduce this other notation where, we want to write a hypothesis, as sum from J equals 0-2 of theta JXJ, so this is the summation, where for conciseness we define X0 to be equal to 1, okay? See we define- if we define X0 to be a dummy feature that always takes on the value of 1, then you can write the hypothesis h of x this way, sum from J equals 0-2, or just theta JXJ, okay? It’s the same with that equation that you saw to the upper right. And so here theta becomes a three-dimensional parameter, theta 0, theta 1, theta 2. This index starting from 0, and the features become a three dimensional feature vector X0, X1, X2, where X0 is always 1, X1 is the size of the house, and X2 is the number of bedrooms of the house, okay? So, to introduce a bit more terminology. Theta is called the parameters, um, of the learning algorithm, and the job of the learning algorithm is to choose parameters theta, that allows you to make good predictions about your prices of houses. and just to lay out some more notation that we’re gonna use throughout this quarter. We’re gonna use a standard that, M, we’ll define as the number of training examples. So M is going to be the number of rows, right, in the table above, um, where, you know, each house you have in your training set. This one training example. you’ve already seen me use X to denote the inputs, and often the inputs are called features. you know, I think, I don’t know, as- as- as a- as a emerging discipline grows up, right, notation kind of emerges depending on what different scientists use for the first time when you write a paper. So I think that, I don’t know, I think that the fact that we call these things hypotheses, frankly, I don’t think that’s a great name. But- but I think someone many decades ago wrote a few papers calling it a hypothesis, and then others followed, and we’re kind of stuck with some of this terminology. But X is called input features, or sometimes input attributes, um, and Y is the output. And sometimes we call this the target variable. Okay. Uh, so x, y is, one training example. and, uh, I’m going to use this notation, um, x_i, y_i in parentheses to denote the i_th training example. Okay. So the superscript parentheses i, that’s not exponentiation. Uh, I think that as suppo- this is- um, this notation x_i, y_ i, this is just a way of, writing an index into the table of training examples above. Okay. So, so maybe, for example, if the first training example is, uh, the size- the house of size 2104, so x_1_1 would be equal to 2104, right, because this is the size of the first house in the training example. And I guess, x, um, second example, feature one would be 1416 with our example above. So the superscript in parentheses is just some, yes, it’s, it’s just the, um, index into the different training examples where i- superscript i here would run from 1 through m, 1 through the number of training examples you have. and then one last bit of notation, um, I’m going to use n to denote the number of features you have for the supervised learning problem. So in this example, uh, n is equal to 2. Because we have two features which is, the size of house and the number of bedrooms, so two features. Which is why you can take this and, and write this, um, as the sum from j equals 0 to n. and so here, x and Theta are n plus 1 dimensional because we added the extra, x_0 and Theta_0. Okay. So- so we have two features then these are three-dimensional vectors. And more generally, if you have n features, you, you end up with x and Theta being n plus 1 dimensional features. All right. And, you know, uh, you see this notation in multiple times, in multiple algorithms throughout this quarter. So if you, you know, don’t manage to memorize all these symbols right now, don’t worry about it. You’ll see them over and over and they become familiar. All right. So, given the data set and given that this is the way you define the hypothesis, how do you choose the parameters. So you- the learning algorithm’s job is to choose values for the parameters Theta so that it can output a hypothesis. So how do you choose parameters Theta? Well, what we’ll do, um, is let’s choose Theta such that h of x is close to y, for the training examples. Okay. So, and I think the final bit of notation, um, I’ve been writing h of x as a function of the features of the house, as a function of the size and number of bedrooms of the house. sometimes we emphasize that h depends both on the parameters Theta and on the input features x. Um, we’re going to use h_Theta of x to emphasize that the hypothesis depends both on the parameters and on the, you know, input features x. But, sometimes for notational convenience, I just write this as h of x, sometimes I include the Theta there, and they mean the same thing. It’s just, maybe a abbreviation in notation. Okay. But so in order to, learn a set of parameters, what we’ll want to do is choose a parameters Theta so that at least for the houses whose prices you know, that, you know, the learning algorithm outputs prices that are close to what you know where the correct price is for that set of houses, what the correct asking price is for those houses. And so more formally, um, in the linear regression algorithm, also called ordinary least squares. With linear regression, um, we will want to minimize, I’m gonna build out this equation one piece at a time, okay? Minimize the square difference between what the hypothesis outputs, h_Theta of x minus y squared. So let’s say we wanna minimize the squared difference between the prediction, which is h of x and y, which is the correct price. and so what we want to do is choose values of Theta that minimizes that. to fill this out, you know, you have m training examples. So I’m going to sum from i equals 1 through m of that square difference. So this is sum over i equals 1 through all, say, 50 examples you have. of the square difference between what your algorithm predicts and what the true price of the house is. and then finally, by convention, we put a one-half there- put a one-half constant there because, uh, when we take derivatives to minimize this later, putting a one-half there would make some of the math a little bit simpler. So, you know, changing one- adding a one-half. Minimizing that formula should give you the same as minimizing one-half of that but we often put a one-half there so to make the math a little bit simpler later, okay? And so in linear regression, we’re gonna define the cost function J of Theta to be equal to that. And, we’ll find parameters Theta that minimizes the cost function J of Theta, okay? and, the questions I’ve often gotten is, you know, why squared error? Why not absolute error, or this error to the power of 4? We’ll talk more about that when we talk about, uh, when, when, when we talk about the generalization of, linear regression. when we talk about generalized linear models, which we’ll do next week, you’ll see that, um, linear regression is a special case of a bigger family of algorithms called generalizing your models. And that, using squared error corresponds to a Gaussian, but the- we, we, we’ll justify maybe a little bit more why squared error rather than absolute error or errors to the power of 4, next week. So, let me just check, see if any questions, at this point. No, okay. Cool. All right. So, um, so let’s- next let’s see how you can implement an algorithm to find the value of Theta that minimizes J of Theta. That- that minimizes the cost function J of Theta. we’re going to use an algorithm called gradient descent. And, you know, this is my first time teaching in this classroom, so trying to figure out logistics like this. All right. Let’s get rid of the chair. Cool, all right. And so with, uh, gradient descent we are going to start with some value of Theta, and it could be, you know, Theta equals the vector of all zeros would be a reasonable default. We can initialize it randomly, the count doesn’t really matter. But, Theta is this three-dimensional vector. And I’m writing 0 with an arrow on top to denote the vector of all 0s. So 0 with an arrow on top that’s a vector that says 0, 0, 0, everywhere, right. So, so sought to some, you know, initial value of Theta and we’re going to keep changing Theta, to reduce J of Theta, okay? So let me show you a, um- vi- vis- let me show you a visualization of gradient descent, and then- and then we’ll write out the math. so- all right. Let’s say you want to minimize some function J of Theta and, it’s important to get the axes right in this diagram. So in this diagram the horizontal axes are Theta 0 and Theta 1. And what you want to do is find values for Theta 0 and Theta 1. In our- I- I- In our example it’s actually Theta 0, Theta 1, Theta 2 because Theta’s 3-dimensional but I can’t plot that. So I’m just using Theta 0 and Theta 1. But what you want to do is find values for Theta 0 and Theta 1. That’s the, right, you wanna find values of Theta 0 and Theta 1 that minimizes the height of the surface j of Theta. So maybe this- this looks like a good- pretty good point or something, okay? and so in gradient descent you, you know, start off at some point on this surface and you do that by initializing Theta 0 and Theta 1 either randomly or to the value of all zeros or something doesn’t- doesn’t matter too much. And, what you do is, uh, im- imagine that you are standing on this lower hill, right standing at the point of that little x or that little cross. what you do in gradient descent is, uh, turn on- turn around all 360 degrees and look all around you and see if you were to take a tiny little step, you know, take a tiny little baby step, in what direction should you take a little step to go downhill as fast as possible because you’re trying to go downhill which is- goes to the lowest possible elevation, goes to the lowest possible point of J of Theta, okay? So what gradient descent will do is, uh, stand at that point look around, look all- all around you and say, well, what direction should I take a little step in to go downhill as quickly as possible because you want to minimize, J of Theta. You wanna minim- reduce the value of J of Theta, you know, go to the lowest possible elevation on this hill. and so gradient descent will take that little baby step. And then- and then repeat. Uh, now you’re a little bit lower on the surface. So you again take a look all around you and say oh it looks like that hill, that- that little direction is the steepest direction or the steepest gradient downhill. So you take another little step, take another step- another step and so on, until, until you- until you get to a hopefully a local optimum. Now one property of gradient descent is that, uh, depend on where you initialize parameters, you can get to local diff- different points. So previously, you had started it at that lower point x. But imagine if, uh, you had started it, you know, just a few steps over to the right. At that- at that new x instead of the one on the left. If you had run gradient descent from that new point then, uh, that would have been the first step, that would be the second step and so on. And you would have gotten to a different local optimum- to a different local minima, okay? it turns out that when you run gradient descents on linear regression, it turns out that, uh, there will not be local optimum but we’ll talk about that in a little bit, okay? So let’s formalize the gradient descent algorithm. In gradient descent, um, each step of gradient descent, is implemented as follows. So- so remember, in- in this example, the training set is fixed. You- You know you’ve collected the data set of housing prices from Portland, Oregon so you just have that stored in your computer memory. And so the data set is fixed. The cost function J is a fixed function there’s function of parameters Theta, and the only thing you’re gonna do is tweak or modify the parameters Theta. One step of gradient descent, can be implemented as follows, which is Theta j gets updated as Theta j minus, I’ll just write this out, okay? so bit more notation, I’m gonna use colon equals, I’m gonna use this notation to denote assignment. So what this means is, we’re gonna take the value on the right and assign it to Theta on the left. And so, so in other words, in the notation we’ll use this quarter, you know, a colon equals a plus 1. This means increment the value of a by 1. whereas, you know, a equals b, if I write a equals b I’m asserting a statement of fact. I’m asserting that the value of a is equal to the value of b. and hopefully, I won’t ever write a equals a plus 1, right because- cos that is rarely true, okay? all right. So, uh, in each step of gradient descent, you’re going to- for each value of j, so you’re gonna do this for j equals 0, 1 ,2 or 0, 1, up to n, where n is the number of features. For each value of j takes either j and update it according to Theta j minus Alpha. which is called the learning rate. Alpha the learning rate times this formula. And this formula is the partial derivative of the cost function J of Theta with respect to the parameter, Theta j, okay? In- and this partial derivative notation. Uh, for those of you that, um, haven’t seen calculus for a while or haven’t seen, you know, some of their prerequisites for a while. We’ll- we’ll- we’ll go over some more of this in a little bit greater detail in discussion section, but I’ll- I’ll- I’ll do this, quickly now. But, I don’t know. If, if you’ve taken a calculus class a while back, you may remember that the derivative of a function is, you know, defines the direction of steepest descent. So it defines the direction that allows you to go downhill as steeply as possible, on the, on the hill like that. There’s a question. How do you determine the learning rate? How do you determine the learning rate? Ah, let me get back to that. It’s a good question. Uh, for now, um, you know, there’s a theory and there’s a practice. Uh, in practice, you set to 0.01. [LAUGHTER]. [LAUGHTER] Let me say a bit more about that later. [NOISE]. Uh, if- if you actually- if- if you scale all the features between 0 and 1, you know, minus 1 and plus 1 or something like that, then, then, yeah. Then, then try- you can try a few values and see what lets you minimize the function best, but if the feature is scaled to plus minus 1, I usually start with 0.01 and then, and then try increasing and decreasing it. Say, say a little bit more about that. all right, cool. So, let’s see. Let me just quickly show how the derivative calculation is done. and you know, I’m, I’m gonna do a few more equations in this lecture, and then, and then over time I think. all, all of these, all of these definitions and derivations are written out in full detail in the lecture notes, posted on the course website. So sometimes, I’ll do more math in class when, um, we want you to see the steps of the derivation and sometimes to save time in class, we’ll gloss over the mathematical details and leave you to read over, the full details in the lecture notes on the CS229 you know, course website. so partial derivative with respect to J of Theta, that’s the partial derivative with respect to that of one-half H of Theta of X minus Y squared. Uh, and so I’m going to do a slightly simpler version assuming we have just one training example. The, the actual deriva- definition of J of Theta has a sum over I from 1 to M over all the training examples. So I’m just forgetting that sum for now. So if you have only one training example. and so from calculus, if you take the derivative of a square, you know, the 2 comes down and so that cancels out with the half. So 2 times 1.5 times, um, the thing inside. Uh, and then by the, uh, chain rule of, derivatives. Uh, that’s times the partial derivative of Theta J of X Theta X minus Y. So if you take the derivative of a square, the two comes down and then you take the derivative of what’s inside and multiply that. and so the two and one-half cancel out. So this leaves you with H minus Y times partial derivative respect to Theta J of Theta 0X0 plus Theta 1X1 plus th- th- that plus Theta NXN minus Y. Where I just took the definition of H of X and expanded it out to that, sum. Because, H of X is just equal to that. So if you look at the partial derivative of each of these terms with respect to Theta J, the partial derivative of every one of these terms with respect to Theta J is going to z- be 0 except for, the term corresponding to J. Because, if J was equal to 1, say. Then this term doesn’t depend on Theta 1. Uh, this term, this term, all of them do not even depend on Theta 1. The only term that depends on Theta 1 is this term over there. and the partial derivative of this term with respect to Theta 1 will be just X1. And so, when you take the partial derivative of this big sum with respect to say the J, uh, in- in- in- instead of just J equals 1 and with respect to Theta J in general, then the only term that even depends on Theta J is the term Theta JXJ. And so the partial derivative of all the other terms end up being 0 and partial derivative of this term with respect to Theta J is equal to XJ, okay? And so this ends up being H Theta X minus Y times XJ, okay? and again, listen, if you haven’t, if you haven’t played with calculus for awhile, if you- you know, don’t quite remember what a partial derivative is, or don’t quite get what we just said. Don’t worry too much about it. We’ll go over a bit more in the section and we- and, and then also read through the lecture notes which kind of goes over this in, in, in, in more detail and more slowly than, than, we might do in class, okay? [NOISE] So, so plugging this- let’s see. So we’ve just calculated that this partial derivative, right, is equal to this, and so plugging it back into that formula, one step of gradient descent is, is the following, which is that we will- that Theta J be updated according to Theta J minus the learning rate times H of X minus Y times XJ, okay? Now, I’m, I’m gonna just add a few more things in this equation. so I did this with one training example, but, uh, this was- I kind of used definition of the cost function J of Theta defined using just one single training example, but you actually have M training examples. And so, the, the correct formula for the derivative is actually if you take this thing and sum it over all M training examples, the derivative of- you know, the derivative of a sum is the sum of the derivatives. So, so you actually- If, if, if you redo this derivation, you know, summing with the correct definition of J of Theta which sums over all M training examples. If you just redo that little derivation, you end up with, uh, sum equals I through M of that. Where remember XI is the Ith training examples input features, YI is the target label, is the, uh, price in the Ith training example, okay? and so this is the actual correct formula for the partial derivative with respect to that of the cost function J of Theta when it’s defined using, all of the, on- when it’s defined using all of the training examples, okay? And so the gradient descent algorithm is to- [NOISE] Repeat until convergence, carry out this update, and in each iteration of gradient descent, uh, you do this update for j equals, 0, 1 up to n. Uh, where n is the number of features. So n was 2 in our example. Okay. and if you do this then, you know, actually let me see. Then what will happen is, well, I’ll show you the animation. As you fit- hopefully, you find a pretty good value of the parameters Theta. Okay. So, it turns out that when you plot the cost function j of Theta for a linear regression model, it turns out that, unlike the earlier diagram I had shown which has local optima, it turns out that if j of Theta is defined the way that, you know, we just defined it for linear regression, is the sum of squared terms, um, then j of Theta turns out to be a quadratic function. It’s a sum of these squares of terms, and so, j of Theta will always look like, look like a big bowl like this. Okay. another way to look at this, uh, and so and so j of Theta does not have local optima, or the only local optima is also the global optimum. The other way to look at the function like this is to look at the contours of this plot. So you plot the contours by looking at the big bowl and taking horizontal slices and plotting where the, where the curves where, where the edges of the horizontal slice is. So the contours of a big bowl or I guess a formal is, of a bigger, of of this quadratic function will be ellipsis, like these or these ovals or these ellipses like this. And so if you run gradient descent on this algorithm, um, let’s say I initialize, uh, my parameters at that little x, shown over here, right. And usually you initialize Theta degree with a 0, but but, you know, but it doesn’t matter too much. So let’s reinitialize over there. Then, with one step of gradient descent, the algorithm will take that step downhill, and then with a second step, it’ll take that step downhill whereby we, fun fact, uh, if you- if you think about the contours of the function, it turns out that the direction of steepest descent is always at 90 degrees, is always orthogonal, uh, to the contour direction, right. So, I don’t know, yeah. I seem to remember that from my high-school something, I think it’s true. All right. And so as you, as you take steps downhill, uh, because there’s only one global minimum, this algorithm will eventually converge to the global minimum. Okay. And so the question just now about the choice of the learning rate Alpha. if you set Alpha to be very very large, to be too large then they can overshoot, right. The steps you take can be too large and you can run past the minimum. Uh, if you set to be too small, then you need a lot of iterations and the algorithm will be slow. And so what happens in practice is, uh, usually you try a few values and and and see what value of the learning rate allows you to most efficiently, you know, drive down the value of j of Theta. and if you see j of Theta increasing rather than decreasing, you see the cost function increasing rather than decreasing, then, there’s a very strong sign that the learning rate is, too large, and so, um. Actually what what I often do is actually try out multiple values of, the learning rate Alpha, and, uh, and and usually try them on an exponential scale. So you try open O1, open O2, open O4, open O8 kinda like a doubling scale or some- uh, or doubling or tripling scale and try a few values and see what value allows you to drive down to the learning rate fastest. Okay. let me just. So I just want to visualize this in one other way, which is with the data. So, this is this is the actual dataset. Uh, they’re, there are actually 49 points in this dataset. So m the number of training examples is 49, and so if you initialize the parameters to 0, that means, initializing your hypothesis or initializing your straight line fit to the data to be that horizontal line. So, if you initialize Theta 0 equals 0, Theta 1 equals 0, then your hypothesis is, you know, for any input size of house or price, the estimated price is 0. And so your hypothesis starts off with a horizontal line, that is whatever the input x the output y is 0. And what you’re doing, um, as you run gradient descent is you’re changing the parameters Theta. So the parameters went from this value to this value to this value to this value and so on. And so, the other way of visualizing gradient descent is, if gradient descent starts off with this hypothesis, with each iteration of gradient descent, you are trying to find different values of the parameters Theta, that allows this straight line to fit the data better. So after one iteration of gradient descent, this is the new hypothesis, you now have different values of Theta 0 and Theta 1 that fits the data a little bit better. after two iterations, you end up with that hypothesis, uh, and with each iteration of gradient descent it’s trying to minimize j of Theta. Is trying to minimize one half of the sum of squares errors of the hypothesis or predictions on the different examples. With three iterations of gradient descent, um, four iterations and so on. And then and then a bunch more iterations, uh, and eventually it converges to that hypothesis, which is a pretty, pretty decent straight line fit to the data. Okay. Is there a question? Yeah, go for it. [inaudible] Uh, sure. Maybe, just to repeat the question. Why is the- why are you subtracting Alpha times the gradient rather than adding Alpha times the gradient? let me suggest, actually let me raise the screen. so let me suggest you work through one example. it turns out that if you add multiple times in a gradient, you’ll be going uphill rather than going downhill, and maybe one way to see that would be if, um, you know, take a quadratic function, excuse me. Right. If you are here, the gradient is a positive direction and you want to reduce, so this would be Theta and this will be j I guess. So you want Theta to decrease, so the gradient is positive. You wanna decrease Theta, so you want to subtract a multiple times the gradient. I think maybe the best way to see that would be the work through an example yourself. Uh, set j of Theta equals Theta squared and set Theta equals 1. So here at the quadratic function of the derivative is equal to 1. So you want to subtract the value from Theta rather than add. Okay? Cool. Um. All right. Great. So you’ve now seen your first learning algorithm, and, you know, gradient descent and linear regression is definitely still one of the most widely used learning algorithms in the world today, and if you implement this- if you, if you, if you implement this today, right, you could use this for, for some actually pretty, pretty decent purposes. now, I wanna I give this algorithm one other name. Uh, so our gradient descent algorithm here, um, calculates this derivative by summing over your entire training set m. And so sometimes this version of gradient descent, has another name, which is batch gradient descent. Oops. All right and the term batch, you know- and again- I think in machine learning, uh, our whole committee, we just make up names and stuff and sometimes the names aren’t great. But the- the term batch gradient descent refers to that, you look at the entire training set, all 49 examples in the example I just had on, PowerPoint. You know, you- you think of all for 49 examples as one batch of data, I’m gonna process all the data as a batch, so hence the name batch gradient descent. The disadvantage of batch gradient descent is that if you have a giant dataset, if you have, um, and- and in the era of big data we’re really, moving to larger and larger datasets, so I’ve used, you know, we train machine learning models of like hundreds of millions of examples. And- and if you are trying to- if you have, uh, if you download the US census database, if your data, the United States census, that’s a very large dataset. And you wanna predict housing prices, from all across the United States, that- that- that may have a dataset with many- many millions of examples. And the disadvantage of batch gradient descent is that, in order to make one update, to your parameters, in order to even take a single step of gradient descent, you need to calculate, this sum. And if m is say a million or 10 million or 100 million, you need to scan through your entire database, scan through your entire dataset and calculate this for, you know, 100 million examples and sum it up. And so every single step of gradient descent becomes very slow because you’re scanning over, you’re reading over, right, like 100 million training examples, uh, and before you can even, you know, make one tiny little step of gradient descent. Okay, yeah, and by the way, I think- I feel like in today’s era of big data people start to lose intuitions about what’s a big data-set. I think even by today’s standards, like a hundred million examples is still very big, right, I- I rarely- only rarely use a hundred million examples. I don’t know, maybe in a few years we’ll look back on a hundred million examples and say that was really small, but at least today. Uh, yeah. So the main disadvantage of batch gradient descent is, every single step of gradient descent requires that you read through, you know, your entire data-set, maybe terabytes of data-sets maybe- maybe- maybe, uh, tens or hundreds of terabytes of data, before you can even update the parameters just once. And if gradient descent needs, you know, hundreds of iterations to converge, then you’ll be scanning through your entire data-set hundreds of times. Right, or-or and then sometimes we train, our algorithms with thousands or tens of thousands of iterations. And so- so this- this gets expensive. So there’s an alternative to batch gradient descent. and let me just write out the algorithm here that we can talk about it, which is going to repeatedly do this. Oops, okay. so this algorithm, which is called stochastic gradient descent. instead of scanning through all million examples before you update the parameters theta even a little bit, in stochastic gradient descent, instead, in the inner loop of the algorithm, you loop through j equals 1 through m of taking a gradient descent step using, the derivative of just one single example of just that, one example, ah, oh, excuse me it’s through i, right. Yeah, so let i go from 1 to m, and update theta j for every j. So you update this for j equals 1 through n, update theta j, using this derivative that when now this derivative is taken just with respect to one training example- example I. Okay, I’ll- I’ll just- alright and I guess you update this for every j. Okay, and so, let me just draw a picture of what this algorithm is doing. If this is the contour, like the one you saw just now. So the axes are, uh, theta 0 and theta 1, and the height of the surface right, denote the contours as j of theta. With stochastic gradient descent, what you do is you initialize the parameters somewhere. And then you will look at your first training example. Hey, lets just look at one house, and see if you can predict that house as better, and you modify the parameters to increase the accuracy where you predict the price of that one house. And because you’re fitting the data just for one house, you know, maybe you end up improving the parameters a little bit, but not quite going in the most direct direction downhill. And you go look at the second house and say, hey, let’s try to fit that house better. And then you update the parameters. And you look at third house, fourth house. Right, and so as you run stochastic gradient descent, it takes a slightly noisy, slightly random path. Uh, but on average, it’s headed toward the global minimokay. So as you run stochastic gradient descent- stochastic gradient descent will actually, never quite converge. In- with- with batch gradient descent, it kind of went to the global minimum and stopped right, with stochastic gradient descent even as you won’t run it, the parameters will oscillate and won’t ever quite converge because you’re always running around looking at different houses and trying to do better than just that one house- and that one house- and that one house. Uh, but when you have a very large data-set, stochastic gradient descent, allows your implementation- allows you algorithm to make much faster progress. Uh, and so, uh, uh- and so when you have very large data-sets, stochastic gradient descent is used much more in practice than batch gradient descent. [BACKGROUND] Uh, yeah, is it possible to start with stochastic gradient descent and then switch over to batch gradient descent? Yes, it is. So, boy, something that wasn’t talked about in this class, it’s talked about in CS230 is Mini-batch gradient descent, where, um, you don’t- where you use say a hundred examples at a time rather than one example at a time. And so- so that’s another algorithm that I should use more often in practice. I think people rarely- actually, so- so in practice, you know, when your dataset is large, we rarely, ever switch to batch gradient descent, because batch gradient descent is just so slow, right. So, I-I know I’m thinking through concrete examples of problems I’ve worked on. And I think that what- maybe actually maybe- I think that uh, for a lot of- for- for modern machine learning, where you have- if you have very- very large data sets, right so you know, whether- if you’re building a speech recognition system, you might have like a terabyte of data, right, and so, um, it’s so expensive to scan through a terabyte of data just reading it from disk, right it’s so expensive that you would probably never even run one iteration of batch gradient descent. Uh, and it turns out the- the- there’s one- one huge saving grace of stochastic gradient descent is, let’s say you run stochastic gradient descent, right, and, you know, you end up with this parameter and that’s the parameter you use, for your machine learning system, rather than the global optimum. It turns out that parameter is actually not that bad, right, you- you probably make perfectly fine predictions even if you don’t quite get to the like the global- global minimum. So, what you said I think it’s a fine thing to do, no harm trying it. Although in practice uh, in practice we don’t bother, I think in practice we usually use stochastic gradient descent. The thing that actually is more common, is to slowly decrease the learning rate. So just keep using stochastic gradient descent, but reduce the learning rate over time. So it takes smaller and smaller steps. So if you do that, then what happens is the size of the oscillations would decrease. Uh, and so you end up oscillating or bouncing around the smaller region. So wherever you end up, may not be the global- global minimum, but at least it’ll- be it’ll be closer to the global minimum. Yeah, so decreasing the learning rate is used much more often. Cool. Question. Yeah. [BACKGROUND] Oh sure, when do you stop with stochastic gradient descent? Uh, plot to j of theta, over time. So j of theta is a cost function that you’re trying to drag down. So monitor j of theta as, you know, is going down over time, and then if it looks like it stopped going down, then you can say, “Oh, it looks like it looks like it stopped going down,” then you stop training. Although- and then- ah, you know, one nice thing about linear regression is that it has no local optimum and so, it- you run into these convergence debugging types of issues less often. Where you’re training highly non-linear things like neural networks, we should talk about later in CS229 as well. Uh, these issues become more acute. Cool. Okay, great. So, yeah. [BACKGROUND]. Oh, would your learning rate be 1 over n times linear regressions then? Not really, it’s usually much bigger than that. Uh, yeah, because if your learning rate was 1 over n times that of what you would use with batch gradient descent then it would end up being as slow as batch gradient descent, so it’s usually much bigger. Okay. So, so that’s stochastic gradient descent and- and- so I’ll tell you what I do. If- if you have a relatively small dataset, you know, if you have- if you have, I don’t know, like hundreds of examples maybe thousands of examples where, it’s computationally efficient to do batch gradient descent. If batch gradient descent doesn’t cost too much, I would almost always just use batch gradient descent because it’s one less thing to fiddle with. It’s just one less thing to have to worry about, the parameters oscillating, but your dataset is too large that batch gradient descent becomes prohibit- prohibitively slow, then almost everyone will use, you know, stochastic gradient descent or whatever more like stochastic gradient descent, okay? All right, so, gradient descent, both batch gradient descent and stochastic gradient descent is an iterative algorithm meaning that you have to take multiple steps to get to, you know, get near hopefully the global optimum. It turns out there is another algorithm, and- and, um, for many other algorithms we’ll talk about in this course including generalized linear models and neural networks and a few other algorithms, uh, you will have to use gradient descent and so- and so we’ll see gradient descent, you know, as we develop multiple different algorithms later this quarter. It turns out that for the special case of linear regression, uh, and I mean linear regression but not the algorithm we’ll talk about next Monday, not the algorithm we’ll talk about next Wednesday, but if the algorithm you’re using is linear regression and exactly linear regression. It turns out that there’s a way to, uh, solve for the optimal value of the parameters theta to just jump in one step to the global optimum without needing to use an iterative algorithm, right, and this- this one I’m gonna present next is called the normal equation. It works only for linear regression, doesn’t work for any of the other algorithms I talk about later this quarter. But uh, let me quickly show you the derivation of that. And, what I want to do is, uh, give you a flavor of how to derive the normal equation and where you end up with is you know, wha- what- what I hope to do is end up with a formula that lets you say theta equals some stuff where you just set theta equals to that and in one step with a few matrix multiplications you end up with the optimal value of theta that lands you right at the global optimum, right, just like that, just in one step. Okay. and if you’ve taken, you know, advanced linear algebra courses before or something, you may have seen, um, this formula for linear regression. Wha- what a lot of linear algebra classes do is, what some linear algebra classes do is cover the board with, you know, pages and pages of matrix derivatives. what I wanna do is describe to you a matrix derivative notation that allows you to derive the normal equation in roughly four lines of linear algebra, rather than some pages and pages of linear algebra and in the work I’ve done in machine learning you know, sometimes notation really matters, right. If you have the right notation you can solve some problems much more easily and what I wanna do is, define this uh, matrix linear algebra notation and then I don’t wanna do all the steps of the derivation, I wanna give you- give you a sense of the flavor of what it looks like and then, I’ll ask you to, get a lot of details yourself, um, in the- in the lecture notes where we work out everything in more detail than I want to do algebra in class. And, in problem set one you’ll get to practice using this yourself to- to- to-, you know, derive some additional things. I’ve- I’ve found this notation really convenient, right, for deriving learning algorithms. Okay. So, I’m going to use the following notation. so J, right. There’s a function mapping from parameters to the real numbers. So I’m going to define this- this is the derivative of J of theta with respect to theta, where- remember theta is a three-dimensional vector says R3, or actually it’s R n+1, right. If you have, two features to the house if n=2, then theta was 3 dimensional, it’s n+1 dimensional so it’s a vector. And so I’m gonna define the derivative with respect to theta of J of theta as follows. this is going to be itself a 3 by 1 vector [NOISE]. Okay, so I hope this notation is clear. So this is a three-dimensional vector with, three components. Alright so that’s what I guess I’m. So that’s the first component is a vector, there’s a second and there’s a third. It’s the partial derivative of J with respect to each of the three elements. and more generally, in the notation we’ll use, let me give you an example. let’s say that a is a matrix. So let’s say that a is a two-by-two matrix. Then, you can have a function, right, so let’s say a is, you know, A1-1, A1-2, A2-1 and A2-2, right. So A is a two-by-two matrix. Then you might have some function um, of a matrix A right, then that’s a real number. So maybe f maps from A 2-by-2 to, excuse me, R 2-by-2, it’s a real number. So, and so for example, if f of A equals A11 plus A12 squared, then f of, you know, 5, 6, 7, 8 would be equal to I guess 5 plus 6 squared, right. So as we derive this, we’ll be working a little bit with functions that map from matrices to real numbers and this is just one made up example of a function that inputs a matrix and maps the matrix, maps the values of matrix to a real number. And when you have a matrix function like this, I’m going to define the derivative with respect to A of f of A to be equal to itself a matrix where the derivative of f of A with respect to the matrix A. Uh, this itself will be a matrix with the same dimension of a and the elements of this are the derivative with respect to the individual elements. Actually, let me just write it like this. [NOISE] Okay. So if A was a 2-by-2 matrix then the derivative of F of A with respect to A is itself a 2-by-2 matrix and you compute this 2-by-2 matrix just by looking at F and taking, derivatives with respect to the different elements and plugging them into the different, the different elements of this matrix. Okay. and so in this particular example, I guess the derivative respect to A of F of A. This would be, right, it would be- it would be that. Ah and I got these four numbers by taking, um, the definition of F and taking the derivative with respect to A_1, 1 and plugging that here. Ah, taking the derivative with respect to A_1,2 and plugging that here and taking the derivative with respect to the remaining elements and plugging them here which- which was 0. Okay? So that’s the definition of a matrix derivative. Yeah? [inaudible]. Oh, yes. We’re just using the definition for a vector. Ah, N by 1 or N by 1 matrix. Yes. And in fact that definition and this definition for the derivative of J with respect to Theta these are consistent. So if you apply that definition to a column vector, treating a column vector as an N by 1 matrix or N, I guess it would be N plus 1 by 1 matrix then that- that specializes to what we described here. [NOISE] All right. So, let’s see. Okay. So, I want to leave the details of the lecture notes because there’s more lines of algebra which I won’t do but it’ll give you an overview of what the derivation of the normal equation looks like. so onto this definition of a derivative of a- of a matrix, the broad outline of what we’re going to do is we’re going to take J of Theta. Right. That’s the cost function. take the derivative with respect to Theta. Right. Ah, since Theta is a vector so you want to take the derivative with respect to Theta and you know well, how do you minimize a function? You take derivatives with respect to Theta and set it equal to 0. And then you solve for the value of Theta so that the derivative is 0. Right. The- the minimyou know, the maximum and minimum of a function is where the derivative is equal to 0. So- so how you derive the normal equation is take this vector. Ah, so J of Theta maps from a vector to a real number. So we’ll, take the derivatives respect to Theta set it to 0,0 and solve for Theta and then we end up with a formula for Theta that lets you just, ah, you know, immediately go to the global minimum of the- of the cost function J of Theta. And, and a lot of the build up, a lot of this notation is, you know, is there- what does this mean and is there an easy way to compute the derivative of J of Theta? Okay? So, ah, so I hope you understand the lecture notes when hopefully you take a look at them, ah, just a couple other derivations. if A is a square matrix. So let’s say A is a N, N by N matrix. So number of rows equals number of columns. I’m going to denote the trace of A to be equal to the sum of the diagonal entries. So sum of i of A_ii. And this is pronounced the trace of A, and, ah, and- and you can- you can also write this as trace operator like the trace function applied to A but by convention we often write trace of A without the parentheses. And so this is called the trace of A. So trace just means sum of diagonal entries and, some facts about the trace of a matrix. You know, trace of A is equal to the trace of A transpose because if you transpose a matrix, right, you’re just flipping it along the- the 45 degree axis. And so the the diagonal entries actually stay the same when you transpose the matrix. So the trace of A is equal to trace of A transpose, um, and then, ah, there-there are some other useful properties of, the trace operator. here’s one that I don’t want to prove but that you could go home and prove yourself with a-with a few with- with a little bit of work, maybe not, not too much which is, ah, if you define, um, F of A equals trace of A times B. So here if B is some fixed matrix, right, ah, and what F of A does is it multiplies A and B and then it takes the sum of diagonal entries. Then it turns out that the derivative with respect to A of F of A is equal to, B transpose [NOISE]. and this is, ah, you could prove this yourself. For any matrix B, if F of A is defined this way, the de- the derivative is equal to B transpose. the trace function or the trace operator has other interesting properties. The trace of AB is equal to the trace of BA. Ah, you could- you could prove this from past principles, it’s a little bit of work to prove, ah, ah, that- that you, if you expand out the definition of A and B it should prove that and the trace of A times B times C is equal to the trace of C times A times B. Ah, this is a cyclic permutation property. If you have a multiply, you know, multiply several matrices together you can always take one from the end and move it to the front and the trace will remain the same. And, another one that is a little bit harder to prove is that the trace, excuse me, the derivative of A trans- of AA transpose C is Okay. Yeah. So I think just as- just as for you know, ordinary, calculus we know the derivative of X squared is 2_X. Right. And so we all figured out that very well. We just use it too much without- without having to re-derive it every time. Ah, this is a little bit like that. The trace of A squared C is, you know, two times CA. Right. It’s a little bit like that but- but with- with matrix notation as there. So think of this as analogous to D, DA of A squared C equals 2AC. Right. But that is like the matrix version of that. [NOISE] All right. So finally, um, what I’d like to do is take J of Theta and express it in this, you know, matrix vector notation. So we can take derivatives with respect to Theta, and set the derivatives equal to 0, and just solve for the value of Theta. And so, let me just write out the definition of J of Theta. So J of Theta was one-half sum from i equals 1 through m of h of x i minus y i squared. and it turns out that, all right. It turns out that, if it is, if you define a matrix capital X as follows. Which is, I’m going to take the matrix capital X and take the training examples we have, you know, and stack them up in rows. So we have m training examples. So so the X’s were column vectors. So I’m taking transpose to just stack up the training examples in, in rows here. So let me call this the design matrix. So the capital X called the design matrix. And, it turns out that if you define X this way, then X times Theta, there’s this thing times Theta. And the way a matrix vector multiplication works is your Theta is now a column vector. So Theta is, you know, Theta_0, Theta_1, Theta_2. So the way that, um, matrix-vector multiplication works is you multiply this column vector with each of these in in turn. And so this ends up being X1 transpose Theta, X2 transpose Theta, down to X_m transpose Theta, which is of course just the vector of all of the predictions of the algorithm. And so if, um, now let me also define a vector y to be taking all of the, labels from your training example, and stacking them up into a big column vector, right. Let me define y that way. it turns out that, um, J of Theta can then be written as one-half of X Theta minus y transpose X Theta minus y. Okay. and let me see. Yeah. Let me just, uh, outline the proof, but I won’t do this in great detail. So X Theta minus y is going to be, right, so this is X Theta, this is y. So, you know, X Theta minus y is going to be this vector of h of x1 minus y1 down to h of xm minus ym, right. So it’s just all the errors your learning algorithm is making on the m examples. It’s the difference between predictions and the actual labels. And if you you remember, so Z transpose Z is equal to sum over i Z squared, right. A vector transpose itself is a sum of squares of elements. And so this vector transpose itself is the sum of squares of the elements, right. So so which is why, uh, so so the cost function J of Theta is computed by taking the sum of squares of all of these elements, of all of these errors, and and the way you do that is to take this vector, your X Theta minus y transpose itself, is the sum of squares of these, which is exactly the error. So that’s why you end up with a, this as the sum of squares of the, those error terms. Okay. And, if some of the steps don’t quite make sense, really don’t worry about it. All this is written out more slowly and carefully in the lecture notes. But I wanted you to have a sense of the, uh, broad arc of the of the big picture of their derivation before you go through them yourself in greater detail in the lecture notes elsewhere. So finally, what we want to do is take the derivative with respect to Theta of J of Theta, and set that to 0. And so this is going to be equal to the derivative of one-half X Theta minus y transpose X Theta minus y. and so I’m gonna, I’m gonna do the steps really quickly, right. So the steps require some of the little properties of traces and matrix derivatives I wrote down briefly just now. But so I’m gonna do these very quickly without getting into the details, but, uh, so this is equal to one-half derivative of Theta of, um. So take transposes of these things. So this becomes Theta transpose X transpose minus y transpose. Right. and then, uh, kind of like expanding out a quadratic function, right. This is, you know, A minus B times C minus D. So you can just AC minus AD this and so on. So I’ll just write this out. All right. And so, uh, what I just did here this is similar to how, you know, ax minus b times ax minus b, is equal to a squared x squared minus axb minus bax plus b squared. Is it’s kind of, it’s just expanding out a quadratic function. and then the final step is, yeah, go ahead. [BACKGROUND] Oh, is that right? Oh yes, thank you. Thank you. and then the final step is, you know, for each of these four terms; first, second, third, and fourth terms, to take the derivative with respect to Theta. And if you use some of the formulas I was alluding to over there, you find that the derivative, um, which which I don’t want to show the derivation of, but it turns out that the derivative is, um, X transpose X Theta plus X transpose X Theta minus, X transpose y minus X transpose y, and we’re going to set this derivative. Actually not, let me just do this. And so this simplifies to X transpose X Theta minus X transpose y. And so as as described earlier, I’m gonna set this derivative to 0. And how to go from this step to that step is using the matrix derivatives, explained in more detail in the lecture notes. And so the final step is, you know, having set this to 0, this implies that X transpose X Theta equals X transpose y. Uh, so this is called the normal equations. And the optimum value for Theta is Theta equals X transpose X inverse, X transpose y. Okay. and if you implement this, um, then, you know, you can in basically one step, get the value of Theta that corresponds to the global minimum. Okay. and and and again, common question I get is one is, well, what if X is non-invertible? Uh, what that usually means is you have have redundant features, that your features are linearly dependent. Uh, but if you use something called the pseudo inverse, you kind of get the right answer if that’s the case. Although I think the, even more right answer is if you have linearly dependent features, probably means you have the same feature repeated twice, and I will usually go and figure out what features are actually repeated, leading to this problem. Okay. All right. Uh, any last questions before- so that so that’s the normal equations. Hope you read through the detailed derivations in the lecture notes. Any last questions before we break? Okay. [BACKGROUND] Oh, yeah. How do you choose a learning rate? It’s, it’s, it’s quite empirical, I think. So most people would try different values, and then just pick one. All right. I think let’s let’s break. If, if people have more questions, when the TAs come up, we’re going to keep taking questions.
Oh, great question. Is there a equivalent of normal equations to logistic regression? short answer is no. So for linear regression the normal equations gives you like a one shot way to just find the best value of theta. There is no known way to just have a close form equation unless you find the best value of theta which is why you always have to use an algorithm, an iterative optimization algorithm such as gradient ascent or ah and we’ll see in a second Newton’s method. |
# Tag Info
4
Your question touches the question of ontology in particle physics. Historically we are used to be thinking of particles as tiny independent entities that behave according to some laws of motion. This stems from the atomistic theory of matter, which was developed some two thousand years ago from the starting point of what would happen if we could split ...
3
Ill answer the second part of your question about effective mass and quasiparticles, since I see that CuriousOne has answered the rest better than I could have. In a metal or semiconductor, the electron is not in the same free state it would be in a vacuum. It is bound to (although delocalised within) a lattice of positive ions. So its dispersion ...
3
The neutron is not a fundamental particle. It carries no electric charge, yet it can interact with photons as its components - the quarks - carry electric charge and thus couple to photons. Macroscopically/classical, these interactions cancel out since its net charge is zero, but quantumly, there is a very big difference between objects with charged ...
3
HInt: Force on what? You need some charge to exert the force on. Otherwise you can calculate the electric field. To do that, you need to know the number of protons in $100$ g of normal matter. Since electrons don't weight anything and (at this level of approximation) there are the same number of neutrons and protons....
2
The Rydberg electron - the electron in the high n level - is highly polarizable and very weakly held. The binding energy of the electron is very small. A small electric field will distort the wavefunction of the Rydberg electron so that it spends more time on one side of the atom than the other. The result is the formation of dipole. Rydberg electrons in ...
2
A propagating EM wave is a field that needs no charges. Likewise, a propagating gravitational wave is a field that needs no masses. However in both cases there is no way (classically) to create the wave without a charge/mass. Considering EM, the divergence of the field is zero unless there is a charge, or put another way since field lines can only begin and ...
1
I don't know cases in which the e.m. field can be produced without charges, however I can tell you how to produce an e.m. field without electric charges. Take a neutral particle, meet it with its antiparticle, have them clash, and you'll get gamma rays. The latter are electromagnetic. Also, gamma emission from excited nuclei, has not much to do with the ...
1
Now per QED, electrical charges interactions are effected by photons. Suppose you are one of the two charges. How do you know to attract or repel the other charge? You want something that does not exist - intuitive picture of physical process within a theory which is a demonstration of how far can one go with mathematisation of experience and ignoring ...
1
The original system as described in inherently unstable (or at best metastable). According to Earnshaw's Theorem, "a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges" http://en.wikipedia.org/wiki/Earnshaw's_theorem So the introduction of the slightest ...
1
I don't think that quasineutrality is "a required condition", but is a property of most plasmas. Quasineutrality is the tendency for plasmas to attain electrical neutrality. It means that if a neutral plasma (with equal numbers of electrons and ions), should generate a region with a slight electrical charge, then because (a) the electric force is huge ...
1
The frequencies are the same but they are 180 degrees out of phase with each other.
1
In short: the laws of conservation (angular momentum, charge, mass-energy, etc.) still work during the process of creation of a black hole. So if a star had some angular momentum/charge before it collapsed, the resulting black hole will also have some (assuming the angular momentum/charge was not radiated away during the collapse). Also, the claim that ...
1
Then does all charges, no matter how much charged are they, ionize the material around them since distance can get smaller and therefore electric field gets bigger. Consequently, the electric field exerted by the charge would be higher than the electrical breakdown limit of the material around it. Let's say you magically stick a (positive) charge inside a ...
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# A Chain rule - legendre transformation
1. Dec 26, 2016
### sgh1324
let
df=∂f/∂x dx+∂f/∂y dy and ∂f/∂x=p,∂f/∂y=q
So we get
df=p dx+q dy
d(f−qy)=p dx−y dq
and now, define g.
g=f−q y
dg = p dx - y dq
and then I faced problem.
∂g/∂x=p←←←←←←←←←←←←←←← book said like this because we can see g is a function of x and p so that chain rule makes ∂g/∂x=p
but I wrote directly ∂g/∂x so i can get a result,
∂g/∂x=∂f/∂x−y ∂q/∂x−q ∂y∂x=p−y ∂q∂x - 0(y is independent of x)
I know that variation y is independent of x, but I'm not sure that q is also the independent function of x. what if the func f is xy??? if I set like that,
g=f−qy=xy−xy=0
it's not same with p!!!
mathematical methods in the physical sciences, Mary L. Boas 3rd edition page231
http://www.utdallas.edu/~pervin/ENGR3300/Boaz.pdf
2. Dec 26, 2016
### Useful nucleus
In taking partial derivatives , it is recommended to explicitly show which variable is maintained constant. So you want to calculate (∂g/∂x)|q. There are two ways. The easiest one, is to look at the differential of g and set dq=0 since you are holding q constant. This way you get (∂g/∂x)|q = p. The second is to use your method. Then,
(∂g/∂x)|q=(∂f/∂x)|q - q (∂y/∂x)|q --------- (1)
notice that (∂f/∂x)|q ≠ p. Correct is (∂f/∂x)|y = p.
It is possible to manipulate expression(1) above to reach to the same conclusion that we obtain easily from the differential which is (∂g/∂x)|q = p.
Also note that there no need to assume that y is independent of x. In fact in the context of applying Legendre Transform to Thermodynamics, the natural variables do depend on each other. For example U=(S,V,N) where U is the internal energy, and we have a dependence of S on N and V. |
# Length contraction and interstellar travel
1. Jan 18, 2010
### Referos
Interstellar travel is always a problem in science fiction: you can't have the hero hibernate for millions of years whenever he or she wants to travel to another star, but it's annoying when spaceships just magically move faster than light.
However, wouldn't length contraction from special relativity partially solve this? Imagine that a ship is travelling at 0.999999c. Maybe we will never reach this speed, but, still, it's not a physical impossibility. Now, at this speed, $$\gamma = 707$$. The distance from Earth to, say, Alpha Centauri is $$4.153 * 10^{16} m$$ (4.39 light years), but the passengers in the ship would observe this length to be contracted to $$5.87*10^{13} m$$. At 0.999999c, this distance can be covered in 195 934 s, which converts to roughly 2.26 days.
Sure, when returning to Earth, they would realize that years have passed due to time dilation.
Still, from the passenger's perspective, they can reach other stars in a somewhat small amount of time.
Now, the fact that I can't remember a science fiction novel or film that used this idea instead of faster-than-light travel must mean that I've got something wrong, but I'm not sure.
2. Jan 18, 2010
### jacksonwalter
The energy required to get to that speed is enormous. I can't see a ship weighing less than 1000kg with enough resources, probably at least 104kg really. In order to get to gamma=707, that's 6 x 1023 J, or at least 7 x 106 kg of anti-matter at 100% efficiency. Good luck.
3. Jan 18, 2010
### dacruick
Correct me if im wrong, but if the ship is travelling almost at the speed of light, doesn't that mean the length of the ship is very small, not the distance it is going.
Or are you also assuming that using relativity you can say that the ship moving from star A to star B is the same as the whole universe traveling in the opposite direction?
4. Jan 18, 2010
### Naty1
Try this for more than you wanted to know....
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
You can also search here on physics forums for things like time travel, space travel, twin paradox and so forth...this has been discussed hundreds of times...
Last edited by a moderator: May 4, 2017
5. Jan 18, 2010
### bcrowell
Staff Emeritus
Referos, your analysis seems right, although I haven't checked the numbers.
Right. In the galaxy's frame, the ship is shortened. In the ship's frame, the galaxy is shortened.
With constant acceleration and deceleration at one gee, I believe the round-trip clock time from earth to the center of the galaxy works out to be on the order of a century (which would correspond to tens of thousands of years on earth).
Re jacksonwalter's point about practical issues -- another problem is that you'd be burned up by frictional heating from the interstellar medium.
6. Jan 18, 2010
### jambaugh
You can't speak of "the length" without qualifying "as seen by...". The ship as seen by itself is unchanged. The distance between stars as seen by the ship is contracted. The ship as seen by people moving with the stars is contracted. The distance between stars as seen by people moving with the stars is unchanged.
To see why this seemingly paradoxical two way contraction is not so paradoxical, consider a somewhat analogous situation.
Imagine a very little planet and two astronauts standing some distance apart looking at each other from atop hills. Suppose the planet is so small that from where they stand the angles of each man's vertical direction is 60deg from the others. Each see's the other's vertical distance as 1/2 their actual height because each sees the other as leaning relative to their own vertical.
Right! It's all relative.
7. Jan 18, 2010
### Nabeshin
General comment: This is the whole reason going fast is so beneficial for futuristic space flights. Sure, in the framework of Newtonian mechanics, extra speed means you get there a bit quicker, but the relativistic effects are the real key.
Two novels which pop into my head which make a big to-do about the time dilation effects of relativistic space travel: Forever War and the Ender's Game series. Oh, and Tau Zero by Paul Anderson, but that one's not as well known. Within any decent hard SF book, these effects are given due consideration.
Cheers!
8. Jan 18, 2010
### Janus
Staff Emeritus
Larry Niven built a whole novel around this idea in A World Out of Time, and Heinlein's Time for the Stars also relies on it. The main reason that it doesn't get used more often is that so much time passes for both Earth and the destination. Sure, the Hero can get to 20 Leonis Minoris in 25 days of his own time, but it will do little good if the situation he set off to resolve transpired 48 yrs ago by planet time when he arrives. (And that's just taking into account his own travel time. If we are restricted to light speed signals, he won't even find out about it for 48 yrs.)
9. Jan 18, 2010
### gpslavov
But very interestingly, in the event that the Earth is about to be destroyed, it wouldn't matter that 50 years have passed between departure and arrival. Humanity can reach another star, hopefully with habitable planets, well within the lifespan of one generation, which is awesome! =)
10. Jan 18, 2010
### Matterwave
Theoretically, this could work. Sadly, 4.36 years would have passed on Earth in your 2.26 day journey, so, everyone you know back home has just aged by 4.36 years. For a trip to the center of the galaxy, everyone you know back home has died.
Communication is also a problem. If you ever wanted to talk with your friends back on Earth, expect a 8.72 year delay in response time...
11. Jan 19, 2010
### devronious
This is interesting, I ran a length contraction / time dilation experiment using sub atomic motion to create relativistic effects of length contraction and what I found is that the space-time surrounding the event was contracted, not just the particle involved. The distance to the next object becomes shorter, but it can also be perceived by outside and seperate frames of reference. This is of course a new experiment, you can find it at wintschlabs.com, its fairly easy to create and if your interested in observing first hand length contraction its worth the time to build.
The interesting thing here is, how is the space surrounding the particle contracted, should just the object in motion which has velocity be the contracted object? It seemed to me that it may have suggested that space was moving with the particles and that the space was the item contracted, not the particle itself. How can a moving object contract something that is separate from it, if velocity is the cause of contraction and the main component wouldn't anything contracted have to have velocity? Including the space-time which clearly the experiment shows is contracted.
The idea lead me to the theory that space-time originates from each and every particle, and that it moves with particles as they travel. If this is the case then relativity makes much more sense and relative motion and everything about it becomes clear why and how they happen. Each particle is its own frame of reference because of this.
You have to remember that both length contraction and time dilation occur for the ship, these offset eachother so that observers don't see it travelling at faster than its actually moving. Imagine if just space's length was contracted, wouldn't its velocity be much greater than it actually was, velocity = d/t and if d is much shorter to the destination its velocity would be massive. But t or time slows counteracting this change. They compliment eachother so as to not create a velocity that does not truely reflect the velocity before relativistic affects. But there is something that does change and that is the passage of time. This is why the muon ages so little and its decay is allowed to pass so far into the earth, see the muon experiment. So I think your people on the ship would age very little and time to them would seem to barely pass by, they wouldn't need cryo sleep would they? The muon didn't, perhaps thats the evidence you need.
-Devin Wintch
Last edited: Jan 19, 2010
12. Jan 21, 2010
### GRDixon
You've got the right idea. During his trip the measuring rods of earth's rest frame are zipping by at .999999c. How can more than 4E16 meters of these rods pass by in only 2.26 days of shipboard time? Because they are LENGTH CONTRACTED. Why Gene Roddenberry (the creator of Star Trek) never played this card is a mystery and a disappointment. Warp 5??? C'mon.
13. Jan 21, 2010
### pervect
Staff Emeritus
1) You've got it right as near as I can tell.
2) Try Gregory Benford's Galactic Center Novels ("In the Ocean of Night, etc).
Of course, even if Benford, a physicist, hadn't written the novels, the science wouldn't change. Also, the fact that Benford is a physicist doesn't make his novels non-fiction - while some elements of the story are inspired by actual physics, other story elements aren't, and it may be hard to distinguish which are which without specialized knowledge.
14. Jan 21, 2010
### DocZaius
The first thing that popped out at me regarding why science fiction novels wouldn't use this, is the acceleration. I'm surprised it's not been brought up in this thread, which makes me think that I'm missing something. The kind of acceleration humans could survive would limit their average speed. The speeds mentioned here would be attained only during a portion of the flight (middle point if the flight is half acceleration half decceleration). The stress on the body is also a consideration if you want a healthy population on the other side of the journey so you might want to limit the acceleration more than merely enough for "survivable."
15. Jan 22, 2010
### jacksonwalter
Nah, if you keep a constant 10 $$\frac{m}{s^{2}}$$ you only have to accelerate for about a year (c/a, convert to years). See https://www.physicsforums.com/showthread.php?t=370572" thread.
Last edited by a moderator: Apr 24, 2017
16. Jan 22, 2010
### Nabeshin
As the poster above me points out, this isn't the reason it's seldom used in science fiction. The reason is, according to observers not aboard the ship, it will take the ship at least the distance the ship is traveling (in light years) years to get there. So when the Enterprise-D gets called to the Neutral zone 1100 ly away on an urgent mission, it would take at least 1100 years for it to arrive, even if those on board only experience hours or minutes! Sort of slows the pace of things, don't you think? |
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