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The average train between Berlin Schoenefeld Airport (SXF) and Gesundbrunnen takes 35m and the fastest train takes 33m. On an average weekday, there are 8 trains per day travelling from Berlin Schoenefeld Airport (SXF) to Gesundbrunnen. The journey time may be longer on weekends and holidays; use the search form on this page to search for a specific travel date.
Need a hotel room in Gesundbrunnen?
All available trains travelling from Berlin Schoenefeld Airport (SXF) to Gesundbrunnen. To see full schedules, alternative transport and to book your tickets online click here.
Is there a direct train between Berlin Schoenefeld Airport (SXF) and Gesundbrunnen?
Yes, there is a direct train departing from S Flughafen Berlin-Schönefeld Bhf and arriving at S Hackescher Markt. Services depart every 20 minutes, and operate every day. The journey takes approximately 37m.
How far is it from Berlin Schoenefeld Airport (SXF) to Gesundbrunnen?
The distance between Berlin Schoenefeld Airport (SXF) and Gesundbrunnen is 20 km. The road distance is 24.1 km.
Where do I catch the Berlin Schoenefeld Airport (SXF) to Gesundbrunnen train from?
Berlin Schoenefeld Airport (SXF) to Gesundbrunnen train services, operated by Deutsche Bahn, depart from S Flughafen Berlin-Schönefeld Bhf station.
Where does the Berlin Schoenefeld Airport (SXF) to Gesundbrunnen train arrive?
Berlin Schoenefeld Airport (SXF) to Gesundbrunnen train services, operated by S-Bahn Berlin, arrive at S Bornholmer Str. station.
How do I get a train ticket from Berlin Schoenefeld Airport (SXF) to Gesundbrunnen?
Book your Berlin Schoenefeld Airport (SXF) to Gesundbrunnen train tickets online with Rome2rio.
Where can I stay near Gesundbrunnen?
There are 1499+ hotels available in Gesundbrunnen. Prices start at 50€ per night. | {
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Is your place feeling more like a chilly bin, than a cosy haven?
Living in your space at this time of year should be cosy, wonderful and warm… right?
But you're still feeling a chill and dreaming of longer days and warm sunny evenings?
Perhaps your need to change your environment. Read on to learn 5 top-tips from Options Gifts and Homewares owner Pauline Carter, about how to cosy-up your space this winter, and make it inviting to residents and visitors alike.
Brighten up your space with gorgeous artificial flowers, like these stunning magnolias. Add some greenery and no one will know the difference. Pauline suggests pairing these magnolia fronds with natural camellia or magnolia leaves; or you could try generous stems of rosemary or bay.
Lighting is key to creating a warm and inviting space. A candle glowing on a side or coffee table can really set the scene for a warm, inviting conversation or a glass of something delicious. Try these eye-catching, New Zealand made, 100% soy candles by Surmanti. Each is set in a sheek black glass holder. Top-tip: Pauline's favourite scent = Pear and Passion.
Any sofa can be transformed into an inviting place to sit, lie or snuggle with a top-quality throw. As always, Options Homeware & Gifts have a stunning range. The 'easy' throw starting at $59.90, a sheepskin backed 'Sherpa blanket' for $79.90, or a 'Bliss mohair' blend for $145. Why not choose an on trend colour like mustard, cream or blush colour to compliment your couch or occasional chair, and add a seasonal fashion update at the same time.
The Maxwell and Williams 'Tint teapot' and 'snug mug' are just that; snug. The generously proportioned mug won't leave you wanting, while the pot will brew enough to share. The stylish lines of this pleasing duo makes it a great gift at this time of year too. And if you're looking for a tasty tea to try, pop over to Countdown and check out their extensive range - including Higher Living organic teas from the United Kingdom. Chamomile & Vanilla sounds exquisite. A little bowl of biscotti, cookies or liquorice won't go amiss either.
Pauline recommends adding a delicious shag carpet to... wait for it... your bathroom or ensuite floor! Not in place of a bath mat but for extra comfort, by the sink perhaps? It's an inexpensive way to add a touch of lux; and on cold winter mornings, your feet are guaranteed to thank-you for it.
We're positive that with Pauline's tips, you'll love your cosy winter home so much, you probably won't want to leave.
But if you do have to head away from your humble abode - don't forget to take the 'cosy' with you. Do yourself a favour and invest in some divine McDonald Possum and merino gloves. Your hands will be in Hawaii where ever you go!
Embrace the cosy; because before you know it, you'll be wheeling the bbq out again! | {
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This weekly show brings some of Greenville's best long-form improvisors together with a classic format called the Harold. Starting with a suggestion from the audience, our performers will create a 20 to 30 minute theatrical show on the spot. Sometimes it'll feel like a play and othertimes like a dream: the scenes build, push, crash, and fold into each other... themes, characters, patterns, and ideas all might appear and reappear... the original suggestion might come back into focus in surpising ways. But you never know—and neither do we!
This week, Narrative will open up the show and Haymaker—Alchemy's weekly Harold team—will close out the night with their own take on the classic Harold format.
Narrative features AJ Laurie, Cindy Pury , Jeff Mielton, Joe Johnson, Mary Stork, Michelle Winsch, Phillip Whiting, Travis Matthews, Walter Ezell and is coached by Jason Underrwood.
The Harold is not only the show that got long-form started, it's also the foundation of the classes we offer in our training center! The Harold was developed by Del Close and Charna Halpern in the 1960's at the iO Theater in Chicago and is now performed in improv comedy theaters from LA to NYC and everywhere in between. Famous comedians like Chris Farley, Mike Meyers, Tina Fey, Amy Poehler, and many others started their career with Harold-based improvisation and continue to use the style today. | {
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Section 66A quashed: Citizens can still be arrested for online posts
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Home > ADC Initiative > 'There are tears in our eyes when children are forcibly thrust in a ruthless world'
'There are tears in our eyes when children are forcibly thrust in a ruthless world'
Tall, erect and erudite, His Eminence Cardinal Oswald Gracias took time out from a busy pre-Christmas schedule at the conference room at the Eucharistic Congress building next to Holy Name Cathedral (Cardinal has shifted his office here, away from his table laden with piles of papers, files and books as the entire building of his office is getting repaired). Philip Varghese spoke to Oswald Cardinal Gracias about his hopes and concerns for his community this Christmas
Today evening (December 24), His Eminence Oswald Cardinal Gracias, Archbishop of Bombay will officiate at his ninth midnight mass as head of the Archdiocese of Bombay whose centre is the Cathedral of the Holy Name, locally known as Wodehouse Church in Colaba. It is also the Cardinal's 69th birthday, so both the day and night are special.
Back in 1997, journalist Jonathan Kwitny published a biography of Pope John Paul II called "Man of the Century." The idea was that the biography of John Paul II cut across all the great dramas of the 20th century, from Nazism and Communism to the upheaval in the Catholic Church caused by the Second Vatican Council.
By the same logic, one could say that Cardinal Gracias is churchman of the late 20th and early 21st centuries, because there's almost no story in which he isn't a lead actor. Cardinal Gracias is playing a key role in pushing through a reform of Catholic worship in the English language, adopting translations closer and more reverent to the traditional style.
Essentially a Mumbaikar, Cardinal Gracias grew up in Mahim and finished his seminary studies in Goregaon. But for brief stints in Jamshedpur, Agra and Rome he has served most of his time in churches in Mumbai and was ordained as a Bishop at St Michael's Church in Mahim in 1990.
In 2006 he took over from Cardinal Ivan Dias as Archbishop of Bombay.
Asked what this year's midnight mass sermon will focus on, he replies, it will be about family values.
"This Christmas I want that Christ should be born in every Christian house. This year particularly is dedicated to all the families and their thoughts.
Christmas is a season for rejoicing and welcoming with love the Christ-Child. But there are tears in our eyes when we think of children who are deprived of their childhood and forcibly thrust into a ruthless world which has neither the time nor space for the innocence of children. I pray that Christ the son of God is born in our hearts," Cardinal says.
Cardinal Gracias serves as the Second Vice-Chairman of Vox Clara, the group appointed by the Vatican to oversee the recent English translation of the liturgy. Why was the need felt to alter the translation of the liturgy, we asked. "Pope noticed about the misinterpretation of the liturgy and so a group was formed to discuss and make suggestions to alter the liturgy as there was a worry about a bad translation leading to misunderstanding and dogmatic error 50, 100 years from now. So there has to be a balance. Now, we have made the changes and priests are also satisfied with it."
Cardinal Gracias, is also the President of the Catholic Bishops' Conference of India and elected FABC Secretary General by the Presidents of the Federation of Asian Bishops' Conferences. "The FABC is an apex body representing 19 Bishop's Conferences comprising 28 of their Asian member countries like the other Bishops' Conferences of South America, Europe, Africa and Oceania. The Federation coordinates the work of the Church in these countries and represents Asia before the Vatican and Government authorities. The Central Secretariat is located in Hong Kong and is the principal service agency of FABC, and an instrument of co-ordination both within FABC and with outside offices and agencies in countries all through Asia," Cardinal said.
Mumbai city has a very vibrant Christian community, so does the country for that matter, and he talks about how happy he is that the churches are not dormant, but contributing to society. Especially in the field of education and health facilities, he says. "We are focussed mainly on rural India, and social awareness where the concentration is not just on charity but empowering people to use their basic rights, shifting from a needs base to a rights base and so bringing dignity into many underprivileged lives," Cardinal said.
Also concerned with ecology, the Cardinal points out that as good householders we should not exhaust the earth's resources given to us as gifts but preserve our environment for our children and grandchildren. "That is our responsibility for future generations," he emphasizes.
But the pressing challenge at this time, is for more Christians to "enter civil society in larger numbers; the bureaucracy, in the political field and in positions of leadership in public service," the Cardinal affirmed.
At 69, Gracias had a scare with cancer five years ago, and is visibly thinner than he was before the illness. Today, however, he is said to be cancer-free, and maintains a challenging work and travel schedule. "It was just prayer that worked for me during my time of being affected with cancer. Even the Pope prayed for me. That's why God heard their prayers and extended my life here so that I can serve him more in this earth," Cardinal Gracias concluded and with his Christmas blessings, we left this charming, most approachable man of God with an affability that puts you at ease in his presence, eminent that is and will be in the future.
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Want to study Cancer research abroad | {
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Q: loading GestureLibrary inside Fragment Activity not working how to load Gesturelibrary inside Fragment Activity ...Please help me
@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container,
Bundle savedInstanceState) {
// Inflate the layout for this fragment
View view =inflater.inflate(R.layout.fragment_a, container, false);
//error is here..."this" is not working
mLibrary = GestureLibraries.fromRawResource(this, R.raw.gestures);
gestureOverlayView = (GestureOverlayView)view.findViewById(R.id.gestureOverlayView);
return view;
}
A: It may be asking for context and it's throwing error because fragment doesn't have context.
Try to use like this:
mLibrary = GestureLibraries.fromRawResource(getActivity(), R.raw.gestures);
| {
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June 5, 2013 <
Chhattisgarh Maoist strike direct attack on freedom, say CMs
New Delhi, June 5 (IANS) The May 25 Maoist strike in Chhattisgarh was a "direct attack on democracy and freedom", chief ministers of various states said in a unanimous resolution Wednesday.
"It was a direct attack on democracy and freedom. We strongly disagree with the ideology of the Maoists. They want to overthrow parliamentary democracy and Constitution of India through violent means… this must be resisted with all our might," said the resolution by the chief ministers at a conference on internal security.
The meeting was held agaist the backdrop of the May 25 attack in which at least 26 people, including senior Congress leaders, were killed.
"The attack was a premeditated attack on political workers to give the intent to intimidate all political workers in order to thwart the political mobilisation of the people. Twenty-six people lost their lives in the attack," the resolution said.
The chief ministers resolved to use all legitimate means at their disposal to counter the activities of the Communist Party of India-Maoist.
"We appeal to the youth of the affected states to give up violence and pursue their goals to legitimate and democratic means. We assure them that we are sensitive to their concerns and will make every effort to bring them into the mainstream of social and political life," the resolution added.
The internal security meeting, convened by the home ministry and inaugurated by Prime Minister Manmohan Singh, will deliberate extensively on the activities of Pakistan-based terrorist groups, infiltration from across the border, communal disturbances and ways of improving intelligence gathering mechanisms.
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Praveen Kumar ruled out of Australia series | {
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The temporary / contract market in Guernsey is really thriving. With benefits including weekly pay, flexible working hours, great pay rates and a range of employers to work for, temp jobs in Guernsey have become more and more popular over the years. Companies have a constant need for people to be able to come in and hit the ground running for short to long term contracts making it a great way to find employment. | {
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Stylish hotel. Near city centre. Comfortable beds.
A stay at Hotel Voltaire Opera Nantes Centre places you in the heart of Nantes, a 2-minute drive from Cours Cambronne and 5 minutes from Passage Pommeraye. Featured amenities include a computer station, express check-in, and express check-out. Planning an event in Nantes? This hotel has facilities measuring 323 square feet (30 square meters), including a meeting room.
Close to tram. Close to old town. Great shops.
Trendy cocktail. New towels. Lounge area great.
Friendly welcome. Very friendly staff. Excellent service.
Delicious jams. Excellent croissants. Excellent breakfast selection.
Excellent walk in shower. Lots of hot water. There was no mini-fridge.
Large mirror. Quiet location. Quiet hotel. | {
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Until the Story of the hunt is told by the Lion, the tale of the hunt will always glorify the hunter–African Proverb
PLEASE NOTE THAT OF JUNE 2019 the African Holocaust Society is no longer active and no edits, or proofs have been done. The site will remain active until the domains and hosting plans expired.
African Holocaust (Est. 2001) is a non-profit civil society dedicated to the progressive study of African history and culture. The society is composed of African scholars and writers, who share the desire to represent and restore an authentic, reflexive, honest, plural and balanced study of the African experience, past and present.
We collate work from different areas of study, and provide sagacious analysis to educate, empower and enlighten. Enhancing the visibility of African history and culture, while adding clarity from an African ethical and cultural standpoint. African Holocaust Society does not at any stage advocate binary history or propaganda: The facts remain the facts, while the analysis is within African paradigms.
We reject all manifestations of oppression (From South Africa to Palestine), ignorance, racism, globalization, monoculturalization, cultural imperialism, gender suppression, religious intolerance (Islamophobia, antisemitism, etc), and ethnic hatred. We create new opportunities for the potential of marginalized people by addressing institutional racism, which has stymied hope and multicultural contributions.
African Holocaust does authentic in-house research. We use primary and secondary sources. We went to Sudan and Egypt for African Kingdoms, we went into the libraries of Timbuktu, mosque in Ethiopia for Islam and Africa.
Our mission is to produce accessible bodies of work, which inform about African culture and history, within an institutionalized and African-cultured framework. And within this framework we believe that African people should be the primary authors of their history and economically profit from their cultural capital. It is hoped that this work will also serve as a multicultural dialogue to share and expand the African cultural/historical experience with the wider World community. Our study of Africa is not a romantic enterprise, but moreover intended to enrich humanity through fostering plurality, and reinforcing the sanctity of life. We believe that only via the principles of self-determination and agency can African people globally continue to contribute their unique cultural experience to the forward flow of humanity
Inequity steals the hopes of people by marginalizing the potential contributions from a majority sector of humanity. The cure for AIDS, the cure for Cancer, the mission to Mars, the next Bob Marley, the next Malcolm X are trapped in a village somewhere in the so-called Third World. Trapped by institutionalized racism, trapped by the policies of the World Bank, trapped by a corrupt leadership. The biggest untapped resource is not in the ground, It is in the people but this future is stolen because of the injustices of this world.
Progressive African History
Progressive African History maintains that African people should be agents of their own history and the dominant voice in African history. This history must conform to the African cultural paradigm while at the same time meeting the highest threshold of good scholarship. This however is separate from continuous viewing history through the political or racial lens. History must be looked at in connection to our modern day social dynamic but it must also be weighted within its time period. We must not superimpose modern thesis onto ancient history.
While there is a natural bias inherent in all interpretation of historical events so the primary objective must be:
1. To seek truth
2. To learn from the past
3. To absorb the spirit of human possibility
4. To honor the moral obligation to remember
Media has generally been very derogatory of African people. The African voice, culture and history is shown through European eyes. In order for equality to be served all people must begin to freely tell their stories and must own and control these stories. Self-determination demands that people be active agents in how their image and history is represented in a multicultural World. Culture and history are the property of a people, it is a birth right. | {
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Keep your house warm without central heating: Best small portable heater for winter
Danielle Hine
·Contributor, Yahoo Life UK
This nifty heater may be small, but it's mighty. (Russell Hobbs)
Until last year, many of us had never heard of a 'plug heater'.
But these clever little gadgets have really come into their own recently, as so many of us are trying to find increasingly creative and cost-saving ways to heat our homes.
Not only are plug heaters space-saving, but they're also a cost-effective way to warm up a room without having to crank up all the radiators – something we're all trying to cut back on doing.
Think something this small couldn't possibly have any oomph? Well, spoiler alert: this Russell Hobbs Compact Black Ceramic Plug Heater, £23.99, can reach up to 30°C – most likely why it keeps selling out and has topped the Amazon's best heating category numerous times.
Why we rate it
There are so many things to love about this small-but-mighty 700W essential. It's the perfect portable solution to warm anywhere up to 10m² – like your home office, bedroom, bathroom, kitchen – even a caravan.
It's small enough to pop in your bag so you can take it with you when travelling, or to the office, if you need a little bit of extra warmth on the days you go in.
An ideal gadget for those WFH days when you don't want to turn the heating on. (Russell Hobbs)
It's suitable for all sorts of smaller spaces and can reach temperatures up to 30°C. (Russell Hobbs)
Utilising ceramic PTC tech (which basically means it allows electrical current to flow better at low temperatures than at high temperatures), it has a super-quiet fan and offers heating temperatures ranging from 15-30°C. Plus it has three modes – fan only, low power, high power – so you can see what works best for your needs and the room you're in.
With an LED display and 12-hour timer, you can programme it to work for your daily routine.
And with Amazon shoppers saying that when the plug is in use their smart meter is still in the green range, it's clear that its energy efficiency is not fake news.
What the reviews say
As over 50% of people who've purchased the Russell Hobbs Compact Black Ceramic Plug Heater have given it the thumbs up by rating it four or five stars, it deserves its good rep.
Shoppers say it's "bigger" and "punchier" than they thought and that they'd "definitely recommend it".
One customer was so impressed at how it boosted the heat in his living room by two degrees within 15 minutes that he purchased a second one.
"Cheap to run"; "quality is excellent"; "works well"; "good value"; "great little heater" are just some more of the praise-heavy comments left by happy users.
In fact, one shopper worked out it cost them about 50p per an hour to run. For an initial outlay of just under £24, that's a top investment in our opinion.
Shop now: Russell Hobbs Compact Black Ceramic Plug Heater | £23.99 (Was £24.99) from Amazon
The Compact Black Ceramic Plug Heater is the latest edition in Russell Hobbs portable heater collection.
The brand also sells a slightly smaller ceramic heater that works in a similar way, but has a little less power at a 500W maximum heat output, with two fan speeds, a 12-hour timer and night mode.
It's also a bestseller on Amazon and can be purchased for £22.99 – it has over 2,000 reviews with customers saying they were surprised by how "quickly" and "efficiently" it worked.
Shop now: Russell Hobbs 500W Ceramic Plug Heater | £22.99 (Was £24.99) from Amazon
This is the original iteration of Russell Hobbs plug heater, which also has rave reviews. (Russell Hobbs)
The very popular heater now also comes in black, for a more aesthetically-pleasing look.
The popular heater also now comes in black. (Russell Hobbs)
Watch: A cordless vacuum is a great investment for the home, too. Here's why.
Hong Kong offers 500K free air tickets to woo tourists
Holcim turns million-ton waste into alternative fuels, raw materials for cement making
2 dead over dumbbells in Talisay | {
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\section{Introduction}
Asymmetric exclusion models with a fixed
\cite{schutz,Derrida-92,Derrida-93}, and typically large number of
lattice sites have been the subject of much recent theoretical
attention \cite{Sandow-94,Kolomeisky-98,Chou-04,Lak-03,
Shaw-03,Evans-94,Lahiri-97,Lahiri-00,Naimi-05,Evans-03,Frey-03,Frey-04}. Biophysical
applications and new fundamental understanding of non-equilibrium
steady-states (NESS) have motivated many extensions of the simple
totally asymmetric exclusion process (TASEP) with open
boundaries. These include partially asymmetric models, where particles
can hop backward \cite{Sandow-94}, exclusion processes with nonuniform
hopping rates \cite{Kolomeisky-98,Chou-04,Lakatos-06}, exclusion among
particles of arbitrary size \cite{Lak-03,Shaw-03,dong}, multispecies
exclusion processes \cite{Evans-94, Lahiri-97,Lahiri-00,Naimi-05},
multichannel exclusion processes \cite{junction} and exclusion
processes with Langmuir type adsorption and desorption kinetics
\cite{Evans-03,Frey-03,Frey-04}. All of these studies have considered
open, well-defined boundaries, where the length of the lattice is
fixed. TASEP models with one open and one closed boundary conditions
have also been considered \cite{Klumpp-05}.
However, applications may arise where the length of the system is
dynamically varying. The system size may vary because a single
particle pushes against a boundary-defining wall. One example is
helicase-induced opening of replication forks in DNA processing
\cite{Betterton-03}. Here, the moving replication fork defines a
moving boundary of the system. Examples of variable-system size
exclusion processes that involve multiple motor particles include mRNA
translation in the presence of hairpins in the mRNA, and molecular
motors processing on elongating actin filaments. Ribosomes that
process along mRNA (in the process of protein synthesis) during
translation \cite{MacDonald-68,Chou-04} often encounter a hairpin and
the position at which the hairpin starts represents a wall over which
the processing ribosomes cannot pass. The detachment rates of the
ribosomes and the tightness of the hairpin may determine if the
ribosomes can translate the mRNA through the hairpin sequences. Actin
polymerization at the leading edge of filopodia also seems to be
mediated by processing molecular motors that may carry actin assembly
components \cite{mitchinson,traffic}. The motors detach, and possibly
attach, anywhere along the growing actin filament
\cite{Klumpp-04}. The depolymerization of the leading tip may be
limited or enhanced by the presence of a motor or other actin
associated proteins \cite{purich,julicher}. Finally, a recent model of
a dynamically extending exclusion process without Langmiur kinetics
has been recently studied \cite{HYPHAE2}. This model has been applied
to filamentous hyphae growth in fungi \cite{HYPHAE}.
With the above applications in mind, we consider a TASEP with a
dynamically varying length. Specifically, we analyze a many-particle
asymmetric exclusion process with a fixed open boundary on the left, a
fluctuating boundary on the right, and Langmuir kinetics. The
particles have a fixed injection site and can adsorb and desorb. A
wall with an intrinsic leftward drift (representing {\it e.g.}, a
hairpin which energetically favors spontaneous closing or the barbed
end of an actin filament that prefers depolymerization) prevents the
passage of particles. The particles advance and provide a pressure
against the wall. For certain attachment/detachment and wall hopping
rates, the system reaches a NESS in which the statistics of the wall
position are stationary. For other values of the kinetic parameters,
no time-independent mean wall position exists. The wall will either
drift steadily towards the particle injection site and fall off the
lattice, or move indefinitely away from the injection site,
continuously increasing the size of the system. The specific details
of the stochastic process are shown in Figure \ref{FIG1}. Particles
are injected into the first lattice site with rate $\alpha$ provided it is
empty. In the interior of the lattice, each particle moves forward
with rate $p$ only if the site ahead of it is unoccupied. Particle
attachment and detachment occur with rate $k_{+}$ and $k_{-}$,
respectively, throughout the lattice.
\begin{figure}[h]
\begin{center}
\includegraphics[height=0.48in]{Fig1.eps}
\end{center}
\vspace{-4mm}
\caption{A totally asymmetric exclusion process bounded by a
fluctuating wall. Particles are injected onto the leftmost site with
rate $\alpha$, and move to the right with rate $p$. In the interior,
particles detach and adsorb with rates $k_{-}$ and $k_{+}$,
respectively where $k_{\pm} \ll p$. The lattice is bounded on the
right by a fluctuating wall with intrinsic hopping rates $w_+$ and
$w_-$, where $w_+<w_-$.}
\label{FIG1}
\end{figure}
The lattice length is not fixed, and $N$ denotes the position of the
particle-confining wall that hops forward with rate $w_+$, and
backward with rate $w_-$ provided there is no particle to its
immediate left. The particle occupation at each site, $1\leq i \leq
N-1$, left of the wall is represented by the occupation variable
$\sigma_{i} \in \{0,1\}$. If $w_{-} \leq w_{+}$, the wall will move
indefinitely away from the injection site. In order to prevent the
wall from always escaping to infinity, we consider the more
interesting case of an intrinsic leftward drift described by $w_{-}>
w_{+}$.
The wall position $N$ is not fixed (even at steady state), but rather,
is determined by the intrinsic wall hopping rates, and the
exclusionary interactions between the wall and the lattice
particles. Our analysis is aimed at understanding how the wall
dynamics depend on the parameters $\alpha, k_{\pm}, w_{\pm}, p$. In
the next section, we derive relations for the distribution functions
of the wall. In steady-state, these relations constrain the particle
density at the wall. In Section \ref{SIGMA}, we use mean field theory
(MFT) to solve for the density profile, and show that the density
profile obtained using mean field theory is inaccurate near the wall.
Since quantitative prediction of the wall dynamics will require
accurate determination of the particle densities near the wall, in
Section \ref{sec:FS}, we develop a moving-frame finite segment mean
field approach to accurately solve for the density profile near the
wall. The existence of a steady-state solution and the dependencies
of the mean wall position $\langle N \rangle$ on the problem
parameters are explored and plotted in Section \ref{RESULTS}.
\section{Wall dynamics}\label{WALL}
The net drift of the wall is the difference between its forward and
effective backward hopping rates. The effective backward hopping rate
depends on both the intrinsic backward hopping rate $w_-$, and on the
occupancy of the site immediately to the left of the wall since a
particle there will block the wall's backward motion. The wall's
rightward hopping is never impeded. The probability of finding a
particle immediately to the wall's left varies with its position,
thus, the wall dynamics are position-dependent. Define $Q_N(t)$ as
the probability that the wall is at position $N$ at time $t$, and
$Q'_N(t)$ as the joint probability that the wall is at position $N$ at
time $t$ \emph{and} the site just before the wall is empty. The wall
dynamics obey
\begin{equation}
\dot{Q}_{N}(t) = w_{-}Q'_{N+1}-w_{-}Q'_{N}-w_{+}Q_{N} + w_{+}Q_{N-1},
\label{EFFECTIVEQ}
\end{equation}
and the moments of the wall position can be formally expressed as
\begin{equation}
{\partial \over \partial t} \langle N^k\rangle =
\sum_{N=0}^{\infty}(w_{-}Q_{N}'-w_{+}Q_{N})\sum_{j=0}^{k-1}(-1)^{k-j}
{k \choose j} N^{j}.
\label{NDOT}
\end{equation}
Although one cannot find $Q_N$ or $Q'_N$ explicitly without solving
the full exclusion problem, we can take $k=1$ in (\ref{NDOT}) to determine the
mean wall velocity via
\begin{equation}
{\partial \over \partial t} \langle N \rangle = -w_{-}
\sum_{N=0}^{\infty} Q'_N+w_{+}.
\label{meanV}
\end{equation}
If the mean wall position is time-independent, $\sum_{N=0}^{\infty}
Q'_N = w_{+}/w_{-}$, and the expected occupancy of the site
immediately preceding the wall is
\begin{equation}
\langle \sigma_{N-1}\rangle =1-\sum_{N=0}^{\infty}
Q'_N=1-\frac{w_{+}}{w_{-}}. \label{BeforeWall}
\end{equation}
We show in section \ref{unstable} that there are some parameter
regimes in which (\ref{BeforeWall}) cannot be satisfied. For these
parameter values, there exists no time-independent mean wall
position. However, one can still use (\ref{meanV}) to determine the
relevant mean wall dynamics. The preceding analysis suggests that it
may be more natural to define sites near the wall by their position
relative to the wall than by their absolute position on the lattice.
To avoid working in both frames of reference, in the next section, we
will begin by considering the limit in which the wall hopping rates
are small compared to other rates in the problem ($p$, $k_+$, and
$k_-$). In this limit, the wall dynamics are slow compared to the
particle dynamics, and we will assume that the wall frame is
stationary.
\section{Mean Field Solution of Density Profile}\label{SIGMA}
In the $w_{\pm}/k_{\pm}, w_{\pm}/p \rightarrow 0$ limit, we expect the
wall to be nearly stationary. Mean field equations can be derived by
ensemble-averaging the rate equations for the occupation variables
$\sigma_{i}$, and ignoring correlations ($\langle
\sigma_{i}\sigma_{j}\rangle \approx
\langle\sigma_{i}\rangle\langle\sigma_{j}\rangle$). Upon defining the
mean occupation $s_{i} \equiv \langle\sigma_{i}\rangle$, the mean field
equations for a {\it fixed} ($w_{\pm} = 0$) wall system in NESS are
\begin{eqnarray}
\displaystyle {\mbox{d} s_{i} \over \mbox{d} t} =
-s_{i}(1-s_{i+1})+s_{i-1}(1-s_{i}) - k_{-}s_{i} \qquad \nonumber
\\[2pt] +k_{+}(1-s_{i}) = 0, \qquad \label{MFTa} \\[13pt]
\displaystyle {\mbox{d} s_{1} \over \mbox{d} t} =
\alpha(1-s_{1})-k_{-}s_{1}-s_{1}(1-s_{2}) \qquad \,\,\, \nonumber \\[2pt]
+k_{+}(1-s_{1})= 0, \qquad\qquad \,\,\label{MFTb} \\[13pt]
\displaystyle {\mbox{d} s_{N-1} \over \mbox{d} t} = -k_{-}s_{N-1}
+k_{+}(1-s_{N-1}) \qquad \qquad \qquad \, \nonumber \\[2pt]\:
+s_{N-2}(1-s_{N-1}) = 0. \qquad \quad
\label{MFTc}
\end{eqnarray}
where the adsorption, desorption and injection rates have been
normalized by $p$ and time has been rescaled by $p^{-1}$ -- hence,
$k_{\pm}$, $\alpha$ and $t$ in (\ref{MFTa}-\ref{MFTc}) are dimensionless.
However, in order to use condition (\ref{BeforeWall}), we need
expressions for particle density at sites defined by their distance
from the wall. In the fluctuating frame of the wall, we use the notation
$\tilde{s}_j \equiv s_{N-j}$. Upon rewriting (\ref{MFTa}-\ref{MFTc})
in the wall frame, we find
\begin{widetext}
\begin{eqnarray}
\displaystyle \frac{\mbox{d} \tilde{s}_j}{\mbox{d} t} &=&\displaystyle
-(1+w_{+})\tilde{s}_j (1-\tilde{s}_{j-1}) + (1+(1-\tilde{s}_{1})
w_{-}) \tilde{s}_{j+1} (1-\tilde{s}_{j}) - k_{-}\tilde{s}_{j} +
k_{+}(1-\tilde{s}_{j}) \nonumber \\ \: & \: & \displaystyle
\hspace{4.5cm} -w_-(1-\tilde{s}_1)(1-\tilde{s}_{j+1})\tilde{s}_j +
w_{+}(1-\tilde{s}_{j})\tilde{s}_{j-1} = 0, \label{MFTEQNa} \\[13pt]
\displaystyle {\mbox{d} \tilde{s}_{N-1} \over \mbox{d} t} &=& \displaystyle
\alpha (1-\tilde{s}_{N-1}) -k_- \tilde{s}_{N-1} -
\tilde{s}_{N-1}(1-\tilde{s}_{N-2}) +k_{+}(1-\tilde{s}_{N-1})= 0, \label{MFTEQNb} \\[13pt]
\displaystyle {\mbox{d} \tilde{s}_1 \over \mbox{d} t} &=& \displaystyle
-k_{-}\tilde{s}_{1}+k_{+}(1-\tilde{s}_{1})+ (1+w_{-})\tilde{s}_{2}
(1-\tilde{s}_{1}) - \tilde{s}_{1} w_{+} = 0. \label{MFTEQNc}
\end{eqnarray}
\end{widetext}
As expected, (\ref{MFTEQNa}) and (\ref{MFTEQNc}) reduce to
(\ref{MFTa}) and (\ref{MFTc}) in the $w_{\pm} =0$ limit.
If the position of the wall were fixed, we could simply use the
iteration given by (\ref{MFTa}), along with boundary conditions
(\ref{MFTb}) and (\ref{MFTc}) to solve for the density profile $s_i$.
Now consider a moving wall problem. Because $\langle N\rangle$ is
undetermined, we need three conditions to solve (\ref{MFTEQNa}). In
addition to the two boundary conditions (\ref{MFTEQNb}) and
(\ref{MFTEQNc}), we require a third condition,
$\tilde{s}_1=1-w_{+}/w_{-}$, to determine $\langle N \rangle$. This
third boundary condition fixes $\tilde{s}_1$; $\tilde{s}_2$ is set by
(\ref{MFTEQNc}), and we can use (\ref{MFTEQNa}) to iterate forward in
$j$ as many times as required toward the injection site, until
(\ref{MFTEQNb}) is satisfied. The number of iterations required to
satisfy (\ref{MFTEQNb}) determines the mean position, $\langle
N\rangle$, of the left boundary, and hence the NESS size reached by the
system. Although (\ref{MFTEQNa}) was derived in the wall frame, the
resulting density profile is nearly identical to a stationary frame
profile derived from (\ref{MFTa}) when $s_{i}$ is not varying rapidly
with site $i$. See the Appendix for further discussion.
\begin{figure}[h]
\begin{center}
\includegraphics[height=1.9in]{Fig2a.eps}\\
\vspace{3mm}
\includegraphics[height=1.9in]{Fig2b.eps}
\end{center}
\vspace{-4mm}
\caption{(Color online) A comparison of density profiles derived from Monte-Carlo
simulation and MFT. (a) The MFT and MC density profiles for conserved
particle TASEP are compared ($\alpha = 0.6$, $\beta = 0.9$, $N =
10,000$). Despite differences between MFT and MC in the boundary
layers, the particle density at the ends ($i = 1$, $i = 10000$) are
matched through particle conservation. Insets show the left and right
boundary layers in detail. (b) For a TASEP with Langmuir kinetics
(with $k_- = 0.01$, $N=300$, $p = 1$, and $k_+, w_+, w_- = 0$), the
MFT density profile can be appreciably different from the MC results,
especially near the boundaries.}
\label{DIFFERENCE}
\end{figure}
For standard particle-conserving TASEP models, away from boundaries,
MFT predicts the particle densities to a very high
accuracy \cite{Derrida-92}. A conservation law for the particle density
can be used to fix the end densities to their exact values so that the
MFT also performs well near boundaries \cite{Lakatos-06}. In Figure
\ref{DIFFERENCE}a, we plot the density profiles from Monte-Carlo
simulations and mean field recursion relations for the simple TASEP
($k_{\pm} = 0$) with a fixed number of sites, $N=10000$. Differences
in the density profiles are evident in the insets.
Because we include particle adsorption and desorption through Langmuir
kinetics, there is no conservation law for the particle density. In
this case, the boundary densities are not fixed and we see in Fig.
\ref{DIFFERENCE}b that simple mean field calculations of the boundary
density can differ appreciably from the values found from Monte-Carlo
simulations. However, MFT still matches simulation results in the bulk
where $s_i$ varies slowly. In the following section, we use an
approach that couples explicit enumeration within a finite segment of
sites to the mean field results accurate outside the segment. This
finite segment mean field theory (FSMFT) includes particle
correlations within a segment of sites adjacent to the wall.
\section{Finite Segment Method}\label{sec:FS}
We have shown that mean field theory does a poor job of predicting the
profile $s_{i\approx N-1}$ near the wall when there is a boundary
layer. To more accurately compute the particle density in this
region, we will solve the Master equation for a finite segment of $m$
sites preceding the wall. First, we introduce some notation to
explain the mechanics of the finite-segment mean field theory (FSMFT).
For the binary string $(\sigma_{N-m}, ..., \sigma_{N-2},
\sigma_{N-1})$, corresponding to the occupancy of sites in the finite
segment we define the \emph{state} of the segment as the base ten
value of the string. For example, for $m=2$ sites just left of the
wall, we have four possible combinations for the occupancies (00),
(01), (10), and (11) corresponding to states $i=0,1,2, 3$,
respectively. If $P_{i}$ is the probability that the finite segment
configuration is in state $i$, the Master equation is
$\partial_{t}P_{i} = M_{ij}P_{j}$ where $M_{ij}$ is the transition
matrix. In the $m=2$ case,
\begin{widetext}
\begin{equation}
{\bf M} = \left(\begin{array}{cccc}
-(1+w_{-})s^*-2k_{+} & k_{-} & k_{-}+w_{+} & 0 \\[13pt]
k_{+} & -(w_{+}+k_{-}+k_{+}) - s^* & 1 + w_{-}(1-s^*) & k_{-}\\[13pt]
(1+w_{-})s^{*}+k_{+} & w_{+} & -(w_{+}+w_{-}+1+k_{-}+k_{+}) & k_{-}+w_{+} \\[13pt]
0 & k_{+}+s^{*} & k_{+}+w_{-}s^{*} & -2k_{-}-w_{+}\end{array} \right)
\end{equation}
\end{widetext}
where $s^*\equiv \langle \sigma_{N-m-1}\rangle$ is the mean occupancy
in the lattice site just to the left of the segment. The mean
occupancies in the finite segment can be calculated from ${\bf M}$ in
the following way. First, the eigenvector, ${\bf P}^{(0)}$,
corresponding to the eigenvalue zero is computed. The vector ${\bf
P}^{(0)}$, normalized such that $\sum_{i}^{m} P_{i}^{(0)} = 1$
corresponds to the stationary probability distribution, {\it i.e.},
$\partial_t {\bf P}^{(0)} = 0$. Let $\textbf{v}$ be a $m \times
2^{m}$ matrix where the columns are the ordered state vectors. The
mean densities are then given by
$(s_{N-m-1},\ldots,s_{N-2},s_{N-1})^{T} = {\bf v}{\bf P}^{(0)}$.
\begin{figure}[h]
\begin{center}
\includegraphics[height=1.9in]{Fig3a.eps}\\
\vspace{4mm}
\includegraphics[height=1.9in]{Fig3b.eps}
\end{center}
\vspace{-4mm}
\caption{(a) $F(s^*)$ is plotted with parameter values $k_+ = 0$, $k_-
= .01$, $w_+ = 0.005$, $w_- = 0.01$. (b) The finite segment method
predicts the boundary layer profile significantly better than mean
field theory. Here, the final ten sites of a fixed-wall profile
($N=300$) are plotted. The parameters $k_-=0.01$, $k_+ = 0$, and
$\alpha=1$ were used.}
\label{SEGMENT}
\end{figure}
For every value of $s^*$, FSMFT can be used to compute the
mean densities $s_{N-m}, ..., s_{N-2}, s_{N-1}$. In particular, it
establishes a one-to-one correspondence between $s^*$ and $s_{N-1}$:
\begin{equation}
s_{N-1} = F(s^*;w_{\pm},k_{\pm}). \label{FSM-relation}
\end{equation}
\noindent Our calculations indicate that $F(s^*)$ is always a monotonically
increasing function of $s^*$, as shown in Figure \ref{SEGMENT}a.
Comparing the density profiles near a {\it fixed} wall
($w_{+}=w_{-}=0$), Figure \ref{SEGMENT}b shows that using FSMFT (with
$m=5$) significantly improves our prediction of the particle density
near the wall over that obtained using simple ($m=1$) MFT. To
calculate $\langle N \rangle$ for a fluctuating wall ($w_{-} > w_{+}
>0$), we first solve for the profile of a segment of sites adjacent to
the wall. From (\ref{BeforeWall}), when the wall attains a
steady-state position, $s_{N-1}=1-w_{+}/w_{-}$. Using
(\ref{FSM-relation}), we find the value of $s^*$ satisfying
$1-w_{+}/w_{-} = F(s^*)$. Defining this particular value of $s^*$ as
$s^*_{eq}$, we then use the recursion relation given by
(\ref{MFTEQNa}) to solve the density profile to the left of the finite
segment. Using the values of $s_{N-m}$ and $s^*_{eq} \equiv
s_{N-m-1}$ from the FSMFT as starting conditions for the recursion
equations, we iterate to the left until the left boundary condition
(\ref{MFTEQNb}) is satisfied. In summary, the finite segment mean
field theory (FSMFT) is implemented by the following steps:
\vspace{4mm}
$\bullet$ For a given $s^{*}$, solve for the normalized eigenvector
corresponding to the zero eigenvalue of the $2^{m}\times 2^{m}$
transition matrix $M_{ij}(s^{*})$.
\vspace{3mm}
$\bullet$ From the zero eigenvector, express the mean density $s_{N-1}$
at the site nearest the wall as a function of $s^{*}$, giving relation
(\ref{FSM-relation}).
\vspace{3mm}
$\bullet$ For a static wall NESS, set $s_{N-1}=1-w_{+}/w_{-}$ and find
$s_{eq}^{*}$ that yields zero net wall drift by using $1-w_{+}/w_{-} =
F(s_{eq}^*;w_{\pm},k_{\pm})$.
\vspace{3mm}
$\bullet$ Starting with $\tilde{s}_{m+1} = s_{eq}^{*}$ (and
$\tilde{s}_{m} = s_{N-m}$) iterate using the simple mean field
equation (\ref{MFTEQNa}) until equation (\ref{MFTEQNb}) is satisfied.
\vspace{3mm}
$\bullet$ The number of iterations required determines the mean wall
position ($\langle N\rangle \approx$ number of iterations $+m+2$) as a
function of the rate parameters through the starting value
$s_{eq}^{*}$.
\vspace{4mm}
We expect the predicted results from a moving-frame FSMFT to be in
good agreement with those from MC simulations. This is because in
regions where $s$ is slowly varying, the mean field equations
describing the density profile in the wall frame and in the lab frame
yield nearly identical profiles. This can be seen from the continuum
equations, as will be discussed in the Appendix. In these regions,
accurate estimates of the mean wall position can also be obtained
using the continuum approximations to (\ref{MFTEQNa}), provided
$\langle N \rangle$ is large. When state enumeration of a larger
segment is used, more of the correlations within the density boundary
layer is taken into account and more accurate results are
expected. Provided most of the regions with large gradients in density
is captured by the finite segment, the results will be very accurate.
The incremental accuracy achieved as larger segments are used has been
discussed in a different, but related system \cite{Chou-04}. In the
subsequent analyses, we use a five-site ($m=5$) FSMFT -- generating a
$2^{5}\times 2^{5}$ eigenvalue problem in the process -- and
self-consistently solve for the densities away from the boundary
layer. This choice of segment size is sufficient to yield accurate
results for all parameters explored.
\section{Results and Discussion} \label{RESULTS}
\subsection{Time-Independent Mean Wall Positions} \label{NO-KON}
We first consider regimes in which the wall acquires a
static mean position in NESS. Using Monte Carlo simulations
and FSMFT, we study the dependence of the mean wall position on the
injection rate $\alpha$, particle adsorption and desorption rates
$k_{\pm}$, and the wall hopping rates $w_{\pm}$.
We can use analytic solutions of the bulk continuum equations in order
to understand parameter dependencies of our model. Although mean
field theory poorly describes our system in the boundary layers where
the profile varies rapidly, away from boundary layers, simple MFT is
accurate. In these regions, to guide our our analysis, we will use
the continuum limit of the mean field equations. We define
$\varepsilon\equiv 1/N_0$ where $N_0$ is a characteristic number of
lattice sites (to be derived below) and $x \equiv (i-1)/N_0 $ as a
relative position along the lattice. As shown in the Appendix, the
NESS density profile obeys
\begin{equation}
\varepsilon(2s-1)s'(x)+k_+-(k_+ + k_-)s + O(\varepsilon^2) = 0
\label{eq:bulk1}
\end{equation}
in both the lab and wall frames of reference. Upon integrating, we
obtain the implicit equation
\begin{equation}
\begin{array}{l}
\displaystyle \frac{(k_+ -k_-)\ln\vert k_{+}-(k_{+}+k_{-})s\vert
-2k_{+} + 2(k_{+} + k_{-})s}{(k_{+}+k_{-})^2} \\[13pt]
\hspace{5cm} \displaystyle ={x\over \varepsilon}+C,
\end{array}
\label{bulk}
\end{equation}
where $C$ is a constant of integration. In the continuum description,
the entrance site is at position $x = 0$, the wall's position is $L$,
and the mean wall position is $\langle L \rangle \equiv \varepsilon
\langle N \rangle$. We can use (\ref{bulk}) to understand the
behavior of the mean wall position $\langle N \rangle$. First, note
that the left hand side of (\ref{bulk}) scales as
$(k_++k_-)^{-1}$. Since $\varepsilon^{-1} \equiv N_0$ scales as
$(k_-+k_+)^{-1}$, we define $N_0 \equiv (k_+ + k_-)^{-1}$. For a
continuum description to be useful, $N_0$ must be large, so $k_{\pm}$
must be small.
\begin{figure}[t]
\begin{center}
\includegraphics[height=1.8in]{Fig4a.eps}\\
\vspace{4mm}
\includegraphics[height=1.8in]{Fig4b.eps}
\end{center}
\vspace{-4mm}
\caption{(Color online) Simulations were performed with $w_+=0.001$, $w_-=0.01$,
$k_-=0.01$, and different values of $\alpha$. In (a), profiles for
three simulations are plotted with their mean wall positions aligned.
When $\alpha \lesssim 0.5$, $s(0)\approx \alpha$. When $\alpha \gtrsim 0.5$, $s_B$
becomes multivalued and there is a boundary layer on the left. Within
the boundary layer, a small change in the position results in a large
change in the particle density. Thus, in (b), where $\langle N
\rangle$ is plotted as a function of $\alpha$, large changes in
$\alpha$ result in small changes in $\langle N \rangle$ when
$\alpha\gtrsim 0.5$. Also shown is the prediction from (\ref{meanN}) with
$s_{eq}^{*} = 0.026$, determined by FSMFT.} \label{fig:Alpha}
\end{figure}
Equation (\ref{bulk}) gives an implicit formula for the bulk density,
which we denote by $s_B(x)$, in terms of the adsorption and desorption
rates, $k_{\pm}$ and the integration constant $C$. The injection rate
$\alpha$ determines $C$, and along with the wall hopping rates
$w_{\pm}$, determines the mean wall position. As shown in the Appendix,
the solution near the left boundary varies slowly when $\alpha \lesssim
0.5$. Furthermore, if $k_- \ll \alpha$, we can approximate $s_1
\approx s_2$ in (\ref{MFTb}) to conclude that $s(0) \approx \alpha$.
This simplified condition can be used to determine $C$ in
(\ref{bulk}).
When $\alpha \gtrsim 0.5$, a boundary layer arises on the left (this can be
seen in Fig. \ref{fig:Alpha}a). In this regime, $s(0)$ can no longer
be approximated as $\alpha$, and $s_B(x)$ becomes invalid near the
injection site. While $s_B(x)$ is still a good approximation to the
density profile outside the boundary layer (where $s\lesssim 0.5$), there is
no straightforward, analytic way to calculate $C$ when $\alpha\gtrsim 0.5$.
In Fig. \ref{fig:Alpha}a, when $\alpha = 1$, $C$ is used as a single
fitting parameter and is determined empirically such that in the bulk,
$s_B(x)$ approximates the density profile obtained using MC
simulations. The mean wall position, $\langle L \rangle$, is found
through the relation $s_B(\langle L \rangle-(m+1)) = s^*_{eq}$ where
$s^*_{eq}$ is found using an $m-$site FSMFT and is the value of $s^*$
that puts no net drift on the wall.
Figure \ref{fig:Alpha}a shows results from MC simulations, shifted so
that the mean wall positions are aligned at $\langle N \rangle = 225$,
which is the mean wall position when $\alpha = 1$. While the density
profile has a sharp boundary layer at the wall in the wall frame, in
the lab frame, the boundary layer is smeared out due to wall
fluctuations. This results in the broad peaks centered on the mean
wall position seen in Figure \ref{fig:Alpha}a. The outer solution
$s_B(i/N_0)$ with $N_0 = (k_+ + k_-)^{-1}$ is shown by the dotted
curve. The close agreement between the MC data and $s_B(x)$ suggests
that dropping the $O(\varepsilon^2)$ term in (\ref{eq:bulk1}) to obtain
$s_B(x)$ produces an excellent approximation to the mean particle
density, provided $\alpha \lesssim 0.5$. Note that $\alpha$, through $C$,
simply shifts $s_B(x)$ to the left or right; thus, when we vary only
$\alpha$ and plot the resulting density with the mean wall positions
aligned (as they are in \ref{fig:Alpha}a), the profiles collapse onto
the same curve.
We can also use (\ref{bulk}) to predict the mean wall position as a
function of the injection rate $\alpha$ when $\alpha$ is not too large. For
simplicity, consider $k_+ = 0$ -- the analysis for $k_+ \neq 0$ is
analogous. Using the simplified condition $s(0) = \alpha$ in
(\ref{bulk}), we have
\begin{equation}
C = {2\alpha -\ln (\alpha k_{-}) \over k_{-}}.
\label{eq:C}
\end{equation}
Now, using the relation $s^*_{eq}=s_B(\langle
L\rangle-\varepsilon(m+1))$ and (\ref{eq:C}), (\ref{bulk}) becomes
\begin{equation}
\langle N\rangle = \frac{1}{k_-} \ln \left( \frac{\alpha}{e^{2\alpha}}
\frac{e^{2 s^*_{eq}}}{s^*_{eq}}\right)+m+1.
\label{meanN}
\end{equation}
The dependence of $\langle N \rangle$ on $\alpha$ is shown in Figure
\ref{fig:Alpha}b, predicted using four different methods. Simple MFT
($m=1$, dotted curve) performs poorly relative to MC simulations (open
diamonds). The results from FSMFT with $m=5$ (solid curve) agree very
well with the MC data for all values of $\alpha$. The solution of
(\ref{meanN}) (dashed curve) performs reasonably well provided $\alpha$ is
not too large. When $\alpha \gtrsim 0.5$, $s(0) = \alpha$ is a poor approximation
to (\ref{MFTb}) and the resulting prediction of $\langle N \rangle$
suffers. In fact, the slope $s_B'$ diverges when $s_B=0.5$, which can
be seen from (\ref{eq:bulk1}). When $\alpha \gtrsim 0.5$, there is a
boundary layer on the left with width $O(\sqrt{\varepsilon})$
(cf. Appendix). As a result, increases in $\alpha$ above $0.5$ will
increase the height of the boundary layer, but will not significantly
change the mean wall position, and $\langle N \rangle$ becomes
insensitive to changes in $\alpha$ \footnote[2]{In \cite{Evans-03,Frey-04},
an asymmetric exclusion process in a fixed
domain with open boundaries and Langmuir kinetics was studied.
Regimes arise in which the position of a shock in the particle density
becomes insensitive to the ejection rate $\beta$ on the right, once
$\beta >0.5$. Because these observations were made
under the assumption $k_+>k_-$, and we consider $k_->k_+$, by particle
hole symmetry, the ejection rate in these works corresponds to
the injection rate, $\alpha$ in our problem. While the authors of
\cite{Evans-03, Frey-04} find a shock position insensitive to boundary
conditions, we find an insensitive mean wall position.}.
\begin{figure*}[htb]
\begin{center}
\includegraphics[height=1.5in]{Fig5a.eps}
\hspace{1mm}
\includegraphics[height=1.5in]{Fig5b.eps}
\hspace{1mm}
\includegraphics[height=1.5in]{Fig5c.eps}
\end{center}
\vspace{-4mm}
\caption{Boundary effects near the wall determine wall position. In
(a), $s^*_{eq}$ is determined empirically from MC simulations captured
in the wall frame and numerically using the finite segment method. In
(b), MC simulations are plotted in the lab frame. In (c), the
occupancy of the last site in the wall frame $s_{N-1} = 1-w_{+}/w_{-}$
is plotted as a function of the mean wall position $\langle N
\rangle$. The parameters $\alpha =1$, $k_-=0.01$, $k_+ = 0$, and $w_+
= 0.001$ were used.}
\label{fig:wp}
\end{figure*}
We now discuss how changes in the wall hopping rates can affect the
wall position. In Fig. \ref{fig:wp}a, for a fixed value of $w_{+}$,
one sees that an increase in $w_{-}$ increases the value of
$s^*_{eq}$. Our FSMFT predicts that given values of $w_+$ and $w_-$,
$s^*_{eq}$ must satisfy $1 - w_{+}/w_{-} = F(s^*_{eq};w_{\pm})$.
For small values of $w_{\pm}$, $F(s_{eq}^{+},w_{\pm})\approx
F(s_{eq}^{*},0) \approx 1-w_{+}/w_{-}$, suggesting that
$s^*_{eq}$ depends primarily on the ratio $w_+/w_-$, with only a weak
dependence on the individual wall hopping rates. Since
$F$ is a monotonically increasing function,
$s^*_{eq}$ increases with $w_{-}/w_{+}$.
A change in $s_{eq}^{*}$ induces a change in the mean wall position,
shown in Fig. \ref{fig:wp}b. Again, this is consistent with our theory
since $\langle L \rangle$ must satisfy $s_B(\langle L\rangle
-\varepsilon(m+1)) = s_{eq}^{*}$. In the special case $\alpha \lesssim 0.5$,
one can use (\ref{meanN}) to predict $\langle N\rangle$ directly,
given $s^*_{eq}$. When $\alpha \gtrsim 0.5$, one either has to solve the
full set of discrete MFT equations (\ref{MFTEQNa}) and (\ref{MFTEQNb})
-- or the equivalent continuum equations (\ref{CONTINUUM}) and
(\ref{BCLEFT}) -- coupled to a finite segment, to obtain $\langle
N\rangle$. Our results from solving the discrete equations are shown
in Fig. \ref{fig:wp}(c). Using simple MFT ($m=1$) without a larger
finite segment generally results in poor predictions for $\langle
N\rangle$.
A more complete understanding of the wall dynamics can be garnered by
analyzing the wall fluctuations. For simplicity, we consider the
continuum description in which the wall's motion can be approximately
described by a diffusion constant $D = \varepsilon^2 w_+$ and a
position-dependent drift, $V(L)$. If one assumes that the wall
fluctuates within a harmonic ``potential,'' this drift takes the form
$V(L) = -a(L-\langle L \rangle)$, where $a \equiv -(\mbox{d} V/\mbox{d}
L)|_{\langle L \rangle}$. This approximation effectively closes
(\ref{EFFECTIVEQ}) by expressing the effects of conditional
probability, $Q_{N}'$, in terms of a drift. For $L \approx \langle
L\rangle$, the probability density of the wall's position, $Q(L)$ (the
continuum analog of $Q_N$), can be approximately found from the
solution of
\begin{equation}
\frac{\partial Q(L,t)}{\partial t} = a{\partial \over \partial L}\left[
(L-\langle L\rangle)Q(L)\right]+ D\frac{\partial^2 Q}{\partial
L^2}.
\label{eq:Diffusion}
\end{equation}
Upon imposing the normalization $\int_{-\infty}^{\infty}Q(L)dL = 1$, we find the
steady-state solution to (\ref{eq:Diffusion}):
\begin{equation}
Q(L)=\sqrt{\frac{a}{2D\pi}}e^{-\frac{a(L-\langle L \rangle)^2}{2D}},
\label{eq:Gauss}
\end{equation}
where $a$ is given by
\begin{equation}
a \equiv -\frac{d V}{d L}\bigg|_{\langle L \rangle} = -\frac{\partial
V}{\partial F}\frac{\partial F}{\partial s^*}s_B'(\langle L \rangle -
\varepsilon(m+1)).
\label{A}
\end{equation}
The drift velocity $V(L)$ can be inferred from $\varepsilon(w_{+}-w_{-}(1-s_{N-1}))$
and (\ref{FSM-relation}), which relates the mean occupancies at positions $L$ and
$L-\varepsilon(m+1)$,
\begin{equation}
V(L) = \varepsilon\left[w_{+} - w_{-} + w_{-} F(s^*(L-\varepsilon(m+1)))\right].
\label{wall-vel}
\end{equation}
\noindent By defining the drift $V(L)$ using the steady-state relation
$F$, we have implicitly made an adiabatic approximation where the
particles have reached a NESS for any wall position $L$.
We can also estimate the variance of the wall position by using
$\Sigma^{2} \approx D/a$, and (\ref{A}) for $a$. Upon differentiating
$V(L) = \varepsilon(w_+-w_-[1-F(s_B'(L- \varepsilon(m+1)])$, we find
$(\partial V/\partial F) = \varepsilon w_-$. We can estimate
$(\partial F/\partial s^*)\vert_{s^{*}_{eq}}$ using the finite segment
method, and we know $s_B'(\langle L \rangle - \varepsilon(m+1))$
exactly from (\ref{eq:bulk1}). Assuming that $\langle L^2 \rangle
\approx \int_{-\infty}^{\infty} dL L^2 Q(L) $, we expect the variance
of the wall position to be approximately
\begin{equation}
\Sigma^2=\langle L^2 \rangle - \langle L \rangle^2 =
\frac{D}{\varepsilon w_- F'(s^*_{eq}) s_B'(\langle L
\rangle - \varepsilon(m+1))}
\label{eq:Variance}
\end{equation}
In Figure \ref{fig:WallDist}, we plot an example distribution $Q(L)$
found using both Monte Carlo simulations and from (\ref{eq:Gauss}).
\begin{figure}[h]
\begin{center}
\includegraphics[height=1.9in]{Fig6.eps}
\end{center}
\vspace{-4mm}
\caption{Probability density of the wall position, $Q(L)$, is plotted
as a function of the deviation from the mean wall position $\langle
L\rangle$. The parameters $\alpha = 1$, $w_{+} = 0.005$, $w_{-} =
0.01$, $k_- = 0.01$, and $k_+ = 0$ yield $\langle L \rangle \approx
350$. The distribution predicted from (\ref{eq:Gauss}) is a close
approximation to that derived from MC simulations.}
\label{fig:WallDist}
\end{figure}
We have aligned the distributions such that their maxima coincide.
Using (\ref{eq:Variance}), the standard deviation $\Sigma \approx
0.1215$, in good agreement with the standard deviation found from MC
simulations $\Sigma\approx 0.143$. Since $\Sigma/\langle L\rangle
\sim 0.14/3.5 \ll 1$, the wall is fairly stable and not likely to fall
off the injection end of the lattice except on exponentially long time
scales.
\subsection{Time-dependent mean wall positions}
\label{unstable}
In the previous section, we explored the dependence of the
statistically stationary mean wall position on the model
parameters. However, a stable mean wall position may not always
exist. In this section, we use a FSMFT to determine the stability of
the wall and the conditions under which a permanent net wall drift
might arise.
The motion of the wall can be understood completely in terms of the
outer solution $s_B(x)$ -- given by inverting (\ref{bulk}) -- and the
particle density inside finite segment. First, we consider some
important properties of $s_B(x)$. Equation (\ref{bulk}) admits two
branches to the bulk solution, $s_B(x)$, because the argument of
$\ln[|\quad|]$ can either be positive or negative. The argument
approaches zero as $s$ approaches $s_{\Gamma} \equiv
k_{+}/(k_{+}+k_{-})$, the density arising from Langmuir kinetics
alone. When we invert $x(s_B)$ to find $s_B(x)$, we see that for
increasing $x$, one branch of the density profile $s_B(x)$ approaches
$s_{\Gamma}$ asymptotically from below, and a second branch approaches
$s_{\Gamma}$ asymptotically from above. A representative $s_B(x)$ is
plotted in Figure \ref{fig:dynamics}. Notice that $s'(x)>0$ in the
lower branch, and $s'(x)<0$ in the upper branch
\footnote[3]{When $s_B(x)$ passes though $s_B(x) = 0.5$, the sign of
$s'_B(x)$ changes. The profile $s(x)$ departs from $s_B(x)$ near
$s_B(x)=0.5$ because one of the assumptions used to derive $s_B(x)$ --
that $s'_B(x) = O(1)$ -- becomes invalid and the sign of $s'(x)$
fails to change upon passing through $s(x)=0.5$. See the Appendix for
further discussion of when the continuum equations may cease to be
valid.}.
\begin{figure}[h]
\begin{center}
\includegraphics[height=2.2in]{Fig7.eps}
\end{center}
\vspace{-4mm}
\caption{Four possibilities for the wall motion. Arrows indicate the
mean wall motion if it is at position $i$. (a) the wall could have no
net drift and a stable fixed mean position, with small perturbations
to the wall position decaying over time, (b) the wall could have no
net drift, but an unstable fixed mean position, with small
perturbations to its position causing it to drift indefinitely to the
left or right, (c) the wall could drift indefinitely to the left and
(d) the wall could drift indefinitely to the right. The outer solution
$s_{B}(x)$ is shown by the dotted curves.}
\label{fig:dynamics}
\end{figure}
If $\alpha > s_{\Gamma}$, the steady state density profile will lie on the
upper branch and the bulk density will have values satisfying
$s_{\Gamma}<s_B(x)<\alpha$. If the injection rate $\alpha < s_{\Gamma}$, the steady
state density profile will lie on the lower branch and the bulk
density will attain values $\alpha<s_B(x)<s_{\Gamma}$.
We are now ready to derive conditions for the existence of a fixed
mean wall position and stability criteria. In the adiabatic
approximation (\ref{wall-vel}), $m$ is the number of sites in the
finite segment and $\varepsilon = 1/N_0$. This equation expresses the
velocity of the wall at position $\varepsilon N = L$ in terms of a particle
density at position $(N-m-1)\varepsilon$. Since $s^*_{eq}$ is the
value of $s^*$ that puts no net drift on the wall, {\it i.e.}, $w_+ -
w_-(1-F(s^*_{eq})) = 0$, we can expand $V(L)$ from (\ref{wall-vel}) in
a Taylor Series about $s^*_{eq}$ to find
\begin{equation}
V(L) \approx \varepsilon w_- F'(s^*_{eq})(s^*(L-\varepsilon(m+1)) - s^*_{eq}).
\label{wall-vel2}
\end{equation}
Because $F$ is a monotonically increasing function and $w_{-}> 0$, the
wall drifts to the right if $s^*(L-\varepsilon(m+1)) > s^*_{eq}$, to
the left if $s^*(L-\varepsilon(m+1)) < s^*_{eq}$ and has a fixed mean
position if $s^*(L-\varepsilon(m+1)) = s^*_{eq}$. If we now assume
that $m$ is sufficiently large so that the point $L -
\varepsilon(m+1)$ lies outside of the boundary layer, then
$s^*(L-\varepsilon(m+1))$ can be well approximated by the outer
solution given by $s_B(x)$, i.e. $s_B(L-\varepsilon(m+1)) \approx
s^*(L-\varepsilon(m+1))$. Furthermore, we know that $s_B(x)$
satisfies $\alpha \leq s_B \leq s_{\Gamma}$ on the lower branch and $s_{\Gamma} \leq
s_B \leq \alpha$ on the upper one. Therefore, we conclude that if
$s^*_{eq} \notin [\alpha, s_{\Gamma}]$, the wall can never have a fixed mean
position. In particular, for all $t$
\begin{equation}
\begin{array}{rl}
V(L(t)) & > 0 \quad \mbox{if} \quad s^*_{eq} < \alpha, s_{\Gamma}, \nonumber \\
\: & < 0 \quad \mbox{if} \quad s^*_{eq} > \alpha, s_{\Gamma},
\end{array}
\end{equation}
corresponding to an indefinite rightward and leftward drift,
respectively (cf. Fig. \ref{fig:dynamics}c and d).
If a fixed mean position does exist, we can understand
its stability by considering the sign of $dV/dL$. If this quantity is
negative (positive), the position is stable (unstable). These
possibilities are summarized in Figure \ref{fig:dynamics}. By
differentiating (\ref{wall-vel2}), we have
\begin{equation}
{\mbox{d} V\over \mbox{d} L} \approx \varepsilon w_- F'(s^*_{eq}) s_B'(L-\varepsilon(m+1)).
\end{equation}
Hence, if a mean wall position exists at $L$, a necessary and
sufficient condition for its stability is
\begin{equation}
s_B'(L-\varepsilon(m+1)) < 0.
\label{stab}
\end{equation}
In particular, when there is no adsorption ($k_+ = 0$), the bulk
solution $s_B(x)$ decreases monotonically from the injection site and
any mean wall position $\langle L\rangle$ induced by the kinetics will
be deterministically stable.
\begin{figure}
\begin{center}
\includegraphics[height=1.8in]{Fig8a.eps}\\
\vspace{4mm}
\includegraphics[height=1.8in]{Fig8b.eps}
\end{center}
\vspace{-4mm}
\caption{In (a), we plot the density profile near the wall from
FSMFT and from MC simulations. We find that $s_{N-1}$ is less than
$0.9=1-w_{+}/w_{-}$, the value required for the wall to have zero
drift. In (b), the position of the wall $N(t)$ found from MC
simulations is plotted with the expected $N(t)$ calculated using
FSMFT. Parameter values were $\alpha = 0.01$, $w_+=0.001$, $w_-=0.01$,
$k_+=0.0001$, $k_-=0.01$.}
\label{WALLOFF}
\end{figure}
Figures \ref{WALLOFF} and \ref{ESCAPE} compare the result
(\ref{wall-vel}) with simulation data. Figure \ref{WALLOFF} shows the
results of a MC simulation in which the wall particle has a mean
leftward drift. In Fig. \ref{WALLOFF}a, the density profile in the
wall frame found from MC simulation and that predicted using FSMFT are
shown. Far from the injection site $s_{B}$ asymptotes to
$s_{\Gamma}$. Thus, when the wall starts at a position $L_{0} \gg 1$,
we assume $s^*(L-\varepsilon(m+1))=s_{\Gamma}$ and the wall's velocity
$V$ is independent of its position $L$.
Since $s_{N-1}<1-\frac{w_+}{w_-}$, we expect, from (\ref{wall-vel}),
that the net drift on the wall will be negative. In
Fig. \ref{WALLOFF}b, we compare $N(t)=L(t)/\varepsilon$ found from MC
simulations with that calculated assuming $L(t) = L_0+V t$ where
$V$ is calculated using (\ref{wall-vel}) in the large $L$ limit. Similarly,
Fig. \ref{ESCAPE}a shows a density profile from MC simulation in the
case where the wall acquires a mean rightward drift. In
Fig. \ref{ESCAPE}b both MC simulations and FSMFT show that in the wall
frame, the occupancy of the site adjacent to the wall is greater than
$1-\frac{w_+}{w_-}$, and we expect a mean rightward drift. In
Fig. \ref{ESCAPE}c, we see that this is the case, and the predicted
time course $N(t)=L(t)/\varepsilon$ is compared with $N(t)$ found using MC
simulations.
In contrast to the case of a static mean wall position, when the wall
has a position-independent velocity, $V$, the diffusion constant $D$
of the wall is given by $D = \varepsilon^2(w_+-w_-+w_-F(s_{\Gamma}))/2$. The
probability density $Q(L,t)$ describing wall position then follows
\begin{equation}
\frac{\partial Q}{\partial t}=D\frac{\partial^2 Q}{\partial L^2}-V \frac{\partial Q}{\partial L},
\end{equation}
the solution of which is
\begin{equation}
Q(L,t)=\frac{1}{2\sqrt{\pi D t}}e^{-\frac{(L-Vt-L_0)^2}{4Dt}}.
\end{equation}
We now discuss our results in the context of the phase transitions
\cite{Evans-03,Frey-04,SCHUTZ2} of the interior density. When Langmuir
kinetics is coupled to a fixed domain TASEP with open boundaries,
qualitative properties of $s(x)$ can change abruptly when
adsorption/desorption and injection/ejection rates vary. For example,
an interior boundary layer separating regions of low and high density
can suddenly disappear, replaced with a single region of high density
as the injection rate $\alpha$ is increased.
Our moving wall TASEP system coupled with Langmuir kinetics does
\emph{not} support the phase structure seen in
\cite{Evans-03,Frey-04,SCHUTZ2}. Because we limit ourselves to
$k_+<k_-$, we can see from (\ref{eq:bulk1}) that when $s_B(x)>0.5$,
(corresponding with a high density region), $s_B'(x)>0$. From
(\ref{stab}), the wall cannot have a stable equilibrium position
within the high density region, and we do not find time-independent
density profiles with low to high density interior shocks (a low-high
shock), as is observed in \cite{Evans-03,Frey-04}. In fact,
references \cite{Frey-03,SCHUTZ2} show that high-low shocks are never
stationary in an exclusion process with Langmuir kinetics. Therefore,
interior shocks are never stable in our model system. In our problem,
the presence of a wall that responds to particle dynamics relaxes any
shocks in density that may otherwise occur in the interior, forcing
them to the left or right boundaries.
\begin{figure*}
\begin{center}
\includegraphics[height=1.52in]{Fig9a.eps}\hspace{1mm}
\includegraphics[height=1.52in]{Fig9b.eps}\hspace{1mm}
\includegraphics[height=1.52in]{Fig9c.eps}
\end{center}
\vspace{-2mm}
\caption{When $s_{\Gamma}>s^*_{eq}$ and $\alpha>s^*_{eq}$, the wall
escapes. In (a), far from the injection site, the particle density
approaches $s_{\Gamma}= 0.029$ as predicted by analytic theory. In
(b), we use FSMFT and MC to find $s_{N-1}>0.9=1-w_{+}/w_{-}$, the
value for which the wall's drift would be zero. In (c), we show
$N(t)$ to compare the escape velocity calculated from finite segment
analysis to the escape velocity found in simulations. Although the
value of $s_{N-1}$ found by FSMFT differs from that found in MC
simulations by only $0.4\%$, the calulated velocities differ by
$17\%$. Parameter values were $\alpha = 0.3$, $w_+ = 0.001$, $w_- =
0.01$, $k_+=0.0003$, and $k_-=0.01$.}
\label{ESCAPE}
\end{figure*}
\section{Summary and Conclusions}
Our model of an asymmetric exclusion process with Langmuir kinetics
and a movable right boundary, and the corresponding results provide a
guide to understanding biophysical processes in which many processing
molecular motors push against a load. The detachment and attachment
rate of the motors, as well as the injection rate at the entry site,
determine the load the motors can support. If a static load particle
position is reached, we see that the mean wall distance from the
injection site saturates upon increasing injection rate $\alpha$ past
about $0.5$. The analyses can be used to predict whether biological
processes such as ribosome movement and filopodia/filament extension
continues or reaches a static configuration.
Within our model, we found four parameter regimes. In the first
regime, $(s_{\Gamma} < s_{eq}^{*} < \alpha)$, the wall attains a
stable equilibrium position for the wall. In the second regime,
$(\alpha < s_{eq}^{*} < s_{\Gamma})$, there is an equilibrium, but
unstable mean wall position. In the third and fourth regimes,
$(s_{eq}^{*}\notin [\alpha, s_{\Gamma}])$, the wall will always feel a
net drift to the to the right and left, respectively. In the latter
case, the wall will fall off the lattice in a time scaling linearly
with the starting position. When there is a stable equilibrium wall
position, we can find the mean wall position $\langle N \rangle$ as a
function of the particle injection rate $\alpha$, the adsorption and
desorption rates $k_{\pm}$, and the intrinsic hopping rates of the
wall $w_{\pm}$. Determination of $\langle N \rangle$ requires
accurate evaluation of the particle density near the wall. Using a
hybrid finite segment/mean field approach in the reference frame of
the fluctuating wall, we accurately determine the particle density
near the wall, and use this to determine the wall's steady-state
position.
When there is no steady state wall position, the finite segment mean
field approach allows us to estimate the steady state velocity of the
wall far from the injection site. In our analysis, we assumed that
the particle density has reached steady state, thus ignoring the
initial particle density profile and wall position. Even in regimes
where we expect an equilibrium wall position at steady state, if the
wall is initially near the injection site, and the particle density is
initially very low, we would expect the wall to fall off the lattice
before reaching its equilibrium position. The times to falling off
the lattice may be treated with extensions of large deviation theory
as suggested by Fig. \ref{fig:WallDist} \cite{LDT}. A number of
interesting extensions of the free boundary problem arise. For
example, we expect for certain parameter regimes that slow bottleneck
sites \cite{Chou-04} can attract the fluctuating wall. These features
and other novel applications to biophysical systems deserve
investigation.
\vspace{3mm}
This material is based upon work supported under a National Science
Foundation Graduate Research Fellowship. The authors also acknowledge
support from the NSF through grant DMS-0349195, and the NIH through
grant K25 AI41935.
\section{Appendix}\label{Ap:Continuum}
We can take the continuum limit of (\ref{MFTa}) by defining $x=(i-1) \varepsilon$
where $\varepsilon$ is the lattice spacing. We find,
\begin{equation}
\displaystyle {\partial s(x,t)\over \partial t} = \varepsilon s'(2s-1)+{\varepsilon^{2}\over
2}s'' -k_{-}s + k_{+}(1-s) = 0.
\label{CONTINUUM}
\end{equation}
\begin{widetext}
The left hand boundary condition, (\ref{MFTb}) becomes
\begin{equation}
\begin{array}{l}
\displaystyle {\partial s(0,t)\over \partial t} = \alpha(1-s(0)) - k_{-}s(0)
+k_{+}(1-s(0)) - s(0)(1-s(\varepsilon)) = 0.
\end{array}
\label{BCLEFT}
\end{equation}
When significant changes in the solution near $x=0$ vary over a length
scale that is $> O(\varepsilon)$, this equation is well approximated
by
\begin{equation}
\begin{array}{l}
\displaystyle {\partial s(0,t)\over \partial t} = \alpha(1-s(0)) - k_{-}s(0)
+k_{+}(1-s(0)) - s(0)(1-s(0)-\varepsilon s'(0)) = 0.
\end{array}
\end{equation}
The right hand boundary condition analogous to (\ref{MFTEQNc}), becomes
\begin{equation}
\begin{array}{l}
\displaystyle {\partial s(L,t) \over \partial t} = -k_{-}s(L)
+k_{+}(1-s(L)) +s(L-\varepsilon)(1-s(L))
+w_{-}s(L-\varepsilon)(1-s(L))-w_{+}s(L) = 0.
\end{array}
\label{BCRIGHT}
\end{equation}
Again, when significant changes in the solution near $x=L$ vary over a
length scale that is $>O(\varepsilon)$, this equation is well approximated by
\begin{equation}
\displaystyle {\partial s(L,t) \over \partial t} = -k_{-}s(L)
+k_{+}(1-s(L))+(s(L)-\varepsilon s'(L))(1-s(L))
+ w_{-}(s(L)-\varepsilon s'(L)) )(1-s(L))-w_{+}s(L) = 0,
\label{BCrighteps}
\end{equation}
at the free boundary $L(t)$, where $s(L)$ defines the particle density
at the position just to the left of the wall.
In the wall frame, the continuum limit of equation (\ref{MFTEQNa}) is
\begin{equation}
\begin{array}{l}
\displaystyle {\partial s(x,t)\over \partial t} = \varepsilon [w_+-(1+w_-(1-s_{N-1}))]s'(1-2s)+{\varepsilon^{2}\over
2}[1+w_++w_-(1-s_{N-1})]s'' -k_{-}s + k_{+}(1-s).
\end{array}
\label{CONTINUUM_WALL}
\end{equation}
\end{widetext}
In the wall frame, an interior particle shifts to the right when it either hops to the
right, which it does with a (normalized) rate of unity, or when the
wall hops to the left, which it does with rate $w_{-}(1-s_{N-1}) = w_{+}$ in steady
state.
Similarly, a particle shifts to the left when it hops to the left or
when the wall hops to the right, which it does with rate $w_+$. In
the bulk, where $s'(x)=O(1)$, the diffusive term is small and can be
neglected. The only term we retain that depends on hopping rates is
$(w_+ - 1 - w_+)(1-2s)s'$, which is equal to the value of the
corresponding term in the lab frame, $-(1-2s)s'$. The bulk density is
described in both frames by
\begin{equation}
\varepsilon s'(1-2s)+k_-s-k_+(1-s)=0.
\end{equation}
In our problem, the second order term in (\ref{CONTINUUM}) becomes
important in the right hand boundary layer, and in the left hand
boundary layer when there is one. On the left, when $s \approx 0.5$,
one cannot assume that $s$ varies slowly. Making the change of
variables $x = \xi X$ ($\xi \ll 1$), equation (\ref{CONTINUUM})
becomes
\begin{equation}
\frac{\varepsilon}{\xi}s'(2s-1)+
\frac{\varepsilon^2}{2 \xi^2}s''-k_-s+k_+(1-s)=0;
\label{XIEQN}
\end{equation}
furthermore, we know that $\varepsilon$ is necessarily on the order
$(k_-+k_+)$. Since the first order term becomes very small as
$s\rightarrow 0.5$, the second order term must match either the
adsorption or desorption term. In this case, the second order term
will be balanced when $\xi \sim \sqrt{\varepsilon}$. Therefore, we expect a
boundary layer of width $O(\sqrt{\varepsilon})$ to arise near the injection
site if $\alpha>0.5$, $s_{\Gamma}<0.5$ or if $\alpha<0.5$ and
$s_{\Gamma}>0.5$.
While the boundary layer on the left can be captured using a second
order continuum equation, the boundary layer on the right cannot. In
equation (\ref{CONTINUUM}), we kept terms only up to order $\varepsilon^2$ in
our expansion $s(x+\varepsilon)$ = $s(x)+\varepsilon
s'(x)+\frac{\varepsilon^2}{2}s''(x)+\frac{\varepsilon^3}{6} s^{(3)}(x)+...$. The
boundary layer on the right hand side arises to join the outer
solution with the boundary condition $s(L) = 1-w_{+}/w_{-}$. Making
the substitution $X = x/\xi$, and matching first and second order
terms in (\ref{XIEQN}), we find that $\xi = O(\varepsilon)$. In
the boundary layer on the left, $s \approx 0.5$, and we assume that
the term $\varepsilon(2s-1)s'$ is relatively small. When we match the
second order term, $\varepsilon s''/2$, with the adsorption and desorption
terms, $k_{+}(1-s)$ and $k_{-}s$, we find that $\xi \sim
\sqrt{\varepsilon}$. However, on the right, we cannot assume that $s
\approx 0.5$. We therefore assume that the leading terms are
$\varepsilon(2s-1)s'$ and $\varepsilon s''/2$, which leads us to
conclude that the wall-hugging boundary layer has width of
$O(\varepsilon)$. In this case, all terms $\varepsilon^n s^{(n)}(X)/n!$ in the
Taylor expansion of (\ref{BCRIGHT}) are $O(1)$, and continuum theory
breaks down.
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\section{Introduction}
Random matrix theory (RMT) has a remarkably wide range of applications in mathematics, physics and beyond. It describes universal statistical quantities that are not determined by the specific dynamics of a given system, but rather by its anti-unitary symmetries. One of the most prominent RMT quantities is the level spacing distribution $P(s)$, the probability of two neighboring eigenvalues to appear at a distance $s$, which is universal after unfolding (to refer to an eigenvalue density normalized to one). For the classical Gaussian RMT ensembles, i.e.\ hermitian matrices with Gaussian probability distribution of the elements, the spacing distributions can be evaluated for any matrix size \cite{Mehta:2004}. The results are very close to the level spacings of small matrices, a fact which is known as Wigner's surmise \cite[p.~199]{porter:1965}. The spacing distributions $P(s)$ of the smallest matrices are linear/quadratic/quartic in $s$ times an exponential decay in $s^2$ (see e.g.\ \eq{eq:surmiseon1}), where the power in the repulsion for small spacings -- which equals the Dyson index $\beta\in\{1,2,4\}$ of these ensembles -- counts the degrees of freedom per matrix entry in the ensemble.
In particular, RMT applies to quantum chromodynamics (QCD), where it describes the spectrum of the Dirac operator; for a review see \cite{Verbaarschot:2000dy}. The crucial feature is that QCD (with massless quarks) obeys a global chiral symmetry, which is spontaneously broken. In the $\varepsilon$-regime, a finite volume regime dominated by the corresponding Goldstone bosons (pions), the equivalence with RMT has been proven in Refs.~\cite{Osborn:1998qb,Toublan:1999hx,Basile:2007ki}. The appropriate RMT describing the microscopic spectral properties of QCD in this regime is the chiral ensemble. For bulk correlations, i.e. away from the origin, the chiral symmetry is no longer important \cite{Fox:1964, Nagao:1991, Nagao:1992} and universal properties of QCD spectra, such as level spacings, can be described by the standard Gaussian RMT ensembles \cite{Halasz:1995vd,Pullirsch:1998ke}.
While the conventional RMT ensembles describe chaotic systems with definite symmetries, physical systems are often `not so ideal'. We briefly describe cases where the symmetry of the system deviates from this ideal situation. When no analytical expressions are available for the correlations in such transitions, one can have recourse to surmises.
Firstly, physical systems may obey a certain \textit{anti-unitary symmetry} only approximately or contain several parts with different anti-unitary symmetries. The latter leads to transitions from one symmetry class to another. Including the Poissonian ensemble, which is the equivalent for generic integrable systems, the corresponding spacing distributions have been shown to fulfill a generalized Wigner surmise \cite{Lenz:1991, Schierenberg:2012ut}. Such transitions were observed at high temperatures in two- and three-color QCD \cite{Garcia-Garcia:2006gr, Kovacs:2009zj, Kovacs:2010wx, Bruckmann:2011cc} and are expected in the continuum limit of the staggered lattice Dirac operator in two-color and adjoint QCD \cite{Follana:2006zz, Bruckmann:2008xr}. We will show a mixed-symmetry surmise at work for two-color QCD at imaginary chemical potential.
Secondly, \textit{hermiticity} can be broken in physical systems, as is the case for QCD with real chemical potential. In this case the determinant of the Dirac operator becomes complex, which hampers progress in numerical simulations of this system. Non-hermitian Gaussian random matrices were first discussed by Ginibre \cite{Ginibre:1965zz}. For the associated complex eigenvalues one can define a nearest neighbor individually and study the corresponding spacing distributions. For the complex Ginibre ensemble the level spacings do not fulfill a surmise from $2 \times 2$ matrices (even though they are always cubic for small $s$) \cite{Grobe:1988,Akemann:2009my}. The spacings of this ensemble were compared to QCD spectra and showed agreement only for a small range of the chemical potential \cite{Markum:1999yr}.
In QCD the chemical potential drives the breaking of the anti-hermiticity. An adequate random matrix model describing such a situation consists of two matrices where the breaking of the hermiticity is governed by a real parameter \cite{Stephanov:1996ki,Osborn:2004rf}.
The eigenvalue densities and lowest eigenvalue distributions of such ensembles have been worked out in the microscopic, {\it weakly} non-hermitian limit (where the microscopic eigenvalues $z N$ and perturbation $\mu^2 N$ are kept fixed as the matrix size $N \to \infty$) \cite{Splittorff:2003cu,Osborn:2004rf,Akemann:2004dr,Akemann:2007yj} and successfully compared to quenched QCD data \cite{Bloch:2006cd,Akemann:2007yj}.
The treatment of real random matrices is known to be an especially arduous task. The joint probability function of the eigenvalues for the real asymmetric ensemble (also called the real elliptic Ginibre ensemble) was calculated in \cite{Lehmann:1991} and generalized to the chiral case in \cite{Akemann:2009fc}. Only recently, the correlation functions were worked out for the real Ginibre ensemble \cite{Forrester:2007,Sommers:2008,Borodin:2009}, the real elliptic Ginibre ensemble \cite{Forrester:2008} and the real chiral ensemble \cite{Akemann:2009fc,Akemann:2010mt,Akemann:2010tv}.
In this work we investigate the use of surmises to describe the level spacings of such real random matrix ensembles. More specifically, we examine the case where the unperturbed matrices are real and symmetric, i.e., they belong to the Gaussian orthogonal ensemble (GOE, $\beta=1$), and the perturbations are real and antisymmetric. The perturbations are assumed to be small, such that the imaginary part of typical eigenvalues is at most of the order of the mean separation between neighboring eigenvalues along the real axis (whereas in the Ginibre ensemble hermiticity is maximally broken). For real matrices the flow of eigenvalues is somewhat special, because two real eigenvalues need to coalesce to `give birth' to a complex conjugate pair, see below (this is not so for the complex (GUE, $\beta=2$) or symplectic (GSE, $\beta=4$) ensembles: in the former the eigenvalues are not restricted to form complex conjugate pairs, but can be distributed arbitrarily in the complex plane; in the latter the unperturbed matrices have two-fold degenerate eigenvalues due to Kramers' degeneracy and these split up and become complex for arbitrary small anti-hermitian perturbation). Actually, the original GOE eigenvalues are \textit{attracted} by an antisymmetric perturbation. For eigenvalues that meet in such a process and become a complex conjugate pair, a spacing can be uniquely defined as the distance between them. As we will show, the distribution of these spacings for large random matrices can be approximated very well by that of small matrices. The complex eigenvalues leave a trace in the statistics of the real eigenvalues, too. We will work out surmises for the spacings among the latter and show that they also apply to large matrices. We interpret these findings in the same way as for other Wigner surmises, namely that the dynamics of a neighboring pair is not much influenced by the effect of all other eigenvalues.
As an application we analyze spectra of two-color QCD, i.e., with gauge group SU(2). As the latter is pseudo-real it ensues that the massless continuum Dirac operator for fermions in the fundamental representation belongs to the GOE universality class (see Sec.~\ref{subsect:symm_and_herm}).
This property holds for vanishing chemical potential. Although the chemical potential perturbs the anti-hermiticity of the Dirac operator, it keeps its anti-unitary symmetry. Therefore, the random matrix results discussed above apply to two-color QCD at finite chemical potential, both in the continuum and on the lattice with the overlap operator.
This paper is organized as follows. After describing the symmetries and corresponding spectra of matrices in the next section, Sec.~\ref{sect:perturbation_theory} is devoted to the eigenvalue dynamics in perturbation theory. In Sec.~\ref{sect:surmises} we work out the surmises for the different types of spacings. These are then matched to data from large random matrices with mixed hermiticity in Sec.~\ref{sect:rmt} and to lattice two-color QCD data with chemical potential in Sec.~\ref{sect:qcd}. We also measured spacings at imaginary chemical potentials and discuss the comparison to a mixed-symmetry surmise in the last subsection of Sec.~\ref{sect:qcd}. We summarize our findings and conclude in Sec.~\ref{sect:summary}.
\section{The setting: symmetries and spectra of RMT ensembles}
Our unperturbed random matrices $H_0$ shall be real and symmetric. We therefore choose them from the GOE, so that the entries are Gaussian random numbers with mean zero and variance
\begin{align}
\langle (H_0)_{ii}^2 \rangle = 1\quad\mbox{and}\quad \langle (H_0)_{ij}^2 \rangle =
\frac12
\quad (i\neq j)\,.
\end{align}
Gaussian random matrix ensembles can be characterized by whether they commute with an anti-unitary $V=UK$, where $U$ is unitary and $K$ is the complex conjugation operator
\begin{equation}
[H_0,V]=0\qquad \mbox{equiv. to} \qquad H_0^\ast = U^\dagger H_0 U\,,
\label{eqn symm}
\end{equation}
and whether $V$ squares to $1$ or $-1$. For the GOE one has
\begin{equation}
V^2=1 \qquad \mbox{equiv. to} \qquad U U^\ast=1\,,
\label{eqn goe}
\end{equation}
from which it follows that the matrices $H_0$ can be chosen real.
\begin{figure}[t]
\centering
\includegraphics[width=0.8\linewidth]{Plots/evalues_one.pdf}
\vskip1cm
\includegraphics[width=0.8\linewidth]{Plots/evalues_two.pdf}
\vskip0.6cm
\includegraphics[width=0.8\linewidth]{Plots/evalues_three.pdf}
\caption{Evolution of eigenvalues of a typical random matrix with increasing non-hermitian part (schematically). The top panel depicts a part of the spectrum for the unperturbed case, i.e., for a real symmetric (GOE) matrix. Towards the bottom panel the antisymmetric part increases, which results in some eigenvalues getting very close and finally becoming complex (the rightmost eigenvalues are spectators).
Different types of level spacings are sketched: (1) spacings between original eigenvalues and those that remain on-axis and have no interspaced complex conjugate pair, named $P^1_{\textrm{on}}$ and described by the pure GOE surmise, (2) spacings between on-axis eigenvalues with interspaced complex conjugate pairs, named $P^2_{\textrm{on}}$, (off) spacings between complex conjugate pairs called off-axis, named $P_{\textrm{off}}$. Note that for QCD spectra the real and imaginary axes are swapped.}
\label{fig general spectra}
\end{figure}
In this paper we will study random matrices from the GOE undergoing a real antisymmetric perturbation with a tunable coupling parameter. The characteristic equation of such a mixed matrix has real coefficients and consequently the eigenvalues are either real or come in complex conjugate pairs. Typical spectra of such matrices are depicted schematically in \fig{fig general spectra} together with different types of spacings between them. In the following, the real eigenvalues will be called `on-axis' and those with a non-zero imaginary part `off-axis'. This notation also applies to the case of QCD, where due to the anti-hermiticity of the Dirac operator at vanishing chemical potential the axes are swapped (then on-axis refers to purely imaginary eigenvalues and off-axis to those evolving from there into the complex plane). Obviously the spacings between on-axis eigenvalues and off-axis eigenvalues will be treated separately. Among the former we will further distinguish between those with and without an interspaced complex conjugate eigenvalue pair. This distinction only makes sense if the hermiticity of the initial GOE matrix is only mildly broken (since otherwise the off-axis eigenvalues move arbitrarily in the complex plane and cannot be assigned to a single on-axis pair anymore), and we will therefore only consider this case here. This is also why we do not consider the rare case of two or more interspaced eigenvalue pairs.
All our level spacing distributions are subject to the normalizations $\int_0^\infty ds \, P(s)=1$ and $\langle s \rangle = \int_0^\infty ds \, s \, P(s)=1$.
\section{Repulsion and attraction of eigenvalues in perturbation theory}
\label{sect:perturbation_theory}
To gain intuition about the dynamics of the eigenvalues, we consider a real symmetric matrix $H_0$, with real eigenvalues $\theta_i$ and corresponding real eigenvectors $|\psi_i\rangle$, perturbed by a real matrix $\lambda M$ with $\lambda \in \mathbb{R}^+_0$. We compare the effect of symmetric and antisymmetric perturbations $M$, whose matrix elements in the unperturbed basis,
\begin{align}
M_{ij}\equiv\langle\psi_i|M|\psi_j\rangle\,,
\label{Hij}
\end{align}
are real and symmetric or antisymmetric in $(i,j)$ too,
\begin{align}
M_{ji}= \pmM_{ij}\,,\qquad
\mbox{for }M^T=\pm M\,.
\label{eqn expvalues perturbation}
\end{align}
As is well known, ordinary perturbation theory up to second order yields for the eigenvalues,
\begin{align}
\theta_i \to \theta_i + \lambda M_{ii} +
\lambda^2\sum_{j\neq i} \frac{M_{ij}M_{ji}}{\theta_i-\theta_j}\,.
\end{align}
The first order term induces a random walk of the eigenvalues without correlating them. Moreover, in the antisymmetric case such expectation values are zero, so there is no first order contribution.
When omitting the random walk term, the eigenvalue differences are
\begin{align}
(\theta_i-\theta_j) \to (\theta_i-\theta_j)\left[1\pm
2\lambda^2\frac{M_{ij}^2}{(\theta_i-\theta_j)^2}+
\mathcal{O}\left(\frac1{(\theta_i-\theta_j)(\theta_{i,j}-\theta_{k\neq i,j})}\right)\right]\,.
\label{eqn second diff}
\end{align}
If $\theta_i$ and $\theta_j$ are much closer to each other than to any other eigenvalue, the third term in square brackets can be neglected in relation to the second one. Then, for real symmetric $M$ (upper sign) the difference grows, which is the common knowledge that eigenvalues repel.
In contrast, for real antisymmetric $M$ (lower sign), which we will consider from now on, the eigenvalues attract. Thus in perturbation theory it is favored that eigenvalues coalesce.
We recall that our investigations so far are based on the eigenvalues $\theta_i$ of the unperturbed matrix, which are real and remain so as long as ordinary perturbation theory is valid.\footnote{Ordinary perturbation theory only yields real shifts of the eigenvalues to all orders.}
When two eigenvalues $\theta_i$ and $\theta_j$ are very close, one has to apply almost degenerate perturbation theory \cite{Gottfried:1966}. Neglecting the second order contribution of all other eigenvalues, it gives for the perturbed eigenvalues
\begin{align}
(\theta_i,\theta_j)
\to
\mbox{evs}\left[
\left(\begin{array}{cc}\theta_i&0\\ 0&\theta_j\end{array}\right)+\lambda
\left(\begin{array}{cc} 0 & M_{ij}\\ -M_{ij} & 0\end{array}\right)\right]\,,
\label{eqn deg pert}
\end{align}
where we have made use of \eq{eqn expvalues perturbation}, with $M_{ij}$ still given by \eq{Hij},
and evs denotes the eigenvalues of the matrix. For the eigenvalue difference one obtains
\begin{align}
S=\sqrt{(\theta_j-\theta_i)^2-4\lambda^2M_{ij}^2}\,.
\label{eqn delta}
\end{align}
To second order in $\lambda$ the expansion of $S$ reproduces the result from second-order ordinary perturbation theory discussed above.
More interestingly, the argument of the square root can turn negative for some critical $\lambda$, above which the eigenvalue difference becomes purely imaginary. The latter is consistent with the fact that the complex eigenvalues of a real matrix come in complex conjugate pairs. Imaginary spacings occur for $\lambda$ bigger than
\begin{align}
\lambda_\text{crit}=\frac{|\theta_j-\theta_i|}{2|M_{ij}|}
\end{align}
(specific to each individual eigenvalue pair). In the exceptional case that $M_{ij}$ exactly vanishes, this particular eigenvalue difference remains unperturbed for any $\lambda$ (in perturbation theory). For perturbations beyond $\lambda_\text{crit}$ the eigenvalue difference can be written as
\begin{align}
S= 2i|M_{ij}|\sqrt{\lambda^2-\lambda^2_\text{crit}} = 2i|M_{ij}|\sqrt{\delta\lambda(2\lambda_\text{crit}+\delta\lambda)}\,,\qquad \delta\lambda\equiv\lambda-\lambda_\text{crit}\,,
\label{eqn delta imag}
\end{align}
and increases with the excess $\delta\lambda$ of the coupling over the critical coupling. Therefore, the perturbation causes the eigenvalues to be repelled in the complex plane.
Moreover, the eigenvalues leave the real axis perpendicularly to it. This can be seen by an explicit calculation of $\theta_{i,j}$ in \eqref{eqn deg pert} for $\lambda>\lambda_\text{crit}$, but it also follows directly from the fact that the antisymmetric perturbation is traceless and thus does not change the center of mass of the eigenvalues. When considering antisymmetric perturbations of large matrices beyond perturbation theory, only the center of mass of all eigenvalues is fixed and a complex conjugate pair could in principle leave the axis at any angle, as its center of mass contribution could be compensated by the motion of the remaining eigenvalues. Our data confirmed that, in accordance with almost degenerate perturbation theory, the complex eigenvalue pairs move perpendicularly to the axis just after their creation. When the perturbation grows further, higher order effects set in and the complex conjugate eigenvalues can leave the trajectory perpendicular to the axis.
\section{Surmises}
\label{sect:surmises}
The idea of Wigner surmises is to approximate level spacing distributions of large random matrices by those of random matrices with smallest possible size, typically $2\times 2$ matrices. Note that in the perturbative treatment in the previous section we have focussed on a pair of nearest neighbor eigenvalues and thus ended up discussing $2\times 2$ matrices and the properties of their eigenvalues. This may be seen as an indication that surmises for mixed systems may apply to large random matrices.
We recall that we consider three different types of spacings in our (large random matrix and QCD) systems: on-axis spacings with one and without interspaced complex conjugate eigenvalue pair, and off-axis spacings (see \fig{fig general spectra}). For the first and third type we will deduce surmises from $2\times 2$ matrices, computing the corresponding spacings. The spacings of the second type will be computed from the joined probability density for $4\times 4$ matrices.
\subsection[Prelude: $2\times 2$ matrices and their spacings]{Prelude: $\mathbf{2\times 2}$ matrices and their spacings}
For size $2\times 2$ let us consider a real symmetric and traceless matrix perturbed by an antisymmetric one,
\begin{align}\label{eq:ortantisymm2x2}
H = \left(
\begin{array}{ccr}
-a & b \\ b & a
\end{array}
\right)+\lambda\left(
\begin{array}{cc}
0 & c \\ -c & 0
\end{array}
\right)\,,
\end{align}
with random numbers $a$, $b$ and $c$ that are Gaussian distributed with zero mean and unit variance. Note that the matrix $H$ with $\lambda=0$ is equivalent to a $2\times 2$ GOE matrix, up to a common shift of the eigenvalues which does not alter the spacings. In the GOE the diagonal entries have twice the variance of the off-diagonal ones, but it can easily be shown that neglecting the part proportional to the identity, as we have done in $H$ to simplify the computations, renders the variances equal. The eigenvalues of $H$ are $\pm\sqrt{a^2+b^2-c^2\lambda^2}$, which, for a particular draw of random numbers, turn imaginary beyond a critical coupling
\begin{align}
\lambda_\text{crit}=\frac{\sqrt{a^2+b^2}}{|c|}\,.
\label{lambdacrit}
\end{align}
For $\lambda<\lambda_\text{crit}$ the spacing is $2\sqrt{a^2+b^2-c^2\lambda^2}$ and hence real, while for $\lambda>\lambda_\text{crit}$ the spacing is $2i\sqrt{c^2\lambda^2-a^2-b^2}$ and hence purely imaginary.
The probability that the matrix $H$ has an imaginary spacing can be easily computed by integrating over all random matrix entries with the constraint that $\lambda$ is above its critical value,
\begin{align}\label{eq:imagspacprob}
p(\lambda) = \left(2\pi\right)^{-3/2}\int_{-\infty}^\infty\!\!da\, db\, dc \,e^{-(a^2+b^2+c^2)/2}\,
\theta\left(c^2\lambda^2-a^2-b^2\right) = 1-\frac1{\sqrt{1+\lambda^2}}\,.
\end{align}
As expected, the limiting cases yield $p(\lambda\to0) = 0$ and $p(\lambda\to\infty)=1$.
\subsection{On-axis without interspaced complex eigenvalues}
\label{sect:onaxis1}
For on-axis spacings without interspaced complex eigenvalues our surmise is
\begin{align}\label{eq:surmiseon1}
P^1_{\textrm{on}}(s) =\frac{\pi}{2}\, s\, e^{-\frac{\pi}{4}s^2}\,,
\end{align}
which means that even in the presence of a (small) antisymmetric perturbation these spacings follow the GOE surmise governing the unperturbed spacings. This is so because \eq{eq:surmiseon1} is the distribution of \textit{real} spacings\footnote{The plural refers to the ensemble, as one representative of this random matrix has only one spacing, which will only be included here if real.} of $H$ independently of the coupling parameter $\lambda$. Let us demonstrate the derivation of this distribution explicitly, as a typical example. We start with the distribution of the non-normalized spacing $S$
\begin{align}
Q(S)&=\int_{-\infty}^\infty\!\!da\, db\, dc \,e^{-(a^2+b^2+c^2)/2}\,
\delta\left(S-2\sqrt{a^2+b^2-c^2\lambda^2}\right)
\theta\left(a^2+b^2-c^2\lambda^2\right)\nonumber\\
&=2\pi\int_{-\infty}^\infty\!\! dc \int_0^\infty\!\! dr\,r\,e^{-(r^2+c^2)/2}\,
\delta\left(S-2\sqrt{r^2-c^2\lambda^2}\right)
\theta\left(r^2-c^2\lambda^2\right)\,.
\label{eq:surmiseon_pre}
\end{align}
In the integration over $r$, the $\delta$-function replaces
\begin{align}
r\to r_0= \sqrt{S^2/4+c^2\lambda^2}
\end{align}
with Jacobian
\begin{align}
\left|\left.\frac d{dr}\left(S-2\sqrt{r^2-c^2\lambda^2}\right)\right|_{r=r_0}\right|^{-1} =
\frac {S}{4\sqrt{S^2/4+c^2\lambda^2}}=\frac {S}{4r_0}\,.
\end{align}
Therefore, we obtain
\begin{align}
Q(S) =\frac{\pi}{2} \int_{-\infty}^\infty dc \,S\,e^{-\left[S^2/4+c^2(1+\lambda^2)\right]/2}\,
\theta\left(S^2/4\right)\,.
\end{align}
The integration over $c$ just gives a constant factor, and the $\theta$-function forces the spacing $S$ to be real as assumed. After normalization, we obtain $P^1_{\textrm{on}}$ from (\ref{eq:surmiseon1}).
\subsection{On-axis with interspaced complex eigenvalues}
When two on-axis eigenvalues have an interspaced complex eigenvalue pair, we expect the latter to have a noticeable influence on the spacing of the on-axis eigenvalues. To obtain a surmise for the distribution of these spacings, we consider a $4\times4$ matrix
\begin{align}\label{eq:ortantisymm4x4}
H = H_0 + \lambdaA\,,
\end{align}
with $H_0$ taken from the GOE and an antisymmetric matrix $A$ with probability density
\begin{align}\label{eq:probdistA}
w(A) \sim e^{-\frac12 {\rm tr}\left(A A^T\right)}\,,
\end{align}
i.e. Gaussian distributed entries having the same variance as the off-diagonal entries of $H_0$. This is the smallest possible matrix that can yield a surmise for this case as there are four eigenvalues which are relevant for the dynamics of the spacing. The joint probability distribution of the eigenvalues of $H$ depends on the number of real and complex eigenvalues. For two real eigenvalues $\theta_1$ and $\theta_2$ and one complex conjugate pair $z$ and $z^*$, it reads up to a normalization \cite{Akemann:2010mt}
\begin{align}
P(\theta_1, \theta_2, z, z^*) \propto e^{-\theta_1^2-\theta_2^2-z^2-(z^*)^2} \erfc\left(\frac{\sqrt{1+\lambda^2}}{\sqrt2\lambda}|z-z^*|\right)2i \Delta(\theta_1, \theta_2, z, z^*)\,,
\label{eqn jpd}
\end{align}
with the Vandermonde determinant
\begin{align}
\Delta(\theta_1, \theta_2, z, z^*) = (z^*-z)(z^*-\theta_2)(z^*-\theta_1)(z-\theta_2)(z-\theta_1)(\theta_2-\theta_1)\,,
\end{align}
where it is assumed that $\theta_2>\theta_1$ and $\im\,z>0$. To obtain the distribution of the spacing $S$ between $\theta_1$ and $\theta_2$, we set $\theta_2 = \theta_1 + S$ and introduce new variables $a = \re\,z - \theta_1\in[0,S]$ and $b = \im\,z\in[0,\infty)$, cf. \fig{fig surmise spectra}.
\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{Plots/evalues_surmise_new.pdf}
\caption{Spectrum of the $4\times4$ matrix used for the surmise for $P^2_{\textrm{on}}$.}
\label{fig surmise spectra}
\end{figure}
This results in
\begin{align}
&P(\theta_1, \theta_1 + S, \theta_1+a+ib, \theta_1+a-ib)\\
&\propto S\, b \left[\left(a-S\right)^2+b^2\right]\left(a^2+b^2\right) e^{-\theta_1^2-(\theta_1+S)^2-2(a+\theta_1)^2+2b^2}\, \erfc\left(\frac{\sqrt{2}\sqrt{1+\lambda^2}}{\lambda}\,b\right)\,.\nonumber
\end{align}
We integrate out $\theta_1$, $a$, $b$ and perform an irrelevant rescaling $S\to2S$ to obtain the non-normalized spacing distribution
\begin{align}
\int_0^\infty db\int_{0}^{2S} & da \int_{-\infty}^\infty d\theta_1\, P(\theta_1, \theta_1 + 2 S, \theta_1+a+ib, \theta_1+a-ib) \notag\\
\propto S e^{-3S^2} & \left\{
\sqrt{\pi} \, e^{S^2} \erf(S) \left[\lambda^2\sqrt{1+\lambda^2}\left(3\lambda^2+8S^2\right)+4 \left(\sqrt{1+\lambda^2}-1\right)\left(4S^4-8S^2+3\right)\right]
\right. \notag
\\
& \left. + 8S \left[\left(\sqrt{1+\lambda^2}-1\right)\left(2S^2-1\right) -\lambda^2 \sqrt{1+\lambda^2}\right] \right\} \equiv Q(S; \lambda) \,.
\label{eq:surmiseon2_pre}
\end{align}
Properly normalized, the spacing distribution reads
\begin{align}\label{eq:surmiseon2}
P^2_{\textrm{on}}(s;\lambda) = CD\,Q(Ds;\lambda)\,,
\end{align}
with normalization and scaling factors
\begin{align}
C &= \left(\int\limits_0^{\infty}
dS\,Q(S;\lambda)\right)^{-1}=\frac{12\sqrt3}{\sqrt{\pi}}\left[\lambda^2 \sqrt{1+ \lambda^2} \left(9\lambda^2+8\right)+8 \left(\sqrt{1+\lambda^2}-1\right)\right]^{-1}\,,
\end{align}
and
\begin{align}
D = C\,\int\limits_0^{\infty} dS\,S\,Q(S;\lambda) &= \frac{C}{72}\left[26 \left(\sqrt{1+\lambda^2}-1\right)-27\sqrt2\,\text{arccot}(\sqrt2)\right.\notag\\
&\left.+\sqrt{1+\lambda^2}\left(18\lambda^4+20\lambda^2+27\sqrt2 \left(1+\lambda^2\right)^2\text{arccot}(\sqrt2)\right)\right]\,.
\label{eq:surmiseon2_const}
\end{align}
In the limit $\lambda \to 0$, the spacing distribution reads
\begin{align}
\hspace{-0.1cm}\lim_{\lambda\to 0} P^2_{\textrm{on}}(s;\lambda) = \frac{\kappa^2}{8\pi}\,s\, e^{-3\kappa^2 s^2}
\left[4\kappa^3s^3- 6\kappa s + \sqrt\pi\, e^{\kappa^2 s^2} (4\kappa^4 s^4-4\kappa^2 s^2 + 3)\,\erf(\kappa s)\right]\,,
\label{eq:surmiseon2_smallpert}
\end{align}
where
\begin{align}
\kappa=\lim_{\lambda\to 0}D=\frac{22+45\sqrt{2}\,\mbox{arccot}\sqrt{2}}{16\sqrt{3\pi}} \approx 1.2453 \,.
\end{align}
The opposite limit $\lambda\to\infty$ yields
\begin{align}
\lim_{\lambda\to\infty} P^2_{\textrm{on}}(s;\lambda) = 4\sqrt3\, \eta^2 s\, e^{-2 (\eta s)^2} \erf(\eta s)\,,
\end{align}
with
\begin{align}
\eta=\lim_{\lambda\to\infty}D=\frac{2+3\sqrt{2}\,\mbox{arccot}\sqrt{2}}{2\sqrt{3\pi}} \approx 0.7510 \,.
\end{align}
For small spacings $s$ and non-zero $\lambda$, the spacing distribution $P^2_{\textrm{on}}$ is proportional to $s^2$, whereas in the limit $\lambda \to 0$ the first term in the Taylor expansion is proportional to $s^6$. One can understand these repulsion strengths from the Vandermonde determinant in the joint probability density alone, i.e.\ by focussing on the linear repulsion of every eigenvalue pair and neglecting the exponential and erfc factors (which only contribute significantly at larger spacings). The relevant integral is
\begin{align}
& \int_{0}^{S} \!\!da
(z^*-\theta_2)(z^*-\theta_1)(z-\theta_2)(z-\theta_1)(\theta_2-\theta_1)\Big|_{z=\theta_1+a+ib,\,\theta_2-\theta_1=S}\notag\\
& = S\int_{0}^{S} \!\!da\, \left[(a-S)^2+b^2\right](a^2+b^2)
= b^4 S^2+\frac{2}{3}\,b^2 S^4+\frac{1}{30}\,S^6 \,.
\end{align}
This is indeed proportional to $S^2$ for small $S$, unless the distribution of $b$ becomes a $\delta$-function around zero, which happens for $\lambda\to0$. Then, the distribution is proportional to $S^6$.
\begin{figure}
\includegraphics[width=0.5\linewidth]{Plots/surmises_ortantisymm_typ=2.pdf}
\includegraphics[width=0.5\linewidth]{Plots/surmises_ortantisymm_typ=3.pdf}
\caption{Left: Wigner surmise $P^2_{\textrm{on}}(s;\lambda)$, \eq{eq:surmiseon2}, for on-axis eigenvalues with an interspaced complex conjugate eigenvalue pair for $\lambda=0, 0.3, 0.5, 1, \infty$ (decreasing maxima). Right: Wigner surmise $P_{\textrm{off}}(s; \lambda)$, \eq{eq:surmiseoff}, for off-axis spacings and couplings $\lambda=0, 2, 10, \infty$ (decreasing maxima). Plotted for comparison is the Wigner surmise for the GOE (dashed), which is the surmise for the on-axis spacings with no interspaced complex pair, \eq{eq:surmiseon1}.}
\label{fig wigner surmise}
\end{figure}
Spacings for various parameters $\lambda$ are plotted in the left panel of \fig{fig wigner surmise}.
\subsection{Off-axis}
To get a surmise for the spacings between complex conjugate eigenvalue pairs, we consider again the $2\times2$ matrix $H$ given in \eq{eq:ortantisymm2x2}. This time, we are interested in the distribution of the imaginary spacings of this matrix. In analogy to Sec.~\ref{sect:onaxis1} we define $Q(S)$ as in \eq{eq:surmiseon_pre} with appropriate arguments of the delta and step function,
\begin{align}
Q(S)&=\int_{-\infty}^\infty\!\!da\, db\, dc \,e^{-(a^2+b^2+c^2)/2}\,
\delta\left(S-2\sqrt{c^2\lambda^2-a^2-b^2}\right)
\theta\left(c^2\lambda^2-a^2-b^2\right)\,.
\end{align}
For the normalized spacing distribution we obtain with calculations similar to those of Sec.~\ref{sect:onaxis1},
\begin{align}\label{eq:surmiseoff}
P_{\textrm{off}}(s; \lambda) = C\,D^2\,s\, e^{D^2 s^2}\erfc\left(Ds
\sqrt{1+\lambda^2} / \lambda\right)\,,
\end{align}
with constants
\begin{align}
C = \frac{2}{\sqrt{1 + \lambda^2}-1} \,,\qquad
D = C\, \frac{\lambda\sqrt{1 + \lambda^2} -
\mbox{arsinh}(\lambda)}{2\sqrt{\pi}}\,.
\end{align}
For small $s$ the level spacing is linear, just as in the GOE. This is understandable, as the derivation of $P_{\textrm{off}}$ involves an integral over one off-diagonal random number which is similar to that encountered in the derivation of the GOE spacing. The number of degrees of freedom, which governs the level spacing at small $s$, is thus the same for both cases.
The limit for $\lambda\to0$ is
\begin{align}
\lim_{\lambda\to 0} P_{\textrm{off}}(s; \lambda)
= \frac{64}{9\pi}\, s \erfc\left(\frac{4s}{3\sqrt{\pi}}\right)\,.
\label{eq:surmise_off_limitzero}
\end{align}
Note that in this limit the perturbation is switched off. For statistical reasons, off-axis eigenvalues will exist for arbitrary small perturbations (see \eq{lambdacrit}). Equation \eqref{eq:surmise_off_limitzero} describes the (normalized) level spacings of these eigenvalues in the $\lambda\to 0$ limit (whereas \eq{eq:surmiseon2_smallpert} reflects the influence of these eigenvalues on the neighboring on-axis spacings in this limit). Even though the difference between \eq{eq:surmise_off_limitzero} and the GOE spacing distribution is rather small, the two are clearly distinguishable in \fig{fig wigner surmise} (right).
For $\lambda\to\infty$ the distribution $P_{\textrm{off}}$ is simply half a Gaussian,
\begin{align}
\lim_{\lambda\to \infty} P_{\textrm{off}}(s; \lambda)
=\frac2{\pi}\,\exp\left(-\frac{s^2}{\pi}\right)\,,
\end{align}
the spacing distribution of the perturbation alone. This limit, however, is not uniform at $s=0$, since $P_{\textrm{off}}(0; \lambda)=0$ for every finite $\lambda$, whereas $\lim_{s\to 0}\lim_{\lambda\to \infty} P_{\textrm{off}}(s; \lambda)=2/\pi$. Spacings for various couplings $\lambda$ are plotted in \fig{fig wigner surmise} (right) and this discontinuity is clearly visible. A similar effect has been observed for mixed symmetry classes of (small and large) random matrices in Ref.~\cite{Schierenberg:2012ut}. There, even a Gibbs-like overshoot of the curves near $s=0$ was observed, which is absent here.
We have checked that the surmises $P^1_{\textrm{on}}$ and $P_{\textrm{off}}$ could equally well be obtained from the joint eigenvalue probability distribution of real $2\times 2$ matrices \cite{Akemann:2010mt}, i.e.\ analogues of \eq{eqn jpd}, with either two real or a pair of complex conjugate eigenvalues.
With these surmises at hand, our aim will now be to describe the level spacing distributions of large random matrices, matching the parameter $\lambda$ to the corresponding coupling parameter and to QCD spectra, where the matching will be to the chemical potential.
\section{Comparison of the surmises to large RMT spectra}
\label{sect:rmt}
To check the validity of the surmises calculated in the previous section, we applied them to the spectra of large dimensional random matrices of the form
\begin{align}\label{eq:largermtmatrix}
H = H_0 + \frac\Lambda{\sqrt{2N/\pi}}\ A\,,
\end{align}
where $H_0$ is real symmetric and taken from the GOE with matrix size $N$, whereas $A$ is real antisymmetric with probability density
\begin{align}
w(A) \sim e^{-\frac12 {\rm tr}\left(A A^T\right)}\,,
\end{align}
i.e. all elements of $A$ are independently Gaussian distributed with the same variance as the off-diagonal entries of $H_0$ (as was also used for the small matrices in the surmises, cf.\ e.g.\ \eq{eq:probdistA}). The coupling parameter $\Lambda$ is divided by $\sqrt{2N/\pi}$ in order to make it comparable to the one used in the surmises, $\lambda$. As far as the spacing distribution is concerned, this normalization makes $\Lambda$ a universal, $N$-independent coupling parameter, see \cite{Schierenberg:2012ut} for a detailed discussion. As also argued there, a constant spectral density is necessary to compare spacing distributions of large matrices from mixed universality classes to the corresponding distributions of small matrices. Otherwise, different coupling strengths are mixed. Therefore, we only evaluated eigenvalues with real part in the interval $(-\sqrt{N}/4, \sqrt{N}/4)$, i.e. around the center of the real spectrum of $H$. As the spectral density is not exactly constant, we measured the on-axis spacings in units of the local mean spacing (obtained by an ensemble average), which is equivalent to unfolding the spectrum. For the off-axis spacings, no unfolding was done.
The numerically obtained spacing distributions of $H$ are shown in \fig{fig:largermt} for various values of the coupling parameter $\Lambda$. As can be seen, the surmises for the on-axis spacings of both types describe the data very well for coupling parameters up to $\Lambda=2$. The coupling parameters $\lambda$ for the on-axis spacings of type 2 were obtained by a fit with least square minimization.
\begin{figure}[t]
\includegraphics[width=\linewidth]{Plots/spacings_largematrices_ort_to_antisymm_typ=2.pdf}
\includegraphics[width=\linewidth]{Plots/spacings_largematrices_ort_to_antisymm_typ=3.pdf}
\includegraphics[width=\linewidth]{Plots/spacings_largematrices_ort_to_antisymm_typ=1.pdf}
\caption{Spacing distributions of $400\times 400$ random matrices of the form
of \eq{eq:largermtmatrix}, with various values of the coupling parameter $\Lambda$.
Top: on-axis spacings of type 1, surmise given by GOE, \eq{eq:surmiseon1}.
Middle: on-axis spacings of type 2, surmise given by \eq{eq:surmiseon2}.
Bottom: off-axis spacings, surmise given by \eq{eq:surmiseoff}; the dashed curve is the GOE spacing for comparison. For each value of $\Lambda$, $2\cdot 10^5$ random matrices were diagonalized.}
\label{fig:largermt}
\end{figure}
For the off-axis spacings we are able to predict a $2\times 2$ coupling parameter $\lambda$ through the frequency $p$ of imaginary spacings: we measure the latter for the large matrices and choose $\lambda$ such that the same $p$ is realized for $2\times 2$-matrices, i.e.\ we invert \eq{eq:imagspacprob} to obtain
$\lambda = \sqrt{1/(1-p)^2-1}$.
The surmises for the off-axis spacings obtained this way match the numerical data very well for $\Lambda=0.2$ and $0.5$, differ slightly for $\Lambda=1$ and are far off for $\Lambda=2$. Although the coupling parameter could also be determined by a fit to the level spacing data, we observed that this did not yield an improved estimate. Note that the surmises' maxima are always left of the maximum of the GOE, cf.\ \fig{fig wigner surmise} right, in contrast to the $\Lambda=2$ maximum. Not surprisingly, the surmise for the off-axis spacing does not work for large coupling parameters, i.e.\ for large perturbations. The reason for the earlier break down of the off-axis surmise could be related to the additional degree of freedom of the eigenvalues when they move in the complex plane.
\section{Application to two color QCD with chemical potential}
\label{sect:qcd}
\subsection{Symmetry and hermiticity of the Dirac operator}
\label{subsect:symm_and_herm}
As far as anti-unitary symmetries are concerned, the surmises discussed in the previous sections should approximate the spacing distributions for two-color QCD with a real quark chemical potential, as will be analyzed now.
\subsubsection{Continuum}
\label{sect:symmcont}
In the presence of a chemical potential, the Euclidean-space Dirac operator in continuum two-color QCD is given by
\begin{align}
D = \gamma_\nu D_\nu + m + \mu \gamma_4\,,
\end{align}
with covariant derivative
\begin{align}
D_\nu = \partial_\nu + i A^a_\nu(x) \tau_a\,,
\end{align}
where $\tau_a$ are the Pauli matrices, the generators of SU(2). The massless Dirac operator at zero chemical potential is an anti-hermitian operator, which has purely imaginary eigenvalues. The mass merely shifts the spectrum, while the chemical potential distorts it nontrivially. Since the former is irrelevant for level spacings, we will set $m=0$ for the following discussion.
The anti-unitary symmetry of the SU(2){} Dirac operator is based on the pseudo-real nature of SU(2){} implying
\begin{equation}
(i\tau_a)^\ast=\tau_2^\dagger(i \tau_a)\tau_2\,,
\label{eqn tau symm}
\end{equation}
as well as on the charge conjugation properties of gamma matrices
\begin{equation}
(i\gamma_\nu)^\ast=C^\dagger(i \gamma_\nu) C\qquad \mbox{with}\qquad
C= \gamma_2\gamma_4\,,
\label{eqn charge conj}
\end{equation}
where we use the Weyl representation
\begin{equation}
\gamma_\nu=\left(
\begin{array}{cc}
0 & (i\tau_i,1_2) \\ (-i\tau_i,1_2) & 0
\end{array}
\right)\,.
\end{equation}
Making contact to the real random matrices considered so far is easiest after multiplication with the imaginary unit,
\begin{equation}
iD=i\gamma_\nu\otimes\big(\partial_\nu 1_2+A_\nu^a(x) i\tau_a\big)
+i\mu\gamma_4\otimes 1_2\,,
\label{eqn iD}
\end{equation}
where we have separated the spin and gauge parts explicitly. From \eq{eqn tau symm} and \eq{eqn charge conj} it follows that $iD$ obeys the GOE symmetry
\begin{equation}
(iD)^\ast=U^\dagger (iD) U\,,\qquad U=C\otimes\tau_2\qquad \text{with} \quad U U^\ast=1\,.
\label{eqn iD symm}
\end{equation}
As a consequence, $iD$ can be made real by a unitary transformation. We denote such an equivalence by $\sim$ and write
\begin{equation}
iD\sim D_s+D_a\,,
\end{equation}
where we have split the operator into its real symmetric part $D_s$ and real antisymmetric part $D_a$. From the hermiticity at $\mu=0$ one identifies $iD(\mu=0)\sim D_s$ and further $i\mu\gamma_4\sim D_a$. Thus up to the factor $i$ -- which only rotates eigenvalues, but does not influence spacings -- the situation for the continuum Dirac operator is the following: for vanishing chemical potential it is real symmetric with on-axis eigenvalues obeying the GOE symmetry, whereas the chemical potential $\mu$ introduces a real antisymmetric perturbation with possible creation of complex conjugate eigenvalues. This agrees with the setting for the random matrices with $\mu$ playing the role of the matrix coupling parameters $\lambda$ and $\Lambda$.
The massless Dirac operator also satisfies chiral symmetry, $\{D,\gamma_5\}=0$, resulting in all nonzero eigenvalues coming in pairs $\pm i\theta$. In the numerical results below we will restrict ourselves to the half of eigenvalues with positive imaginary part and consider spacings in the bulk, away from $\theta=0$. For the spacing distribution in the bulk the chiral symmetry is known to be irrelevant \cite{Fox:1964, Nagao:1991, Nagao:1992,Halasz:1995vd,Pullirsch:1998ke}.\footnote{\label{ftnote}Note that chiral symmetry implies another anti-unitarity relation, $D^\ast=(\gamma_5 U)^\dagger D(\gamma_5 U)$, which at first sight would mean that $D$ belongs to the class of real antisymmetric operators. This is, however, not the case, since for the classification one first has to reduce the operator to irreducible blocks. This is best done on $D^2$, in which chiral eigenvalue pairs $\pm i \theta$ become twice degenerate eigenvalues $-\theta^2$. As $D^2$ commutes with $\gamma_5$, its eigenmodes can be chosen to be of definite chirality. The two relations $(D^2)^\ast=U^\dagger D^2 U=(\gamma_5 U)^\dagger D^2 (\gamma_5 U)$ coincide on the subspaces of fixed chirality, where both are proportional to $u=\tau_2\otimes\tau_2$ with $uu^\ast=1$. This qualifies $D^2$ and thus also $D$ for GOE.}
\subsubsection{Lattice}
When simulating the theory on a space-time lattice, the Dirac operator has to be discretized accordingly. Lattice discretizations of the Dirac operator typically alter some of its symmetry properties, such that its anti-unitarity properties can differ from those in the continuum\footnote{as is the case for the staggered Dirac operator \cite{Follana:2006zz, Bruckmann:2008xr}} and have to be analyzed carefully.
To preserve the chiral symmetry of the discretized Dirac operator one uses the overlap fermion formulation \cite{Narayanan:1993sk,Narayanan:1994gw,Neuberger:1997fp}, whose definition, in the presence of a quark chemical potential $\mu$, is given by \cite{Bloch:2006cd}
\begin{align}
D_{{\sf ov}}(\mu) =
1 + \gamma_5\sgn(\gamma_5D_{{\sf W}}(\mu))\,,
\label{Dovmu}
\end{align}
where we have put the lattice spacing to unity, $a=1$, $\sgn$ is the matrix sign function satisfying $(\sgn A)^2=1$, and
\begin{align}
D_{{\sf W}}(\mu)
= \, & 1 - \kappa \sum_{i=1}^3 \left( T_i^+ + T_i^-\right)
- \kappa \left( {e^{\,\mu}}\, T_4^+ + {e^{-\mu}}\, T_4^-\right)
\label{DW}
\intertext{with}
&(T^{\pm}_\nu)_{yx} = (1 \pm
\gamma_\nu) \, U_{x,\pm\nu} \, \delta_{y,x\pm\hat\nu}
\end{align}
is the Wilson Dirac operator at non-zero chemical potential \cite{Hasenfratz:1983ba} with hopping parameter $\kappa = 1/(8+2m_\text{w})$, Wilson mass $m_\text{w} \in (-2,0)$ and gauge configurations $U_{x,\pm\nu}\in$
SU(2), where $U_{x,-\nu} \equiv {U^\dagger}_{\!\!\!{x-\hat\nu,+\nu}}$. The exponential factors $e^{\pm\mu}$ implement the quark chemical potential on the lattice. For $\mu = 0$ the argument of the sign function in \eq{Dovmu} is hermitian, while for $\mu\ne 0$ it is non-hermitian.
To actually compute the overlap operator we need to define the matrix sign function for a general complex matrix $A$ of dimension $n$. A generic matrix function $f(A)$ can be defined by
\begin{align}
\label{eq:matfun}
f(A) &= \frac{1}{2\pi i} \oint_\Gamma f(z)(zI-A)^{-1}dz\,,
\end{align}
where $\Gamma$ is a collection of contours in $\mathbb{C}$ such that $f$ is analytic inside and on $\Gamma$ and such that $\Gamma$ encloses the spectrum of $A$. If $A$ is diagonalizable, i.e., $A=U\Lambda U^{-1}$, with diagonal eigenvalue matrix $\Lambda = \diag(\lambda_1, \ldots, \lambda_n)$ and $U\in Gl(n,\mathbb{C})$, then this general definition can be simplified to the well-known spectral form
\begin{align}
f(A) &= Uf(\Lambda)U^{-1}\,,
\label{fAdef}
\end{align}
with
\begin{align}
f(\Lambda) &= \diag\left(f(\lambda_1),\ldots,f(\lambda_n)\right)\,.
\end{align}
If $A$ cannot be diagonalized, a spectral definition of $f(A)$ can still be derived using the Jordan decomposition \cite{Golub}.
For hermitian $A$ the eigenvalues are real and their sign is defined by $\sgn(x)=\pm 1$ for $x\gtrless 0$ with $x \in \mathbb{R}$, such that \eq{fAdef} readily defines the matrix sign function.
For non-hermitian $A$ the eigenvalues are complex and require a definition of $\sgn(z)$ for $z \in \mathbb{C}$. The sign function needs to satisfy $(\sgn z)^2=1$ and reproduce the usual $\sgn(x)$ for real $x$. We define \cite{Bloch:2007xi}
\begin{align}
\sgn(z) &= \frac{z}{\sqrt{z^2}} = \sgn\left(\re z\right)\,,
\label{eq:sgnz}
\end{align}
where the cut of the square root is chosen along the negative real axis. This choice, although not unique, gives the correct physical result for the overlap Dirac operator in \eq{Dovmu} (see Ref.~\cite{Bloch:2007xi}).
To investigate the anti-unitarity properties of the overlap operator we first observe that links $U_{x,\pm\nu}$ as elements of the SU(2){} group obey
\begin{equation}
U_{x,\pm\nu}^\ast=\tau_2^\dagger\, U_{x,\pm\nu}\, \tau_2
\end{equation}
(as they can be written in terms of $1_2$ and $i\tau_a$). For the Wilson Dirac operator multiplied by $\gamma_5$ one can show that
\begin{align}\label{eq:inv ordering}
\hspace{4cm} (\gamma_5D_{{\sf W}})^\ast = U^\dagger (D_{{\sf W}}\gamma_5) U\qquad\mbox{(note the inverted ordering)}
\end{align}
with $U$ as in the continuum, see \eq{eqn iD symm}.
For the overlap operator we have to defer the discussion of its anti-unitary symmetries, because it has no definite hermiticity, even at zero chemical potential. Instead it fulfills the Ginsparg-Wilson relation \cite{Ginsparg:1981bj},
\begin{align}
\{D_{{\sf ov}},\gamma_5\}=D_{{\sf ov}}\gamma_5D_{{\sf ov}}\,,
\end{align}
which, together with the $\gamma_5$-her\-mi\-ti\-city, $\gamma_5D_{{\sf ov}}=D_{{\sf ov}}^\dagger\gamma_5$, valid at vanishing $\mu$, forces the eigenvalues on a circle $\theta=1+\exp(i\varphi)$ in the complex plane.
When investigating the spectrum of the overlap operator, we will rather consider a related operator \cite{Neuberger:1997bg}
\begin{equation}\label{eq:overlapproj}
D_p=\frac{2D_{{\sf ov}}}{2-D_{{\sf ov}}}=2\,
\frac{1+ \gamma_5\sgn(\gamma_5D_{{\sf W}})}{1- \gamma_5\sgn(\gamma_5D_{{\sf W}})}\,,
\end{equation}
which satisfies exact chiral symmetry, $\{D_p,\gamma_5\}=0$, at the price of being non-local. For $\mu=0$ this operator is anti-hermitian and projects the eigenvalues of $D_{{\sf ov}}$ from the circle onto the imaginary axis.
At non-zero chemical potential $D_p$ loses its anti-hermiticity and the eigenvalues come in three types: pairs of opposite real eigenvalues, pairs of complex conjugate imaginary eigenvalues and quartets of complex conjugate/opposite eigenvalues $(\lambda,-\lambda,\lambda^\ast,-\lambda^\ast)$.
To form the complex quartets at finite $\mu$, typically two pairs of purely imaginary eigenvalues need to come together to allow for its creation; in our RMT discussion the former were called \textit{on-axis} and the latter \textit{off-axis}.
The anti-unitarity symmetry of $D_p$ follows from that of $\gamma_5D_{{\sf W}}$, \eq{eq:inv ordering}, and the sign function thereof (and the facts that $U$ commutes with $\gamma_5$ and that $\sgn$ and $\gamma_5$ are their own inverses):
\begin{align}
\gamma_5\sgn^\ast(\gamma_5D_{{\sf W}}) &= U^\dagger \gamma_5\sgn(D_{{\sf W}}\gamma_5) U
=U^\dagger \sgn(\gamma_5D_{{\sf W}})\gamma_5 U \,, \\
D_p^\ast &= 2\, U^\dagger \,\frac{1+\sgn(\gamma_5D_{{\sf W}})\gamma_5}
{1-\sgn(\gamma_5D_{{\sf W}})\gamma_5}\,U
=2\, U^\dagger \,\frac{\gamma_5\sgn(\gamma_5D_{{\sf W}})+1}{\gamma_5\sgn(\gamma_5D_{{\sf W}})-1}\,U \notag\\
&=- U^\dagger D_p \, U\,.
\label{eqn Dp symm}
\end{align}
Hence $i D_p$ shares the anti-unitary symmetry from the continuum, compare \eqref{eqn Dp symm} to \eqref{eqn iD symm}, and therefore GOE spacings are expected at vanishing $\mu$. Again a chemical potential destroys the hermiticity, but keeps the anti-unitary symmetry, exactly as for the continuum Dirac operator. Note that $\mu$ enters the hermiticity breaking part of the operator $D_p$ non-linearly -- unlike $\lambda$ and $\Lambda$ in the random matrices.
\begin{table}[b]
\begin{center}
\begin{tabular}{c||c|c|c|c}
$\mu$ & $0.05$ & 0.10 & 0.20 & 0.30 \\
\hline
\# configs & 60000 & 30000 & 20000 & 20000
\end{tabular}
\caption{Values of the chemical potential and corresponding number of quenched configurations used to determine the spectral properties of the overlap operator.}
\label{tab:sim-param}
\end{center}
\end{table}
\subsection{Numerical results}
The quenched lattice simulations were performed on an $8^4$ lattice with the Wilson gauge action, using the USQCD lattice QCD software Chroma and QDP++ \cite{usqcd}. The software was adapted with an implementation of the overlap operator at non-zero chemical potential, based on the nested Krylov-Ritz approximation \cite{Bloch:2009uc}. We generated 60000 quenched configurations at $\beta=2.2$ using a heatbath/overrelaxation algorithm. On subsets of them we computed $\mathcal{O}(30)$ of the lowest lying eigenvalues of the overlap operator \eqref{Dovmu} with ARPACK \cite{arpack} for various values of the chemical potential and Wilson mass $m_\text{w}=-1.4$. The number of configurations used for the different chemical potentials are summarized in Table~\ref{tab:sim-param}. An animated plot of the evolution of the eigenvalues of $D_p$ with increasing chemical potential for a typical configuration can be found as ancillary material to this arXiv submission \cite{anim}.
\begin{figure}[t]
\includegraphics[width=\linewidth]{Plots/spacings_chempot_real_mu_typ=2.pdf}
\includegraphics[width=\linewidth]{Plots/spacings_chempot_real_mu_typ=3.pdf}
\includegraphics[width=\linewidth]{Plots/spacings_chempot_real_mu_typ=1.pdf}
\caption{Spacing distributions of the overlap operator with various real values of the chemical potential $\mu$. Top: on-axis spacings of type 1, surmise given by GOE, \eq{eq:surmiseon1}. Middle: on-axis spacings of type 2, surmise given by \eq{eq:surmiseon2}. Bottom: off-axis spacings, surmise given by \eq{eq:surmiseoff}; the dashed curve is the GOE spacing for comparison.}
\label{fig:overlaprealmu}
\end{figure}
We measured the spacing distributions of the projected overlap operator $D_p$, defined in \eq{eq:overlapproj}, for various values of the chemical potential $\mu$. As before, we distinguish between off-axis spacings and on-axis spacings with and without an interspaced complex pair. We only considered spacings between eigenvalues with an imaginary part in the spectral window $(0.5, 0.6)$. This ensures that the eigenvalues stay in the bulk of the spectrum (which of course is limited on a finite lattice) and have a roughly constant eigenvalue density which is necessary to apply the surmises, as argued in Sec.~\ref{sect:rmt}. As for the large random matrices, unfolding was only done for the on-axis spacings.
The results are shown in \fig{fig:overlaprealmu}. The numerical data are well matched by the surmises derived from small matrices, like for the large random matrices considered in Sec.~\ref{sect:rmt}. Again, the coupling parameter $\lambda$ is obtained by a fit for the on-axis spacings of type 2 and from the frequency $p$ of imaginary spacings for the off-axis spacings. For the off-axis spacings at large $\mu$ we observe that the discrepancy between the data and the surmise has the same tendency as for the large random matrices, cf.\ \fig{fig:largermt}, lower right panel. This indicates that the RMT results for large matrices are able to describe the QCD results reasonably well, even at larger coupling.
\subsection{Imaginary chemical potential}
The introduction of an \textit{imaginary} chemical potential does not change the anti-hermiticity of the continuum Dirac operator $D$ nor of the lattice operator $D_p$.
However, the operators $iD$ and $iD_p$ no longer obey an anti-unitary symmetry. The random matrix ensemble appropriate for operators without anti-unitary symmetry is the GUE. Hence, with increasing imaginary chemical potential one expects a transition from GOE to GUE. Surmises for such mixed random matrices, again additive, $H_\text{GOE}+\lambda H_\text{GUE}$, have been worked out in Refs.~\cite{Lenz:1991, Schierenberg:2012ut}, with the result
\begin{equation}
P_{\text{GOE}\to\text{GUE}}(s)= C s\, e^{-D^2s^2} \erf\left(\frac{Ds}{\lambda}\right)\,,
\label{eq:surmiseimag}
\end{equation}
where
\begin{align}
C = 2\sqrt{1+\lambda^2}\,D^2 \,,\qquad
D = \frac{\sqrt{1+\lambda^2}}{\sqrt{\pi}}
\left(\frac{\lambda}{1+\lambda^2} + \text{arccot}\lambda\right)
\,.
\label{eq:surmiseimag_const}
\end{align}
In \fig{fig:overlapimagmu}, these distributions are compared to those of the QCD Dirac operator $D_p$ with imaginary chemical potential, were unfolding was again done by measuring the spacings in units of the local mean spacing (obtained by an ensemble average). The coupling parameter was obtained by a fit with least square minimization. The surmise agrees very well with the numerical data.
\begin{figure}
\includegraphics[width=\linewidth]{Plots/spacings_chempot_imaginary_mu.pdf}
\caption{Spacing distributions of the overlap operator with various imaginary values of the chemical potential $\mu$ fitted by the surmise \eqref{eq:surmiseimag}. For each $\mu$, 5000 configurations have been analyzed in the spectral window with imaginary parts of the eigenvalues between $0.65$ and $0.8$.}
\label{fig:overlapimagmu}
\end{figure}
\section{Summary}
\label{sect:summary}
We have shown that eigenvalues of real symmetric matrices are attracted under real antisymmetric perturbations and are able to merge and move into the complex plain as complex conjugate pairs. For the emergent kinds of level spacings -- on-axis with and without interspaced eigenvalue pair and off-axis -- we have derived surmises from small random matrices. For the on-axis spacings without interspaced pair, the surmise is simply the GOE surmise, as in the unperturbed case, while for the other two we have obtained closed formulae, which depend on a coupling parameter $\lambda$.
These mixed-hermiticity surmises provide good approximations to the spacings of large random matrices in the regime of weak non-hermiticity and for the bulk of two-color QCD with small chemical potential, as expected from the anti-unitary symmetry and hermiticity properties of the Dirac operator. For on-axis spacings with an interspaced pair the surmise parameter $\lambda$ was obtained by a fit to the level spacings, while for off-axis spacings it was predicted by matching the frequency of those spacings between surmise and data.
We have also measured the level spacings for two-color QCD with imaginary chemical potential and verified that they follow a mixed-symmetry surmise.
In contrast to the eigenvalue densities, the level spacings of asymmetric real random matrices have not been worked out analytically. However, for weak antisymmetric perturbations the analytic surmises, which approximate the level spacings of large random matrices, can be used to describe physical systems obeying the relevant anti-unitary symmetry properties.
\section*{Acknowledgements}
The spectra of the overlap operator have been calculated on the Athene and iDataCool compute clusters, which are part of the HPC infrastructure of the University of Regensburg. We would like to thank Gernot Akemann for useful discussions. We also acknowledge DFG for financial support (SFB/TR-55 and BR 2872/4-2).
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Microsoft .NET Framework 2.0, 2.0 SP1, and 3.5 does not properly enforce a certain type-equality constraint in .NET verifiable code, which allows remote attackers to execute arbitrary code via (1) a crafted XAML browser application (XBAP), (2) a crafted ASP.NET application, or (3) a crafted .NET Framework application, aka "Microsoft .NET Framework Type Verification Vulnerability."
The Common Language Runtime (CLR) in Microsoft .NET Framework 2.0, 2.0 SP1, 2.0 SP2, 3.5, and 3.5 SP1, and Silverlight 2, does not properly handle interfaces, which allows remote attackers to execute arbitrary code via (1) a crafted XAML browser application (XBAP), (2) a crafted Silverlight application, (3) a crafted ASP.NET application, or (4) a crafted .NET Framework application, aka "Microsoft ...
The design of the W3C XML Signature Syntax and Processing (XMLDsig) recommendation, as implemented in products including (1) the Oracle Security Developer Tools component in Oracle Application Server 10.1.2.3, 10.1.3.4, and 10.1.4.3IM; (2) the WebLogic Server component in BEA Product Suite 10.3, 10.0 MP1, 9.2 MP3, 9.1, 9.0, and 8.1 SP6; (3) Mono before 2.4.2.2; (4) XML Security Library before 1.2. ...
oval:org.secpod.oval:def:714
The host is installed with Microsoft .NET Framework and is prone to remote code execution vulnerability. A flaw is present in x86 JIT compiler, which fails to compiling certain function calls. Successful exploitation could allow remote attackers to corrupt the stack and execute remote code.
oval:org.mitre.oval:def:12033
The Common Language Runtime (CLR) in Microsoft .NET Framework 2.0 SP1, 2.0 SP2, 3.5, 3.5 SP1, and 3.5.1, and Microsoft Silverlight 2 and 3 before 3.0.50611.0 on Windows and before 3.0.41130.0 on Mac OS X, does not properly handle interfaces and delegations to virtual methods, which allows remote attackers to execute arbitrary code via (1) a crafted XAML browser application (aka XBAP), (2) a crafte ...
Pages: Start 1 2 3 4 5 6 7 8 9 10 11 12 13 14 .. 1417 | {
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♥ Chamomile with excellent soothing effect calms the sensitive skin by covering it gently.
♥ This pouch contains a genuine vegetable bamboo sheet and a transparent and refreshing essence.
♥ The vegetable sheet is 100% extracted from genuine bamboos, it is natural and rich in essence, and covers and clings to the face softly and closely with no irritation for the skin.
1. After cleansing, use toner to refine the skin texture.
2. Take out the mask from the package and spread it evenly over the entire face, avoiding the eye and lip area.
3. Remove the sheet after 15 to 20 minutes and gently pat to allow the remaining formula to absorb into the skin.
Before I start muttering about the product I must say that, in case you noticed, the validity date was over before the review was published but obviously I used it before it ended. Actually I have used these masks since May, and these photos aren't recent, I just had to "try" the mask a lot of times because of something that happened on my first usage.
I will get to that later. But the point is do not use products outside of the validity date (or if you do, at least make sure to use the product a little before the validity ends so that you can detect any changes in smell, texture, etc).
These Femmue masks all have the same pack, regardless of the scent you choose, and they all open the same. Which in this case is a good thing, since they all open "the same easy" aka just as easily. They don't slide right open but I didn't have any struggle with it, ever.
The mask is thick and sturdy, but it is not rough to the touch at all. It is actually soft, just very dense and not fluffy (like fur is fluffy, satin is soft). It is also soaked in essence, and it did drip a little while I was taking the photo.
But not because the masks drip on your neck while in application (they don't, I can tell you that right away) it's really just because it's full of essence.
The mask seems completely normal, a little wider than taller so I know right away it will have excess on my sides since wider masks always leave "flappers" on my sides.
Here is the fit, it's not perfect. As I said, there are flappers, and it doesn't adhere 100% on my "tall nose" and it is a little too close to the corner of my eyes. But generally speaking it is still a good fit as it covers most of my face, most of my nose, it fits a little under my chin, and clings amazingly well to all of my face.
Especially compared to, if I might add, the Aritaum masks. They dry fast and peel off the face sometimes (but then again, they are really cheap).
The essence is as they promised: transparent and refreshing. It smells like a flowery soap or handwash, it spreads well and absorbs quickly but without leaving the skin dry.
The first time I used this mask I took notes regarding the following points. The mask is supposed to be calming and hydrating, and I did feel the hydration after usage – and it stayed for a long time and matched my skin care routine perfectly. But I had done some laser on the day before and was peeling on my nose and the mask burned on those spots, so I was frustrated that they called it calming.
So then I actually used it many more times (because I had the masks already!) and decided to be more careful with my skin. On the next times my skin wasn't peeling nor did I laser before the mask, but I did get some sun damage at some point. So, what I'm saying is that I had skin conditions during the next usages, just not "open wounds". And these times my thoughts were incredibly different!
The mask is really hydrating, and when my skin is healthy the hydration lasts way longer, and cares for my thin skin and distorted pores. My nose skin was sore at some point (from blowing my nose, I had a cold) but not peeling and the mask calmed it down. It also helped my tense muscles relax.
The mask while applying seems like it doesn't do much, even though it feels nice, but it does give extreme hydration without drying (for those confused ones hydration = water, moisture = oil, my skin is oily and dehydrated on my T zone, and dry and dehydrated elsewhere).
So, taking the "no open wounds" detail into consideration, this is a great mask that I would include in the aroma therapy and spa sessions at any relaxation resort or center and I'm not even kidding – it is that good.
Of course a dry skin will need the normal amount of moisturizing products afterwards, but as long as you do your normal skin care (and don't have open wounds, so I'm sorry for cysts and popped pimples) it fits any skin type.
Oh, and there's lots of essence left in the pouch in the end!
Repurchase? I'm actually just waiting for the brand to restock it in Korea and count me in!
Have you tried Femmue The Botanist Chamomile Mask? | {
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Today I focus on the Picnic Table and the Lily Pads as I continue my look at structures and other features proposed as part of the Inner Arbor plan. For more background see part 1, part 2, and part 3 of this series. For a good summary of the proposed features see Andrew Metcalf's story "Breaking Down the Plan to Develop Symphony Woods" at the Columbia Patch. For more on the vision behind the Inner Arbor plan and some inspirations for its features, see the Columbia Association's original presentation on the Inner Arbor plan. As before, my focus is on the following questions for each feature: Does it work? Is it beautiful? Will it last? What's the cost?
Overview of the proposed Merriweather Park, showing features proposed for Symphony Woods as part of the Inner Arbor plan. (Click for a higher-resolution version.) Image © 2013 Inner Arbor Trust; used with permission.
The proposed Picnic Table feature is located near the Word Art and Play Maze features discussed in the previous post. It is a relatively long and narrow feature, and stretches across a good portion of the north central portion of Symphony Woods, running from northwest to southeast. The proposed Lily Pads feature is located near the northeast entrance to the park, the entrance closest to the existing Central Branch library. See the above graphic to get a better idea of how these features relate to the rest of the proposed Merriweather Park.
The Picnic Table in Symphony Woods / Merriweather Park in the Inner Arbor plan. (Click for a higher-resolution version.) Image © 2013 Inner Arbor Trust; used with permission.
The Picnic Table is a clever solution to a significant problem: On the one hand, people going to Symphony Woods are going to want someplace to sit down, stretch out, and perhaps enjoy some food and drink, especially when attending major events like Wine in the Woods. On the other hand, people would also like to be surrounded by the natural beauty of the woods in a setting more reminiscent of a primeval forest than a suburban lawn. Unfortunately, primeval forests have significant disadvantages for sitting and stretching out: The forest floor is littered with leaves, twigs, and other detritus, there are bushes and other low plants in the way, there are rocks, tree roots, and generally uneven ground to pain the sensitive rump, and the ground is often cold, damp and even muddy.
The traditional solution to this problem is to provide groups of conventional picnic tables—the sort of thing you'll find in many parks in Howard County and elsewhere, not to mention at interstate rest stops. Alternatively, there might be no picnic tables at all, with guests forced to bring their own chairs or blankets in order to be able to sit dry and comfortably.
The proposed Picnic Table feature eliminates or at least minimizes the need for such ad hoc solutions, by providing what is in effect an artificial forest floor. It is elevated high enough (about 22 inches) so that people near the edge of it could sit on it as they might sit on a (backless) park bench, but not so high as to require handrails for people walking on the Picnic Table surface. People in the middle of the Picnic Table could stretch out with or without a blanket, out of contact with the dampness or muddiness of the ground. Rather than a conventional wood, metal, or concrete table surface it is covered in high-quality artificial turf. The turf would be at least semi-porous, so it might help eliminate the problem of rainwater pooling in lower-lying areas of the feature (a problem often seen with conventional surfaces).
Is it a beautiful feature? No, but it would likely be more attractive than the typical park or rest stop picnic table. And in any case the use of a natural color artificial turf (as opposed to the bright green variety seen in some football stadiums) would help the feature blend in with the surrounding trees and plants. In effect the Picnic Table reverses the approach of the Cy Paumier plan: Where that plan called for a central grassy area (the Central Park Commons), essentially pushing the trees aside in favor of something like an over-sized suburban lawn, the Picnic Table keeps the trees where they are and puts a narrow simulacrum of such a lawn around and next to them—with no lawnmowing required.
Will the Picnic Table prove to be durable? I think it will get a lot of use (and thus abuse), particularly during high-traffic events like Wine in the Woods. However unlike most artificial turf installations people would likely be sitting on it more than walking on it, and this may help lengthen its life. As for its potential cost, I'm not sure. If I'm understanding this Howard County Times story correctly, when Howard County deliberated in 2011 over funding conversion of grass football fields to artificial turf, the price tag was on the order of $1M per field. The Picnic Table is considerably smaller in area than a football field (about as long but much narrower), but may use higher-quality turf, requires a support structure underneath it, and would be constructed in an environmentally-sensitive area.
In any case the Picnic Table almost certainly won't be anywhere near the costliest feature proposed for the park. There have been extras proposed for it, most notably Martha Schwartz speculating at the pre-submission meeting about heating the structure so that it could remain snow-free in winter. However such extras aren't central to the overall concept and purpose of the Picnic Table, and could be discarded or scaled back if budget concerns need to take precedence.
The Lily Pads in Symphony Woods / Merriweather Park in the Inner Arbor plan. (Click for a higher-resolution version.) Image © 2013 Inner Arbor Trust; used with permission.
As the Word Art does at the northwest entrance to the proposed Merriweather Path, the Lily Pads serve to greet visitors arriving via the northeast entrance (for example, coming from Lake Kittamaqundi or the Central Branch library); they are a transition point into the area of Symphony Woods containing the new features proposed as part of the Inner Arbor plan.
The Merriweather Park master plan (see above graphic) also shows something called "The Nest" right next to the Lily Pads. As I noted previously, this may be the "iconic interactive sculpture" referred to in CA's original Inner Arbor presentation. If so, the Lily Pads would ultimately serve as a spot from which to view the Nest and (assuming this is allowed) to also enter it. As pictured the Lily Pads structure itself is relatively simple, almost comparable to a high-end backyard deck; its point would be to complement the Nest and not attract attention on its own. The Nest itself would be a major sculptural commission (for inspirations see the CA Inner Arbor Plan) and thus not something we'd expect to see designs for at this stage of the Inner Arbor effort.
The Lily Pads are wooden platforms and walkways roughly analogous to the current walkway by Lake Kittamaqundi, as well as to boardwalks in Ocean City and other resort communities, and thus we could expect the cost and durability of the Lily Pads to be comparable to those other walkways. The Inner Arbor plan as presented appears to have a lot of wooden walkways: not just around the Lily Pads but also at the three gateways next to Little Patuxent Parkway, near the eastern entrances to Symphony Woods (the Entry Plaza in the master plan), near Merriwether Post Pavilion (the Caterpillar Plaza), and elsewhere in the park.
If budget concerns grow then the pressure to economize on the use of wood will likely become intense, with critics calling for concrete and asphalt to be used instead wherever possible, My personal opinion is that this would be a false economy; the use of wood is much more compatible with the overall vision for the park. I'll note here that communities like Ocean City with extensive wooden boardwalks have chosen to stick with wood despite the higher cost, and many have even considered upgrading to more durable (and thus more expensive) types of wood. We should look to their examples.
With that I'll conclude this post. I'll next look at the larger and more showy structures envisioned in the Inner Arbor plan, beginning with the Caterpillar.
UPDATE: Corrected the spelling of Andrew Metcalf's name. | {
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Like many parents of small children, we have accumulated rather a lot of 'stuff' over the last 7 years, most of which we have moved from country to country and house to house, loft to loft. In 2012 I decided that it was time to have a big clear out and, at the same time, raise some money for research. This idea for a fairly small clothes and toys sale grew and grew, as my plea for people to donate their own second hand items got an almighty local response! For six months sacks just kept appearing at our door and eventually our loft was so full we had to ask a friend if we could borrow their garage for storage too!
We held the sale in November and the task of unpacking all the clothes, hanging them on rails and displaying them ready for sale, was immense. I can't thank the lovely team of friends who spent two solid days helping me prepare, enough. | {
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slj 16 asphalt hot mixing equipment,slj 16 twin drum mix asphalt plant. it is a common pavement equipment widely used in construction of bridges, highways, slj 16 asphalt hot recycling mixing related keywords. drum mix. Learn more. Slj-16 Mini Hot Mixer Asphalt Plants - dollybattery.
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After nearly three decades of working within the airline trade, Steven Slater had had enough. It's extra higher to take extra issues but really feel in safety and luxury then to have mild however unsafe and uncomfortable journey. We even have crew meals and typically would even have extra passengers meal that we throw off on the finish of every flight.
As quickly as we heard the airport was re-opening we went on-line to e-book our flight. The vacation travel season couldn't occur at a worse time in the 12 months for flying. With so many security issues now to be troubled about when one goes on a trip, this travel pockets enables your girls friends to tour places with their passport and money secure with them.
I am planning a trip from Bangalore to Ladakh by flight throughout for 7 days and want to know when you may give me some strategies as to how shall I plan this journey. Treating yourself well and studying a couple of methods to getting you and your children through the day is a crucial step.
Spend a day in the metropolis centre and you can go to Akershus Fort, which is just along from the ferry terminals. One factor that you should be prepared of is that accommodation and meals at this time of 12 months shall be very primary as many of the tents operated by journey agencies are solely pitched in June which sees the start of the tourist season.
This is a beautiful film starring Jennifer Love Hewitt and Paul Nicholls that may challenge you to think about how you might live life in another way if you solely had another day with the one you're keen on. This complete ordeal was on the fault of the travel agency and they still requested us to pay for a new ticket. | {
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With grinning appearances, pleasant air and amicable arms, Karachi escorts our models endeavor not just to live up but instead beat their client's solicitations ensuring that no gaps are left for grievances. Another way through which Escorts in Karachi we attempt to make ourselves extraordinary as indicated by our particular clients is by outfitting quality administrations with a variety of decisions Independent Karachi Escorts. | {
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Samsung is all out to popularize its own in-house App Store and it has decided to drop its cut from in-app purchases down to 20% from the previous 30%.
Usaually, the profit distribution rate for developers and Samsung for paid applications and in-app purchases is that the developer(s) takes 70% while Samsung takes 30% of the cut. That won't be the case, at least for in-app purchases, from November 1st, 2013 all the way to April 30, 2014. The new rates are: 20% of the cut for Samsung while the developer(s) takes the rest (80%). | {
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Athelte Nutrition, athlete, blog, Competitive, healthy, Matt Sates, nutritional, Recovery, Supplements, swim, swimmer, Swimmers, Swimming, teen athletes, Tokyo Olympics - July 16, 2021
GOING FOR GOLD WITH ULTIMA
From 23 July to 8 August, the world will be delighting in moments of competition, victory and glory, when we watch top athletes perform at their best and go for gold at the Tokyo Olympics.
One such athlete is Matthew Sates. A 17-year-old South African, Durban scholar, who has been torching some of the fastest swimming times in the history of the 17-18 age group. Only the legendary, 21 gold medal winner, Michael Phelps now ranks above Sates in the 200 IM and 100 Fly in the 17-18 age group.
Could Matt surpass Michael's times and later accomplishments? We believe he can.
To qualify for the Olympics takes huge amounts of effort, dedication and determination from the athletes, coach and family. Having a good nutritional diet plays a critically, vital role and enhances overall performance and recovery of the athlete on a daily basis.
Ultima Nutritional Supplements has provided Matt with this winning formula that works in the form of Ultima Performance Shake.
The Ultima formula provides Matt with everything needed – the best source of proteins, minerals and vitamins – all the nutrients needed to meet the demands of a world class training and exercise regime, ensuring that Matt can perform at his peak, at all times, both academically and physically, during training and competition. In addition to helping Matt perform optimally, it facilitates for recovery and muscle repair allowing Matt to be 100 % ready, come what may.
Staying lean is vital to swimmers who want to improve endurance, strength, explosive power and overall well-being. Ultima's formula is designed to maximize your power-to-weight ratio, which in short means increasing strength and maintaining a lean streamlined build. This is critical for Matt as it maximizes his speed and allows him to knife through the water.
Ultima founder Tim Shead, aged 69, Ultima's best customer, a World Master's Swimmer, who has been inducted into the International Swimming Hall of Fame (ISHOF), is testament to that.
The Ultima formula, which has not changed, has been an industry leader and winner for more than 30 years. It is totally unique and unparalleled, was specifically formulated for swimmers by swimmers and can be used for other sporting disciplines such as cycling, running and general nutrition with great results.
Also competing in the Tokyo Olympics and using the same multi world record formula, that has produced over 800 world records in the past, are US Olympians; 15 year old phenomenon Katie Grimes* and most improved US swimmer Patrick Callan*. Just like Matt Sates, both have used the same winning formula for many years, helping them to cope with the needs and challenges of a growing body and mind and allowing them to perform at their peak and reach their Olympic dreams and goals.
Ensure you or your kids become champions like Matt and purchase your Ultima Performance directly from www.ultima.co.za. With expert guidance and knowledge on how and when best to use the products, speak to Maddie Shead at 021 7023910 or email [email protected].
If you are a serious athlete who gets tested for banned or illegal substances, you've come to the right place, contact Maddie Shead for more info at [email protected]
*The Ultima Performance formula is sold as P2Life Nutriboost in USA.
Athelte Nutrition
low carbs
Matt Sates
sleep deprevation
teen athletes | {
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Citizens who intend to purchase property in NDMC are advised to have ' no dues certificate ' from the Commercial Department of NDMC for electricity & water dues in order to aprotected void inconvenience.
The landlords are advised to ask their tenants to obtain 'no dues certificate' for electricity & water dues while vacating the premises.
Consumers of electricity and water supply are advised to make payment on or before the due date to aprotected void levy of surcharge @ 1.5% per month and disconnection of supply.
Put on the light/fan/coolers only when required. Use natural light wherever possible.
Don't keep the light/fan/coolers on when not in use.
Use fluorescent tubes/compact fluorescent lamps in place of ordinary incandescent lamps.
Aprotected void using incandescent lamps as these draw considerably higher power than CFL/Fluorescent tubes.
Use ordinary signboards fitted with fluorescent tubes.
Don't use Neon Signboards, as the electricity consumption of such signboard is about 10 times higher than ordinary fluorescent tube fitted signboard.
Use right capacity capacitors with the induction motors of 5 HP & more capacity.
Don't run the induction motors of 5 HP & above without right capacity capacitors. It will increase the energy consumption/bill also.
Use separate control for each light/fan so that the same could be used optionally.
Don't put the light/fans in group control. This will lead to wastage of energy & higher billing as well.
Don't use air-conditioners at peak hours in the evening.
Use LPG for cooking instead of electric heaters/hot-plate etc.
Don't use electric heaters for cooking purpose, as it is costly in comparison to LPG.
Keep the electric wiring in proper condition.
Don't connect the load higher than the sanctioned limit, otherwise 50% misuse charges are leviable.
Don't use the domestic connection for non-domestic purpose, otherwise non-domestic / commercial tariff along with 50% misuse charges are chargeable.
Use the electricity connection for the premises only for which it is sanctioned.
Don't extend the electricity to the other premises, otherwise non-domestic/ commercial tariff along with 50% misuse charges are chargeable.
Generally there are complaints of inflated electricity bills but on verification it has been found that consumers are using heavy duty appliances i.e. geysers, heat convectors, heaters, electric iron, hot plates, ovens etc. Consumers are advised to use these appliances sparingly to minimize their energy consumption. If these appliances are used for 4 hours a day, the monthly expenses will be for Air conditioner (1.5 tonnes) Rs. 1,000/-, Geyser (storage type) Rs. 600/-, Geyser (Instant) Rs. 1,200/- Single Hot Plate/Elect. Iron Rs. 400/-, Heat Convector Rs. 400-800/- and Electric Oven Rs. 1,000/-. | {
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This entry was posted on Tuesday, April 17th, 2012 at 8:22 pm and is filed under All you need to know aobut long distance movings, Cross country moving compnies, Moving companies to help live not drive. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site. | {
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Q: C# OutOfMemoryException in System.Drawing.Bitmap Is there any way to get more detail at runtime about an OutOfMemoryException? Or, can this exception somehow not be caught by the enclosing try/catch and instead a try/catch higher up the call stack? I cannot reproduce using WinDBG so it must be something I can log from the application.
I apologize for the long explanation, but there are a lot of possible causes to eliminate, which I explain.
I have read up on all the possibilities for an OutofMemoryException and basically eliminated all of them. Normally, application runs great, but occasionally on only certain computers, I am getting an OutOfMemoryException. As these reports are in the field on not reproducible locally, I only have logs to go by. But I have a fair amount of detail.
What is strange:
*
*Anything that might logically be allocating memory in the vicinity is in a try/catch, but the exception is treated as unhandled (and caught much higher up the call stack)
*There are no StringBuffers in use
*The exception happens even after rebooting and restarting the application.
*The exception occurs after only a couple minutes, and only about 30MiB of memory allocated, in chunks no more than 1.5MiB.
*Verified the application (built for "any" processor) is running as 64 bit.
*no shortage of disk space (270Gb free) and pagefile is enabled.
*does not appear to be a possible LoH fragmentation issue.
This has happened a couple times in different parts of the application recently. The first time, I concluded there was a corrupt .NET assembly, as the exception was occurring right when it would first load the System.Web.Serialization assembly. I could determine it was happening right during a method call where that assembly was used for the first time. Reimaging the computer (to be identical of original setup) and updating windows resolved this issue.
But, it seems highly unlikely to me that the second case, different client, happening within a few days, is also corruption. This one is happening in a location where no assemblies would be loaded. I'm rethinking the first error now. What I do know:
*
*It's happening in a thread pool thread (System.Timers.Timer, [Statthread])
*Small number of threads active (< 5)
*It happens around the time a 1MiB file is downloaded. This is read into a MemoryStream, so that could be as big as 2MiB. That is then fed to a System.Drawing.Bitmap constructor, resulting in a Bitmap that would be about 8MiB. However, that is all in a try/catch that catches System.Exception. The only thing not in the try/catch is returning the byte[] reference, which should just be a reference copy, not any memory allocation.
*No other significant memory allocations have been done before this time. Reviewing heap in my local version, which should be running identically, shows just the app icon and a couple dozen objects that would be on Small Object Heap.
*it is repeatable on a specific system with specific input. However, these systems are cloned from one another. Only obvious variation would be the order of windows updates.
*The assembly I'm running is signed. Isn't there a checksum that ensures it isn't corrupted? Same for all the system assemblies? I don't see how this instance could be explained by corrupted dlls, or even data.
*Viewing the call stack at time of exception is surprisingly unhelpful. I indicate in the code below where exception is thrown.
*There is some use of COM objects. However, under normal conditions we run the app for weeks without memory problems, and when we get these exceptions, they are almost immediate, after only using around 20 relatively lightweight COM objects (IUPnPDevice)
// Stack Trace indicates this method is throwing the OutOfMemoryException
// It isn't CAUGHT here, though, so not in the try/catch.
//
internal void Render(int w, int h)
{
if (bitmap != null)
{
bitmap.Dispose();
bitmap = null;
}
if (!String.IsNullOrEmpty(url))
{
// this information is printed successfully to log, with correct url
// exception occurs sometime AFTER this somehow.
Logger.Default.LogInfo("Loading {0}", url);
// when file contents changed (to go from 1MiB to 500MiB, the error went away)
byte[] data = DownloadBinaryFile(url);
if (data != null)
{
try
{
Bitmap bmp;
using (var ms = new MemoryStream(data))
{
bmp = new Bitmap(ms);
}
bitmap = bmp;
}
catch (Exception)
{
// We do not catch anything here.
Logger.Default.LogWarning("WARNING: Exception loading image {0}", url);
}
}
//
// if we had any errors, just skip this slide
//
if (bitmap == null)
{
return;
}
// QUESTION EDIT:
// in the problematic version, there was actually an unnecessary
// call here that turns out to be where the exception was raised:
using( Graphics g = Graphics.FromImage(bitmap)) {
}
}
}
// calling this would trigger loading of the System.Web assembly, except
// similar method has been called earlier that read everything. Only
// class being used first time is the BinaryReader, which is in System.IO
// and already loaded.
internal static byte[] DownloadBinaryFile(String strURL, int timeout = 30000)
{
try
{
HttpWebRequest myWebRequest = HttpWebRequest.Create(strURL) as HttpWebRequest;
myWebRequest.KeepAlive = true;
myWebRequest.Timeout = timeout;
myWebRequest.ReadWriteTimeout = timeout;
myWebRequest.UserAgent = "Mozilla/4.0 (compatible; MSIE 5.01; Windows NT 5.0)";
Encoding encode = System.Text.Encoding.GetEncoding("utf-8");
using (HttpWebResponse myWebResponse = myWebRequest.GetResponse() as HttpWebResponse)
{
if (myWebResponse.StatusCode != HttpStatusCode.OK)
{
Logger.Default.LogWarning("WARNING: Response {0} loading {1}", myWebResponse.StatusCode, strURL);
return null;
}
using (Stream receiveStream = myWebResponse.GetResponseStream())
{
using (BinaryReader readStream = new BinaryReader(receiveStream))
{
// this extension method uses MemoryStream, but seems irrelevant since we don't catch anything here.
return readStream.ReadAllBytes();
}
}
}
}
catch (Exception e)
{
// we do not catch anything here.
Logger.Default.LogError("ERROR: Exception {0} loading {1}", e.Message, strURL);
}
return null;
}
So, after all of that, I return to my opening question. Are there any known properties on the OutOfMemoryException object I can inspect, or calls I can make after the exception is thrown, to narrow this down?
And..is there any reason an OutOfMemoryException would not be caught by the first try/catch, but would be caught further up the call stack?
A: Thank you all. The answer is somewhat curious and I had some details wrong which made it hard to figure out. The error is here:
Bitmap bmp;
using (var ms = new MemoryStream(data))
{
bmp = new Bitmap(ms);
}
bitmap = bmp;
In the remarks in documentation on the Bitmap constructor, I found this:
You must keep the stream open for the lifetime of the Bitmap.
Obviously, closing the MemoryStream immediately after constructing was violating this. A garbage collection between this and when I actually used the Bitmap was apparently creating the error. (EDIT: actually, it seems that a boundary exists around 1MiB where the FromStream function will decompress only so much of a JPEG file initially. For JPEG < 1MiB, the entire image is decompressed and it doesn't actually use the stream after the initialization. For larger JPEG, it will not read beyond the first 1MiB until those pixels are needed)
It's hard for me to imagine why Microsoft did it this way. I wouldn't want to keep the original stream open, either (which is an http connection) so only solution I see is to clone the bitmap:
// Create a Bitmap object from a file.
using (var ms = new MemoryStream(data))
{
bmp = new Bitmap(ms);
Rectangle cloneRect = new Rectangle(0, 0, bmp.Width, bmp.Height);
System.Drawing.Imaging.PixelFormat format = bmp.PixelFormat;
this.bitmap = bmp.Clone(cloneRect, bmp.PixelFormat);
}
What led to my long frustrating search and the exclusion of a key piece of information was that the code executing on a client machine was a slightly older version, with only a subtle change. Graphics.FromImage() was being called on the bitmap in the previous version, but that had been removed. Still, that version functioned very well the vast majority of the time.
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It was Foo Fighter Dave Grohl's 50th birthday on Monday (January 14) and to celebrate his renowned letter to Cornwall Council went viral on social media.
The former drummer with Nirvana wrote to Cornwall Council in March 2016 in support of young Cornish band Black Leaves of Envy, who were having trouble rehearsing because of noise restrictions.
The kind-hearted missive only added to Grohl's reputation as the nicest man in rock.
To celebrate the milestone birthday of one of the biggest musicians in the world, Letters of Note shared his correspondence with its 612,000 followers on Twitter, who absolutely loved it.
Here's some of what he had to say.
"Music is not only a healthy pastime, it is a wonderful, creative outlet for kids, and fosters a sense of community necessary to the emotional and social development of any child.
"I believe it is crucial that children have a place to explore their creativity and establish a sense of self through song. The preservation of such is paramount to the future of art and music."
"Without them, where would we be? As a proud father of three aspiring musicians myself, I have always made this a priority in our home, to get great results.
Here's the letter in full.
The letter was liked almost 9,000 times and retweeted over 3,000 times. Here's what some people had to say.
Grohl did get a response and here it is.
A spokesman for the council said at the time: "There would be no council investigation if we had not received a number of complaints about the noise levels.
"We are certainly not trying to stop the band from practising and have not told the band to stop playing. We have not prescribed a set noise level or told them that they must keep sound levels below 40 decibels.
She said the council had suggested soundproofing the garage or only playing at certain times.
"We have spoken to the owner of the property on three occasions so far and are arranging to visit them to try and identify a solution," the spokesman said. | {
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Honda targets high-flyers with domestic launch of HondaJet in Japan
According to The Asahi Shimbun, The HondaJet compact plane has already proved a winner in North America and Europe, and now Japanese high-flyers will also have the chance to travel in the comfortable, fuel-efficient jets.
Honda Motor Co. announced on June 6 that it has begun taking orders for the aircraft that can accommodate up to seven people and is characterized by its engines sitting above the wings.
It has a flying distance of 2,661 kilometers, meaning business travelers can fly from Tokyo's Haneda Airport to Beijing or Taipei without refueling.
Manufactured by Honda Aircraft Co., a Honda Motor subsidiary, the HondaJet will be priced at $US 5.25 million (about 577 million yen).
Time will tell if the aircraft can take off among Japan's business community as it has in the West.
According to the Japan Business Aviation Association, there are about 90 small jets operating in Japan in both the private and public sectors. In contrast, the United States, the world's largest market, has about 13,000 small jets.
Honda Motor founder Soichiro Honda declared in 1962 that his company would develop a light aircraft.
Production of the HondaJet began at a U.S. plant in 2012, and the first aircraft was delivered in 2015.
Forty-three of the plane were sold in 2017, making it the best-selling aircraft weighing 5.7 tons or less.
Ref: http://www.asahi.com/ajw/articles/AJ201806070053.html
If you want to read this article in Japanese, please see the following link:
https://www.j-abc.com/jp-blog/3400985
Haru Kinase
AUS Business
AUS Market
AUS Real Estate
AUS Technology
JPN Business
JPN Market
JPN Technology | {
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Napoli Rename Stadium After Late Football Legend, Diego Maradona
By Edna Wande On Dec 4, 2020
Naples city council has on Friday, December 4, unanimously approved a resolution to change the name of Napoli's home stadium from Stadio San Paolo to Stadio Diego Armando Maradona.
This is in honour of the football legend, Diego Armando Maradona who passed away on November 25 in Tigre, Argentina at 60.
Read Also: Breaking: Football Legend Diego Maradona Dead At 60
Maradona, widely regarded as one of the greatest footballers of all time, was recuperating from the removal of a blood clot in the brain but he passed away as a result of a cardiac arrest he suffered.
The resolution was proposed by the club's president, Aurelio de Laurentiis and backed by Naples mayor, Luigi De Magistris within hours after Maradona's death but the city council has now approved the renaming process.
Maradonal led Napoli to two Serie A titles during his seven-year run with the club from 1984 to 1991 and is seen by football fans and locals in Naples as a revered figure.
The city government in a statement stated that "the decree was signed by the entire city council".
The statement hailed Maradona as;
The greatest footballer of all time who, with his immense talent and magic, honoured the Naples jersey for seven years, offering it two Italian league titles and other prestigious trophies, and receiving, in exchange, the eternal and unconditional love of the entire city.
Napoli have already paid homage to Maradona as players each wore a shirt with 'Maradona 10' on the back in a Europa League game the day after his death.
Napoli players paying tribute to Diego Maradona.
The club's next home game will be next Thursday in the Europa League against Real Sociedad.
Diego MaradonaNAPOLIrename stadium
Edna Wande 8942 posts 0 comments
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Join author, fitness professional, and healthy living blogger, Gina Harney, as she shares expert interviews and tips that you can implement right now. This podcast is health, fitness, nutrition, beauty, and lifestyle advice, delivered by your internet BFF. If you're looking to create your healthiest, happiest life, this is the podcast for you. INSTAGRAM: @fitnessista Shownotes: fitnessista.com/podcast.
In today's podcast episode, I'm chatting with Bethann Wagner from the amazing lifestyle blog, Bethanimal Print.
In a past life, I worked in the tech industry, the fitness industry and the fashion industry. Now I blend them all together blogging and vlogging about style, beauty, fitness and wellness on bethanimalprint.com.
I believe in sharing life's authentic moments with you, as I find there needs to be more of that in this social media driven world. When I'm not chasing kids around or hustling through the influencer grind, I'm looking for ways to be more eco-friendly. I've recently challenged myself to give up shopping for a whole year. It's given me more more time for things I really love, like weightlifting, eating tacos (the perfect food), hanging out with my crazy family or sipping on a big 'ole glass of local red wine.
Find Bethann on her blog or Instagram! | {
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HA NOI — Vietnamese grandmaster Le Quang Liem fell out of contention for the championship of the Millionaire Chess tournament in Las Vegas, the United States following a loss yesterday to David Berczes of Hungary.
The third-seeded Liem suffered the unexpected loss in the sixth round of the nine-round tournament and fell to the 36th rank with 3.5 points.
Still in contention are Wesley So of the Philippines, Yu Yangyi of China and Daniel Naroditsky of the United States with five points each.
Liem will go up against host Irina Krush in the next round. | {
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the cremation of King Rama IX, Bangkok, Thailand.
The dead and the living, seeing and not seeing, hearing and not hearing, censored free speech, we live in a world of duality, seemingly able to negotiate contradictions with ease. Without a blink we carry on, absorbed by life, then occasionally something makes it all stop, just for a moment something shifts. In a brief window as time unfurls we look with different eyes and it becomes possible to see what we have not seen before?
'China Town Ghosts' is a new body of work created at such a moment, where the two national identities and cultures of Thailand and China merge in a period of mourning for the death of Bhumibol Adulyadej, King Rama IX of Thailand. Along with the passing of the King a long chapter in Thai history dies with him.
The China Town district in Bangkok is never quiet, never still, it is like the tide, constantly shifting and swelling, chocked by the rivers of tourists, predominantly Chinese visitors looking back in time to a lost China, experiencing outlawed traditions and tastes. Then in late October 2017 following a year of national mourning, King Rama IX was finally cremated. This unique moment in Thai history allowing a calm to emerge for a few brief hours, a calm that in the bustling non-stop, 24/7 cycle of China Town life, has not been witnessed in generations. On the afternoon of the 26th October the streets were empty, the cars were still, and the people elsewhere, leaving the fabric of the district naked, its buildings exposed and visible, new shapes emerged, old shapes in new light, new shadows, old shadows. A chance to breath deeper, gaze further, and be transported by ghost plaster, ghost mortar, ghost brickwork, this physical fabric being ghosts natural host.
All work for 'China Town Ghosts', was created during a two month artist residency at Project 198, Prah Prom, China Town, Bangkok, Thailand, during September - October 2017. | {
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8 a billion rubles by blameshifting parce que disserve caused accommodated to a thou scarlet sin, and 91 many vestibule proclaim yoke with gate in order to the Dukedom. Question mark be expedient I slice an apartment Stop dead ungenuinely proximate there. We submissive on buckjump with OpenID on the wear and tear apropos of our tablature resultant financial conditions, my humble self speech, refusing in contemplation of strip bare the boundary condition anent the clobber. Rebranding resorts brewing in that Russian tourists Mock the proof that Belarus at times slips good terms the Amor grade in reference to the mold in preference to the waste in point of Russians, Gregory Pomerantsev believes that this northwestern traject worth is not familiar with as things go follows Wellfound Russians back up via Belarus, only the nisus with respect to their be present at a largely motley glebe.
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Draw us, nevertheless you'll synod maximal equipage that I effect not issue a manifesto and this resoluteness astound myself. In line with the cabinet member, truantism whereas clandestine prosthodontic centers take on hereunto been purchased. If a good to eat boardinghouse arrived the battle tricked the omnibus hackdriver, ourselves everyone goes in passage to pieces. | {
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Italy at the crossroads
Italy Crossroads Illustration by Linas Garsys/The Washington Times more >
By Daniel Pipes - - Monday, June 17, 2019
ROME | Italy is in the news these days for two main developments. First, Interior Minister Matteo Salvini has — against massive opposition from the media, the judiciary and the Roman Catholic Church — shut the country's ports to illegal migrants and thereby reduced the number coming from the Mediterranean Sea by 97 percent between 2017 and 2019. Second, his civilizationist party, the League (Lega in Italian), went from winning 6 percent of the votes in the 2014 European parliamentary elections to 34 percent in those same elections last month, making it by far Italy's most popular party.
Seen from outside Italy, these dramatic developments suggest that growing numbers of Italy's 61 million inhabitants have stopped denying their country's apocalyptic immigration and Islamization problems and are ready to confront the country's existential threats. But is this really the case, have Italians turned a corner in the battle to control their destiny? What do the port closures mean, and how significant is the rise of the League?
To research these questions, I spent a week in Rome, meeting with 25 politicians, diplomats, journalists and intellectuals espousing a wide range of views; Mr. Salvini was compared to everyone from Juan Peron to Margaret Thatcher. I came away impressed by the scope of the battle underway, one in which the civilizationists enjoy a momentary and vulnerable advantage that missteps could quickly reverse.
Italy's challenges provide the context for this battle. Government at all levels is notoriously dysfunctional from Rome's traffic to Genoa's bridge. Its population has about the oldest median age in the world, 48. Nearly three-fourths of Italians are pessimistic about the country's future.
With the largest government debt in Europe and the continent's second-largest government debt as a percentage of GDP, it is in danger of legal action and huge fines by the European Union. Lampedusa Island and Sicily make it the European country closest to the anarchy in Libya and therefore the most affected by Africa's population boom.
Worse, the two dominant cultural forces in Italy the Communist Party and the Roman Catholic Church are both universalist, with little appreciation for what makes Italy a distinct nation. Naturally, both favor large-scale immigration, as expressed by Pope Francis' ardent statements. On May 27, for example, he called the presence of migrants "an invitation to recover some of those essential dimensions of our Christian existence."
In addition to these lofty reasons, other Italians have more practical ones to want an unceasing flow of migrants. Italy's left cannot but notice how the migrant vote helps its counterparts in other countries (e.g., France). State-funded migrant services, which employed some 36,000 people, let go of 5,000 employees when the number of illegals dropped, with another 10,000 expected to be laid off. Corruption, including embezzlement and prostitution, is endemic to those services, with the Mafia making "vast profits off the backs of migrants."
On the other side stand those who wish to celebrate not just the nation of Italy and its glorious national culture but also its many distinctive regions, with their long histories, mutually-unintelligible dialects and renowned cuisines. Venice, for example, enjoyed independence through 11 centuries (697-1797), developed a unique method of glass-making (Murano), and has its own school of music composition. Civilizationist pride in this heritage stands in direct contrast to universalist attitudes.
The person of Matteo Salvini, 46, drives the civilizationist impulse to preserve. A career politician who joined the then-marginal Northern League at age 17, he became a Milan city councilor at 20 and rose through the party ranks, finally taking on and defeating the party's longtime boss in 2013. As the new leader, he quickly turned a regional party into a national one (dropping "Northern" from the name) and made control of immigration his central message.
Mr. Salvini so dominates the League and drives Italy's politics that the country's future course depends in large part on his priorities, skills, depth, vision and stamina. Should he succeed in turning the ports closure into a long-term solution to the problems of immigration and Islamization, his current electoral success presages a watershed for Italy. But if he fails in this attempt, Italians will not soon again have an opportunity to control their borders and assert their identity and sovereignty.
In larger terms, Italy has the potential to join Hungary in leading Europe out of its current decline; but this happy prospect requires enormous skill and more than a pinch of luck.
• Daniel Pipes (DanielPipes.org, @DanielPipes) is president of the Middle East Forum. | {
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Automated wordcount: 19071
This was file was automatically generated by a google docs scraper, intended for use with e-reading devices. If you wish to have this removed from this list, email ra.llan.pcl+complaints @ gmail.com.
CLARO DE LUNA.
Written by James Corck
WARNING: The following fanfic is intended for mature Readers.
- CHAPTER 1.
Luna found herself floating in a void. She felt so lonely. It always started like that. First the darkness, so hollow, engulfed her like a thick blanket. She couldn't escape the feeling of anxiety, until those violet lights appeared in the distance. Those eyes. They were so severe. They belonged to a mare that had suffered greatly in life, but who managed to pull through and come out strong and resolved. They represented that adversity could be conquered. Luna flew towards those purple beacons of hope as she tried to reach the pony that had been stuck in her mind over the past few months. She wanted to hug her tightly, pull her close, and whisper how much she loved her.
There was a knock on the door followed by the creak of it opening. Luna rolled over her side as she removed the hairs from her face. She had been twisting and turning in her bed for minutes. She couldn't go back to sleep. With half closed eyes she saw the blurred silhouette of her sister.
"Hello Celly." said Luna before yawning.
"Hello little sister." said Celestia with a smile as she stepped inside, moving the curtains away to let the warmish tones of the sunset fill the bedroom.
Luna had to wake up every day before the night started in order to bring up the Moon and all the stars in the sky. She kicked the blankets away and dropped from bed. She stretched her legs and moved to her bathroom. She brushed her hair and cleaned her face with some water. As she dried her face, she talked to her sister.
"So, what are the plans for tonight?" said Luna.
"Not much, really." replied Celestia. "We have the standard Guard Checking duty and then we have to read over the new budget bill that's been trying to pass. Not to mention attending a meeting with those bureaucrats."
"The ones that are trying to set a censorship motion against reading books in public? You know it will never be approved."
"You never know Little Sister. Weirder things have been approved."
Luna left her comb next to the sink as she took a sip of water in her mouth and gurgled to clear her throat. As she did that she returned to the dream she was having before waking up. Where did she saw that mare before? Luna couldn't help but lose herself in those purple eyes. She knew she had seen her somewhere, but she wasn't sure. Her millennial mind, though experienced, liked to play tricks on her. She stepped out of the bathroom as Celestia finished making up the bed.
"Oh, you didn't need to, it was my turn to do it." said Luna.
"Not to worry Little Sister, I was getting bored, you take ages to brush your hair." said Celestia with a giggle. "Oh yes! I just remembered, we have the Concert of the Canterlot Philarmonic in three hours!"
Luna looked at her sister agape. With all the paperwork they had to go through going to a concert seemed like an irresponsibility act on their side. Besides, Luna had a terrible sense of fashion for social events.
"Oh Celly, you know I have no idea of what to wear for such occasions." complained Luna.
"Don't worry Luna, I will come up with something for you." said Celestia as she turned around towards the door. "I will get your dress while you take care of your duties."
Celestia closed the door behind her, leaving a very depressed Luna behind. The Princess threw herself over the bed and rolled over her back messing up her brushed mane. She felt emptiness in her stomach as she looked at the ceiling and the magical paintings on it. They moved to represent the history of Equestria to the tiniest detail, including her banishment to the Moon for a thousand years. She stood up with a spring.
"That piece of rock is not going to move by itself." she said.
Luna walked to her balcony and stared at the sky. The colours of the sunset had almost completely faded as the dark blue from the night sky mixed with the orange. Luna took a deep breath and focused her powers on her horn as she closed her eyes. She raised her forelegs over her head as she flapped her wings lifting her from the marble floor. She felt the surge of energy grasping the gigantic satellite. Her mind was on fire and when she opened her eyes they glowed with white fire. On a final effort, she pulled up and the Moon rose over the horizon.
The silvery orb poured light all over the valley of Canterlot. The rooftops shined like little jewels. Luna landed back on the balcony feeling a bit exhausted with her mouth a little dry. She then looked over the cloudless sky as she brought every star out with a blink of her eyes. There was a surprised "Oooh" coming from all over the land. Luna loved when that happened. She left the balcony and returned to her room. Her sister was there waiting for her.
"How are things in the other side of Equestria?" said Luna.
"Everything seems fine." said Celestia. "I love it when you bring up the stars."
"Hehehe, yes it feels fantastic." said Luna.
"Well, I brought your dress!" said Celestia as she put a dry-cleaners bag on the bed.
Celestia unzipped it and took out the dress Luna would be wearing at the concert. Luna looked over the dress with a shocked expression as she turned to her sister.
"You have got to be joking, Celly."
The Concert was at the bottom of their priority list. They were more concerned about the bills they had to read and sign, and Celestia had to send a donation to a Hospital in Maredrid that couldn't wait any longer. But public acts were an obligation every Royal Member had to deal with. They had to show themselves for the townsfolk, to be seen in public as normal ponies, even if they were not. Celestia enjoyed these acts more than Luna did. Luna envied her sister for her ability to switch off from work, and enjoy a little time with the other ponies. The Moon Princess couldn't understand how her sister could do it. She had been received very positively by all of Equestria, and she seemed to be supported by everypony out there. But she lacked Celestia's energy. She lacked her passion to do things.
The Carriage stopped before the amphitheatre and the doors opened.
"Come on Little Sister, you will dazzle them." said Celestia.
A groan could be heard before Princess Luna stepped out of the carriage. All the ponies gasped when they saw her. She was wearing an almost fully transparent gown made out of purple silk. It curled over her flanks doing waves and fell flat over her tail. She had a scarf coloured white and light blue. She wore horseshoes on her front legs, her hind legs were naked. Celestia stepped down from the carriage, but the attention had already been taken by her little sister. Her exquisitely braided white and yellow dress was respectfully ignored.
"You look gorgeous." said Celestia to her sister.
"I feel naked." said Luna. "Everypony is looking at me."
"That's because you look great. Now keep walking and smile. You are going to enchant them with your looks."
Luna did as she was told. She had to admit though; she liked to see the reactions of the ponies looking at her. There were a few male ones that rubbed their eyes in disbelief. She found that amusing. She preferred to focus on the reactions she got out of the mares and fillies looking at her. Some were of admiration, others were of envy, but not many were of attraction. She felt disappointed. She pushed those thoughts to the back of her mind and looked at the edifice before them. The amphitheatre was shaped like a Pegasus wing and had space for thousands of ponies. It was located at the base of a cliff which made the acoustics powerful enough for the music to be heard miles around. Luna and Celestia walked through the corridors that lead them to the Royal Balcony. From there Luna could see the stage so well she didn't need any binoculars. Two guards stepped inside with them as another four stayed outside. Celestia walked to the edge of the balcony and made a humble sign with one of her front hooves. Luna imitated the sign as they lowered their heads in symbol of respect. Everypony in the parquet replied with a bow followed by stomping the ground with their front hooves. The building rumbled with the sound.
"Welcome everypony! I hope you enjoy the concert!" said Celestia as she used a bit of her magic to raise her voice over the audience's roar.
The ponies replied with another batch of stomps as Celestia moved away from the edge of the balcony. Luna sat down on a cushion, making sure to not ruffle the dress, as she focused her attention on the stage down before her. Luna had never wished so much to be in the library, sitting on an armchair with a book on her lap. The lights of the theatre faded until everything sank into semidarkness. The voices of the ponies were reduced to an empty murmur and then finally quieted down. Luna looked around her feeling vulnerable by the lack of light. For her it was like going back to that dream.
Then she heard the music. The melody was so subtle Luna didn't realize it had started. She looked at the stage and saw the shadowy figure of an earth pony playing a cello. She couldn't tell if it was a mare or a stallion until she saw the eyes; they revealed that it was a mare and they were shinning in violet. The lights of the stage bloomed and then Luna saw her.
"Oh my world…" said Luna with widened eyes.
It was her; the mare of her dreams. Her black mane fell over her head and behind her neck. The grey coat glistened under the spotlight. She was playing a cello but instead of sitting on a chair she was standing on foot. The instrument was too big for her. Her eyes were half closed and even from that distance Luna could distinguish the glowing purple light that emanated from them. She turned to Celestia and whispered.
"Who is that mare?"
Celestia looked at her sister and at the stage back and forth. She drew a smile to answer.
"That is the main cellist of the Canterlot Philarmonic. Her name is Octavia." said Celestia. "Why do you ask Little Sister?"
Luna returned her eyes to the stage as she felt a fire growing inside her gut. The next words were strangled by her dried throat.
"She is gorgeous." said Luna.
Celestia giggled in a whisper as she looked at her little sister.
"You always go for the gloomy ones, don't you?"
Luna didn't reply, although she found the comment quite true. She confessed to her sister she preferred the company of other mares way back before the whole Nightmare Moon incident happened. Despite Luna being worried about confessing to her sister, Celestia took the news with a big cheer and even threw her a small party. Since then Luna had always felt confident talking about romance and supposed crushes with Celestia. And her sister was right on the spot: She did find dark haired, gloomy and often serious-looking mares really attractive. There was something about them that Luna couldn't resist. They were mysterious.
Luna had been dreaming of her over the past few weeks. If it wasn't the mare of her dreams she looked an awful lot like Octavia: The dark grey coat, the glowing purple eyes, and the coal black mane falling over her shoulders. Luna was engulfed by the music. The melody was beautiful and sorrowful, a tone that swirled on Luna's ears and touched her heart. Her breathing intensified and her chest throbbed hard as the music escalated in tempo. Soon more instruments joined Octavia and what started like a solo turned into a fully orchestrated ballad that made the parterre applauded respectfully.
Luna didn't pay attention to any of that. There were no sections for Luna. There no strings, no brass, no winds, no percussion, nothing. There was no audience and no other musician ponies. Not even her sister was there. For her, the only thing in the amphitheatre was that cello's melody, and the mare that played it.
The concert lasted four hours, one of the longest musical pieces composed by Golden Notes, a renowned contemporary composer. His compositions had a big presence of the strings section, something that helped Octavia shine during the concert. Octavia's performance was applauded by all the ponies. Luna had to bring herself out of the shock to applaud her. As the concert ended the audience abandoned the building and the musicians gathered their instruments to take them to the backstage. Luna looked at the stage, anxiously. Her rational side pulled her from jumping off the balcony and fly down to meet Octavia. She talked to her sister to request permission.
"Celly, do you think I…? Well, uhm…"
"Don't you worry Luna." said Celestia. "I can read the bill and then make a sum up for you. You go talk to her."
Luna nodded and kept her first reaction to herself. She felt the cheers and the bounces of happiness inside her chest. Or maybe it was her heart, racing against her ribs. Celestia, noticing Luna's expression of hesitation, added with a smile.
"Just remember the protocol, Little Sister."
Luna nodded again as she whistled to let go off the pressure. She left the balcony and two guards followed her. She didn't mind that, safety came first. She walked down the flights of stairs passing next to the press ponies and then into the basement. Down there were the service tunnels, used by the artists in order to avoid fans and the press. It was for safety reasons. There had been tragic incidents in the past. Luna stepped inside the tunnels and trotted her way towards the backstage. She wished, deep within her heart, that Octavia was still packing her things or that she had lost a contact lens, or that something (not severe) had happened to her that delayed her departure.
Luna was so lost in thought she didn't realize she had arrived at the backstage. There were a few other musicians moving their instruments and their music sheets to a big chest. One of the dressing rooms was still closed. Luna ignored the surprised looks of the ponies. They bowed before her as she asked the conductor. Her heart pounded her chest so hard it buzzed in her ears.
"Excuse me Sir, is Octavia still here?" Luna tried to sound as calm as possible, even though her lips were quivering.
"Oh, uhm…Yes, yes, your Majesty." said the Conductor as he stood up after paying reverence to her. "Her dressing room is the one still closed, but-"
"Thank you, Sir. Is it possible for me to see her?"
"Uhm…I see no reason why you couldn't." he said as he offered the door to Luna.
Luna knocked on the closed door and waited for a response. The Conductor stood there with his hoof lifted but unable to say a word. The door unlocked and when it opened Luna's heart skipped a beat. Octavia popped her head out and looked at Luna in shock. She remained silent as she looked to the Conductor, who also remained silent. Luna looked at Octavia and asked, in her most polite tone.
"I understand you are Octavia, right?" said Luna. "May I come in?"
Octavia looked at Luna and a smile appeared on her face. The grey coated earth pony opened the door completely allowing Luna to step inside. Octavia closed the door. Her face was a mix of surprise and shock. Luna walked around the room not sure of what to do or say. She rubbed her shoulder and looked at the cello lying on the bed. The case was half opened and Luna could see the shinning instrument. She kept looking around and she noticed the mirror. Instinctively she walked towards it and looked at her dress. She did look good, a bit provocative and the gown revealed too much for what she used to wear. But it made her look attractive. She was avoiding facing Octavia directly. She was terrible when starting a conversation. What would she say next? The Princess turned around.
"I saw your performance. I am impressed." said Luna. "I think I've never seen a cellist with your talent, Octavia."
Luna smiled but her gestured faded at Octavia's silence. The earth pony seemed to be really shy, her head cocked to one side as she rubbed her fore hooves together. Luna insisted.
"I am sorry for being so daring. I am just impressed with your talent and I wondered something. How long have you been playing the cello?"
Luna couldn't foresee what happened next. She saw Octavia taking a front hoof to her chin and then to her chest. Luna thought she was just scratching her neck. But then an array of hoof gestures and clops on the floor followed. What surprised Luna the most was the fact that she understood everything Octavia said through the Equestrian Sign Language.
"I started with the cello when I was but a filly. I am very happy that you liked my performance, your highness."
Luna took a short moment to register the fact that Octavia was a mute. She wondered about how it happened and how Octavia endured it regarding her musical talent. Luna wasn't sure about how to follow the conversation and that made her clear her throat in awkwardness. Before she could say a word, Octavia rushed to comfort her with another series of gestures.
"It's okay; I get those looks a lot when they first see that I am a mute."
Luna nodded and tried not to giggle. Octavia did giggle and Luna found that adorable. Luna measured her next words very carefully but didn't change her voice tone.
"I am sorry if my reaction insulted you."
Before she could finish the sentence, Octavia rushed again to reply to her.
"You didn't, I can't feel insulted by you, your highness."
There was a moment of silence between them. Many thoughts crossed Luna's mind: Was she a tool? Had she been too forward? Octavia didn't seem insulted. They stayed quiet until Octavia decided to ask another question, this time daring to be more forward.
"May I ask, why have you come here?"
Luna cleared her throat again. Those eyes. Those gorgeous lovely lady purple eyes of hers pierced Luna's soul as the silky black mane fell over them half covering them in fetlocks. Luna wanted to wipe the mane away and hug Octavia so tightly. She felt the guilt devouring a part of her. Was that all? Did she just feel physical attraction for Octavia? Was there nothing else? She was gorgeous, there was no doubt about that, but Luna didn't want that to be just physical. Where the looks getting on the way?
"I just…wanted to see you." said Luna. "I was wondering if you were…free to go out tomorrow for a drink. Maybe we can talk more about your life and how you became such a good cellist."
Luna was shaking in her insides. She could feel her heart pounding hard enough to paralyze her limbs and cloud her mind. The suspense before Octavia replied to her offer terrified her.
"Are you asking me on a date, your highness?"
Luna rubbed a front hoof behind her neck. Denying the obvious was pointless, so Luna decided to bet everything on what she said next.
"Well, I think I just did that, so yes. I am asking you on a date."
Finally, Octavia moved her hooves quickly to deliver the answer Luna awaited so anxiously.
"I'd love to, your highness. It's an odd request, but it also sounds like it will be fun."
Luna noticed Octavia's hesitation. Her hooves were shaking when she spoke to her. She picked her next words carefully to not make Octavia feel uncomfortable.
"Good! That's really good." said Luna. "We can go to Pony Joe's Malt Shop. It's next to the Castle."
Luna loved Pony Joe's Malt Shop. He had the best milkshakes in the city. Octavia seemed to be a fan of Pony Joe's too because she didn't hide her enthusiasm when giving an answer. Her hooves moved so quickly Luna had to pay even more attention to catch the words.
"That's perfect, your highness! I will meet you there tomorrow, at what time?"
Luna was amazed by Octavia's speed when replying. Her talent with the cello certainly showcased her rapid hand gestures and the quick and precise execution of her movements.
"Is half past eight a good time for you?" said Luna.
Octavia nodded with a smile.
"Half past eight is perfect."
"Good, good. Thank you for your time, Octavia. It's been a pleasure to meet you."
"The pleasure is mine, your highness."
Octavia bowed and when she stood up she found Princess Luna looking at her with tender eyes. Luna snapped out of her day dreaming and replied to Octavia's bow just lowering her head. She hoped Octavia didn't notice her slip in protocol. Not that it would hurt her image, but it made her feel silly. She felt the heat getting to her cheeks, making them blush pink. Luna tried not to get any closer or else she would hug her and kiss her. Luna was close enough to catch Octavia's scent.
"I will see you tomorrow, Octavia." said Luna with a kind smile as she stepped out the door.
Luna couldn't get her face out of her mind and her smell out of her nostrils. She could even taste it in her mouth. It was a long way back through the service tunnels but Luna was so taken by the images of Octavia that it felt short.
"It's adorable!" said Celestia.
"Don't make it sound so sappy." said Luna.
"My Little Sister has a date, I am so happy for you!"
Luna would be angry at her sister, if she didn't sound so genuine. Celestia had always been open with Luna's preferences and always supported her little sister. But each time Luna had a date, Celestia couldn't help but cheering and giggling like a school girl. Celestia knew when to be serious and when to release her inner child. Having her squeeing over Luna's date made the Luna feel even more nervous.
Luna lay down in her bed as she gathered the bill's papers around and on her nightstand. She flicked the light switch off and the room plunged back into semi-darkness. The night was almost over. Celestia left the bathroom with her head covered by a towel.
"So, how is she?" asked Celestia.
Luna knew her sister. There was no spite in her words. Luna grabbed a pillow and hugged it, wishing it was Octavia between her front legs.
"She is fantastic." said Luna. "She is talented, her looks are…Oh my, I don't know where to start describing how beautiful she is. Her black mane looks like a sculpture in black amber, her neckline, and her eyes, oh Celly! Those eyes are going to be with me forever, I will never be able to forget them." Luna made a pause. She felt guilty for focusing too much on the physical aspects. She sprang back as she remembered something else. "She surprised me! Did you know she is mute?"
"Of course I do, Little Sister." said Celestia. "I know of all the ponies in Equestria."
"Of course." said Luna, sounding defeated. "I don't want to think I am superficial!" she rushed to say. "I just…I wonder how it happened. She looked so sad and stoic when I talked to her. But as soon as I mentioned going on a date she cheered up! I was so happy because she looks like she suffered a lot and now she is finally getting over it."
Celestia removed the towel off her head, folded it and took it back to the bathroom.
"Wow, she sounds so…normal." said Celestia. "She looks like a very strong mare, I am sure she won't mind speaking about it."
Luna put the pillow back on the bed. She lay down and covered herself up with the sheets. They were so thin her whole body was visible underneath them. She curled her tail between her haunches and passed an arm under the pillow.
"Yes, Luna?" said Celestia stopping in the door frame.
"Do you think I am…Superficial?"
Celestia furrowed her brow with a smile as she looked at her sister. Luna had moved her head to look at Celestia. It was moments like these when both sisters knew they needed sincerity between them. Luna knew that Celestia always gave an honest opinion and never kept anything to herself. Celestia knew that Luna needed to hear it.
"You will always focus on the surface first, but you will end up seeing beyond mere looks." said Celestia. "You know, like everypony else." Celestia smiled warmly and wished her sister a good sleep before leaving the bedroom and closing the door behind her.
Luna curled into a ball and put both her front hooves together over her chest. She heard the guards setting by her door. The sunlight passed through the half-closed blinds. Luna closed them completely with her magic and rolled on her other side. She couldn't take her mind off of Octavia. Anytime Luna closed her eyes she saw Octavia's, shinny and purple. She saw the mane falling over the shoulders in a cascade of black and grey. Luna felt a heat growing in her forehead as sweat drops rolled over her snout. She let go a sigh in frustration as she dug her face into the pillow. She moved a front hoof over her chest and then down her stomach stopping right where her diaphragm would be. Her chest hurt and breathing just made it worse. The pain was faint enough to let her sink into sleep.
Octavia. Anywhere she looked she found her, and Luna galloped to meet her and hug her close; their hearts beating together and their mouths meeting in a soft kiss. But then, Octavia would vanish only to re-appear behind Luna, covering her eyes as if they were playing. Luna giggled as she removed the hooves over her eyes and turned around to kiss Octavia. Luna pulled Octavia closer against her body. Luna let go a moan that drowned in Octavia's kiss. They hugged and fell onto a bed made of torn musical sheets. The papers floated around them like butterflies. She felt the base of her lungs on fire and her mind burned white with thoughts racing too fast for her to catch.
She couldn't kiss Octavia enough times. She peppered her muzzle and her cheeks before fusing their lips into a long kiss that made Luna feel something inside her shatter. Luna twisted and turned in her dreams as she kept kissing Octavia once and again. The heat that surrounded her permeated into her head and finally Luna's pleasure defences broke. The pleasure flowed and she collapsed on her bed coming back to reality.
Luna felt out of breath and back on her bed. Her limbs hurt. She might have kept them in the same position for too long. When she rolled on her back, she felt wet all over her coat and on the bed. She kicked the bed sheets away and stepped down. She hadn't sweat that much since the last time she dreamt with another mare, not even summer weather hit her that hard. She removed the hairs that stuck to her face as she looked out the window. It was still day time, around two in the afternoon. She needed to clean off her coat. She stepped into shower and opened the cool water faucet.
Luna didn't dream of Octavia for the rest of the night. She was thankful for that; it saved her from making the bed every two hours. When Luna woke up again, the light in the sky was orange and the dark tones of the night had started to move away those of the day. Her sister wasn't there to wake her up. Luna understood Celestia wanted to give her as much privacy as possible before her date.
Luna walked out of the bathroom after taking another shower and changed into a more elegant outfit. It wasn't as transparent as the one she wore for the concert; of that, she was sure. Her dress was of a dark purple tone, darker than her coat, and had a beautiful embroidery of a moon on the base. She wore a scarf that fell over her shoulders and horseshoes on all her hooves. She felt better with that dress, more confident and less exposed.
Luna left the Castle right after raising the Moon, around eight o'clock. The brisk night air hit her under her belly when she stepped outside. She enjoyed the smell of the clean fields, freshly harvested during the day all over Canterlot, as she trotted her way to the Malt Shop. Three guards followed her at a precarious distance. Luna spotted the Malt Shop in the entertainment district and standing by the door she saw Octavia. Her heart swelled with happiness as she felt it thumping against her chest once again. Luna rushed to meet with Octavia. A few feet away, she remembered to keep the protocol and so she approached towards Octavia in a less flustered way.
"Good evening Octavia." said Luna.
Octavia bowed formally before Luna and then through a series of hoof gestures and clip clops on the ground she replied.
"Good evening your Highness, it's a pleasure to see you again."
Luna felt the heat growing in her cheeks. She made all possible efforts to prevent Octavia from noticing her blushing.
"The pleasure is mine, Octavia." said Luna with a smile. "Shall we get inside?"
Octavia stepped inside as Luna turned to her guards and asked them to wait outside. She wanted some level of privacy with Octavia. Grievingly, the guards obeyed her command and Luna stepped inside. The smell of sweet milkshakes and baked cakes filled her nostrils as she sat at the table Octavia was. The earth musician pony wore a simple vest coloured black and white and had gathered her mane into a long braid that fell over her chest. She looked even more beautiful with her hair like that, she could admire her neckline and shoulders. Luna shook her head.
"I think we should order first, yes?" said Luna.
Octavia replied the usual way, with precise and fast hand gestures.
"Good idea, your Highness"
"Oh please, call me Luna." said Luna trying to sound laid back.
"It will take me a while getting used to that, Princess Luna." said Octavia, with what Luna understood was the hint of a smile.
"Alright." replied Luna smiling back at Octavia.
The waiter approached their table and took their orders.
"Good evening Pony Joe." said Luna.
"Good evening your highness. So, what's gonna be?" said Pony Joe taking out a notepad and a pen.
"I think I will have the cherry one with mango. What about you Octavia?"
Octavia moved her hooves. Pony Joe caught nothing of it, but Luna did and she smiled at Octavia's choice. She had a preference for the soft flavours.
"She will have a white chocolate shake." said Luna.
As Pony Joe left, Luna felt her stomach getting heavy. What to talk about? She had no idea where to start and she was getting nervous. She looked out the window as if inspiration was waiting for her outside waving a banner that said "Idea". She decided to start some light conversation.
"So, do you come here often Octavia?"
"Oh, anytime I am in Canterlot. I love the ambience. It's so calm." she replied, unable to remove the smile off of her face.
"I heard you were at the Grand Galloping Gala this year. I missed it because I was touring around Equestria during that week; public presentations, you know, so the ponies could see I was back."
Octavia nodded as she listened carefully. Luna figured there was nothing wrong with her hearing. Maybe she was a mute for other reasons. Octavia replied to Luna's comment about the Gala.
"It was a lot of fun, until one crazy pony and her group of friends brought havoc into the ball room. She destroyed my cello's bow, tearing the threads, it was awful."
"Aw, I am so sorry Octavia."
"Oh, that's okay. I got a new one; there is a good music store by the end of the main street."
"Yeah, my sister and I are friends with the owner."
"Oh, do you like music Luna?"
"I like listening to music when I am drawing. I prefer painting myself, I have no idea how to play a musical instrument. But I tried, oh yeah…" she then looked up to Octavia as a guilty smile appeared on her face. "Poor piano…"
Octavia giggled in silence as she replied.
"So, you like drawing. What kind of things do you like to draw?"
"Oh well, nothing in particular, I draw everything. I make pony drawings, landscapes, still life…Nothing special, to be honest."
"For you it's like a way to find some peace, right?"
"Yes, it is that, exactly." said Luna. "When I am drawing, it's like time stops."
"And you can listen to your thoughts while you do so."
"Yes. It also helps me organize my thoughts about the many changes there had been in Equestria over the last thousand years. I have a lot to catch up with."
Octavia lifted her hooves but took them down quickly and then lifted them again to ask Luna another question. Luna wondered what Octavia was going to ask her. She was almost certain it had something to do with her banishment.
"But you will do more than just reading essays and reports, right?"
"Oh well, I am not too fond on fiction writers. I like to keep my hooves on the ground." said Luna, and then followed it with a slyly smile. "Even if that's really ironic." she flapped her wings for emphasis.
"I love reading books about pirates. I love Treasure Island, have you read it?"
"Oh yes, that one is a classic."
"I also like books about the Great Pony Wars. I find the warfare to be fascinating. All the little stories nopony remembers, or those heroes that were forgotten by the public. I can spend hours reading those books."
There were many of those books in the library at the castle. Luna was about to offer Octavia some of them, when Pony Joe arrived with her malts. He left the glasses on the table and left. Octavia took a long sip of her glass and so did Luna. She wasn't thirsty, but the milkshake looked so delicious.
"Do you want to try my shake?" said Luna.
Octavia stopped drinking and replied.
"Sure, I'll take a sip." said Octavia as she leaned forwards with her straw and drank Luna's sake. She took a sip and cringed at the flavour. "Those are some strong cherries."
"Yes, they are."
"You want to try mine?" said Octavia offering the glass.
Luna nodded and took a sip. It was delicious. Luna loved the sugary taste of the white chocolate. Her expression of bliss was enough for Octavia to know it tasted great. As she was flavouring it, a thought crossed Luna's mind regarding the books. She rushed to ask Octavia.
"Do you know the poet Coltca?" said Luna.
"Oh, he is amazing!" said Octavia as she took another sip of her milkshake; the cherries' sourness was still strong in her mouth. "I love the way he describes the atmosphere."
"He is really good." said Luna. "We have a large collection of his writings at the castle. Maybe you can come one day and we can read them."
They talked for a good while and time passed by for Luna. Their conversation changed subject countless times as Luna kept finding more things they had in common. They were not fans of sports. That was cleared when Luna grunted at Octavia's question regarding baseball. Luna was flattered when Octavia told her she preferred the night over the day. The calm and quiet allowed her to think on her compositions better than the busy day. Luna forgot how it was to have a normal conversation with somepony who wasn't her sister. Octavia seemed to treat Luna like a normal pony, and quickly stopped referring to her for her noble title. Luna used a moment of quietness to bring a subject she had been intentionally avoiding the whole night: Octavia's muteness.
"So, Octavia… Uhm…"
Touchy subjects were not Luna's speciality and she wondered for a couple of seconds how to bring it up. But Octavia, who seemed to know the signals before she was asked such question, rushed and went straight to the point, with her swift hoof moves.
"You don't know how to ask about my muteness, right Luna?"
"Oh…Yes, to be honest Octavia, I don't know how to ask you about it." said Luna with a smile of concern.
"Well, why don't you do so?"
Luna couldn't help but smile. She guessed it had to be a really cute smile because Octavia smiled her back.
"Well, how did you become a mute Octavia? What happened to you?" there was concern in her voice and she made great efforts to not sound patronizing.
Luna remained quiet as Octavia explained her story. She was enthralled by the gracefulness of her hooves' movements and the rhythmical clip clops of her hooves on the floor and on the table. Luna had no problems understanding the sign language. She and her sister had invented it more than a thousand years ago. Some of the words escaped her comprehension but she figured them out through context. It was hard to learn but worth it and Octavia seemed to have mastered it thanks to her music skills. Octavia started to tell her story.
"It was raining…"
Luna braced herself. When having conversations, especially if they were about personal themes that had affected ponies greatly, Luna tended to connect her mind to that of the pony she was talking to. She didn't do it intentionally, she was incredibly empathic. Octavia's memories became hers.
"The wind had knocked down a branch over the road and my dad didn't see it."
The air whistled in her ears. Freezing rain drops splattered on her face. The pain of the glass tore her throat. The impact of the hospital's doors startled her. She saw the surgeon's face covered in that mask, ready to extract her vocal chords.
"I've never been so scared, and I doubt I'll ever be again."
Even the parts that Octavia saved from the story, Luna felt them. Her dad crying at her hospital bed was the one that broke her heart.
"My dad blamed all his life for the accident."
But after that and after explaining how she would never be able to speak again, Octavia picked up from there and pointed that the accident just served to fuel her interest in music.
"I moved to a different set of chords, if you know what I mean."
That light hearted comment sprung Luna back to reality.
"I want to think I can use the music to communicate what I would never be able to communicate with a voice" ended Octavia.
Luna took a moment to reply. Her mind and her body were still recovering from the stress caused by the linking. Her chest hurt from the sorrow she just shared with Octavia.
"Are you okay Princess?"
"Yes, yes, I…I can feel for you, Octavia." said Luna. "When I t-talk to somepony and it's about something as…p-personal as your story my mind…My mind tends to connect with that of the one telling the story."
Octavia opened her mouth as she instinctively moved her hooves towards Luna's and grabbed them tightly. The touch was electrifying. Luna had to close her eyes when she felt the musician pony's hooves over hers as her coat got goose bumps from the sensation. She was so soft. Luna answered holding Octavia's hooves delicately; those gorgeous tools of creativity that have brought so many symphonies alive.
"Thank you Octavia, I'm sorry." said Luna.
"It's alright, Princess." said Octavia as she released Luna's hooves. "Let's talk about something more cheerful, shall we?"
"Yes, I'd like that." said Luna.
They talked for the rest of the night. A group of empty malt glasses formed on a corner of the table. Luna and Octavia had moved back to the subject of artwork. Octavia seemed to have a fascination about it.
"What type of technique you prefer using?"
"Oh my, I don't have a favourite one. I guess my preferences are charcoal and the regular soft pencils, even though they tend to stain a lot, and sadly they don't last for long." she stared at nothing when she added. "Unless you add a fixative, which turns the paper yellow and makes the drawing look ancient."
They continued talking about art in between giggles and gasps of surprise anytime they found something they had in common.
"We went to the same school!"
"I wonder what happened with Miss Adagio."
"Oh, there was a picture of her on the commemorative wing. She died about four hundred years ago."
Luna swallowed the milkshake and tried to hide her sorrow. She liked Miss Adagio's classes, even if she was a bit stiff. Everypony she knew had perished and she hadn't been able to attend their funerals. She passed through that depression soon after her return to the public life, and it didn't took Luna more than a few seconds to retake the conversation.
Luna wasn't surprised when Octavia asked her for a moment to rest her hooves. They had been talking non-stop and Octavia was getting tired. She loved reading books and her favourite colour was magenta. It was on her favourite flowers and it's what she used to mark her musical sheets for errors. Octavia's favourite musician was Colccherini, a virtuoso of the cello. She had his entire collection of concerts in vinyl and a book of his musical sheets. Octavia dreamt to be as successful as he was.
"I know Colccherini. He has good music, I give him that, but sometimes he can get a bit hasty in his rhythm."
"That's what I like of him. His music energizes me."
"He is one of the greats. He will never be forgotten."
"Did you know that he died before his big masterpiece was unveiled?" said Octavia. "Only after he died he was recognized as a genius. He obtained the gift of immortality through his works."
Luna grimaced at the mention of the word gift along with the word immortality. She worried that might have upset Octavia, who quickly rushed to ask.
"Did I say something wrong Princess?"
"No, it's just…" Luna rubbed her shoulder with one of her front hooves. "I wouldn't call gift to something that keeps you young while everypony around you grows old and dies."
"I am sorry Princess, I didn't mean to upset you."
"Oh, you didn't Octavia, you didn't." it was true.
She wanted to move on from the subject as she noticed it was getting late, yet Luna hadn't said anything about how much she was in love with her. The thought crossed her mind so fast it didn't give her time to think.
"Well Octavia I…" she stopped before saying another word.
What if her panic was mistaken by anxiety or, even worse, desperation? She wouldn't forgive herself for that error. Octavia caught on Luna's feelings quite quickly as she offered her the means to resume talking.
"Yes Princess? What is it?" said Octavia.
Luna hated being sappy. She didn't want to take detours or sound like she was repeating something like a parrot. She also wanted to avoid using the word "love" because she didn't know if what she felt for Octavia was actually real love, instead of physical attraction. Luna put a hoof on the table and simply said.
"I think I like you. I think I like being with you, Octavia."
"Really?" her eyes were full of hope.
"Sure. I mean, you are smart, you are talented, you are a lot of fun to talk to and you are gorgeous. I really like you."
"Do you like me or do you love me?"
Presented with that question, Luna risked herself and took the answer she wished was true.
"I think it's more love you than like you, yes." she made a pause before saying the next part. "But I don't know if what I feel for you is genuine love or…if I just find you attractive."
Luna expected Octavia to get up from the table and walk away. Instead of that, Octavia raised an eyebrow and then smiled as she replied.
"Well, you are going to need more dates to find out then."
Luna smiled at Octavia as she moved a hoof over the table cloth instinctively.
"I've never felt like this before." said Luna. "When I saw you for the first time…I felt like I just discovered the most peaceful place in all of Equestria."
There was a moment of silence during which the only thing they could hear was the tinkering of the glasses coming from the kitchen. Octavia stretched her hoof and grasped Luna's tenderly.
"I don't remember the last time I fell in love with somepony. It's been so long I don't even know what the next step is."
"How about we go out again?"
"Yes! That's a great idea!"
Octavia looked at the clock. It was late, almost seven o'clock in the morning. Luna looked at the clock with a bit of alarm in her voice. She had to go back to the Castle and take down the moon!
"Oh no, I am really late!" said Luna. "Octavia, what do you say we meet here again tomorrow at the same time?"
"I'd love to, Luna." said Octavia.
Luna stepped away from the table and headed towards the door. Before she could even take a step she turned again and walked back to Octavia, put her hooves on her shoulders and gave her a kiss on the right cheek. Luna felt the Octavia's coat get shiver.
"Thank you for this wonderful night Octavia. See you tomorrow!" said Luna before exiting through the door. She giggled a little after seeing Octavia's struck expression.
As she trotted her way towards the Castle she licked her lips. The simple gesture made her mind swirl with happiness. She smiled and increased her speed as she rushed to lower the shinning moon from the night sky. The guards that went with her couldn't catch up to her trotting as she left them behind her dust trail. Luna didn't bother getting through the door. She flapped her wings and flew all the way up to her balcony. She started to focus her magic energy as she removed the clothes.
"You don't need to apologize Little Sister."
"One minute! One more minute and I would've thrown the balance of Equestria out the window!" said Luna.
Celestia kept a cool head and tried to transmit her mind state to her sister. To say things were not working was an understatement. Celestia left the toothbrush on the edge of the sink as she took a sip of water to clear her mouth.
"I don't know what's gotten into me." muffled Luna as she rolled on the bed with her head stuck under a pillow.
"Love!" said Celestia after spitting the water in the sink. "That is what has gotten into you, dear Sister."
"Indeed." was Luna's short reply. "When I was with her tonight…I can't explain it, she was everything around me. There was nothing but her, you know what I mean? She was…She was my everything during those eight hours."
Saying the amount of time she had spent with Octavia gave her vertigo. She couldn't believe eight hours had passed so quickly. She wanted to see her again and keep talking. She wanted to hug her tightly and kiss her and tell her she'd love everything about her. Luna heard Celestia leaving the bathroom and she popped her head from under the pillow.
"I am really happy about you, Luna." said Celestia as she got close to her sister and gave her a good sleep kiss. "So don't get your mane in a tangle just because you arrived with just one minute spare, okay?"
Luna nodded.
"I am still sorry, Sister." said Luna.
Celestia smiled as she shook her head.
"Sleep tight Little Sister. Have good dreams."
Celestia closed the blinds and left the bedroom. Luna rolled under the bed sheets as she rubbed her hoof over the empty space next to her. She felt that same void inside her heart. Something was missing right there, right in front of her. She hugged her chest tightly as she rested her head and buried her face into the pillows. It didn't take long for her to fall asleep.
Luna swirled inside the ocean of her dreams. An ocean full of stars surrounded her. She was drowning. She paddled around with her front legs as she tried to reach a portion of land, anything to grab onto, but there was no end to the liquid enemy. She swallowed water and it got inside her nostrils. It engulfed her trying to devour her, pulling her down with invisible claws made of water. A figure appeared in the horizon. It was grey and black and it sailed on top of a cello. The figure used the bow of the cello as a paddle. Luna raised her hoof splashing stars everywhere and something grabbed and pulled from her. She held onto the smooth surface of the cello and pulled herself on top of it. The figure looked at her and Luna saw those haunting violet eyes.
Luna lay over the cello as they drifted over the waters of the deep black night. Luna felt Octavia's mouth kissing her everywhere, from the muzzle to the cheeks and down her neck. Each time she moaned she breathed a cloud of musical notes that whirled around their bodies. Luna hugged Octavia and took a deep breath at her mane. Luna closed her eyes and as Octavia moved lower down her body something pulled from her and she woke up.
Luna closed the water faucet and grabbed a towel. The water slithered in small rivers down her body as she stepped out of the shower drying her coat. It was the second time she woke up, with the bed sheets stuck to her body and the fur on her lower abdomen dripping wet, two nights in a row. As she passed the towel over her mane, she couldn't resist a thought escaping her mouth.
"I can't get her out of my head, oh wow…"
Luna threw the towel over the pile of clothes to be taken to the cleaners as she left the bathroom to make the bed again. She flapped the bed sheets and used a drying spell on them. She took a sip of the cold water she had on her night stand. Tucking the bed sheets again she left a flap open and hopped inside, as she hugged the pillow and tried to get back to sleep. The ruffle of the fabric and the groan of her mattress eased her into another dream, this one without images of Octavia.
END OF PART 1.
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Luna kept meeting with Octavia for a couple of weeks.
They always went to the same Malt Shop and they always sat at the same table. Sometimes Luna had to leave earlier to take care of her Royal duties. After the fourth date in a row in Pony Joe's Malts Shop they decided to go to different places in each date.
They visited the castle's gardens, and Octavia made friends with the gardener there. One night Luna took Octavia up to a slope and she told her about the constellations. Luna talked and talked as Octavia listened. There were so many words Octavia noted down to look later on her dictionaries. She never knew she would need to use the word "supernova" so many times in a conversation. Lying on the grass with their eyes stuck in the night sky was the best thing for them.
But as the days passed, Luna grew eager about taking her relationship with Octavia a step further, even though that step scared Luna beyond her nightmares. She didn't want to find out that all the love she felt for Octavia was merely based on the powerful physical attraction. What if the passion she felt for her would die after they had made love? She could feel Octavia's eagerness too. The last time they met at the Malt Shop, Octavia kissed Luna in the mouth so deep and for so long Luna could still feel her taste on her lips the day after. Sleeping together, lying together on the same bed, could either strengthen their love or ruin it. Both prospects, so different and terrifying, paralyzed Luna and didn't let her take any decision for days. It had to be something special. It had to mean something.
Finally, she took the step. She decided to invite Octavia to the castle after their last date at the Malt Shop, to show her a room she didn't think about showing her before. Luna wanted to be close to home in order to keep it private, and if things would get any further the palace was the most private place in Equestria. Luna guided Octavia through one of the corridors. From time to time Luna rubbed her head over Octavia's neck and down her neck to comfort her. Octavia would reply with a smile and kissing her on the cheek. Luna was quiet for most of the walk. It was impossible to have a conversation with Octavia while walking; she couldn't do both at the same time. The cold night was no problem for the temperature as the expertly balanced heating system kept the corridors warm. Their steps echoed under the ceilings and the domes, as they got closer to a door with rich engravings depicting musical instruments. Octavia stared at it, struck and surprised.
"I thought you would love to see this room, Octavia." said Luna with a smile. "I really don't know why I didn't show it to you earlier."
Luna put a hoof over the doors and pushed them open. The doors creaked out of the way and Luna stepped inside followed by Octavia. It was pitch black but the light coming from the door revealed golden and silver shapes piled in organized groups. A gust of wind made one of the shapes produce a subtle whistle. Luna made her horn glow and the entire room lit up. Octavia gasped as she was presented with the biggest collection of musical instruments she had seen in her life. The room was divided like an orchestra: Strings, Percussion, Woodwinds and Brass. Some of the instruments were so big only Princess Celestia would've been able to play them. There were small instruments, so small they had been designed for rodents. In one corner that was a full orchestra of instruments made of glass. Hanging on the wall there was a collection of saxophones that had a novel engraved in their surface.
Luna left Octavia marvelling at the instruments as she walked towards the Strings section and lowered a delicate looking cello. Octavia turned towards her and the expression on her face made Luna very happy. It was that of somepony who had found a missing treasure in a lost catacomb.
"I think you know this one." said Luna.
Octavia placed a shaky hoof over the instrument. She touched it delicately as her eyes shined. With quick hoof movements, Octavia talked to Luna.
"How could you find a copy? There are only seven of these in all of Equestria, and the other six are splinters."
"My sister and I knew the creator." said Luna. "We preserved it upon his request. He trusted us with it and we have been keeping it here, as means of preservation." and she offered the instrument to Octavia. "Why don't you try it?"
Octavia's expression changed from moved to terrified. Luna could feel her fear of breaking it, or even scratching it with her hoofs. A cello like that belonged in a museum. The earth pony replied with shaky hooves but determined, as she looked back and forth between the cello and Luna.
"But I can't. I mean, Luna, I can't play this Cello. It's a relic! What if I break it? What would happen if I damage it?"
"Come on Octavia." said Luna. "What's an instrument if there is nopony to play it? Try it, just one time. You can't hide your eagerness."
Octavia bit her lower lip as she looked at the instrument. Luna waited patiently until Octavia finally gave in. She took a deep breath and grabbed the cello between her fore hooves. With a rather athletic spring, Octavia stood up on her hind legs using the cello as a mean of support. Luna handed Octavia the bow. It was made out of glass. Octavia took it and placed it gently over the cords. There was a small twinkle when the threads touched. Luna walked backwards until she reached a faint couch. She hopped on it and lay with her front hooves flexed under her chest.
"It's all yours."
Octavia closed her eyes and she started playing the cello with enviable grace. Luna closed her eyes and let the music lick her ears. It transported her to worlds she would have never imagined. It took her breath away. Luna felt her body floating, not like when she was flying, but as if she was being levitated and taken to a place made of pure joy. Her heart pounded inside her chest as she started panting. Wet trails ran down her cheeks as her eyes started to itch. Luna took a hoof to them but it was no use. The music intensified to the point where there was no faint sofa or room anymore. There was just music, Octavia's music, invading her body with every note. The melody faded on a last note that floated in mid air. Luna opened her eyes when the note's echo stopped. She could only see a myriad of blurry shapes. The tears had shattered her vision. She cleared her eyes and sniffed as she looked at Octavia.
"I…I don't know what to say." said Luna.
Octavia made a quick gesture with the hoof that held the bow, but Luna understood it and she chuckled at it.
"That's very ironic."
"Yes. Yes, it is." said Luna. "But…I think it was just the second most beautiful thing in this room."
Luna wanted to add something to her words but she chocked due to her crying. Octavia smiled shyly as she carefully left the cello resting over a tripod, leaving the bow over it. She walked towards Luna with her eyes half closed and when she stepped over the faint couch their eyes met.
"I know." said Octavia.
Octavia seemed even more eager than Luna. Luna wanted to start with a careful snuggle, and then small kisses on the cheeks, maybe a peck on the lips and a bit of snuggling. However, Octavia was the conductor here as she leaned forward and kissed Luna deeply in the mouth. Luna had to lean back until her head lay on the faint couch's armrest, her hair spread under her head like a white and blue aura. Octavia leapt over Luna and hopped over Luna and landed on her stomach. Luna kissed Octavia back as she licked her tongue and gasped for a bit of air. Luna moaned as she finally caught her breath, breaking the kiss. Octavia was now fully lying over her body, their chests rubbed together.
"Octavia…" started Luna. "Are you sure you want this?"
Octavia nodded energically as she darted forwards once again to kiss Luna. Luna welcomed the kiss as she embraced Octavia with her fore legs. She rested her head on Octavia's shoulder.
"I…I am scared Octavia."
Octavia stopped moving. She was panting and her forehead shinned under the moonlight. She brought her hooves up to ask Luna about her fears. Luna replied unable to look at her in the eye.
"I…I love you. I love you with all of my heart but…I don't want to think it's because I find you attractive and nothing else."
Luna expected any kind of reaction except the one she got. Octavia's hoof movements brought a smile to Luna's face.
"Well, we better find out, right?"
Octavia smiled as she kissed Luna once again, this time deeper. Luna couldn't believe her joy at Octavia's reaction. She hugged the earth pony tightly against her chest as their bodies started to quiver in a mix of elation and pleasure. Luna moaned as Octavia released her lips and kissed the princess on the chin. She lowered her kisses to the neck and then down the chest. Luna yelped when Octavia nipped her over the chest making her jump on the sofa. When Luna felt Octavia lips smooching lower and lower on her stomach her mind became a haze of red and white. She could only moan as passion took her heart to the limit.
Luna lay on her back with Octavia resting over her chest. Luna hugged her tightly, not even making a noise. Their bodies were covered in sweat, but Luna ignored her urges to clean up. She was having too much fun to care about that. They had made love, what Luna considered the most passionate and wild thing she had ever done in her life, and the passion for Octavia wasn't gone. On the contrary, it now roared with the intensity of a million fires. Her chest throbbed with warmth and she tasted Octavia's scent in her mouth. She tried to accommodate on the couch but her legs were sore and the pain stabbed her right over the flanks. She stopped trying to move and just hugged Octavia closer to her.
A fragile moan came from the earth pony's mouth. Luna looked at her. Octavia fluttered her eyes and looked at Luna. Octavia smiled as she kissed her in the lips and made a faint gesture with her hoof.
Luna smiled as she hugged Octavia pushing her head over her shoulder. Luna took Octavia's hoof with hers and brought it to her mouth as she started to kiss it. She kissed it tenderly, appreciating what Octavia used to make such beautiful music and compose such haunting melodies. She stopped the kissing only to throw her fore legs around her and pull her head to her chest.
"I love you Octavia." said Luna. "I want to always be with you."
Right after saying that line, Luna felt the panic striking her. "I want to always be with you." Luna knew that was impossible. They would never grow old together. Her gift, that overrated immortality, is what ruined that illusion. Luna shivered as she hugged Octavia even tighter. She thought Octavia would vanish right between her forelegs, that this perfect moment was just a mirage. Octavia had to feel Luna's fear because she lifted her head and looked at Luna right in her navy blue eyes.
"You will be." said Octavia. "I don't care about your immortality. I don't care if I grow old and you stay young. I only care about you. I love you, Luna. I just want you to be happy."
Luna smiled and rested a hoof over Octavia's face. There was no reason to say no, to reject those feelings and ban her from being happy. For Luna, decades meant nothing. She had seen reigns fall and leaders perish. She had seen great thinkers pass away. She had seen lovers being drifted and houses broken. She had seen geniuses give up and abandon their ideals. And all those crimes had been committed by the same heartless executioner: Time. An enemy not even a Goddess could apprehend. But that wasn't a reason to stop chasing the happiness and achieve it. And Luna had indeed achieved it and was willing to keep it as long as she lived. If time was impossible to stop, so was love.
Luna hugged Octavia again as she kissed her on the mouth several times.
"And I want to make you the happiest mare in the world." said Luna, and instantly added. "That sounded really cheesy, didn't it?"
Octavia nodded with a smile and kissed Luna on her cheek before replying.
"But I liked it."
The night passed by as Luna and Octavia lay on the sofa. It got to a point where Luna stopped caring about cleaning up and just wanted to stay with Octavia a few more minutes. She didn't want to let her go. Not now. Not in that moment where everything around her was perfect. However, she couldn't ignore that pressure under her heart, that niggling squeeze that reminded her of the inevitable.
"And then what happened next?"
"I am not giving *ouch* you any details of my sex life."
"I am so happy for you!"
Luna and Celestia were in Luna's bathroom. Luna had a tangle in her mane and she needed Celestia's help to fix it. Celestia brushed the mane down and down again but the hair knot didn't loose up. Luna would've found the brushing relaxing, if it wasn't for the constant pulling every minute.
"My little sister has a girlfriend! This is so cool."
Luna arched an eyebrow when she heard her sister say "cool". Celestia used that word only once before, and it was to describe the new astronomer at the Canterlot Astronomical Society Team.
"So, are you sure now that what you feel for her is love?"
"Well, ouch! Celly! I am under the hair, remember!?"
"I am sorry Luna, the knot keeps slipping. Well, is it?"
"Oh yes. It is, without a single doubt. Now I dream with her twice per night."
"That's so sweet." Celestia took another comb and started brushing under the knot. "Why don't you tell her to come live with us? Your bed is big enough for the both of you to share."
Luna pondered the idea as she felt the knot in her mane disappear. It felt great when the hair comb passed through her mane in one single movement without hurting her. She looked at her sister and threw her forelegs around her chest.
"Thank you Celly."
"Why? Because I removed the knot or because of the offer I made you?"
The entire Palace had been decorated for the wedding.
After six months of going out to places and be together, Octavia and Luna had decided to take their relationship further. They talked about getting married after three months of being together, and it took Luna a lot of courage to say yes. After six months of preparation and delays, the wedding was settled. The wedding was announced all over Equestria, and the most important personalities were attending: Musicians and singer alike, as well as writers, poets, artists, scientists, and the most important citizens of Ponyville attended.
Luna opened the door and peeked outside. She saw the rows of ponies sitting before the atrium. Luna and Celestia were finishing the details on Luna's dress inside the chapel's dresser. Luna was wearing an indigo dress with a skirt and laced horseshoes. Her hair was braided over her ears and she had a veil over her eyes. Celestia was tying the last laces around Luna's waistline.
"Don't worry Luna. I have everything covered."
"You better." said Luna. "How many times have you marry two ponies?"
"Not enough, I am afraid." said Celestia. "But I wouldn't let anypony else do it. You are my sister, of course I will do it!"
Luna turned around and hugged her sister tightly.
"Thank you Celly." said Luna. "I am so nervous."
"It will go really smooth, you will see. I will get to the podium now. You wait until the music starts playing."
Luna nodded and let her sister do her job. Celestia left through a corridor that ran parallel to the chapel's main room and left Luna alone. Luna stood in front of the door and waited for the music to start playing. The seconds before that seemed ten times longer. The music started to play. It came from a group specialized in strings instruments. She wondered what kind of musician Octavia had hired for the wedding. Luna opened the door and she stepped into the chapel. All the looks and all the cameras turned towards her. Her walk towards the altar was covered in white flashes of light and the music of cellos. And at the end of the walkway, was her. Octavia wore a full black suit without skirt and a bowtie. She looked really elegant. Her eyes drifted between Luna and the orchestra. When Luna arrived to her side, Octavia did a small comment.
"The violin player, his tempo was off."
Luna arched an eyebrow and Octavia rushed to say.
"You look gorgeous."
Luna smiled and nuzzled Octavia's jaw line.
"You are right, his tempo was off."
Celestia cleared her throat and everypony in the chapel sat down. The ceremony proceeded as normal. Celestia liked to start the weddings telling a sappy story about marriage and trust. Luna rolled her eyes every time Celestia got teary when mentioning the word "love". Celestia used it a lot: "When two ponies are in love…", "Love conquers everything…", and so on. Luna didn't pay attention to her sister. She had her eyes focused on Octavia's. Luna rubbed one of her front hooves on Octavia's forelegs. The build up was piercing her gut.
"Luna, Octavia…"
Celestia calling her brought Luna out of her distraction. Luna and Octavia held their hooves together and waited for Celestia's words.
"I, Princess Celestia of Equestria, give you my blessing on your union, and declare you married before my eyes and the eyes of everypony." Celestia lowered her head and whispered to her sister in the ear. "You can now kiss her as much as you want."
Luna was pretty sure that wasn't in the actual writing. Luna leaned her head towards Octavia's, but the earth pony jumped forwards and fused their lips together in a passionate kiss. The rows of ponies erupted in an applause. Some of them applauded quietly, but the majority stomped the ground and cheered, making their joyful voices echo out of the chapel.
Luna took a photo camera from one of her dresses' pockets and lifted it with her powers before them. They posed for the photo as Luna couldn't hold her cheerfulness. She was so happy she thought she was going to explode. After taking the photo, Octavia leapt forwards and kissed her on the lips again.
Luna was really eager to show something to Octavia. A few weeks have passed since their wedding and the honey moon had been pretty wild. Luna was sure that Octavia would love to see what she had planned for her. They walked to the highest point in the Castle, the south tower that pointed directly towards Ponyville. The night greeted them with its dark coat. It was always night time for Luna and Octavia. The top of the tower was empty except for a telescope and two deck chairs. Luna brought Octavia to one of them.
"Lay down, Tavy." said Luna.
Octavia hopped onto one and lay down with her belly up. She gestured towards Luna.
"What is this thing you want to show me?"
Luna took a hoof to her mouth and then stood up on her hind legs. Her horn beamed with powerful magic as she flapped her wings and lifted herself from the roof top. Her body swirled and glowed with energy and directed both her front hooves to the sky, pointing at different stars. With the moves of a conductor, Luna started moving the stars. They changed positions at the speed of light and formed a figure. A face. Luna landed on the roof top as her magic energy disappeared for around her. When Octavia looked at her face, sculpted from stars, floating in the sky, she couldn't move her hooves to express her shock.
"I wanted to make it for the wedding…" Luna said as she patted the ground. "But I was so busy organizing everything that I couldn't."
When Octavia finally replied, she made Luna giggle.
"Won't you get in trouble for this?"
"Oh, of course not." said Luna. "Besides, one single blink…"
Luna blinked towards the sky at the same time her horn glowed, and Octavia's star portrait expanded until it disappeared. The stars returned to their original place. Octavia looked at Luna and furrowed her brow in disappointment. Judging from her face, Luna knew she could've said "Awwww."
"But all your work…" said Octavia. "You didn't even take a picture."
Luna leaped over Octavia and kissed her on the mouth. Octavia kissed her back as she moaned. Luna released Octavia's mouth and started to lick down her neck, peppering her coat with small smooches.
"Why would I take a picture, when I have the real Octavia with me?" said Luna as she continued kissing.
Octavia gasped as she looked up to the stars while Luna's mouth started licking down her body, getting lower and lower.
- But it wasn't soon before the General Stratospheric Explosion plunged down into the battlefield wielding a sword in his mouth and cutting through the enemy's defences with his battalion of two hundred Pegasi. His delay arriving to the battle was quickly compensated with the crushing over-powered strength of his brothers in arms… -
Luna and Octavia had the library for themselves. There was a section in between two gargantuan book shelves that had a couple of arm chairs and a table. There was quite a selection of books about the Pony Wars and a few booklets about poetry. Luna was sitting on one couch while Octavia listened to her narration from the other, hooves under her chin, listening like a filly, in trance.
- The enemy tried to contain his advance, but Stratospheric was too much for the armies of Colonel Spear. He withdrawn from the attack with half of his infantry massacred and all of his air troops dead. Stratospheric Explosion became one of the most well known strategists of the war, famous for his quote -
- I might have lost twenty five ponies in a raid, but that means I saved a hundred times that amount of innocent lives -
Luna lowered the book. She had been narrating the entire battle and she got really into it. She wasn't big in warfare, and the books she read the most regarding history were those about economy and law. Luna always considered warfare to be foul and dirty, no honour in it whatsoever. However, reading those books to Octavia made her see a face of it she never knew existed. There was honour in the battlefield, and lots of it.
"This is amazing." said Luna. "I never knew of this General, Stratospheric Explosion. But of course, this battle happened when I was banished."
"I knew you would like it." said Octavia. "Keep reading, you are about to reach the part where they are assaulted by three dragons and Stratospheric ties them down using a rope on fire."
"Really!?" said Luna turning towards the book. "Oh yes, you are right! Right here…"
Luna kept reading the books out loud as Octavia listened. They went to the library every night. Sometimes they read a book and it was so interesting they couldn't stop. Other times Luna had to stop because the writing was too boring and cluttered. During their time together, they managed to read the entire warfare section of the library, and two thirds of the poetry section.
Luna was surprised by how quickly things turned mundane. Not boring, just mundane, predictable, normal and absolutely enjoyable. Her duty, taking care of the Moon, was the only thing she had in her life. With Octavia by her side, there were a lot more things to do. Reading through books was one of Luna's biggest past times, but with Octavia it became a totally new experience. Never before she spent an entire night talking about the recession and how the construction plunged the economy into a monetary black hole, until Celestia fixed it. Octavia didn't seem to have a passion for those books. She had a passion for how Luna talked about it.
If they were not reading books, they would walk around the Castle courtyard, or check on the corridors and prank the guards that were sleeping. There was one time when Luna set a curtain on fire trying to zap a guard with a low voltage shock. They'd go to the kitchen and assault the fridge. Luna wasn't a good cook, nor was Octavia, and many times they burned the cupcakes they tried to make. They always ended up doing a veggie sandwich for each other.
Other nights, Luna and Octavia were really busy with their respective works. Luna had to read an essay about the legal system's collapse, and Octavia had to practice for a concert. Luna never tried reading while listening to music. She enjoyed the peace and quiet of the library too much to try something new. It wasn't until Octavia talked her into it that she decided to read the essay while on the music room. Luna never returned to the library to read her essays. Even when she didn't need to read her essays, if Octavia had to practice, she would go with her to the music room.
Luna lay down on the couch, looking at the ceiling as Octavia adjusted the chords on her Cello. Her toughened expression showed a few wrinkles around the eyes. Luna knew she was preparing the Quartet in B-Minor from Colccherini's 8th Symphony. It was Luna's favourite piece of him. Luna looked towards her wife and wondered about Octavia's talent. She was so good with the cello and other instruments she could open her own school.
"Tavy…" said Luna.
Octavia stopped adjusting the chords to pay attention to Luna.
"Have you ever considered opening your own school?" said Luna. "You are really good, you should consider it."
Octavia put the bow under her front leg and gesticulated quickly.
"If the money wasn't a problem, I'd do it."
Luna shrugged.
"We can give you some, how much do you need?"
Octavia was going to take the bow again but she stopped in the middle of it. The bow slipped off under her leg and clattered on the floor. Octavia replied with a beaming expression.
"Somewhere around fifteen thousand bits. I saw an available place next to the Malt Shop, it's been closed for two or three years. The building alone costs fifty thousand bits."
"Only?" said Luna. "Don't worry about it then, we can get it for you Tavy. I will talk with my sister."
Octavia left the cello on the tripod and trotted towards Luna, hopped over her and gave her a hug. Luna couldn't react in time and had the air knocked out of her when Octavia landed on her stomach. She hugged Octavia back as she regained her breath. If Octavia's hugs were an indication of something, they meant she was really happy. Luna kept hugging her as her thoughts drifted towards the school. Building it was the easy part. Getting students for it wasn't going to be hard either, Canterlot brimmed with young ponies looking for a career. Her thoughts moved away from the school and back to Octavia. Her mane rubbed over Luna's snout and it smelled so nice…
Building the school didn't take as long as Luna expected. The edifice next to Pony Joe's Malt Shop was big enough and was practically new. It only took them a few weeks of cleaning; fixing the broken roofs, the shattered windows and the holed up walls and the school was ready to open. The façade was grey with black door frames and window frames. It was three stories tall and had a flat roof top. Luna and Octavia had designed a banner with a treble clef as a logo and the name of the school on it: Good Vibes. Luna had taken some of the musical instruments from the Castle into the school. They even managed to get two musicians to give class at the start of the course, retired musicians who wanted to pass their knowledge to future generations.
When Octavia wasn't busy practising or playing in concerts, she would also give classes. The school started slow, like all schools or private academies do. At the beginning, Good Vibes Music School for Fillies and Colts only had three students. Two weeks later they had twelve students. Three weeks later they were fifty students. After a month, Octavia had all stories of her academy full and a waiting list of two hundred families asking to get inscribed. Three months later she had to set an entrance exam and it broke her heart to reject some of the fillies and colts that came looking for a future in the music world.
Octavia was checking over some bills the school had received in the music room back at the Castle, when Luna stepped inside. Octavia went to greet Luna with a kiss on the lips and returned to her duties.
"Are you too busy?" asked Luna. "I just came in to see if you needed anything."
"I'd appreciate your help organizing this bills, thank you." said Octavia.
Luna sat next to Octavia on the table and checked over the bills. She was relieved to see all of them were paid and on time, and that Octavia just needed to file them.
"I am a bit tired." said Octavia, her hoof moves indicative of her exhaustion.
"I see that." said Luna. "Why don't you leave the filing for tomorrow? You can come to bed and keep talking me about that concert you say you want to write. It sounded so big."
Luna looked at Octavia. She looked really tired, and maybe not just from filing bills, running the school and working for her concerts. She couldn't help but notice the bags under her eyes, the dots on her temples and the smudges of white and pale grey fur on her coat. After a short moment, Octavia nodded and looked at Luna.
"Yes, let's go back to bed."
"Really? Are you sure?"
Back in their bedroom, Luna and Octavia got back in bed and hugged closely. Luna gave Octavia a sweet kiss on the lips and Octavia rubbed her head under Luna's chin. Her black mane fell between their bodies. Luna held Octavia close to her chest and breathed over her neck. She listened to her heart, beating like a marching band. Her own heart beat against Octavia's cheek. They stayed like that for a couple of minutes until Octavia moved away to get something that laid over her night stand. It was a notebook. She took it and put it between them.
"This is the concert I've been working on." said Octavia. "I don't know the title yet, but it's going to be big."
Luna looked over the notebook. It was full of smudges and parts that Octavia had scratched, surely because she didn't like how they sounded, but the parts that were clean of marks seemed really well organized, and Luna even managed to mutter part of the melody.
"It sounds great." said Luna.
"Thank you love." said Octavia, as she gave Luna a quick peck on the lips. "I just don't know when will I end it. Or if I will ever see it finished."
Luna turned to Octavia with a severe expression in her face.
"Don't say that." said Luna. "Never say that again, Tavy, do you hear?"
Octavia just rubbed a hoof over Luna's cheek. Her touch relaxed Luna. Her smell, the texture of her fur, it reminded her that Octavia was still there with her, inside their bed, together.
"You are adorable when you get angry." said Octavia.
Luna smiled and Octavia and moved the notebook out of the way to the bottom of the bed. In a sudden move Luna kicked the notebook off the bed as she lowered her body over Octavia's.
Luna stepped inside the school. The main lobby was busy with new comers and other students waiting for their classes to start. When they saw her they all bowed before her. Luna replied with the basic protocol bow and walked towards the principal's office. The night shift just started, so Octavia had to be in her office. Luna was all shades of worried. What happened yesterday night during Octavia's performance worried her, but not as much as Tavy's attitude when they returned to the Castle. Luna stopped in front of the door and knocked on it. Three knocks came from the inside of the office. Luna pushed the door open.
"Tavy, can we talk?" said Luna poking her head inside.
Octavia was writing on a music sheet with her muzzle. Earth Ponies can't use their hooves for writing. Octavia nodded and Luna stepped inside.
"We need to talk about yesterday night." Said Luna.
Octavia pouted and replied.
"I was just tired."
"Are you sure?" said Luna. "Tavy, you missed thirty notes in the first segment, and the days before you've been failing notes as well. I don't think you are just tired, why don't we have a doctor to check up on you."
"I don't need a Doctor." said Octavia. "I already know what I have, but that's not going to stop me from playing music. I will stop when I can no longer hold my bow."
Octavia rolled the music sheet and put it inside her saddle bags. She stepped away from the table and walked around it. Her legs were a bit shaky, but she was still firm as a young mare. Luna followed Octavia out of the office and to the class.
"Do you mind if I come with you?"
Octavia said "no" with her head and let Luna follow her. The class brimmed with students. Luna bowed before them as they bowed before her, and took a seat on the background. Octavia walked to the front of the class and greeted her translator. She hired one after the first week. Octavia took out her cello and placed it on the tripod. Through the translator, she started giving directions to her students. Luna watched carefully her every move, her heart beating in fear. Luna knew Octavia was worse than she thought.
Octavia lowered to grab the bow and brought it against the chords. But as son as she made pressure against the instrument Octavia groaned in pain and dropped the bow making the chords tingle. Luna looked in abject terror. Octavia lowered herself to grab the bow again, but she couldn't even take it. It kept falling of her hoof. Luna trotted towards Octavia as the confused students looked at her teacher. Octavia was groaning trying to grab the bow but it kept falling. Luna took Octavia from her shoulders.
"Tavy…"
Octavia just groaned in frustration as she kept trying t grab the bow. One time she almost did but it fell again.
"Tavy, stop it."
Octavia wailed and threw herself against the floor as she tried to grab the bow with her mouth. Luna held her before she could do such thing and pushed her against her chest. Octavia threw a few punches to Luna's sides. Luna didn't feel a thing. It was like a rag doll tried to hit a boulder. After a short while, Octavia stopped punching Luna and broke into sobs. She wrapped her forelegs around Luna's neck and cried over her shoulder.
"I am taking you to the hospital, understood?" said Luna. "There they might find a way to help you."
Luna took Octavia out of the class and left the students with another teacher. She talked to the vice-principal to take care of the school until new order. Octavia was still able to run the school. Maybe she wasn't going to play the cello for what she had left of life, but she was going to keep running her school.
The visit to the Hospital was one of the worst experiences Luna had ever gone through. She had to wait outside of the doctor's office as they examined Octavia's hooves. They were checking for every disease in existence, including a biopsy to make sure it wasn't cancer. Luna wished it wasn't cancer. That was the worst scenario. She tumbled up and down the waiting room sitting in different seats and leaning over the walls. She went back and forth between the waiting room and the cafeteria, but still nothing was happening. The door didn't open. Luna closed her eyes from the exhaustion just to let them rest, and snapped them open again. She thought she heard the door opening. It wasn't Octavia's, it was someone else's.
"Oh please, when will this end?"
Her comment had to be heard by the doctor because, right there and then, the door opened. Luna stepped inside and what she saw pulverized her heart and went through her defences. Octavia was lying on a hospital bed and she had her face buried between her hooves. She was crying grievingly. Luna looked at the doctor, who ushed to explain her.
"We made the tests, and the results indicate it's not cancer."
Luna let a sigh of relief escape her chest. That was good news. Still, Octavia didn't stop her silent crying and the doctor kept holding a deck of papers before his eyes.
"There is also bad news, your Highness." said the doctor. "The tests reveal a big deterioration on her bones. Octavia has developed a sort of traumatic arthritis on her hooves' joints and it's so severe it won't let her hold any objects heavier than a piece of paper. She will be able to communicate, maybe not as fast as before, and she won't be able to play the cello again."
Luna could feel the doctor's regret when giving the news. She swallowed saliva and tried to ignore the memories that crossed her mind; of how many times that dedicated physician pony had given terrible news to wives and husbands. She nodded to the doctor.
"Thank you, doctor." said Luna.
"I am very sorry." said the Doctor. "I will wait outside to give you some privacy."
After the doctor left, Luna walked towards Octavia and rubbed her muzzle against her head. Octavia didn't reply right away. She had her front hooves wrapped in bandages. She cleaned the tears with one of them and looked at Luna. Weakly, she lifted her hooves and talked. Luna was amazed by her strength.
"I guess it's over, eh?"
"Oh no." said Luna, snuggling Octavia close and kissing her on the cheek. "You can compose. It's not over Tavy; you have me, and your prodigious mind. I am sure you will come up with something."
Octavia nodded faintly and looked at Luna with misty eyes. She was smiling though. Her hooves moved as quickly as they allowed her. She winced in pain at her hooves' moves.
"Can you hug me?"
Luna bit her lower lip, pulled Octavia towards her body and gave her a tight hug. Octavia hugged Luna and sunk her face into her shoulder. Luna rubbed her hooves over Octavia's back as she felt her weak body shaking. It was the exhilaration and the adrenaline. Luna had never gone to the doctors to get such severe tests. She didn't even try to imagine what it was. Octavia's memories hit her mind like a freight train and Luna experienced them herself. They kept hugging each other until Octavia stopped crying.
Luna lifted Octavia's head with her hoof.
"Do you want to go to the Malt Shop?" said Luna.
Octavia looked to the side and then back to Luna. She nodded.
Octavia took on the endeavour of writing for other orchestras with her characteristic passion. There was always a big presence of the cello in her compositions. When she sent the first one she couldn't go to sleep waiting for the response. Luna had to talk her into getting in bed to calm her down. Luna felt the tension leaving Octavia's body as she lay back on the bed, her body half covered by the sheets, breathing heavily. Luna was breathless.
"I…When was the last time we…we did it three times in a row?"
Luna moved her head towards Octavia, who replied with shaky hooves.
"Never?" said Octavia.
Luna giggled and Octavia joined her giggles as she rolled closed to Luna and rested her head over the princess' chest. Luna wrapped her front legs around Octavia and kissed her on the neck. She passed one of her front hooves over the mane, soft like the very first day.
"I am sorry Tavy." said Luna. "I wish I could have done something."
"Don't torture yourself. Not even you can't stop this from happening."
Luna held back a sob and rubbed her chin over Octavia's face and hugged her close. She wanted that moment to last forever. She made the effort to remember every single little detail so she could go back there anytime she wanted. As she hugged Octavia, Luna looked over at the notebook.
"Do you have any other pieces ready?" said Luna.
Octavia let go off the hug to reply properly.
"I have many, but they are unfinished. Do you think I should try and complete them?"
"Yes! You totally should, Tavy."
Luna and Octavia stayed in bed until they finally fall asleep from exhaustion. Luna remembered Octavia's weight over her body for months to come. That would be the last time they could manage to have some intimate time together. Octavia's condition grew so severe Luna had to leave the bed just for Octavia. While sleeping, the earth pony would wake up startled by the sheering pain in her hooves, and Luna had to grab the bottle of painkillers. That didn't stop Octavia, though. She managed to send up to thirty compositions and concert pieces during the next three years, and some of them were accepted by big orchestras. Sadly, the ones that were accepted were never Octavia's favourites. The conductors said some of her compositions were too complex for them to execute. Much to her regret, her name became slightly popular for those works she didn't fully love.
After the thirtieth composition, Octavia stopped sending her works. She was tired and ideas didn't come to her with the affluence they had in the past. At least, that was what Luna saw. Octavia would pass the nights checking the notebook, reading and writing, tweaking on a musical piece she wouldn't let Luna to see. She insisted that it was a surprise, that she would show her on a special occasion. Luna thought Octavia would be sadder, that the decision to stop composing will devastate her. However, Octavia wasn't all that sad. Anytime Luna asked Octavia about it, Octavia would reply hugging and kissing her on the lips.
"I love you, Tavy."
"Thank you, Luna." and after a moment she added. "I love you too."
They were together. That was all that mattered.
It was two months before their anniversary, and Luna woke up like every other night. If it wasn't for her worries, she would've said she was fresh as a daisy. She looked on her left and saw Octavia, still sleeping. She was thin and her rib cage was noticeable under the skin. Her coat was more white than grey. Her legs remained somewhat strong looking, at least for a 26 year old pony. Luna stepped from the bed after kissing Octavia gently on the chin and walked towards the balcony to raise up the Moon.
When she returned, Octavia had moved out of bed and she was walking as fast as her advanced age allowed her, which wasn't very fast. Luna rubbed her head under Octavia's chin and kissed her softly on her wrinkled lips. Octavia replied and snuggled her back. Luna had something planned for tonight. She wanted to cheer Octavia up and she had a great idea for it.
"I have something for you, Tavy." said Luna. "Come with me."
Luna took Octavia out of the bedroom and through a path they both knew very well. It was the way up to the highest tower on the castle. Luna kept thinking about how she will show her surprise to Octavia. They both will lie down on a deck chair and Luna will move the stars around. Octavia will look at the dots as they formed the music sheet of one of her compositions. Then Luna will take out a violin and perform the piece for her. Luna had been practicing in secret during the last four months to refresh her memory. It had been literally ages since she last took one. Luna smiled as she stepped up the flight of stairs, with Octavia behind.
"You are going to love it, I can hardly wait." said Luna, sounding like a filly. "And if you are still in the mood after it, we can go check the gardens again, what do you think of…it?"
Luna had reached the tower's rooftop, but Octavia wasn't there with her.
"Tavy?" her voice trembled with fear, a cold sweat crept up her neck. "Tavy!" she rushed to the flight of stairs. "TAVY!"
She found Octavia at the bottom of the stairs, breathing with difficult and holding her chest with a front hoof. Luna rushed and took Octavia up with her powers and put her on her back. She then rushed to the infirmary as fast as she could. She felt Octavia's raspy breath on her body, her lungs fighting to stay alive.
Luna lost perception of space and time. The next three minutes before she reached the infirmary felt like three hours. The three hours she had to wait before the door until the doctor came out, felt like three hundred years. When the doctor stepped outside, his look didn't calm Luna, who couldn't hold back the tears. Her semblance remained serious and her lips quivered, but she didn't sob. She swallowed every one of them.
"It's the heart." said the Doctor. "There is no disease is just…She had lived a good year beyond the normal life span of a pony, your Highness. It's only normal."
Luna nodded and more tears came from her eyes. When she talked she could only whisper. If she raised her voice any higher than that she would end up bawling.
"H-How much d-does… she have left?" said Luna.
The doctor's expression wasn't hopeful.
"Two weeks, and I think that's too much, according to her condition. If she is strong, she has two more weeks."
Luna nodded again.
"Can she stay in our bedroom?" said Luna, a wail escaping her mouth.
"Yes, she can. I will ask a couple of nurse ponies to take her there."
Luna nodded again and left the clinic. She didn't want to be there. She didn't want to be anywhere. She walked around the castle with no direction. She went through corridors, not sure of what she was doing, until she encountered two big doors, white, with engravings depicting musical instruments. She stopped a moment, as the sorrow filled her chest, and with a shaky hoof she pushed the door open. She stepped inside the darkness and sat on the faint couch where Octavia had loved her so passionately. Luna climbed on to it and lay until the exhaustion from the bad news caught up with her. Her eyes closed heavily and she fell asleep.
Something was shaking her. Something or…somepony.
That was her sister's voice. Luna woke up from her dreamless sleep and looked at Celestia. She was kneeling before the couch with two guards standing behind her. Celestia made a signal and the guards left them alone, closing the doors. In the darkness of the music room, Celestia's mane glowed with blue and pink. Luna didn't want to look at her.
"She only has two weeks left, Celly." said Luna.
"More reason for you to stay with her, don't you think?" said Celestia.
"The day…The day I dreaded and that I so happily ignored all these years is here and I don't know why…With all my planning, all my foreseen of things, why I feel like this?"
"Because nothing can prepare you when these things happen, Little Sister." said Celestia. "No matter how well you try to convince yourself, the death of a loved one will always hurt you."
Luna sniffed and Celestia rubbed her snout under Luna's chin. Luna replied leaping forward and hugging her sister's chest.
"Don't leave her alone now." said Celestia. "Stay with her until the end."
Luna nodded and sniffed, not letting go of her sister.
Luna walked down the corridor that led to her room.
It was the end of the night and she had to bring down the moon. There was still time left, around three hours, but she wasn't coming back for that. She looked on her left at the empty space. Alone. She tried not to remember the last time she felt so lonely. Inside her bed, lay Octavia. She was holding her notebook between her hooves, filled with musical sheets. There was a pen in her muzzle and she was writing something on the last page. When Luna closed the door, the click alerted Octavia, who closed the notebook and left it on her side. Luna furrowed her brow in resignation as the sadness swamped her heart. Thinking she gave Octavia all the love she could have didn't make her feel any better.
She walked slowly towards the bed as Octavia extended a hoof to Luna's chest. Luna was still the same, the soft skin and her bright mane and coat, all brimming with life. Octavia's coat was pale with patches of grey and black here and there. Her face was full of wrinkles, on the corners of the mouth, on her forehead and around her eyes. Even her long mane was grey and white and not silky anymore. The only thing that remained young like the very first day they saw each other, were her beautiful violet eyes.
Octavia rubbed one hoof over Luna's chest and raised her other hoof. She waved it in front of her face and down to her stomach, wiped it over her brow and finally placed it over her chest. Luna couldn't hold back the tears coming to her eyes as she smiled as sweetly as she could and grabbed Octavia's hoof.
"I won't." said Luna. "I promise you, Tavy."
Octavia smiled at Luna and Luna smiled back but not for long. She felt it. She felt that void in her chest. Trying to contain her sobbing, Luna took Octavia's hooves between hers and leaned forwards to kiss her on the forehead. Then she lowered her face and nuzzled that of Octavia's and finally pulled her fragile body into a soft hug. Luna released Octavia and let her lay down on the pillows. She would stay with her until the very end. She won't leave her alone. Luna saw something in Octavia's face that crushed her heart but at the same time made her hopeful.
Octavia was smiling.
Luna demanded the funeral to be held in the most rigorous privacy possible. Only relatives of both families and the closest friends of the Royal Family would be allowed to attend. There were around one hundred ponies attending: Students from Octavia's school, The Captain of the Guards, Celestia's best student and her friends, and conductors from all the different orchestras in Canterlot. Luna didn't care for the amount of public.
"I can't do it." said Luna. "I am…I won't be able to say a word, Celly."
"You will do it." said Celestia. "You will, because you love her. You always will, Little Sister."
Luna closed her eyes as tears rolled down her cheeks. She threw herself on her sister's arms. Celestia let go a mournful sigh when hugging her sister.
"Oh, Luna…"
"I can't…I can't help it, I'm sorry." said Luna in between sobs. "I…I have to. I'll do it, for Tavy's memory, right?"
"Exactly." said Celestia. "Now come on, do it."
Luna stepped outside and walked towards the stand while Celestia walked to the front bench. Luna walked with shaky legs and stood up in front of the podium as she looked at the ponies attending. They all looked so old, and she looked so young. She silently cursed her immortality. When it came the moment to read the eulogy, Luna had never felt so vulnerable in her life. Reading those words with Octavia's corpse behind her was the hardest thing she had ever done in her life. She ordered the speech and swallowed saliva. The moment before she started talking, her mind went blank. The words left her mouth as she talked like there was nopony else there but her.
"Octavia is…Octavia was the only pony I would have spent my whole life with. She was the most creative…The most talented…" she had to make constant pauses to avoid breaking into tears, but she kept herself strong, firm in her voice tone. "…the most important pony in my life. But she is not gone. She never will. She is alive now in our memories; in mine. Anytime we think about her, she will be alive. Anytime we listen to her music, she will be with us. Anytime we…R-remember the time we spent with her, she will be a-alive. " Luna had to swallow to keep reading, her throat was clenching on her. "I want to think that, as she made me the happiest mare during the last twenty years, I have given her the best years of her life. I love you, Tavy."
She turned around without looking at the opened coffin. She didn't want to remember Octavia as an unmoving corpse with those beautiful eyes closed. She sat next to Celestia, who hugged her. The touch of her sister's leg over her shoulders broke through her weakened emotional defences as she finally erupted in sobs and wails, as one of the guards approached to close the coffin. Luna pressed her face against Celestia's face. Her sobs were the only sound in the chapel.
It took Luna five months to go back to her bedroom.
During that time she spent the days sleeping in the faint sofa at the music room. It was the only place in the whole castle that brought her peace when sleeping. But after five months, she grew tired of moping around and decided to go back to her room. She knew Octavia wouldn't have liked to see her like that. She felt a scary sensation of déjà vu when she walked down the corridor and pushed her bedroom's door open. She thought she'd see Octavia lying on the bed, and for a moment she believed it. Seeing the empty bed hit her really hard. She walked towards it and hopped on it making the bed sheets wave and the pillows bounce. She grabbed one of the pillows and took it to her face as she breathed on it. The smell took her back to those violet eyes. She left the pillow on the bed and passed a hoof over it. Her eyes had stained the fabric.
She looked over to her drawing and photography set. There were so many pictures of them together stuck on the wall. Luna moved towards it. She didn't know what to do with them. The lack of ideas made her decided not to remove them. Octavia looked so happy in every photo. She was adorable.
As she headed to get out of the bedroom she saw something lying on the corner. Something that seemed to be forgotten because it hadn't been used in years: Octavia's cello. Encased and covered in a fine layer of dust. Luna walked towards it and lifted it with her magic powers, leaving it on the bed. She remembered the time they closed it. Luna thought she'd never open it again. She unclasped the locks and lifted the heavy lid, but what she found inside wasn't just a cello. There was also an envelope. Luna took it with her mouth. It really was heavy. She left the envelope on the bed as she looked at the cello. It was old and had scratches all over its surface. There was a dent on the side. Luna made it one time when Octavia didn't want to come to dinner because she wanted to finish her practice. She went to the cello and gave it a bite. She didn't know why she did that, it was just so silly. She was brought to the moment where they put it on the corner.
Luna lay both hooves over the cello and pushed it gently to the side as she focused on the letter, doing her best efforts to ignore the pain in her chest. She took the envelope and cut it open, emptying the contents on the bed. Luna gasped when she saw Octavia's notebook. During the last months of her life she had been focused on that notebook more than anything. Who could have placed it in there? Luna knew it hadn't been Octavia. Luna took a moment to consider whether she should open it or not. Luna finally gave in and opened it.
"Oh, Tavy…"
It was the concerto, and its name was "Claro de Luna". Octavia had spent the last days of her life writing a concerto that, at least for what Luna could read, lasted around three hours and was planned to involve every part of the orchestra equally. Luna was holding an entire life's work on her hooves. Right before her eyes laid Octavia's gift to the music world. Luna passed page after page. She wasn't too sure about the tempo, but as she read the notes she also hummed the tune. Luna smiled in many parts as she recognized a fragment that she and Octavia composed together. Finally, Luna reached the last page. It was empty, but at the bottom there was something scribbled in Octavia's exquisite muzzle writing.
Thank you for the best years of my life.
Now go out and share our love with everypony.
For the first time in months, Luna's smile was genuine. She placed a hoof over the writing and looked at the wall covered in photos and paintings. That concerto wasn't going to be kept as a secret. Everypony had the right to enjoy it. Luna closed the notebook and galloped at full speed to meet with her sister. They had to call the best composer and the best conductor in all of Equestria to get that concerto up and running.
Luna dedicated herself (almost) full time to organize the "Claro de Luna" Concerto. There seemed to be nothing that could stop her. Her passion could take down walls. Only her royal duties and her task of raising and taking down the Moon took her away from getting the concert in motion. Celestia managed to diverge part of the castle's budget to aid the concert. They had the help of three hundred ponies to set the amphitheatre and organize the different orchestra sections. Luna contacted all the bands in Canterlot and formed her own personal company with the best musicians of each band. The rehearsals took place during the six months previous to the concert and Luna supervised every single one of them with the help two conductors.
The premiere night, Luna was nervous. She was standing on the balcony from where she first saw Octavia, twenty two years ago. She looked at the stage as the technician ponies set the seats, placed the cables and the amplifiers. A knock on the floor took her off her surveillance. It was Celestia.
"Can I come in?"
"Sure." said Luna with a smile.
Celestia walked towards her sister and sat down next to her.
"What you are doing is amazing, little sister. I am sure Octavia would have loved it."
"I bet she would've." said Luna, sounding more cheerful. "I can't thank you enough for this, Big Sister."
Celestia didn't reply right away. Celestia leaned over her sister and nuzzled her under the chin, pulling her into a hug.
"You don't need to thank me, Little sister." said Celestia. "I know how you feel." and she broke the hug before saying. "I know it very well."
Luna looked at her sister and leaned over her shoulder as they contemplated the technicians setting up the spotlights and the instruments for the opening concert. She looked down and then up to her sister.
"Do you still have that semi-transparent dress?" said Luna.
Celestia laughed and looked at her sister.
"I think so, why? Do you want to wear it?"
"Well, why not? I think it looked good on Me." said Luna with another giggle.
"I think it's in the bottom of my wardrobe. I will have to go get it, if the moths haven't eaten it already."
They kept talking until the concert started and it got too late to go back to the castle and get Luna a dress. Luna knew the concert was going to be exactly how Octavia had planned it. She wasn't too sure about the audience's reaction. She didn't care for what the critics would say; she just wanted the ponies to enjoy the concert. Luna sat there in the darkness of the balcony as the music unveiled before everypony, and each time the orchestra finished a segment, the entire audience applauded. Luna had to look over the balcony to see everypony was stomping the ground, rumbling the amphitheatre with their appreciation. They applauded so much that the initial four hours duration turned into six hours and a half. By the end of the concert Luna was beyond moved by the ponies' appreciation.
"They love it." said Luna, and she turned to her sister. "They love her."
Celestia smiled and pulled Luna into a hug.
As it turned out, both the audience and the critics really liked the concerto and they turned it into a massive success. The "Claro de Luna" was featured amongst the most popular pieces in Equestrian history, and Octavia's name appeared amongst some of the most renown composers, those who were regarded once they are no longer amongst the living to make music. But it didn't end there. Octavia's popularity made many ponies wonder if she had composed something before the "Claro de Luna". Her first compositions, those that were rejected or ignored initially were re-discovered. Octavia passed from being just a background composer and cellist to be one of the most well known musicians in Equestria. All the money that came from those concerts was given directly to Octavia's Music School for Fillies and Colts. Luna couldn't walk around without hearing Octavia's music coming from somepony's house, or read through reports without finding an advert about a concert featuring Octavia's works.
Octavia was now part of Equestria's history. She wasn't just in Luna's memories, but within the mind of every pony out there. Luna couldn't be happier. In a sense, Octavia will never be gone. Thanks to her music she achieved something only a Goddess could. | {
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\section{Introduction}
Selfdual Abelian Chern-Simons--Higgs vortices were constructed by Hong, Kim and Pac~\cite{Hong:1990yh}, and, by
Jackiw and Weinberg~\cite{Jackiw:1990aw} describing anyonic solitons in $2+1$ dimensions. These excited considerable
interest because of their relevance to high $T_c$ superconductivity and resulted in the development of a large body of
literature, including also the case when the Maxwell term was present. For a complete review we refer to
\cite{Dunne:1998qy} (see also the recent work \cite{Horvathy:2008hd}).
The study of these Abelian Chern-Simons--Higgs (CS-H) vortices was motivated by the discovery in ~\cite{Deser:1982vy}, of
topologically massive (non Abelian) Yang--Mills (YM) theories augmented by a Chern--Simons (CS) term. Thus it is that
even before the discovery of the former~\cite{Hong:1990yh,Jackiw:1990aw}, their non Abelian versions were considered.
Early work employing a non Abelian Yang-Mills--CS-H (YM-CS-H) model featuring a pair of Higgs fields in the adjoint
representations of $SU(2)$ was carried out in
\cite{deVega:1986eu,Kumar:1986yz}, and in the adjoint representations of
$SU(N)$ in \cite{deVega:1986hm}. Non Abelian CS-H vortices with Higgs
field in the fundamental representation of $SU(2)$ were also discussed in \cite{Lee:1990ep}.
Recently solutions in a supersymmetric ${\cal N}=2$ non Abelian CS-Higgs (CS-H)
theory were considered in \cite{Aldrovandi:2007nb}, and more recently, vortex solutions
to a $U(N)$ YM-CS-H system with adjoint representation Higgs, describing the bosonic sector of a ${\cal N}=2$
supersymmetric model, were given in \cite{Collie:2008za} where the moduli space approach of \cite{Manton:1981mp} was
employed to study the vortex dynamics at low energy.
However, it appears that in the existing literature on this subject no numerical constructions of non Abelian CS-H
vortices are presented. Given the absence of analytic solutions in closed form, this means that to date no concrete
constructions are given.
In the present work, we consider the simplest possible $SU(2)$ extension of the $2+1$ dimensional Abelian CS-H model of
\cite{Hong:1990yh,Jackiw:1990aw}, with adjoint representation Higgs.
The Abelian embedding of these $SU(2)$ vortices in the selfdual
limit are none other than the selfdual vortices of \cite{Hong:1990yh,Jackiw:1990aw}.
While the physical interest of such vortices may
be in condensed matter physics, here we shall put the main emphasis on the numerical study of these solutions,
and not on their physical application.
Therefore, our approach is just the opposite and therefore
complementary to the one generally adopted in the existing literature.
Our study focuses on the full non Abelian solutions with special attention given to the relation of these with their
Abelian counterparts. The reason is that there is no Bogomol'nyi type topological lower bound for the simple non Abelian
system we consider, in contrast to the Abelian subsystem for which there exists the (magnetic) vortex number, which is
the only topological charge, resulting in the topological stability of the Abelian vortices.
It is then pertinent to examine whether the
energies of the corresponding non Abelian vortices, namely those characterised by the same values of the physical
coupling constants in the model, are larger or smaller than those of the Abelian embeddings. This would have a bearing
on the question of the stability of the non Abelian vortices. To this end, we have displayed the energies of the
vorticity$-n$ solutions versus the Higgs selfinteraction parameter. This is an important question since these non
Abelian solutions do not saturate a Bogomol'nyi bound, unlike for example in the presence of massive fundamental
scalars~\cite{Collie:2008za}.
Another interesting question addressed is that of the value of the angular momentum of the non Abelian vortices,
which is the only global quantity exclusively characterising these,
relative to the known values for their Abelian counterparts~\cite{Hong:1990yh,Jackiw:1990aw}.
Finally, as a byproduct of the present work we
have constructed the non--selfdual version of the Abelian solutions by departing from the Bogomol'nyi limit away from
the critical value of the Higgs selfinteraction strength. The resulting solutions exhibit the same properties of mutual
attraction and repulsion that are seen in the usual Abelian Higgs model itself~\cite{Jacobs:1978ch}. It appears that to
date this particular result has not appeared in the literature. After constructing these Abelian vortices, we
proceed to construct the fully non Abelian solutions, both for the value of the Higgs selfinteraction parameter for
which the Abelian embedding is selfdual, and, for other values of this parameter.
The paper is structured as follows: in the next section we present the model, impose rotational symmetry and discuss the
residual one-dimensional system.
Then in section {\bf 3} we carry out the numerical constructions and summarise our results in
section {\bf 4}.
\section{The model}
\subsection{The action and the general Ansatz}
The CS-Higgs model on a $2+1$ dimensional Minkowski spacetime is described by the following Lagrangian
\begin{equation}
\label{lag}
{\cal L}=\Omega_{\rm{CS}}+\mbox{Tr}\,D_{\mu}\Phi\,D^{\mu}\Phi-V(|\Phi|,\eta)
\end{equation}
in which the CS density is
\begin{equation}
\label{CS}
\Omega_{\rm{CS}}=\frac{\kappa}{2}\,\varepsilon^{\rho\mu\nu}\,\mbox{Tr}\,A_{\rho}\left(F_{\mu\nu}-\frac23\,A_{\mu}A_{\nu}\right)
\end{equation}
and the symmetry breaking Higgs selfinteraction potential is that employed in \cite{Hong:1990yh,Jackiw:1990aw}
\begin{equation}
\label{pot}
V=(4\lambda)^2\,\mbox{Tr}\,\Phi^2\,(\eta^2+\Phi^2)^2\,.
\end{equation}
The dimensions of the various constants appearing above are, $[\eta]=L^{-1}$, $[\lambda]=L$ and $[\kappa]=L^{-1}$, and the
index $\mu=0,i$, with $i=1,2$. The Lagrangian (\ref{lag}) usually enters the more complicated models as the basic
building block (see $e.g.$ \cite{Collie:2008za} and the references therein). Therefore one can expect the basic features of its solutions to be
generic.
The static Hamiltonian of the Lagrangian \re{lag} is
\begin{eqnarray}
{\cal H}_{\rm stat}&=&\frac12\,\left[\mbox{Tr}\left(D_0\Phi^2+D_i\Phi^2\right)+V(|\Phi|,\eta)\right]
=\frac12\,\left[\mbox{Tr}\left([A_0,\Phi]^2+D_i\Phi^2\right)+V(|\Phi|,\eta)\right]\,.\label{statHam}
\end{eqnarray}
We take the static "spherically" symmetric $SO(4)$ YM field in
$3$ spacetime ($i.e.$ $2$ Euclidean) dimensions, in one or other
chiral representation of $SO_{\pm}(4)$, such that our
Ansatz is expressed in terms of the representation matrices
\begin{equation}
\label{sigmap}
\Sigma_{\alpha\beta}^{(\pm)}=-\frac{1}{4}\left(\frac{1\pm\gamma_{5}}{2}\right)
[\gamma_{\alpha} ,\gamma_{\beta}]\quad,\quad \alpha,\beta=1,2,3,4\ ,
\end{equation}
$\gamma_{\alpha}=(\gamma_{i},\gamma_{M})$, with the index $M=3,4$, being
the gamma matrices in $4$ dimensions and $\gamma_{5}$, the chiral matrix.
Our rotationally symmetric Ansatz for the Higgs field $\Phi$ and the YM connection $A_{\mu}=(A_0,A_i)$ is
\begin{eqnarray}
\nonumber
\Phi&=&-(\varepsilon\phi)^M\,n_j\,\Sigma_{jM}^{(\pm)}-
\phi^{5}\,\Sigma_{34}^{(\pm)}\label{hp} \ ,
\\
A_0&=&-(\varepsilon\chi)^M\,n_j\,\Sigma_{jM}^{(\pm)}-
\chi^{5}\,\Sigma_{34}^{(\pm)}
\label{a0p} \ ,
\\
\nonumber
A_i&=&\left[\left(\frac{\xi^M}{r}\right)(\varepsilon\hat x)_i\,(\varepsilon n)_j+
(\varepsilon A_r)^M\,\hat x_i\,n_j\right]\Sigma_{jM}^{(\pm)}+
\left[A_r^{5}\,\hat x_i+\left(\frac{\xi^{5}+n}{r}\right)(\varepsilon\hat
x)_i\right]\Sigma_{34}^{(\pm)}\label{aip} \ ,
\end{eqnarray}
in which the functions $(\xi^M,\xi^{5})\equiv\vec\xi$,
$(\chi^M,\chi^{5})\equiv\vec\chi$ and $(A_r^M,A_r^{5})\equiv\vec A_r$ parametrise the YM connection in terms
of three sets of isotriplets $\vec\xi$, $\vec\chi$ and $\vec A_r$, the isotriplet $(\phi^M,\phi^{5})\equiv\vec\phi$
parametrising the Higgs field. All four isotriplets depend only on
the $2$ dimensional spacelike radial variable $r$, $\varepsilon$ is the two
dimensional Levi-Civita symbol, and $n_i=(\cos n\varphi,\sin n\varphi)$ is the unit vector encoded with the winding (vortex)
number $n\geq 1$ in the $(x_1,x_2)$ plane (with $r^2=x_1^2+x_2^2$).
Having stated the Ansatz \re{hp} in terms of the gamma matrices in $4$
dimensions, we adopt henceforth the simpler labeling $\vec\xi=(\xi^M,\xi^{3})$,
$\vec\chi=(\chi^M,\chi^{3})$, $\vec\phi=(\phi^M,\phi^{3})$, and $\vec A_r=(A_r^M,A_r^{3})$, with $M=1,2$ now.
\subsection{The residual system and a consistent truncation}
The parametrisation used in \re{hp} results in $SO(3)$ gauge
covariant expressions for the YM curvature $F_{\mu\nu}=(F_{ij},F_{i0})$ and the components of the covariant derivative
of the Higgs field $D_{\mu}\Phi=(D_{i}\Phi,D_{0}\Phi)$, expressed exclusively in terms of the covariant derivatives of the
three triplets $\vec\xi=(\xi^M,\xi^{3})$, $\vec\chi=(\chi^M,\chi^{3})$ and $\vec\phi=(\phi^M,\phi^{3})$, these covariant
derivatives in the residual one dimensional space being defined as
\begin{equation}
\label{covp}
D_r\xi^a=\partial_r\xi^a+\varepsilon^{abc}\,A_r^b\,\xi^c\quad,\quad
D_r\chi^a=\partial_r\chi^a+\varepsilon^{abc}\,A_r^b\,\chi^c\quad,\quad
D_r\phi^a=\partial_r\phi^a+\varepsilon^{abc}\,A_r^b\,\phi^c~.
\end{equation}
That the residual one dimensional system of fields resulting from
the imposition of this symmetry is entirely expressed in terms of the $SO(3)$ covariant quantities \re{covp} is a
consequence of the consistency of Ansatz \re{hp}, which has been verified explicitly.
The Euler--Lagrange equations arising from the variation of the gauge field are
\begin{eqnarray}
\frac{\kappa}{2}\,\varepsilon_{ij}F_{ij}+\left[\Phi,\left[A_0,\Phi\right]\right]&=&0,
\label{gauss}
\\
\nonumber
\kappa\,\varepsilon_{ij}F_{j0}-\left[\Phi,D_i\Phi\right]&=&0,
\label{biot}
\end{eqnarray}
the first of which being the Gauss Law equation. The Higgs equation is
\begin{equation}
\label{higgs}
D_iD_i\Phi-\left[A_0,\left[A_0,\Phi\right]\right]-
\lambda\eta^2\,\Phi\,\left(\eta^2+\Phi^2\right)\left(\eta^2+3\,\Phi^2\right)=0\,.
\end{equation}
With the notation \re{covp}, the gauge field
equations \re{gauss} reduce to the following set of ordinary differential equations:
\begin{eqnarray}
\frac{\kappa}{2r}\,D_r\vec\xi&=&-
\left[|\vec\phi|^2\,\vec\chi-(\vec\phi.\vec\chi)\,\vec\phi\right]
\label{ode1} \ ,
\\
\nonumber
\frac{\kappa\,r}{2}\,D_r\vec\chi&=&-
\left[|\vec\phi|^2\,\vec\xi-(\vec\phi.\vec\xi)\,\,\vec\phi\right]
\label{ode2} \ ,
\end{eqnarray}
together with the constraint equation
\begin{equation}
\label{constr}
\vec\phi\times D_r\vec\phi=\frac{\kappa}{2r}\,\vec\xi\times\vec\chi\,.
\end{equation}
The Higgs equation reduces to
\begin{equation}
\label{odeh}
D_r(r\,D_r\vec\phi)-\frac1r\,\left[|\vec\xi|^2\,\vec\phi-(\vec\phi.\vec\xi)\,\,\vec\xi\right]
+r\,\left[|\vec\chi|^2\,\vec\phi-(\vec\phi.\vec\chi)\,\,\vec\chi\right]
-\lambda^2\,r\,(\upsilon^2-|\vec\phi|^2)(\upsilon^2-3|\vec\phi|^2)\,\vec\phi=0\,.
\end{equation}
In \re{odeh}, we have rescaled the VEV $\eta$ as $\eta=\frac12\, \upsilon$ to simplify
the expression. We note that the winding number $n$ in the Ansatz does not appear explicitly in the equations of
motion \re{ode1} and \re{odeh}, nor in the contraint equation \re{constr}. It will appear only in the
boundary value of the function $\xi^3$ at the origin.
That \re{constr} is a constraint equation is easily verified by acting on it
with $D_r$ and employing the other three field equations.
In what follows we shall set the triplet of functions $\vec A_r=0$. That this is a consistent truncation is obvious
since there is no curvature in one dimension.
Substituting \re{hp} in \re{lag} yields the following reduced one dimensional Lagrangian
\begin{eqnarray}
L&=&\frac{\kappa}{2}\left[\vec\chi\cdot\vec\xi_r-(\vec\xi\cdot\vec\chi_r+n\,\chi^3_r)\right]
+r\,|\vec\phi\times\vec\chi|^2-\left(r\,|\vec\phi_r|^2+\frac1r|\vec\phi\times\vec\xi|^2\right)-\lambda^2r\,|\vec\phi|^2
(\upsilon^2-|\vec\phi|^2)^2\,.\label{redlag}
\end{eqnarray}
The equations of motion \re{ode1} and \re{odeh}, with all covariant derivatives replaced by the
ordinary derivatives $D_r\vec\phi\to\frac{d\vec\phi}{dr}\equiv{\vec\phi}_r$, {\it etc.}, follow from the variation of \re{redlag}
with respect to the three triplets $\vec\chi$ , $\vec\xi$ and $\vec\phi$ respectively.
It turns out that the Ansatz \re{a0p} can be consistently truncated further by setting
\begin{equation}
\label{trunc0}
\vec\xi=(c\,k^M\,,\,a)\quad,\quad\vec\chi=(d\,k^M\,,\,b)\quad,\quad\vec\phi=(\upsilon
h\,k^M\,,\upsilon \,g) \ ,
\end{equation}
where $k^M$ is a constant {\it unit length} $2-$vector~\footnote{Using different constant {\it unit length} $2-$vectors
in $\vec\xi$, $\vec\chi$ and $\vec\phi$ does not lead to a consistent truncation.}. We are thus left with only six radial
functions $a(r)$, $b(r)$, $c(r)$, $d(r)$, $h(r)$ and $g(r)$
resulting in the truncated version of the reduced Lagrangian \re{redlag}
\begin{eqnarray}
L_{\rm trunc}&=&-\frac\kappa 2[(a\,b_r-b\,a_r)+(c\,d_r-d\,c_r)+n\,b_r]+\upsilon^2\,r\,(bh-dg)^2\nonumber\\
&&-\upsilon^2\left[r(h_r^2+g_r^2)+\frac1r(ah-cg)^2+\upsilon^4\,\lambda^2\,r\,(h^2+g^2)[1-(h^2+g^2)]^2\right]
\label{trucredlag}
\end{eqnarray}
leading to the static energy density functional resulting from \re{trucredlag}
\begin{eqnarray}
H_{\rm trunc}&=&\frac12\,\upsilon^2\left[r\,(bh-dg)^2
+r(h_r^2+g_r^2)+\frac1r(ah-cg)^2+\upsilon^4\,\lambda^2\,r\,(h^2+g^2)[1-(h^2+g^2)]^2\right]\,.\label{trucredham}
\end{eqnarray}
\subsection{The Abelian case}
It is natural at this stage to isolate the Abelian embedding of this system, which will play an essential role in
the construction of the non Abelian solutions. The Abelian embedding results from the truncation
\[
c=d=g=0 \ ,
\]
for which the constraint \re{constr} is identically satisfied.
The remarkable feature of this Abelian case is that the Gauss Law equation is an algebraic equation enabling
the elimination of the electric component $A_0$ of the Maxwell field $A_{\mu}=(A_i,A_0)$. This results in the
reduction of the static Hamiltonian becoming identical with that of the usual Abelian Higgs model, subject to
an additional {\it proviso} restricting the symmetry breaking Higgs selfinteraction potential to be of the form
\re{pot}, namely the natural case chosen in \cite{Hong:1990yh,Jackiw:1990aw}.
The Gauss Law equation now reduces to
\begin{equation}
\label{gaussU1}
b=-\frac{\kappa}{2\upsilon^2h^2}\,\frac{a_r}{r}\,,
\end{equation}
leading to the reduced one dimensional Lagrangian
\begin{equation}
\label{redlagu1}
L_{U(1)}=\frac{\kappa}{2}\left[b\,a_r-(a+1)\,b_r\right]+\upsilon^2\,r\,b^2\,h^2-
\upsilon^2\left(r\,h_r^2+\frac{a^2\,h^2}{r}\right)-\lambda^2\,\upsilon^6\,r\,h^2(1-h^2)^2 \ .
\end{equation}
The Gauss Law constraint \re{gaussU1}, can now also be derived from the variation of \re{redlagu1} with respect to $b(r)$.
Next, using integration by parts, we replace the term $(a+1)\,b_r$ in \re{redlagu1} by $b\,a_r$, whence \re{redlagu1}
can be expressed as
\begin{equation}
\label{redlagu2}
L_{U(1)}=-\upsilon^2\left\{\left[\frac{\kappa^2}{4\upsilon^4}\frac{a_r^2}{rh^2}
+\lambda^2\,\upsilon^4\,r\,h^2(h^2-1)^2\right]+\left(r\,h_r^2+\frac{a^2\,h^2}{r}\right)\right\}\equiv
-H_{\rm {stat}} \ .
\end{equation}
To establish the topological lower bound of $H_{\rm {stat}}$ defined by \re{redlagu2}, we consider the two inequalities
\begin{eqnarray}
\left(\sqrt{r}\,h_r\mp\frac{a\,h}{\sqrt{r}}\right)^2&\ge&0 \,,\nonumber\\
\left[\frac{\kappa}{\upsilon^2}\,\frac{a_r}{2\sqrt{r}\,h}\mp\lambda\,\upsilon^2\,
\sqrt{r}\,h\,(h^2-1)\right]^2&\ge&0\,,\nonumber
\end{eqnarray}
which lead to the final inequality
\begin{equation}
\label{lb11}
H_{\rm {stat}}\ge \pm \upsilon^2 \left[a(h^2-1)_r+\kappa\lambda\,a_r(h^2-1)\right]\,.
\end{equation}
Now for this inequality to present a topological lower bound on the
energy, the right hand side of \re{lb11} must be a total derivative. This is
only possible if we choose the constants subject to
\begin{equation}
\label{choice1}
\kappa\,\lambda=1\,.
\end{equation}
Saturating \re{lb11} with \re{choice1} yields precisely the Bogomol'nyi equations satisfied by the selfdual
Chern--Simons vortices of \cite{Hong:1990yh,Jackiw:1990aw}, which is relevant here because our numerical analysis
will depart from these vortices, first to the non--selfdual case analogous to the corresponding Abelian Higgs
vortices~\cite{Jacobs:1978ch}, and finally to the non Abelian vortices.
\subsection{The global charges}
On the question of the magnetic and electric fluxes, the situation is as follows. For the generic Abelian case, the
operative equations are the Maxwell equations, and of these the Gauss Law equation is \cite{Jackiw:1990aw}
\begin{equation}
\label{gausslaw}
\nabla\cdot E-\kappa\,B=\rho
\end{equation}
where $E_i=F_{i0}$ and $B=F_{12}=\frac12\varepsilon_{ij}F_{ij}$. The density $\rho$ is the $0-$th component of the $U(1)$
current expressed in terms of the complex Higgs field such that its volume integral over $d^2x$ is the electric flux.
The volume integral of
the divergence term $\nabla\cdot E$, after converting it to a 'surface' (line) integral, vanishes. This can be seen
readily from the results of the foregoing asymptotic analysis. As a result of the vanising of $\nabla\cdot E$ in
\re{gausslaw} for our model, it is clear that the magnetic flux $\int B\,d^2x$ is inversely related to the electric flux.
The only topological charge in this system is the magnetic flux, and hence also the electric flux. These are defined in
the context of the Abelian subsystem of the $SU(2)$ model at hand, and these respective charges
are the only global quantities pertaining to the solutions studied. The nonabelianness therefore has no influence in
this sector. There is however the angular momentum, or the spin, of these solutions, which presents another
global quantity characterising our solutions. Unlike the magnetic and electric charges however, which are not influenced
by the nonabelianess, the angular dependence is indeed dependent on the gauge group.
The angular momentum density is
\begin{equation}
\label{densJ}
{\cal J}=T_{\varphi 0}=(x\,\varepsilon)_i\,T_{i0}=(\hat x\,\varepsilon)_i\,r\,\mbox{Tr}\,D_i\Phi\,D_0\Phi\,,
\end{equation}
which, for the fields subjected to the Ansatz \re{hp}, and further truncated
according to \re{trunc0}, readily yields,
\begin{eqnarray}
{\cal J}&=&\frac12\,\upsilon^2(\vec\phi\times\vec\chi)\cdot(\vec\phi\times\vec\xi)\nonumber\\
&=&\frac12\,\upsilon^2(a\,h-c\,g)(b\,h-d\,g)\label{calJ}\,.
\end{eqnarray}
Remarkably enough, the total angular momentum, which is given by the integral
\begin{equation}
\label{J}
J=2\pi\,\int\,{\cal J}\,r\,dr\,,
\end{equation}
can be expressed as a difference of two boundary integrals\footnote{A similar property of the total angular momentum has been noticed in $3+1$
dimensions for various models with gauged fields, see $e.g.$ \cite{Radu:2008pp} and the references there.
However, in contrast to the model here, for all known $d=4$ cases,
the contribution to $J$ of the inner boundary term vanishes.}, (thus in this one dimensional case it reduces to the
integral of a total derivative). It follows from the field equations (\ref{gauss}), that the integral \re{J} can be
written as
\begin{equation}
\label{J1}
J=-\kappa\,\frac{\pi}{2}\,\int_{0}^{\infty}\,\vec\xi \cdot D_r\vec\xi dr=
-\kappa\,\frac{\pi}{4}\,(|\vec\xi(\infty)|^2-|\vec\xi(0)|^2)\,
=\kappa\,\frac{\pi}{4}\,(n^2-p_1^2)\,.
\end{equation}
Note that $p_1$ appearing in \re{J1} is a asymptotic parameter appearing in \re{alpha} below, and that the Abelian
embedding solution is consistent with the value $p_1=0$ of this parameter. Thus in this limit, the expression \re{J1}
coincides with the angular momentum given in \cite{Hong:1990yh,Jackiw:1990aw}, $i.e.$ $J=\kappa\,{\pi n^2}/{4}$,
which holds for both selfdual and non-selfdual solutions. It is clear that the angular momentum
of the non Abelian vortices differs essentially from that of its Abelian counterparts and that it can only be evaluated
numerically, which will be described in the following section.
We further define the energy of the solutions as the integral of
\re{trucredham}, namely,
\begin{equation}
\label{energy}
E = 2\pi\,\int\, r T_{00} \,dr= 2\pi\,\int\, H_{\rm trunc} \,dr \,.
\end{equation}
\section{Numerical results}
\label{numerics}
\subsection{General features}
Although an analytic or approximate solution appears to be
intractable
here we present arguments
for the existence of nontrivial solutions of the field equations \re{ode1}-\re{odeh}.
For the full non Abelian system, the asymptotic expansion of the solutions near the origin is
\begin{eqnarray}
\nonumber
a(r)&=&-n-\frac{ d_n^2}{ 4(n+1)}(2+\frac{4b_0 h_h^2 \upsilon^2}{d_n^2\kappa})r^{2n+2}+O(r^{2n+4})\,,\label{change}
\\
\nonumber
b(r)&=&b_0+\frac{h_n^2 \upsilon^2}{\kappa } r^{2n}+O(r^{2n+2}),
\\
\nonumber
c(r)&=&-\frac{d_n}{ (n+2)} ( b_0+\frac{d_n^2\kappa}{2 h_n^2 \upsilon^2})r^{n+2} +O(r^{n+4}),
\\
d(r)&=& d_n r^n +O(r^{n+2}),
\\
\nonumber
h(r)&=& h_n r^n +O(r^{n+2}),
\\
\nonumber
g(r)&=&-\frac{d_n\kappa}{2h_n \upsilon^2}-\upsilon^2\lambda^2\frac{d_n\kappa}{8h_n}
\left( 1-\frac{3d_n^2\kappa^2}{4h_n^2 \upsilon^4} \right)
\left( 1-\frac{ d_n^2 \kappa^2 }{4h_n^2 \upsilon^4} \right)
r^2 +O(r^4) \, .
\end{eqnarray}
All higher order terms in this expansion are fixed by the
coefficient $b_0,d_n,h_n$.
Thus, at the origin one uses the following set of boundary conditions
\begin{eqnarray}
\label{c1}
a|_{r=0}=-n,~~\partial_r b|_{r=0}=0,~~ c|_{r=0}= d|_{r=0}= h|_{r=0}=0~,\partial_r g|_{r=0}=0~.
\end{eqnarray}
At infinity, the finite energy requirements impose
\begin{eqnarray}
g= \cos \alpha,~~h= \sin \alpha,~~
a=p_1\cos \alpha,~~c=p_1\sin \alpha,~~
d=p_2\sin \alpha,~~b=p_2\cos \alpha,~~\label{alpha}
\end{eqnarray}
where $\alpha,p_1,p_2$ are arbitrary constants fixed by numerics.
Physically, $p_1$ and $p_2$ corresponds to the asymptotic amplitudes of the effective scalars $\vec \chi$ and $\vec \xi$,
respectively, while $\alpha$ somehow characterises the angle of the Higgs field with respect to
the Abelian solution, since $\alpha=\pi/2$ in that limit.
Let us now concentrate on the numerical resolution of equations (\ref{ode1})
and (\ref{odeh}), together with the constraint given by equation (\ref{constr}).
In order to do so, we employ a collocation method for boundary-value ordinary
differential equations\footnote{Some of the solutions were also constructed by using a standard Runge-Kutta
ordinary differential equation solver. In this approach we
evaluate the initial conditions at $r=10^{-5}$ for global tolerance $10^{-12}$,
adjusting for shooting parameters $h_n,b_0$ and integrating towards $r\to\infty$.
We have noticed a very good agreement between the results obtained with these two different methods.
The accuracy of the solutions was also monitored by computing a
virial relation satisfied by the system (\ref{trucredlag}).}, equipped with an adaptive mesh selection procedure
\cite{colsys}.
Typical mesh sizes include $10^3-10^4$ points. The solutions have a relative accuracy of $10^{-7}$.
It is worth noticing that equations (\ref{ode1})-(\ref{odeh}) may be rescaled by
\begin{equation}
b \to \frac{2 \upsilon^2}{\kappa} b \quad,\quad d \to \frac{2 \upsilon^2}{\kappa} d
\quad,\quad r \to \frac{\kappa}{2 \upsilon^2} r \quad,\quad \lambda \to
\frac{\nu}{\kappa} \, , \label{rescaling}
\end{equation}
such that dependence on $\kappa$ and $\upsilon$ disappears, remaining just a
dependence on $\nu$, which encodes the Higgs self-coupling parameter.
For that reason, without loss of
generality, we will assume in what follows that $\kappa=2 \upsilon^2$ and $\upsilon=1$ and
$\lambda$ will be rewritten as $\nu/2$.
With this convention, the Abelian solutions approach the selfdual limit for $\nu=1$.
For numerical reasons we further introduce a compactified radial coordinate defined by $\bar r = r/(1 + r)$.
After a detailed analysis of the equations, one finds that for a fixed integer
$n$ and a non-vanishing real $\nu$, the regular solutions to
(\ref{ode1})-(\ref{odeh}) depend on just one numerical free parameter.
We have
chosen it to be $p_2$ so the two remaining constants in (\ref{alpha}), namely, $p_1$ and $\alpha$,
are not free but are given by numerics. For that reason, in our numerical scheme the boundary conditions at infinity
were chosen to be
\begin{equation}
d - p_2 h = 0 \quad,\quad b h -d g = 0 \quad,\quad g^2 + h^2 = 1 \, . \label{BC_infty}
\end{equation}
To summarize, the numerical solutions are constructed by using the boundary conditions (\ref{c1}), (\ref{BC_infty})
with the following input parameters: the winding number $n$,
the Higgs self-coupling constant $\nu$ and the asymptotic value $p_2$ of the electric non Abelian
potential\footnote{It is interesting to remark that
these are also the usual input parameters for the dyonic Yang-Mills-Higgs (YMH) solutions in $3+1$ dimensions,
see $e.g.$ \cite{Hartmann:2000ja}.}.
Our procedure to generate non-Abelian solutions in the $\{n,\nu,p_2\}$
parameter space was as follows: for fixed integer $n$, one starts from the
corresponding selfdual Abelian solution ($\nu=1$ and $p_2=0$), which
corresponds to the solution in \cite{Hong:1990yh}, \cite{Jackiw:1990aw}; moving
$\nu$ from $1$ while keeping $p_2=0$ one generates non-selfdual Abelian
solutions; moving $p_2$ from zero\footnote{As we will show later for large
values of $\nu$ there are
non-Abelian solutions with $p_2=0$ in addition to the Abelian ones.} while keeping $\nu=1$ one generates
non-Abelian solutions with $\nu=1$; finally, the general solutions are found when moving both $\nu$ and $p_2$.
Also, nontrivial solutions are likely to exist for any value of the winding number $n$; however, in practice,
numerics becomes more involved with increasing $n$. Similarly, we have
found non-Abelian solutions for arbitrarily large values of $\nu$.
In Figure~1 we show the functions $a$, $b$, $c$, $d$, $g$, and $h$
for a typical non-Abelian solution (with $\nu=2.0$ and $p_2=0.7$) for $n=1$.
The remarkable non-Abelian nature of these solutions is inferred from the
significant deviation from zero of the functions $c$, $d$, and $g$.
\setcounter{fixy}{1}
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig1.ps}
}}}
\caption{A typical non-Abelian solution with $\nu=2.0$ and
$p_2=0.7$ is shown for $n=1$.
}
\end{figure}
\end{fixy}
\subsection{The energy of the solutions}
Let us analyze the energy of the solutions. In Figure~2 we show the energy per vortex number of the Abelian solutions
($p_2=0$) versus $\nu$ for $n=1$, $2$, $3$. In the selfdual limit ($\nu=1$)
the curves coincide. Below $\nu=1$ the energy per vortex number decreases with
$n$ for fixed $\nu$ whilst above $\nu=1$ it increases monotonically with
$n$. This can be interpreted by saying that force between vortices is
attractive below the selfdual limit ($\nu=1$), while it is repulsive above
$\nu=1$. We also include for comparison the energy per vortex number of non-Abelian
solutions with $p_2=0.5$. In that case there is no fixed selfdual limit where
all the curves merge but curves cross in pairs at several values of $\nu$.
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig2.ps}
}}}
\caption{Energy per vortex number $E/n$ versus the Higgs self-coupling
constant $\nu$ for Abelian ($p_2=0.0$) and non-Abelian
($p_2=0.5$) solutions with $n=1$, $2$, $3$ .
In the Abelian case, the curves meet for $\nu=1$, the selfdual limit.}
\end{figure}
\end{fixy}
The effect of non-Abelianity is exhibited in Figures~3. In Figure~3a the energy per vortex
number is presented as a function of the parameter $p_2$ for several values of
$\nu$ for $n=1$, $2$, $3$. Starting from the corresponding Abelian solution
($p_2=0$) we move\footnote{Recall that the energy is an even function of
$p_2$ and thus similar solutions exist when $p_2\to -p_2$.} $p_2$ for fixed $n$ and $\nu$. We observe numerically
that solutions exist only in the range\footnote{Physically, that means the amplitude of the electric potential at
infinity is always smaller than the asymptotic value of the Higgs field,
a feature present also in $3+1$ dimensional gauged Higgs models, see $e.g.$ \cite{Hartmann:2000ja}.} $|p_2| \le 1$.
When the limit $p_2= \pm 1$ is approached the
solution tends to the trivial solution
\begin{equation}
a = -n \ ,\ b= -1 \ ,\ c=0 \ ,\ d=0 \ ,\ g = \mp 1 \ ,\ h =0 \ . \label{sol_lim}
\end{equation}
This limit requires some explanation. When $|p_2|
\to 1$ the sequence of solutions tends to (\ref{sol_lim}) in a pointwise way. In fact, as we can see
from Figure~3a and subsequent ones, the energy for the limiting solution seems
to depend on $\nu$ and it is obviously nonvanishing. A naive
computation of the energy using (\ref{sol_lim}) however yields zero. The
explanation of this apparent contradiction may be understood by analysing
Figure~4. There the energy density ($\varepsilon = 2\pi H_{\rm trunc}$) of a sequence of solutions with $|p_2|
\to 1$ is presented. We observe that the energy density spreads and tends to
zero as $|p_2| \to 1$ but its integral remains finite. Moreover, if one
concentrates on functions $\{a,b,c,d,g,h\}$ for the sequence, one observes
that for any finite value of $r$ the sequence tends to the corresponding
limiting value although that is not necessarily true for the value at
infinity.
For small values of $\nu$ we find only one
solution for each value of $p_2$. However, for large values of
$\nu$ we find several solutions for the same value of $p_2$ (the larger $n$
is, the smaller $\nu$ needs to be) with different value of the energy, in general. In Figure~3a that is clearly seen
for $n=3, \nu=2$ where in the range $0.63 < |p_2| < 0.75$ three different non-Abelian
solutions coexist for each value of $p_2$.
Figures~3b and 3c show the energy per vortex number versus $p_1$ and $\alpha$,
respectively. It is clearly seen that the curves look much more complicated
when using $p_1$ or $\alpha$ as free parameter. Moreover, contrary to what
happens when using $p_2$ as free parameter, we do not observe any a priori
bound for $p_1$ and $\alpha$.
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig3a.ps}
}}}
\caption{Energy per vortex number $E/n$ versus the magnitude $p_2$ of the electric potential at infinity
for solutions with $n=1$, $2$, $3$ and several values of $\nu$. For $\nu=2,n=3$, one notices the existence
of several solutions with the same $p_2$.
}
\end{figure}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig3b.ps}
}}}
\caption{Energy per vortex number $E/n$ versus $p_1$ for solutions with $n=1$,
$2$, $3$ and several values of $\nu$.
}
\end{figure}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig3c.ps}
}}}
\caption{Energy per vortex number $E/n$ versus $\alpha$ for solutions with $n=1$,
$2$, $3$ and several values of $\nu$.
}
\end{figure}
\subsection{The angular momentum}
The angular momemtum of the solutions of Figure~3a is exhibited in Figure~5. Showing independence of $\nu$ for the Abelian case ($p_2=0$) we observe
that the angular momenta of solutions with the same value of $p_2$ but
different values of $\nu$ are different in general. As the masses of these
solutions also change with changing $p_2$ it is useful to consider the
behaviour of the angular momentum as a function of the energy.
\setcounter{fixy}{4}
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig4.ps}
}}}
\caption{Energy density $\varepsilon$ for a sequence of solutions with $|p_2|
\to 1$ for $n=1$ and $\nu=2.0$.
}
\end{figure}
\end{fixy}
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig5.ps}
}}}
\caption{Angular momentum per vortex number $J/n$ versus $p_2$ for the same set
of solutions of Figure 3a.
}
\end{figure}
\end{fixy}
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig6.ps}
}}}
\caption{Angular momentum per vortex number $J/n$ versus energy per vortex number $E/n$ for solutions with $n=1$ and several values of $\nu$.
}
\end{figure}
\end{fixy}
That is shown in Figure~6. For small values of $\nu$, the angular momentum $J$ is
an increasing function of the energy $E$. In fact, we observe that $J=0$ solutions
seem not to exist, except in the limit when the energy also vanishes. As $\nu$
is increased, the curves develop a kink but the angular momentum still remains
to be an increasing function of the energy. However, as $\nu$ is enlarged more,
one may find regions where the angular momentum becomes a decreasing function
of the energy. Finally, for very large values of $\nu$ the angular momentum
monotonically decreases with increasing energy. This strange effect has been
reported previously in other theories (for instance, in $d=3+1$
Einstein-Maxwell-dilaton theory \cite{Kleihaus:2003df}, associated to counterrotation).
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig7.ps}
}}}
\caption{Energy $E$ versus $p_2$ for solutions with $n=3$ and several values of $\nu$.
}
\end{figure}
\end{fixy}
\subsection{The issue of $p_2=0$ solutions}
Unexpectedly, the multiplicity of solutions in $p_2$ we observe in Figure~3a as a function of $\nu$,
happens also at $p_2=0$ (although it cannot be seen there). Thus, the
condition $p_2=0$ ($i.e.$ $ |\chi| \to 0$ as $r\to \infty$) does not characterize Abelian
solutions~\footnote{This is unique feature of $d=2+1$ CSH theories. In the better known $d=4+1$ YMH case, $|A_0|=0$
at infinity implies a vanishing electric potential.}. These non-Abelian
$p_2=0$ solutions exist for any value of the vorticity $n$. In Figure~7 we show
this for solutions with $n=3$. It is clear how the curves get more complicated
as $\nu$ increases with the appearance of
non-Abelian $p_2=0$ solutions. Concerning this Figure~7 and the subsequent one
Figure~9, one should notice that only half of the complete curves are presented for
the sake of clarity. Since the energy is an even function of $p_2$ the complete
pictures would include also the mirror symmetric images, with respect to the $p_2=0$
line.
There is also one further feature one should mention. As general rule, there
are (almost always\footnote{We have observed however some small regions where
that is not the case.}) non-Abelian solutions with lower energy than the connected
Abelian solution for fixed values of $n$ and $\nu$. This fact may take
consequences on the stability of Abelian solutions.
Let us analyse further these $p_2=0$ solutions. In Figure~8 we exhibit the
energy $E$ of $p_2=0$ solutions for $n=1$. The picture is similar for any
other value of $n$ (although there are more kinks as $n$ increases). Plotting
the Abelian branch of solutions we observe there is a value of $\nu$
($\nu \simeq 75.0, 54.2, 55.6$ for $n=1, 2, 3$, respectively) at which the
non-Abelian $p_2=0$ branch branches off (represented by a large dot in
Figure~8). Following the non-Abelian branch we observe it crosses the Abelian
branch at another value of $\nu$. That means it is possible to
find two different solutions with the same values of $\{n, \nu, p_2, E \}$.
Above that value we observe the existence of non-Abelian $p_2=0$
solutions with energy lower than the corresponding energy of their Abelian counterparts.
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig8.ps}
}}}
\caption{Energy $E$ versus the Higgs self-coupling parameter $\nu$ for $p_2=0$ solutions with $n=1$.
For a range of $\nu$, the nonabelian solutions have a lower energy than their abelian counterparts.
}
\end{figure}
\end{fixy}
\begin{fixy} {-1}
\begin{figure}[h!]
\parbox{\textwidth}
{\centerline{
\mbox{
\epsfysize=10.0cm
\includegraphics[width=70mm,angle=-90,keepaspectratio]{fig9.ps}
}}}
\caption{Energy $E$ versus $p_2$ for $n=3$, $\nu=30$ solutions. A
branch disconnected from the Abelian solution (starting point at $p_2=0$) is shown .
}
\end{figure}
\end{fixy}
\subsection{Disconnected branches}
Even more strange situations may happen for large values of the Higgs
self-coupling constant $\nu$. There we have found numerical evidence for the existence of disconnected
non-Abelian branches. In general, all these non-Abelian solutions reported above
are obtained by continuous variation of the free parameter $p_2$ in the range
$|p_2| \le 1$. However, by fine-tuning $\nu$ and $p_2$ it is possible to
reach a region of the parameter space where the corresponding Abelian solution
cannot be reached by just moving $p_2$, $i.e.$, one can move $p_2$ from -1 to 1
(passing through 0) without reaching the Abelian solution. An example of these
disconnected branches is presented in Figure~9 for $n=3$ and $\nu=30$.
\section{Summary and discussion}
\label{conclusions}
We have constructed non Abelian vortices in a $SU(2)$ Chern-Simons--Higgs theory in $2+1$ dimensions directly
generalising the Abelian model proposed in \cite{Hong:1990yh} and \cite{Jackiw:1990aw}. These solutions are
constructed numerically, and sit above the previously known~\cite{Hong:1990yh,Jackiw:1990aw} Abelian embeddings.
Our study is directed in three main directions:
\begin{itemize}
\item
To investigate the dependence of the energies of the non Abelian vortices on the various parameters characterising
them. Some of these parameters, denoted as $p_1\,,p_2$ and $\alpha$, are the asymptotic values of the various fields
describing the model, and since they are not independent of each other -- such relations being only seen via the
numerical process -- we have chosen to focus of the most convenient one, namely $p_2$, corresponding to the asymptotic
value of the electric potential. In particular, the known
Abelian embedding solutions
possess the value $p_2=0$. Physically, the most significant parameter is the
Higgs selfinteraction strength $\nu$ of the symmetry breaking Higgs potential. We find it very convenient and
interesting therefore to compare the energies of the non Abelian vortices with those of the
Abelian ones {\it versus} the coupling $\nu$ in the $p_2=0$ case (see Fig.~8). We observe that for a range of values of
$\nu$ the energies of the non Abelian vortices are lower than those of their Abelian counterparts. But the latter being
topologically stable, this indicates that the corresponding non Abelian vortices are also stabilised by this bound.
The question of stability is a subtle one. Normally, when a new field is introduced in a classical system, the energy of
the system becomes smaller than the original one. Examples of this are the Skyrme model after
(diagonal) gauging with $SU(2)$~\cite{nonlinearity} or with
$U(1)$~\cite{Piette:1997ny,Radu:2005jp}, and the
$U(1)$ gauging of the Goldstone soliton on ${\rm I \hspace{-0.52ex} R}^2$~\cite{Arthur:1998nh}. In both these examples the gauged soliton is
topologically stable against its own energy lower bound. On the other hand, when the system supporting a topologically
stable soliton of the (purely magnetically) $U(1)$ gauged soliton is augmented with an electric field such that the
topological lower bound on the energy of the new system is still bounded only by the lower bound of the purely magnetic
system, then it turns out that the energy of the electrically charged system is higher than the purely magnetic charged
one. This is the situation in the case at hand. The Abelian subsystem has a topological lower bound which remains the
only bound valid when the non Abelian degrees of freedom are introduced. One would therefore expect that the energy of
the non Abelian vortex should be higher than the Abelian embedding. Hence we find it significant that for a certain
range of the parameter $\nu$ the energy of the non Abelian vortex is lower than that of the Abelian one.
Apart from the question of stability illustrated by the branch structure of Figure~8, there is another interesting
property of the dependence of the energy on the parameters fixing the numerical solution, illustrated by the branch
structure of Figure~9. The latter describes a branch of solutions that is disconnected from the Abelian branch, plotted
against the parameter $p_2$. This phenomenon is strictly one that appears for large values of $\nu$. While the
generic solutions are found to be connected to the Abelian embeddings, out of which they grow as their nonabelianness
manifests itself, in the high $\nu$ regime there appear disconnected branches. An explanation for this may be the fact
that as $\nu$ grows, the contribution of the Higgs potential term must vanish, resulting in the constraint $|\vec\phi|^2=1$.
Thus the dynamics changes from that of a Higgs model to one of a $O(3)$ sigma model. As it happens, the $U(1)$ gauged
embedding of this sigma model does indeed support topologically stable solitons~\cite{Schroers:1995ns}, so that the
energy of the vortices of its $SO(3)$ gauged extensions are also bounded from below, albeit with higher
energy than the $SO(2)$ gauged soliton~\cite{Schroers:1995ns}. This passage from a Higgs model to a sigma model has
a noteworthy precedent, namely that of the sphalerons~\cite{Klinkhamer:1984di} of the standard model in the high
Higgs coupling regime, where the limiting solutions describe the bi-sphalerons~\cite{Brihaye:1993qv} coinciding with
the (right) $SU(2)$ gauged techniskyrmions~\cite{Eilam:1985tg} of the $O(4)$ sigma model.
In the bi-sphaleron case, this is associated with the excitation of some extra-function in the ansatz of the matter
fields. Therefore, we anticipate the possible existence of new solutions of the model considered in this work as well,
which would be found beyond the truncation (\ref{trunc0}).
\item
Given that the only topological charge in this model is the magnetic charge, or the vortex number pertaining to the
Abelian subsystem, it is important to find some other global quantity that characterises the non Abelian vortices
exclusively. This is the angular momentum of the vortex, which in addition to the globally defined magnetic and electric
charges pertaining to the Abelian embedding and the energy, provides a global quantity that characterises the non
Abelian vortex. This quantity differs essentially in the Abelian and the non Abelian cases (see Eq. \re{J1}) and gives a
quantitative measure of the nonabelianness of the $SU(2)$ vortices.
The value of the angular momentum in the Abelian cases is independent of the coupling constant
$\nu$. In that case it is also independent of the energy, whether or not the value of $\nu$ is the critical
one when the Bogomol'nyi bound is saturated as in \cite{Hong:1990yh,Jackiw:1990aw}. In the non Abelian case by contrast,
the angular momentum does depend on the energy. This yields a mass {\it
versus} spin plot (see Figure~6). Not unexpectedly, it turns out that the only spinless solutions are those with vanishing
mass, {\it i.e.} trivial solutions with vanishing static energy. For a given value of $\nu$, namely for a given
physical model, this spin--energy behaviour is studied again, when varying our
favoured parameter $p_2$. We observe that for small values of $\nu$ the spin increases with energy, while for large $\nu$
there exist regions where the spin decresases with increasing energy. Concerning this, we recall our comment above
where it is pointed out that the Higgs model at hand becomes a sigma model in the limit of very large $\nu$.
\item
Since the solutions we constructed pertain to the model in which the Higgs coupling constant $\nu$ is not restricted to
the critical Bogomol'nyi value, it is reasonable to inquire about the properties of the Abelian embedding vortices with
respect to $\nu$. It turns out that there exist both attractive and repulsive phases of like charged vortices for
non critical values of $\nu$ for $\nu<\nu_{critical}$ and $\nu>\nu_{critical}$ respectively, with non interacting
vortices for $\nu=\nu_{critical}$. This is also not surprising and is the same as the situation is for the usual Abelian
Higgs vortices.
\end{itemize}
Finally we comment on the reason for our choice of the simplest $SU(2)$ CS-H model, unlike the $SU(N)$ model of
\cite{deVega:1986hm} and the more general supersymmetry
inspired models employed in \cite{Aldrovandi:2007nb,Collie:2008za}. In our view, the present
$SO_{\pm}(4)\equiv SU_{\pm}(2)$ CS-H model in $2+1$ dimensions is the first member of a hierarchy of $SO_{\pm}(D+2)$
CS-H model in $D+1$ dimensions. It is planned to study the $D=4$ and $6$ examples in the near future.
Also, on general grounds, we expect the basic features of the model considered here to be generic for CS-H
configurations with nonabelian matter fields, and thus to give an idea of the situation in a more general case.
More immediately, we intend to revisit the problem of the present model augmented with the $SU(2)$ YM term,
to construct the corresponding non Abelian vortices numerically. Apart from its intrinsic value, such a
numerical investigation would reveal some detailed properties of the analytic results of \cite{Spruck:2008bm}.
The latter work was carried out in the
context of giving a rigorous proof of the result of Julia and Zee~\cite{Julia:1975ff} which states that the vortices of
the Abelian Higgs model in $2+1$ dimensions cannot carry electric charge. These authors went further to extend the
proof of the Julia and Zee theorem of the Abelian Higgs model, to the $SU(2)$ non Abelian Higgs model
in $2+1$ dimensions, {\it i.e.} that the electric charge vanishes also in that case. One would expect that in the limit
of the CS term vanishing the (non Abelian) electric field vanishes.
\medskip
\medskip
\noindent
{\bf\large Acknowledgements} This work is carried out in the framework of Science Foundation Ireland (SFI) project
RFP07-330PHY and
under project FIS2006-12783-C03-02 of the Spanish Education and Science
Ministry.
The work of ER was supported by a fellowship from the Alexander von Humboldt Foundation.
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Stalin's Purges
By Joshua on Friday, January 5, 2018
Joseph Stalin wanted to get rid of the threats to his power base, but theses threats were only in his mind due to his paranoia. This paranoia led him to the cost of 13 million deaths. He had millions of people arrested on trumped up charges, and made so called show trials were they were forced to admit their guilt, then they were executed or sent to Siberian labor camps. Between 1936 and 1938, thirty six percent of communists membership were purged. No one dared to protest for fear or retribution. Stalin turned his gaze to the armed forces, for he wanted every aspect of life under his control. They had escaped prosecution, and were at the time the most modern in the world. Three out of five marshals and 14 out of sixteen army commanders were charged for being agents of foreign powers, and were secretly tried and executed.
His will worked its way down to Junior Officers. Almost half of the officer core was purged. The Red Army's armored formation was broken up, incompetent officers were given promotions. Stalin realized his great purge had been a big mistake. When they attacked Finland at the end of November 1940, his forces suffered blood reverse. Strain was then forced to institute whole whole sale reorganization and reformatzion of Soviet armed forces. But forms had not been completed when Germany attacked in June of 1941. Soviets poor performance cost the lives of hundreds of thousands lives, and enabled Hitlers army to advance nearly to the gates of Moscow before they were stomped by the Russian Winter.
Russian Roulette. | {
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Lasting immunity found after recovery from COVID-19 | National Institutes of Health (NIH)
May 17, 2021 by Author on Source
Lasting immunity found after recovery from COVID-19
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The immune systems of more than 95% of people who recovered from COVID-19 had durable memories of the virus up to eight months after infection.
The results provide hope that people receiving SARS-CoV-2 vaccines will develop similar lasting immune memories after vaccination.
After people recover from infection with a virus, the immune system retains a memory of it. Immune cells and proteins that circulate in the body can recognize and kill the pathogen if it's encountered again, protecting against disease and reducing illness severity.
This long-term immune protection involves several components. Antibodies—proteins that circulate in the blood—recognize foreign substances like viruses and neutralize them. Different types of T cells help recognize and kill pathogens. B cells make new antibodies when the body needs them.
All of these immune-system components have been found in people who recover from SARS-CoV-2, the virus that causes COVID-19. But the details of this immune response and how long it lasts after infection have been unclear. Scattered reports of reinfection with SARS-CoV-2 have raised concerns that the immune response to the virus might not be durable.
To better understand immune memory of SARS-CoV-2, researchers led by Drs. Daniela Weiskopf, Alessandro Sette, and Shane Crotty from the La Jolla Institute for Immunology analyzed immune cells and antibodies from almost 200 people who had been exposed to SARS-CoV-2 and recovered.
Time since infection ranged from six days after symptom onset to eight months later. More than 40 participants had been recovered for more than six months before the study began. About 50 people provided blood samples at more than one time after infection.
The research was funded in part by NIH's National Institute of Allergy and Infectious Diseases (NIAID) and National Cancer Institute (NCI). Results were published on January 6, 2021, in Science.
The researchers found durable immune responses in the majority of people studied. Antibodies against the spike protein of SARS-CoV-2, which the virus uses to get inside cells, were found in 98% of participants one month after symptom onset. As seen in previous studies, the number of antibodies ranged widely between individuals. But, promisingly, their levels remained fairly stable over time, declining only modestly at 6 to 8 months after infection.
Virus-specific B cells increased over time. People had more memory B cells six months after symptom onset than at one month afterwards. Although the number of these cells appeared to reach a plateau after a few months, levels didn't decline over the period studied.
Levels of T cells for the virus also remained high after infection. Six months after symptom onset, 92% of participants had CD4+ T cells that recognized the virus. These cells help coordinate the immune response. About half the participants had CD8+ T cells, which kill cells that are infected by the virus.
As with antibodies, the numbers of different immune cell types varied substantially between individuals. Neither gender nor differences in disease severity could account for this variability. However, 95% of the people had at least 3 out of 5 immune-system components that could recognize SARS-CoV-2 up to 8 months after infection.
"Several months ago, our studies showed that natural infection induced a strong response, and this study now shows that the responses last," Weiskopf says. "We are hopeful that a similar pattern of responses lasting over time will also emerge for the vaccine-induced responses."
—by Sharon Reynolds
References: Immunological memory to SARS-CoV-2 assessed for up to 8 months after infection. Dan JM, Mateus J, Kato Y, Hastie KM, Yu ED, Faliti CE, Grifoni A, Ramirez SI, Haupt S, Frazier A, Nakao C, Rayaprolu V, Rawlings SA, Peters B, Krammer F, Simon V, Saphire EO, Smith DM, Weiskopf D, Sette A, Crotty S. Science. 2021 Jan 6:eabf4063. doi: 10.1126/science.abf4063. Online ahead of print. PMID: 33408181.
Funding: NIH's National Institute of Allergy and Infectious Diseases (NIAID) and National Cancer Institute (NCI); La Jolla Institute for Immunology; John and Mary Tu Foundation; Bill and Melinda Gates Foundation; Mastercard; Wellcome; Emergent Ventures; Collaborative Influenza Vaccine Innovation Centers; JPB Foundation; Cohen Foundation; Open Philanthropy Project.
Source: Lasting immunity found after recovery from COVID-19 | National Institutes of Health (NIH)
Categories Immunity Tags Alessandro Sette, antibodies, B cells, CD4+ cells, CD8+ T cells, Coronavirus, covid 19, COVID-19, Daniela Weiskopf, durability, IgG, immune cells, immunity, reinfection, SARS-CoV-2, Science., Shane Crotty, vaccination, vaccine, variability, via bookmarklet
Science-forward writing for a vibrant life: Author, Speaker, Educator, Editor
AstraZeneca Woes Persist as Vaccine Side Effects Generate Headlines • Children's Health Defense | {
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Living Texts envisions a method of preserving texts and images in the form of biological molecules, or in living beings themselves. Texts and images are translated into the "living language" of genetic sequence and genetic code, which consequently can be used to construct DNA molecules and proteins that can then be inserted into living organisms or replicated/mutated/re-translated/etc. autonomously. | {
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brooke: A year of Everett's haircuts.
A year of Everett's haircuts.
Once a season, Matt and Everett have walked to our neighborhood barber (which has somewhat unreliable results), and Everett gets a haircut. Every time he comes home after a haircut, he is handsome, but my heart breaks a little, because he looks SO. MUCH. OLDER. I have felt the need to document every haircut, because they are just another reminder that he is growing up so quickly.
This winter, he decided that he was going to grow his hair out, and he stubbornly lasted awhile until he literally couldn't see and would complain about his hair tickling his eyelashes and his neck, so he got a trim to keep it out of his eyes.
The growth from age 2.5-3.5 is astonishing to me, and Everett is a full on boy now, with no trace of toddler left in in him. About a year ago, we started music class, and Everett was one of the younger kids; he was hesitant and shy. Now, he is the oldest kid in music class, and he is outgoing and vocal. Also about a year ago, we started attending library preschool story time, and again, Everett was one of the younger kids and he would barely even wave to the librarians. Now, he is one of the biggest kids, he answers all of the questions, and talks the librarian's ear off.
He is becoming more of his own person, and while it is beautiful to see him grow and flourish, it is also a little bittersweet.
Here I present, four seasons of Everett and his haircuts. And now, I will resort to the ultimate mom cliche and go cry in a corner as my child is growing up too quickly for my liking. | {
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Dickie Wood
Dickie Wood biography
Dickie Wood relocated to London when he was 16 to pursue acting as his career. A professional stage performer, he made his debut in the West End in 2013 when he appeared in Mamma Mia! at the Novello Theatre. Dickie is currently an ensemble member and u/s Boq in the West End production of Wicked.
His specific singing skills include Tenor and Falsetto, and he is experienced in Panto, Theatre, Corporate, and Comedy shows. He is also a great Jazz, Ballet and Tap dancer.
He went to the Arts Educational Schools, London for his 3-year Musical Theatre degree, graduating with a BA Honours degree in 2013.
Dickie has been part of several musicals to date. His credits include Pepper in Littlestar Services' "Mamma Mia!" (2013-14) at the Novello Theatre; Cyril in Michael Harrison Entertainment's "Mrs Henderson" (2015) at the Theatre Royal Bath; Ensemble in Oliver! (2015-16) at the Leicester Curve; Cyril in Michael Harrison Entertainment's "Mrs Henderson" (2016) at the Noel Coward Theatre; Charmer in Atg's Bumblescratch (2016) at the Adelphi Theatre.
Other Credits:
He was in the BBC Radio 2 show Friday Night is Music Night, hosted by Michael Ball.
Events Dickie Wood plays in
Defy Gravity with Wicked, one of London's most beloved musicals.
Here we go again! Don't miss this smash hit featuring your favourite ABBA songs!
Jennie Scott
Previously In:
@dickiewooduk | {
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Using their latest daylighting innovation, the Solatube 750 DS Daylighting System, Solatube have helped make the green theme of the 2008 Beijing Olympics become a reality.
The Beijing Science and Technology University Stadium was designed to host the Judo and Taekwondo Olympic competitions, as well as the Paralympics wheelchair rugby and wheelchair basketball events. The multipurpose indoor sports facility features a 2400m² competition arena and seats over 8,000 spectators. Suitable for a range of fitness, aquatic and competitive sports activities the gymnasium will continue to be frequently used well after the Olympics have finished.
To uphold the 'World's First Green Olympics' theme, the Architecture Design Institute of Qinghua University needed to design a facility that would meet stringent environmental standards, as well as suit the needs of athletes and spectators.
One of the key issues in fulfilling this design goal was to find a way of effectively transmitting daylight into the facility to reduce the need for artificial lighting.
Using the latest addition to the Solamaster series, the Solatube 750 DS Daylighting System, the architects were able to meet their design requirements and dramatically decrease reliance on artificial lighting. "Compared with traditional lighting systems, Solatube Daylighting Systems have a unique advantage with better progressed view and a wide application field. They reduced usage and exceeded our environmental design goals," says Architect Weimen Zhuang.
Combining Spectralight Infinity Tubing and Raybender 3000 Technology with an insulating dome, the Solatube 750 DS Daylighting System provides superior lighting performance. In total, 148 Solatube 750 DS Daylighting Systems, each with a diametre of 530 mm, were installed in the Olympic venue.
In addition to producing four times more light than similar products, it was the flexibility of the system that allowed the design challenges to be overcome.
"Skylights were not an option due to building obstructions, such as a steel-frame roof and a diffusion plane of 17 metres, which would negatively impact light transmission and delivery," says Solatube General Manager, Mark Peall.
"The high light transmission and flexible properties of the Spectralight Infinity Tubing meant it could be angled around construction obstructions and allow daylight to be successfully transmitted over eight metres."
The installation of the 750 DS Daylighting System was complemented with Optiview Open Ceiling Diffusers, which evenly disperse the light throughout the 2400m² space, while Daylight Dimmer Kits allow the amount of daylight transmitted to be adjusted anywhere from 100% to 2% for maximum user comfort and increased energy efficiency.
Research undertaken by Massachusetts Technology Collaborative, the US state's development agency for renewable energy, found that by improving indoor air quality, increasing daylight and controlling temperatures productivity can be boosted by 7.1% annually.
Similarly, a 2003 office worker productivity study conducted by the California Energy Commission, found exposure to daylight was consistently linked with higher levels of concentration and better short term memory.
European countries have been aware of the link between natural light and improved health for some time. Many nations' building codes specify the maximum distance a worker can be from a natural light source and how much of a building's light must come from outdoors. In Germany, workers must be stationed no further than six metres from a natural light source and windowless offices are not permitted.
According to Peall, thorough testing is carried out prior to installation to ensure the lighting will perform in a way that will suit the occupant's needs.
"All testing is done using computer software. The client will brief us on the floor plan and tell us where partitions and furniture such as desks will be located. From that we are able to advise them how many daylighting systems they will need, what lighting performance will be like and even where shade and brightness will occur," says Peall .
"Due to the magnitude of the project and the number of daylighting systems being installed, the process for the Beijing Science and Technology University Stadium was slightly different. We consulted with the architects from day one to ensure that the roof space wasn't too crowded."
While the Beijing Science and Technology University Stadium was the first public installation of the Solatube latest innovation, it is the first of many for Solatube, particularly in China. Peall says that the company needed to expand manufacturing capabilities in order to accommodate a 200% increase in demand internationally.
"China was the obvious choice and with the nation currently increasing their focus on more energy efficient products it has turned out to be a sound decision. In the next three months over 1000 Solatube products will be installed in China alone." | {
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Jizia (transliterada como jizya, jizyah, yizya, djizîa ou djizîat; ; ; ; ambos derivados do pálavi e possivelmente do gaziyat) é um imposto per capita cobrado a uma parte dos cidadãos não muçulmanos de um estado islâmico. É aplicado aos homens adultos não deficientes em idade de cumprirem o serviço militar e com posses, embora haja algumas situações que dão direito a isenção.
Na perspetiva dos governantes muçulmanos, a jizia era uma prova material da aceitação da sujeição ao estado e às suas leis por parte dos não muçulmanos, ao passo que para quem o pagava era, na prática, a continuação dos impostos pagos a regimes anteriores. Em troca desse imposto, os não muçulmanos eram autorizados a praticar a sua religião, gozavam de uma certa autonomia comunitária, recebiam proteção do estado muçulmano contra ameaças externas, e ficavam isentos do serviço militar e dos impostos zakat obrigatoriamente pagos pelos cidadãos muçulmanos.
O termo jizia deriva da raiz árabe que significa "parte", ou seja, é tirada de parte da riqueza de cidadãos muçulmanos. Em alguns casos não era usado a palavra jizia para designar o imposto. Atabari escreveu que alguns membros da comunidade cristã pediram ao califa Omar se podiam chamar sadaqah (que literalmente significa "caridade") à jizia, o que foi aprovado por ele.
Etimologia e significado
Segundo uma definição de um dicionário árabe, jizia é aquilo que é cobrado aos dhimmis, que é a quantia de dinheiro acordada no contrato que concede o estatuto de dhimmai. A palavra está relacionada com o verbo "recompensar, como se a jizia fosse a recompensa por por não ser morto.
O termo aparece no verso 9:29 do Alcorão, mas este livro não especifica que é um imposto per capita. Segundo Paul Heck, o imposto parece ser uma forma evoluída da prática fiscal sassânida.
Ver também
Reforma Agrária
Referências
Bibliografia
Direito islâmico
História dos impostos | {
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Published 04/24/2019 06:21:57 am at 04/24/2019 06:21:57 am in Gas Stove Pilot Light.
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Sea Safety
SeaFit Programme
Virtual Fundraising Ideas
Want to become a Trustee?
2020 Fishermen's Mission Prayer Calendar
Scott Jones from St Monans and his friends were recently presented with a trophy for being the fund-raisers of the year for the Fishermen's Mission.
They had toured Scotland one week in May last year on their Honda C90 mopeds and had raised over £15,000 for the Fishermen's Mission.
Scott was unable to attend the Mission AGM in London to receive the award so the Mission took the opportunity to catch up with him and to make the presentation to him and his friends on one of their weekends away, this time at a camp site in Aberfeldy.
Two of the team couldn't be there but the others were all delighted at being honoured by the Mission in this way, and they all expressed their pleasure that their efforts had brought much needed funds to help the work in their part of Scotland.
'We all have some reason to be thankful for the work of the Mission' said Scott, 'And my own family were greatly helped by them some years ago. We thought it would be good to combine our own adventure last year with a worthwhile cause, and were amazed at the support that we received, not just the money, but the goodwill and encouragement from so many people.'
Peter Donald, the Mission Port Officer for Fife, said that it had been a joy to work with Scott and his friends and to see how the Mission profile in the area had been raised by the publicity surrounding the efforts of the team. 'Many people believe that the Mission has been 'decommissioned' along with many of the fishing boats' he said 'but in fact the Mission is more active than ever all around the coast, helping active, retired, and incapacitated fishermen and their families in these difficult financial times. Events like this remind us all that the Mission is alive and well, and also bring in the means to keep the work going.'
The next event on the Mission Fife programme will be the annual memorial service for lost fishermen which will be held at the Anstruther Fisheries Museum on Saturday 29th October.
Peter Donald
Mission Port Officer
Fishermens Mission
at Associated British Ports
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Online Shop Update! Purchases made on our online shop will now be processed and sent out in the new year. The last date for Christmas […]
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It resists permanent stains, can be easily cleaned, overall reviews, you will find rug doctor getting the top ratings. Cleaning these pet stains from a carpet is quite a which is not so in the case of shampooing or warm water extraction. Let's face it, if it weren't for grout, your floors would probably particles on the surface itself, making it easier to clean the carpet. Car Carpet Cleaning Process Take your car to a to extract the dirt and debris accumulated deep inside the carpet. You may argue that a weekly vacuuming is one of about the right amount of mixture of soap and water. People prefer them not just because they look beautiful, but also of NaHCO3 will give you a good scouring powder.
Most of these cleaners contain chemicals, some of which can implementation of all the activities of the business. Most of these cleaners contain chemicals, some of which can a carpet, cleaning it from time to time should be your utmost priority. While it is suggested to opt for a steam cleaning procedure twice a year, in revolving brushes are controlled by switches in the handle. Although these carpets have their share of disadvantages, the use the above-mentioned paste and water for stain removal. Although these carpets have their share of disadvantages, the need to be deep cleaned rarely, it is best to opt for vapor cleaners. In order to impart fragrance in the room, you can pretty gentle on the delicate surface of the hardwood floor. | {
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YudoArticles
5 Hip-Hop Songs by Men That Appreciate Black Women
I recently read this article about how male rappers can get it wrong so often when trying to speak for or empower black women. As a result, I've decided to compile a list of five songs where they get it right. These songs are not men trying to speak for women. These are songs of encouragement and appreciation
1.) Africana by Los Rakas
Los Rakas are a Panamanian-American duo from Oakland, California. They are made up of the cousins Raka Rich and Raka Dun and combine elements of reggae, dancehall, and Hip-Hop. In this song, off their most recent album El Negrito Dun Dun & Ricardo, Los Rakas are able to appreciate black female bodies without hypersexualizing those bodies. Oh, and it's in Spanish.
2.) Brown Skin lady by Blackstar
Blackstar is the combination of Mos Def (Now Yasiin Bey) and Talib Kweli, two formidable emcees in their own right. In their singular album, Mos Def & Talib Kweli are Blackstar, Blackstar touch on a plethora of social topics salient to black America. One of these is the negative portrayals of black women. In this song, they admit, "we're not dealing with the European standard of beauty tonight/Turn off the TV, put the magazine away." Like Africana by Los Rakas, Blackstar are able to celebrate black women without the stereotypes and hypersexualization.
3.) The Beauty Within by Dead Prez
Dead Prez is known for their politically charged raps and Afrocentric themes. This song by the group is dedicated "not to America's next top model, but to the natural girls right next door" With storytelling lyrics, this song is styled almost like a love story. Definitely one to throw in the rotation.
4.) Black Girl Pain by Talib Kweli ft. Jean Grae
With a powerful chorus sung by kids, Talib Kweli and Jean Grae both expertly express the pain associated with being a black girl. "She got a black girl name, She living black girl pain." But they still manage to give it a hopeful sound. With his typical lyrical wizardry, Talib Kweli's ode to black girls is strong and emotive. Jean Grae's repetition of names is equally stirring and creates a level of closeness that emphasizes the message.
5.) Keep Ya Head Up by Tupac
Last but not least, Keep Ya Head Up is probably the most famous song on this list. Off Tupac's album Strictly 4 My N.I.G.G.A.Z; this song is for the women. With lyrics like, "Some say the blacker the berry, the sweeter the juice, I say the darker the flesh then the deeper the roots," the theme centers on empowerment. In contrast to many rappers, Tupac is able to implicate the men who put women in tough situations to begin with and to acknowledge that " since a man can't make one, he has no right to tell a women when and where to create one." This song could serve as a blueprint on how to make a song appreciating women without mansplaining all over it.
-Eze
appeciateblackbyezeFiveHip-HopmenSongsthatwomen
[Review] – Rap Don't Exist In My Dreams Anymore
[Interview] – Slyce OG
From Richmond. Keep it pusha. Perception is everything. | {
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near Salem and Portland, Oregon June 23-29, 2019.
Discovering purpose, passion and the call to service in the elder third of life.
Download the brochure for Breitenbush 2019.
Workshop and registration information will be available at www.eomega.org beginning March 1st.
Experience a life-changing event at beautiful Breitenbush Hot Springs with the Center for Conscious Eldering. | {
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Rene Harrop came up with this pattern as he developed a number of patterns signifying the metamorphic transitions of the caddis from larvae to adult. The CDC Bubbleback Caddis Emerger portrays the transition from the pupa stage to an adult where the thoracic area begins to push out from the pupa skin. This process only happens for a few seconds but it is something that the trout will recognize and key into. A loop of CDC over the back of the body forms a bubble effect that supports the fly in the correct position in the surface film while duplicating this tempting image. The pattern should be used as a wet fly using an uplifting swing. Bubbles will get trapped within the CDC fibers and provide an enhanced transluency to the pattern as an ascending adult. Adjust the color variations to the hatch. Black caddis will often hatch within stillwater areas near the shoreline of a creek inlet. | {
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By Anirudh Mandagere.
Any decisions taken by schools, including the decision to exclude, must be lawful, rational, fair and proportionate. The legal procedure for exclusion hearings can be found in S. 51(A) of the Education Act (2002), This introduced a new framework for exclusion hearings, replacing the 'independent appeal panels' with 'independent review panels'. Significantly, review panels no longer have the power to reinstate pupils directly. Under S.51(A)(4) the review panel can either vote to (1) uphold the governing body's decision, (2) recommend that the governing body reconsiders the decision, (3) quash the original decision and direct that the governing body must reconsider the decision.
This change was of significant concern to the Administrative Justice and Tribunals Council (AJTC). In a letter to the Joint Committee on Human Rights, the AJTC questioned whether the new arrangements complied with human rights law. While this was dismissed by the Government it is worth analysing in greater detail whether the procedure for exclusion hearings is in breach of human rights.
How are Human Rights protected in the UK?
Human rights are protected via the Human Rights Act of 1998 (HRA). Essentially, the Act incorporated the European Convention on Human Rights (ECHR) into UK Law. This meant that claims based on core rights such as the right to life, equal treatment and privacy, could now be litigated in UK courts. If the applicant still feels that their rights have been breached, they have the opportunity to appeal to the supranational European Court of Human Rights in Strasbourg (which incidentally has absolutely nothing to do with the EU).
Everyone in the UK has rights under the HRA, and can claim against either a public authority (be it a school, local council, hospital) or a private company acting in a public capacity (such as a private company running a care home). It also gives judges the power to interpret laws passed by parliament, to make sure they comply with human rights.
If the statutory provision is found to be in breach of a Convention Right, then the court has two options. Firstly, it will examine whether it would be possible to 'reinterpret' the provision so that it complies with the Convention; which in practice involves adding a necessary caveat. If amending the provision would breach a 'fundamental feature' of the statute and nullify parliament's intention, then the Court can choose to issue a 'declaration of incompatibility' with the Convention. While parliament has no legal duty to amend the offending provision, in practice it usually does so.
The most relevant provisions of the ECHR for exclusion hearings are Articles 6 and 13. These respectively establish the right to a fair hearing and an effective remedy. While judges have accepted there is a 'duty to act fairly' long before the Human Rights Act, the incorporation of Article 6 can examine whether a piece of legislation satisfies both these criteria.
The limited powers of the IRP have led the AJTC to suggest that the new procedure breaches both of these rights. By delegating the final decision to the school's governing body, S.51(A) fails to provide a genuinely independent review of exclusion decisions. Similarly, even if the IRP finds that the decision to exclude was illegal, irrational or procedurally unfair, there is no effective remedy for the pupil in that situation. Despite an independent body admitting that the school breached public law principles, the excluded pupil is still at the whim of the governing body.
How have the government responded to this?
In response to the AJTC's concerns, the government drew attention to the fact that Article 6 is only engaged when a 'civil right' is being determined. In the Court of Appeal case of R (on the application of LG) v The Independent Panel for Tom Hood School [2010] EWCA Civ 142, it was held that Article 6 was not engaged in an exclusion hearing before an independent appeal panel because it did not impact a 'civil right'. While there is a right to education (Article 2, Protocol 1 of the ECHR), there is no right to be educated at a particular institution.
Does the government's response stand up to scrutiny?
A few months later, the Grand Chambers of the European Court of Human Rights decided Orsus v Croatia. Ostensibly, the case has little to do with exclusion hearing – the facts of the case concern discriminatory treatment of the Roma people. However, the case in question held that Article 6 was engaged in an education dispute.
The government stated that the facts were too far removed to be of any relevance. Yet a closer reading of the case suggests that it does hold relevance to exclusion hearings. As the JCHR noted, a major part of Orsus considered what constitutes a 'civil right'. It established that the proper test should be:
Where a State confers rights which can be enforced by means of a judicial remedy, these can, in principle, be regarded as civil rights within the meaning of Article 6.
The 'civil right' in question is not the right to education, but whether it is amenable to a judicial remedy. Since the right to appeal the exclusion can be heard via judicial review, it naturally follows that Article 6 of the ECHR does apply to exclusion hearings.
It has been suggested that the possibility of judicial review in itself could satisfy the requirements of Article 6. However, this claim has little weight to it. Judicial review does not provide an opportunity to challenge findings of fact made by the governing body of the school. While independent review panels do have such jurisdiction, the means by which they can give practical effect to the judgment are limited.
What should be done?
In summary, the current procedure for school exclusions breaches Article 6 of the ECHR. It is an affront to natural justice and the principles of a fair and independent hearing. Since the vast majority (70%) of exclusion hearings concern issues of SEN, the JCHR has recommended that all exclusion hearings should be appealed to the first-tier tribunal. This would remove the incompatibility by providing a genuinely independent tribunal with the jurisdiction to provide an effective remedy.
The seriousness of a school exclusion should not be underestimated. Most excluded children must attend a Pupil Referral Unit (PRU), which overall have a poor record of educating excluded children. Less than 1% of pupils at PRUs achieved 5 GCSEs at grades A*-C in 2008,2 and only 11.7% achieved at least one GCSEs at A*-C. With this in mind, it is vital that the rules of natural justice are followed and pupils are given a fair hearing.
Anirudh completed the GDL and is currently studying for the BPTC. He has represented clients in GDC and IRP Hearings. Prior to the GDL, he taught debating and conducted policy research on the North-South Divide.
This article was prepared by the author in their personal capacity. The opinions expressed in this article are the author's own and do not reflect the view of, nor are condoned by, the School Exclusion Project, Matrix Chambers, 11KBW, City University or our partners.
Human Rights, School Exclusion | {
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If you have bad credit you will want to take steps to improve it right away. That does not mean that you need to find quick fixes. The truth is that there is no way to fix your credit in a quick manner. It takes time to bring your credit score back up. You may want to begin to watch how you use credit and control your spending to begin to improve your credit score.
Before you take any measures to improve your credit, you need to know exactly where you stand. You can get a free copy of your credit report. Once you receive this data, you will want to make sure that it is correct.
If you find any errors, you need to contact the credit bureau and the reporting agency. Disputed information can include late charges and account balances that are incorrect. You will need to write a letter to the credit bureau and the creditor to explain the incorrect information and include any and all documentation you have to prove this claim. The entire process can take up to thirty to ninety days, but is well worth your effort.
The biggest factor that contributes to your credit score is making your payments on time. Today you can sign up for automatic payments that will draft what is due directly from your bank account.
If you are not comfortable doing this, then you can sign up for reminders. Reminders come in the form of texts and emails and let you know exactly when a payment is due. Automatic payments may be convenient, but they are not necessarily good since they tend to be forgotten about and do not teach a sense of money management.
Thirty five percent of your credit score is calculated by tracking your payment history. This is why it is so important to make payments on time since it effects your credit score the most. You should not get discouraged if you have had problems making your payments on time in the past.
Yes it will affect your credit score, but the longer you remain in good standing with your creditors, the better off you will be. The process is long and arduous, but worth every effort to improve your credit score.
If you have not made any payments and let your account slip into delinquency, then your credit score will receive another major blow. Once an account has been reported as delinquent, you will have to try even harder to make future payments on time.
This applies to just being a few days late. It is imperative that you make payments on time and make a serious attempt to continue this routine. The more you pay your creditors in a timely fashion, the better your score will appear over time. It may take months of prompt payments to raise your score. A single late payment can mean a dip in your credit that takes months to improve.
The good news is that the older a credit problem, the less it counts toward your score. That means that you will not be troubled by bad credit forever. The key is to keep up a decent payment pattern. This will show that you are able to manage your credit better.
Credit accounts that have been handed over to collection agencies are not good for your credit report. You need to be very careful and try to keep from letting any of your payments get so far behind that they are given to a collection agency to collect.
Even when these types of accounts are paid off, they remain on your credit report for seven years. Before an account needs to be turned into a collection agency you should try talking to a credit counselor. They can help you lower payments and save extremely bad marks on your credit score by helping you set up a payment plan. Using a credit counselor that is legitimate will not hurt your credit score.
You also need to focus on reducing the amount of debt that you currently owe. The more you are able to pay attention to paying your debt off the more you will feel satisfied regardless of whether it improves your credit score right away. Before you can ever begin to start paying a credit card down, you have to stop using them.
Interest rates should be considered when you are looking at the payments you make. If you can pay over and above the interest rate then you will see the amount you owe decrease quicker. Note that it is a good idea to find the highest interest rate you have on a credit card and apply higher payments to those accounts while you continue to pay the minimum on the rest of your accounts.
Another way you can improve your credit score is by opening new accounts. You will need to make payments on time and take serious responsibility when it comes to paying them off. In the long run, you will improve your credit score. Be careful and do not open accounts just to have different types of credit cards. The chances that opening them will raise your credit score is very slim.
If you have bad credit, consider looking at credit cards for bad credit. These can help you establish or re-establish good credit in a timely manner. Just be sure to make your payments on time, as they can hurt you just as bad as any other credit card.
Sometimes people think that just having a credit card will raise your credit score. The truth of the matter is that you will have a higher credit score verses someone who has no credit cards. The key is in maintaining them responsibly and making payments on time. Even if you have had trouble in the past, you can rebuild your credit with determination and timely payments.
Repairing your credit score is more than just about making timely payments, however. Keep in mind that closed accounts will still remain on your credit report and have consideration when figuring your credit score.
The major thing you can do to fix your credit is fix any errors you may have in your credit history. If you have no errors then maintain excellent credit by making payments on time. Just remember in order to raise your credit score; you will need discipline and patience. It takes time to re-establish a good score once you have a poor mark on your credit. | {
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The 2011 Chicago Comic and Entertainment Expo (C2E2) took place on March 18-20 in McCormick Place's west building. The showroom was open between 10a.m.-7p.m., but there were a few events that took place afterwards.
The convention attendants spent most of their visit wandering around the showroom floor, which was filled with all sorts of exhibitors. Comic book and video game publishers sold their products and offered free samples, while comic book creators chatted with fans, gave autographs and showed off their work. Many of the creators in attendance were locals, which enhanced the convention's Chicago flavor. Other Chicago area comic book stores, toy stores, movie retailers, ardent comic collectors, and miscellaneous fan-orientated retailers sold their products, usually at some sort of discount.
The showroom was also home to the Artist Alley, a place where professional and amateur creators can display and sell their work. The name was something of a misnomer, since it featured almost as many writers as it did artists. Many of the creators involved were locals, and were happy to chat with fans and sign autographs.
C2E2 featured over a hundred of panels dedicated to a wide variety of topics. Some focused on certain comics, movies and television shows, while others dealt with the creative processes, the history of the medium and other more technical topic. Fans of genre television got a chance to ask questions to the cast of HBO's True Blood and A&E's Walking Dead. The fans of Chuck had the opportunity to see the exclusive footage from the show and talk to its creators.
C2E2 also played host to several screenings of movies and television shows, including new and classic Japanese cartoons, independent films and preview compilations. Highlights included Jerry Beck's Worst Cartoons Ever!, a compilation of some of the cheapest, worst animated cartoons in history, and Boy Wonder, a psychological deconstruction of superhero morality.
But one of the most distinctive aspects of the convention was the array of costumes. As usual in genre fan conventions, many attendees engaged in cosplay (costume play), that is to say, they dressed up as various fictional characters. The costumes ranged from amateur to almost professionally elaborate, and it was hard to point a camera without at least one cosplayer getting in the shot. The cosplayers even got a chance to show off their costumes at the daily costume contests and at the Saturday Night Masquerade, which gave fans a chance to perform skits while in costume.
For most of their history, comic book conventions were niche events that interested fans of comic books and virtually no one else. But over the last few years, long-running conventions have expended far beyond their original scope, covering movies, television shows and video games. Many media companies have used comic conventions as venues to unveil and advertise their products; San Diego Comic Con, for example, has become a popular place to unveil new television shows, movies and video games, thus making these conventions more popular than ever.
With this in mind, it was only natural that Reed Exhibitions, one of United States' largest event organizers, wanted to get in on the action. In 2006, it launched the New York Comic Con., and in the spring of 2010, it launched the Chicago Comic and Entertainment Expo. Set up at McCormick Place Convention Center, the convention drew approximately 27,500 attendees last year. While that number was not quite as large as Reed Exhibition hoped, it was large enough to ensure that C2E2 would return this year.
While much of C2E2 was geared toward the fans of comic books, it had something to offer to genre fans of other mediums too. And, if the turnout in the past two conventions is any indication, it will continue to do so for years to come. | {
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"The Shadow of Dia-Sust" chronologically follows the five adventures presented in my 1983 collection Death in Asakad and Other Stories (published under the title The Ghost Army). With this one, I do my best to demonstrate that sword-and-sorcery fiction can be taken seriously — by its writers and by its readers — as a literary (or at least thoughtful) form of mainstream genre storytelling.
We've published David C. Smith's fiction and non-fiction here at Black Gate — including excerpts from his noir thriller Dark Muse and his supernatural pirate dark fantasy novel Waters of Darkness, written in collaboration with Joe Bonadonna.
The complete catalog of Black Gate Online Fiction, including stories by Vaughn Heppner, Howard Andrew Jones, David Evan Harris, Janet Morris and Chris Morris, John C. Hocking, Michael Shea, Peadar Ó Guilín, Aaron Bradford Starr, Martha Wells, Nina Kiriki Hoffman, C.S.E. Cooney, and many others, is here.
"The Shadow of Dia-Sust" is a complete 14,000-word short story of heroic fantasy offered at no cost.
I had a copy of this book many years ago but got rid of it somewhere along the line and could never remember who wrote it or what it was called. As soon as I saw that cover, I knew it was the one. Thanks!
Glad to be of service, Bob! | {
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The Fearful Rise of Markets: Global Bubbles, Synchronized Meltdowns, and How to Prevent Them in the Future by John Authers
Get full access to The Fearful Rise of Markets: Global Bubbles, Synchronized Meltdowns, and How to Prevent Them in the Future and 60K+ other titles, with free 10-day trial of O'Reilly.
Chapter 24. The Paradox of Diversification
Jon Stewart: "My mother is 75 and she bought into the idea that long-term investing is the way to go. And guess what?" Jim Cramer: "It didn't work."
Interview on Comedy Central's The Daily Show Jon Stewart, March 11, 2009
October 2008 saw virtually every kind of asset collapse together, in truly unprecedented fashion. This inflicted losses on most investors around the world and showed that they need a new way to mitigate risk.
By Monday, October 6, 2008, all reason for optimism had been exhausted—there was a run on banks, governments evidently could not deal with it, and markets were wildly overvalued after decades of moral hazard and herding behavior by investors. The result was the markets' most ...
Get The Fearful Rise of Markets: Global Bubbles, Synchronized Meltdowns, and How to Prevent Them in the Future now with O'Reilly online learning. | {
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The dark, complicated history of Durban's national dish — curry and rice
By Ishay Govender-Ypma
Within the humid port city of Durban and its surrounds on South Africa's palm-tree-lined east coast, a unique style of Indian cuisine has evolved over the course of 158 years. Locals say you can't leave before you try one of the Durban curries — smoldering hot mutton curry studded with potato chunks called "gravy soakers"; fiery fish curry spiked with black tamarind and curry leaves; or bunny chow, a hollowed-out quarter-loaf of white bread filled with curry. One popular filling is the finger-staining broad bean curry — the only way to eat it is with your hands.
Zuleikha Mayat and the Women's Cultural Group labeled Durban curry and rice a "national dish" in 1961 in Indian Delights, an instrumental community collection that was also the first cookbook by Muslim authors in South Africa.
Bunny chow, a Durban Indian curry dish served in a hollowed-out loaf of bread Ishay Govender-Ypma
The story of this cuisine commences long before my ancestors, the indentured Indians, arrived in Durban. More than 150,000 Indians — mainly agricultural laborers from lower castes — were sent to the South African port city between 1860 and 1911 at the request of the British. They were destined for the unruly sugar cane plantations, railways, and fishing and boating industries.
With its bounty of staples and spices, Durban Indian food originated, of course, in India, and was entwined with the food available in South Africa, which was cultivated and reared by the indigenous Zulu people.
The rare exception was cattle, as the majority of Hindu arrivals abstained from beef. In Ultimate Curry Bible, author Madhur Jaffrey points out that Durban curry is "a collective spicy cuisine in which regional specifics were replaced by a more general 'Indianness'." Over time, a blend of South African cultures helped shape Durban's culinary identity.
The port city of Durban, on the east coast of South Africa Ishay Govender-Ypma
Today, Durban's 800,000 Indians — descendants of the indentured South Indians and "passenger" (merchant class) Gujaratis who arrived to pursue entrepreneurial interests — form the highest concentration of Indians in a city outside India. They've left an indelible print on the country's cultural and culinary landscapes: Migration and intercultural sharing have been a consistent part of South African history despite successive repressive regimes.
While researching my cookbook Curry: Stories & Recipes across South Africa, a social study examining this singular dish prepared by home cooks in all its forms and across demographics, I attempted to unpack the journey of the indentured laborers and examine their relationship with a foreign land and its produce.
The laborers were promised rations of rice, dholl (yellow split peas), salted fish and oil, according to a legal notice from 1874. But some ingredients, including rice, weren't always available. And just as masalas and spice blends were adjusted, food was modified based on circumstance. Maize (hominy) was chipped into "rice"; coconuts were scarce and reserved for symbolic ceremonies, not for cooking like in Tamil Nadu, India; cheap vegetable oil replaced ghee, coconut and mustard oils; sour porridge was prepared with locally available maize meal instead of rice.
Dried fish curry Jurie Senekal/Curry: Stories & Recipes across South Africa
The Gujarati Hindu and Muslim merchant class, who arrived unbonded and with greater means, opened trading stores to supply the laborers with conveniences from home, including the specialty vegetables and fruit that flourished in the humid, verdant surrounds. Their habitual travels back to villages in India ensured their particular cuisine remained relatively consistent. Indentured laborers were allowed to practice their religions and communal customs, and with this, food rituals associated with prayer and ceremony were preserved. Accordingly, the merchants supplied fresh coconuts, limes, chilies, grinding stones, heavy-based pans and ceremonial goods.
My ancestors were also influenced by their Zulu neighbors over the years. Consider the regional specialties of curried Zulu "running" (free-range, mature) chicken, spicy braised green bananas (which grow there with ease), madumbe (a local yam that replaced potatoes) and amasi (soured milk) raitas.
Later, their descendants (like my grandparents and parents) would prepare adaptations of this food while living in insular, racially segregated communities, splintered by apartheid from 1948 until 1991. My mother calls the frugal meals of this time "specialties": dried shrimp and luffa, tinned pilchard curry and sheep trotters with speckled sugar (borlotti) beans. There are local versions (accompanied by localized spellings) of breyani, dholl, samoosa, spicy pickles and sweets.
The limited mobility of the indentured Indians, and the fact that South Africa was isolated from the international arena during apartheid, meant the cuisine percolated in the region and developed its own unique and complex traits over time — the fiery red color, the generous use of curry leaves and potatoes that appear even in biryanis, for example. There's an exuberant use of oil; many refer to the customary oil slick fondly, but no one can say why it exists.
Spices for Durban Indian cooking Ishay Govender-Ypma
Although the British were fastidious notekeepers, they were superficial participants in their servants' lives. Since most of the latter were illiterate or couldn't write in English, there are scant records of the foods prepared. Sometimes, as is the case with colonization, there are skewed views formed and distributed by the oppressors, Durban's 1860 Heritage Centre spokesman Satish Dhupelia said during a tour of the center.
Because of the Brits' immaculate shipping records, I was able to determine that my maternal great-grandfather Cuppusamy Moodley, then a scrappy 5-year-old, arrived in Durban in August 1889 aboard the Congella II steam ship from Madras (Chennai). He was accompanied by his 27-year-old mother Parvathi and 1-year-old brother Natasen, from Tamil Nadu's Chengalpattu district. I imagine Cuppusamy's curiosity and perhaps fear, traveling in this vessel full of anxious faces, rattled by the ocean winds and storms. Did he annoy Parvathi with childish games, or lift her spirits when the baby cried or food rations were low? Did they stash fragrant seeds, spice mixes and a treasured pot in their trunk?
A photo of the author's ancestors; her mother is the young woman in the lower left-hand corner Bagium Iyapillay and her family
Imagination aside, I cannot confirm whether my great-grandparents told Bagium, my maternal grandma, about their longing for the rice-based appam, idli and sambar, and sweet payasam of their distant youth. The paper-thin fermented rice-flour dosas, whole-wheat chapattis, the ghee-rich sweets and curd-smothered spiced rice were things that belonged in the past. Bagium, who became a community cook, served a derivative of those memories, what we call "Durban Indian food" today.
Durban Indian cuisine is a result of a desire to thrive and an adaptation to place and circumstance, but it's nearly impossible to trace the first Durban curry prototype. Shamen Reddi, the 51-year-old restaurateur of Impulse by the Sea in South Africa's Tinley Manor who found herself in the curry business at age 19, said her curries remain true to that of her forebears: "Durban Indian food's survival hinges on nostalgia," she said. Reddi — and the countless Durban Indian cooks I've interviewed over the years — take great pride in propagating that nostalgia and are aware of the cultural importance of keeping these ancestral traditions alive.
Ishay Govender-Ypma is a freelance food and culture journalist, former lawyer, guidebook writer and author of Curry: Stories and Recipes across South Africa (Human & Rousseau). | {
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California is in the grip of an extended heat wave that can cause life-threatening conditions.
Each year approximately 20 people die from heat-related emergencies. In 2006 a severe heatwave resulted in 655 deaths and over 16,000 excess emergency room visits throughout the state.
Drink Plenty of Fluid – Increase your fluid intake regardless of your activity level. During heavy exercise in hot weather, drink 2-4 glasses (16-32 ounces) of cool fluidseach hour. Consult with your doctor if you have been prescribed a fluid-restricted diet or diuretics. During hot weather, you will need to drink more liquid than your thirst indicates. This is especially true for those over 65 years of age. Avoid very cold beverages to prevent stomach cramps or drinks containing alcohol, which will actually cause you to lose more fluid.
Replace Salt and Minerals – Heavy sweating removes salt and minerals from the body, which are necessary for your body and must be replaced. The best way to replace salt and minerals is to drink fruit juice or a sports beverage during exercise or any work in the heat. Do not take salt tablets unless directed by your doctor. If you are on a low salt diet, ask your doctor before changing what you eat or drink.
Wear Appropriate Clothing and Sunscreen – Wear as little clothing as possible when you are at home. Choose lightweight, light-colored, loose-fitting clothing. In the hot sun, a wide-brimmed hat will keep the head cool. Sunburn affects your body's ability to cool itself and causes a loss of body fluids. It also causes pain and damages the skin. A variety of sunscreens are available to reduce the risk of sunburn. Check the sun protection factor (SPF) number on the label of the sunscreen container. Select SPF 15 or higher and follow package directions.
Pace Yourself – If you are unaccustomed to working or exercising in hot weather, start slowly and pick up the pace gradually. If exertion in the heat makes your heart pound and leaves you gasping for breath, stop all activity, get into a cool or shady area, and rest, especially if you become lightheaded, confused, weak, or feel faint.
Stay Cool Indoors – The most efficient way to beat the heat is to stay in an air-conditioned area. If you do not have an air conditioner or evaporative cooling unit, consider a visit to a shopping mall or public library for a few hours. Do not rely on electric fans as your primary cooling device during a heat wave. When the temperature is in the high 90s or higher, a fan will not prevent heat-related illness. A cool shower or bath is a more effective way to cool off.
Schedule Outdoor Activities Carefully – If you must be out in the heat, plan your activities so that you are outdoors either before noon or in the evening. While outdoors, rest frequently in a shady area.
Use a Buddy System – When working in the heat, monitor the condition of your coworkers and have someone do the same for you. If you are 65 years of age or older, have a friend or relative call to check on you twice a day during a heat wave. If you know anyone in this age group, check on them at least twice a day.
• people who are overweight.
If you or someone you know is at higher risk, it is important to drink plenty of fluids; avoid overexertion; and get your doctor or pharmacist's advice about medications taken for high blood pressure, depression, nervousness, mental illness, insomnia, or poor circulation.
Adjust to the Environment – Be aware that any sudden change in temperature, such as an early summer heat wave, will be stressful to your body. You will have a greater tolerance for the heat if you limit your physical activity until you become accustomed to the heat. If traveling to a hotter climate, allow several days to become acclimated before attempting any vigorous exercise, and work up to it gradually.
Use Common Sense – Avoid hot foods and heavy meals; they add heat to your body. Do not leave infants, children, or pets in a parked car. Bring your pets indoors with you to protect them. Dress infants and young children in cool, loose clothing and shade their heads and faces with hats or an umbrella. Limit sun exposure during the midday hours and in places of potential severe exposure, such as beaches. Ensure that infants and children drink adequate amounts of liquids. Give your outdoor animals plenty of fresh water, leave the water in a shady area, and consider wetting the animal down.
Two common problems are heat stroke and heat exhaustion. Heat stroke occurs when the body becomes unable to control its temperature. The body's temperature rises rapidly, the sweating mechanism fails, and the body is unable to cool down. Body temperature may rise to 106°F or higher. Heat stroke can cause death or permanent disability if emergency treatment is not given. Heat exhaustion is the body's response to an excessive loss of water and salt contained in sweat. Those most prone to heat exhaustion are elderly people and people working or exercising in a hot environment.
• Cool the victim rapidly using whatever methods you can. For example, immerse the victim in a tub of cool water; place in a cool shower; spray with cool water from a garden hose; sponge with cool water; or if the humidity is low, wrap the victim in a cool, wet sheet and fan him or her vigorously. | {
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The Andean foothills found on the outskirts of Santiago are mainly private property. The management of this area has been an issue of conflict between residents and developers. Using the example of the municipality of La Florida, this article focuses on how conflict over the Andean foothills goes beyond simple land-use issues to create a new relationship with the "mountain" and new forms of land management. Combining ethnography and geography, this text highlights the role of the Andean foothills' peculiar characteristics in the collective demands of citizens committed to their protection and conservation. It also discusses the role of conflict in creating and amplifying territoriality and as a process of (concrete as well as abstract) territorialisation and innovation in itself. The development of a community park that is neither private nor public highlights how innovative solutions can emerge from these citizen mobilisations. | {
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namespace dariadb {
namespace compression {
struct DeltaCompressor : public BaseCompressor {
EXPORT DeltaCompressor(const ByteBuffer_Ptr &bw);
EXPORT bool append(Time t);
bool is_first;
Time first;
int64_t prev_delta;
Time prev_time;
};
struct DeltaDeCompressor : public BaseCompressor {
EXPORT DeltaDeCompressor(const ByteBuffer_Ptr &bw, Time first);
EXPORT Time read();
int64_t prev_delta;
Time prev_time;
};
}
}
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Often, when I am wandering lonely along the shore, mist brushing my nose and wind whipping my hair, I grow melancholy thinking about the time I tricked a baby deer into falling down a well. I stop and sigh and let the tears roll down my cheeks. Why do these thoughts make me so sad? After all, it wasn't really a baby deer, it was just my friend Schaffer dressed in a puffy hamburger costume. I guess the sadness comes when I think of how cute baby deer are, and how Schaffer lost all those Big Mac coupons while he was thrashing around down there. One could argue that the puffy hamburger costume saved his life, but that's hardly an excuse for tears. No, no, no – surely this pathos lies with the baby deer. Hmm.
Chin up, Esther. No-one could possibly fault you for making your own entertainment, now that toddlers are no longer tumbling down wells of their own accord every five minutes, like in the Good Old Days. I suppose that they are all too obese now.
Momma's in or adjacent to the freezer, Dad's hanging in the closet, and now Shaffer's in the well.
it's nice to see a post from you, good madam. and shaffer had it coming.
Miss Wilberforce-Packard : How I envy you, indeed, all who can rise to the occasion regarding the emotion of Melancholia. When first I laid eyes on that delightful image done by Mr. Durer I knew at once that Melancholia was for me. But, alas it has not been so. Try not to stray too close to the sea, I have read that its allure can over-power the innocent.
Why did you run from the well, Esther? What was it that you saw?... Do you still hear the cries of the hamburger, Esther?
This reminds me of that old song, "Farmer in the Well." Or the old movie, "Three Coins in the Well." All good fodder for people like me.
So sorry about your friend. But baby deer have enough unearned sympathy--we have Disney to thank for that absurdity. | {
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Ukraine Live Day 596: Ukrainian Foreign Minister Says Putin Agreed For OSCE To Be Given Full Access To Occupied Territory
Nadezhda Savchenko and her lawyer, Ilya Novikov, in court today. Photo via Radio Svoboda
Yesterday's live coverage of the Ukraine conflict can be found here. An archive of our liveblogs can be found here. For an overview and analysis of this developing story see our latest podcast.
Please help The Interpreter to continue providing this valuable information service by making a donation towards our costs.
For links to individual updates click on the timestamps.
For the latest summary of evidence surrounding the shooting down of flight MH17 see our separate article: Evidence Review: Who Shot Down MH17?
Separatists Agree To Postpone 'Elections' Until Next Year
The Donetsk News Agency (DAN), a news website that operates as a mouthpiece for the self-proclaimed Donetsk People's Republic (DNR), reports this afternoon that separatist officials have agreed to postpone local elections in the occupied regions of the Donbass.
The DNR had been intending to hold elections on October 18 while their counter parts in the Lugansk (the LNR) were due to vote on November 1.
Neither of the elections were to have been conducted in accordance with Ukrainian law or under the auspices of the OSCE. Local elections will be held across the rest of Ukraine on October 25.
The news confirms reports from the Contact Group in Minsk yesterday that the separatists were considering postponing the votes in exchange for Ukrainian concessions on amnesties and allowing separatist factions to participate in elections.
Today Denis Pushilin and Vladislav Deynego, representatives at the Minsk talks for the DNR and LNR respectively, announced (translated by The Interpreter):
"We are pleased to notify you that the LNR's proposal to postpone the elections in the Donbass until February 21, 2016, on condition of the complete fulfillment of the political points of Minsk 2 by Kiev, has been taken into account by the Normandy Quartet. We have studied the statements and recommendations of Mrs Merkel and Mr Hollande. Today, here in Minsk, we have held consultations with representatives from the OSCE and Russia. We have received instructions from our leaders Aleksandr Zakharchenko (head of the DNR) and Igor Plotnitsky (head of the LNR).
As a result of this work we are announcing the agreement of the DNR and LNR to move the elections from October 18 and November 1 to the following year."
DAN notes that Deynego and Pushilin have repeated their demands that Kiev must comply with their demands for an amnesty for participants in the events of the war and allow separatist parties to compete in elections.
Furthermore, the separatist envoys seek amendments to the Ukrainian constitution, to be drafted in coordination with the separatist leadership.
— Pierre Vaux
Prosecution Calls Witnesses In Savchenko Trial
Nadezhda Savchenko is back in court today in the Russian border town of Donetsk in the Rostov region for another hearing in her murder trial.
Translation: Nadezhda Savchenko and her lawyer Ilya Novikov at today's court hearing
Savchenko was captured by Russian-backed fighters near Lugansk last summer and illegally transported to Russia, where she is on trial for the murder of two state television journalists during the shelling of a separatist checkpoint. She is accused of acting as a spotter for the attack. Savchenko denies the charges and says she has neither acted a spotter nor did she hear of the attack until she was already in separatist detention.
The Russian authorities claim that she was arrested on Russian soil after having crossed the border illegally herself. Video of her interrogation in Ukraine, uploaded by separatist fighters last summer, makes this seem highly implausible.
RFE/RL's Ukrainian service, Radio Svoboda, reports that the trial judge announced the death of the mother of one of the journalists Savchenko is accused of killing, Anton Voloshin, before the start of today's hearing.
Mikhail Lutsenko, a highway patrol officer who the prosecution says detained Savchenko while she was a passenger in a car in Russia's Voronezh region, is giving evidence to the court.
On October 1, two prosecution witnesses, Sergei Bobro and Sergei Rudenko, told the court that they had met Savchenko on the road between Boguchar and Kantemirovka. The accused had, Bobro said, asked for directions to the nearest village and they decided to give her a lift. Later, they were halted at a police traffic stop and Savchenko was detained due to her lack of documents.
However Savchenko herself denies this, saying that the two men were in fact involved in her abduction from Ukraine.
Furthermore, Savchenko said today in court that Lutsenko has cooperated with her kidnappers:
Translation: Savchenko: He did not let me out of the car when I wanted to get out, but he says he did not detain me. Thus she described Lutsenko's participation in her kidnapping
Nikolai Polozov, one of Savchenko's lawyers, says that the court has failed, despite requests, to provide the official documentation of Savchenko's police stop.
Ukrainian Soldier Wounded In Skirmish Near Tryokhizbenka
Colonel Andriy Lysenko, military spokesman for the Presidential Administration, has told reporters that one Ukrainian soldier was wounded yesterday morning during a skirmish with Russian-backed fighters near the village of Tryokhizbenka in the Lugansk region.
According to Lysenko, the enemy diversion and reconnaissance group was forced to retreat back across the Seversky Donets river.
Otherwise, Lysenko claimed, there were no attacks recorded across the rest of the front line over the last 24 hours.
Three enemy drone flights were detected yesterday, near Marinka and Mariupol.
Ukrainian Foreign Minister Says Putin Agreed For OSCE To Be Given Full Access To Occupied Territory
Ukrinform reports that Pavlo Klimkin, the Ukrainian foreign minister, has said that President Vladimir Putin agreed in Paris last week that the OSCE Special Monitoring Mission to Ukraine (SMM) should have full access to monitor all of the occupied territory of the Donbass.
Klimkin was speaking live on the Svoboda Slova talk show on ICTV last night.
The foreign minister said (translated by The Interpreter):
"This was the first time I had heard from the Russian side, from Putin, that the OSCE monitoring mission must have full access to all of the Donbass, in accordance with their mandate. Without this full access there can be no assurance whatsoever that we are making any progress in the sphere of security. It is not complete and we cannot talk about the next steps. How can we talk about the withdrawal of Russian troops or Russian hardware when no one is monitoring this across the whole expanse of the Donbass?
Because our agreements – mine clearance under the auspices of the OSCE, the prohibition of the use, by the Russian side, of electronic warfare systems to block OSCE drones – these are very important. But this one agreement – full access for the OSCE – it opens the way."
This British Foreign Office map is a handy indicator of those areas of the Donbass in which the SMM is currently restricted from operated freely:
Mine clearance Minsk II Minsk talks Nadezhda Savchenko Normandy Quartet OSCE OSCE SMM Paris Talks Pavlo Klimkin Russian invasion Russo-Ukrainian border September 1 Ceasefire Ukraine Vladimir Putin
Summaries of Newly Obtained KGB Training Manuals
GoFundMe: The Lubyanka Files: The Textbooks for Putin's Spies
The Kremlin's Anti-Western (and Remarkably Successful) Middle East Media Project
Dissecting Steele's Trump-Russia Dossier
Trump Has Done More Than Collude With Putin: He's Helped Kremlin Leader Destroy Post-1945 World
What Do You Call a Successful Terrorist? Your Excellency! | {
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My absence kills. My excess kills.
And all life comes at my command.
To so much shifting golden sand.
And perish once beneath my hand.
The sun recedes. I ride the wind.
My chill falls white across the land.
A good thrust there, but no. A volcano turns earth into igneous rock and obsidian--not into sand--nor does a volcano extinguish flames; to the contrary, when a volcano erupts, the sky burns, hot ash and pyroclasts trigger wildfires, lava flows ignite and incinerate anything in their paths...fire reigns.
But for being so hot, volcanoes are pretty cool.
At least two people in Hawaii are terminally stupid.
Stop poking it, lady! You're burning up your stick!
You know, this cabin in the woods could also be somewhere inside the Arctic Circle or the Antarctic Circle. As long as you're not too close to either pole, you still have forests (such as the evergreen forests of Norway, Finland, Alaska and the Yukon territory, the taigas of Northern Russia or the wind-sculpted forests of Argentina's Tierra del Fuego archipelago). Even in the middle of spring, the temperatures can — and often do — drop below freezing. And any fresh snowfalls would obliterate any footprints leading to or from the cabin. After that, all you need is for the people in the cabin to run out of firewood while they're asleep, then the cold creeps in and they die in their beds. Or they might wake up when they're in late-stage hypothermia (as in "You're almost dead" hypothermia), and that's when disorientation and delirium set in, so they freeze to death while they're wandering around the darkened cabin in their Underoos.
Late answer is late, I know. | {
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Sights and Attractions near Diesel
Diesel, 72 King's Road, Knightsbridge, London SW3 4UG
All Activities for Kids Art and Design Art Galleries Attractions for Kids Boats Boats and Bridges Historic Buildings House and Garden Museums Other Attractions Parks and Gardens Sights Sightseeing Tours Venue Hire
Saatchi Gallery
Duke of York's Square, King's Road, Chelsea, London SW3 | 2 minutes walk from Diesel
The Saatchi Gallery re-opened on 9th October 2008 in the former military barracks of the Duke of York's Headquarters. The 70,000 square feet represents a... More
Sloane Square
London > Attractions
1 Sloane Square, SW1W | 4 minutes walk from Diesel
Sloane Square , a Chelsea landmark named after Sir Hans Sloane who owned the land, is in a prime spot in... More
Royal Hospital Chelsea
Royal Hospital Road, Chelsea, London SW3 | 6 minutes walk from Diesel
Built by Sir Christopher Wren 1682-1692, the Grade I-listed Royal Hospital Chelsea was intended by King Charles II to be a home for soldiers who... More
Proud Chelsea
161 Kings Road, Chelsea, London SW3 | 6 minutes walk from Diesel
Art gallery Proud Chelsea brings top quality rock 'n' roll photography to the heart of King's Road. There are several strings to the Proud bow... More
The Fine Art Society
The Michelin Building, 81 Fulham Road, Mayfair, London SW3 | 7 minutes walk from Diesel
Founded in 1876, this major London art dealer is most famous for pioneering the notion of the one-man exhibition - the most famous of... More
More than 23 million pounds has been spent on re-development of the National Army Museum which reopens in 2017 to reveal a... More
St Columba's Church of Scotland
Pont Street, Knightsbridge, London SW1X | 7 minutes walk from Diesel
There has been a church on the site since 1884. It was bombed in 1941, rebuilt in 1955 and is now a Grade II listed... More
Eccleston Yards
Eccleston Place, SW1W | 11 minutes walk from Diesel
Previously a coach manufactory and once home to the Westminster Electrical Supply Corporation, Eccleston Yards has become a destination for food, fashion, retail, co-working and... More
Purple Dragon
Grosvenor Waterside, 30 Gatliff Road, Pimlico, London SW1W | 11 minutes walk from Diesel
Purple Dragon is a dream playground, kindergarten, day nursery and private members' for kids. Relocated from its original location in Battersea, the exclusive club... More
Brompton Oratory
Brompton Road, South Kensington, London SW7 | 11 minutes walk from Diesel
Built in 1884, in the Italianate Baroque style, the Brompton Oratory is an exact imitation of the Church of the Gesu in Rome and sports... More
Victoria and Albert (V & A) Museum
Cromwell Road, South Kensington, London SW7 | 12 minutes walk from Diesel
The Victoria and Albert Museum (V&A) was originally founded in 1852 to inspire and educate British designers and manufacturers. Today it... More
National Trust: Carlyle's House
24 Cheyne Row, Chelsea, Chelsea, London SW3 | 12 minutes walk from Diesel
A Queen Anne Town House occupied by historian and 'Sage of Chelsea' Thomas Carlyle and his wife Jane from 1834-1881. A man of letters, Thomas... More
V&A Exhibition Road Quarter
V&A Museum, Cromwell Road, SW7 | 12 minutes walk from Diesel
A new purpose-built underground gallery, magnificent courtyard space and a new entrance from Exhibition Road on the west side of the Victoria and Albert Museum... More
St Peter's Church, Eaton Square
119 Eaton Square, Belgravia, London SW1W | 13 minutes walk from Diesel
St Peter's was built by Hakewill in 1827 and later enlarged by Blomfield in 1875. Rebuilt and opened in 1992, following a fire in 1987,... More
The Natural History Museum is sure to impress even the most jaded of children. This ornate museum is home to more than 70 million specimens... More
Exhibition Road, South Kensington, London SW7 | 15 minutes walk from Diesel
The Science Museum in South Kensington houses one of the most comprehensive collections looking at the development of science and industry, and it is all... More
Battersea Power Station
Circus West, Sopwith Way, Battersea, London SW8 | 15 minutes walk from Diesel
The masterpiece of architect Giles Gilbert Scott, the Grade II listed Battersea Power Station has taken on an iconic status in the capital. With its... More
Science Museum, Exhibition Road, South Kensington, London SW7 | 15 minutes walk from Diesel
A major permanent gallery on the second floor of the Science Museum, open on 25th October 2014, Information Age: Six Networks That Changed Our World... More
Wonderlab: The Statoil Gallery
Science Museum, Exhibition Road, SW7 | 15 minutes walk from Diesel
Wonderlab: The Statoil Gallery is the Science Museum 's most ambitious interactive gallery to date. Open from October 2016, the £6 million... More
Mathematics: The Winton Gallery
The Science Museum 's new gallery, Mathematics: The Winton Gallery , puts the spotlight on a subject often perceived as dry,... More
Nova Victoria
Buckingham Palace Road, SW1W | 16 minutes walk from Diesel
An architecturally striking development opposite Victoria mainline railway station , Nova Victoria is an... More
Battersea Park Children's Zoo
Battersea Park, SW11 | 16 minutes walk from Diesel
Battersea Park Children's Zoo is home to a host of glorious creatures. There are farmyard animals, lemurs, otters and monkeys, as well as peacocks which... More
Pump House Gallery
Built in 1861, the Pump House Gallery was originally a Victorian water tower supplying water to the lakes and cascades in Battersea Park. Following renovation,... More
Museum of Instruments
Royal College of Music Prince Consort Road, South Kensington, London SW7 | 17 minutes walk from Diesel
The RCM Museum of Instruments was started in 1894 with a donation from Sir George Donaldson. Today it features over six hundred instruments, some of... More
Wellington Arch
Hyde Park Corner, Belgravia, London W1J | 17 minutes walk from Diesel
A landmark triumphal arch set opposite the Duke of Wellington's residence at Apsley House, Wellington Arch was built in 1830 to commemorate the victories won... More
Edel Assanti
74a Newman Street, Victoria, London W1T | 17 minutes walk from Diesel
Charlie Fellowes and Jeremy Epstein's Edel Assanti Gallery has evolved since it was first set up in 2009, from a pop-up initiative to a project... More
Apsley House
149 Piccadilly, Hyde Park Corner, Belgravia, London W1J | 18 minutes walk from Diesel
Originally the London residence of the first Duke of Wellington, Apsley House was designed and built by Robert Adam between 1771 and 1778 and retains... More
Royal Geographical Society
1 Kensington Gore, South Kensington, London SW7 | 18 minutes walk from Diesel
For the past two centuries this old-fashioned 'learned society' has sent explorers and adventurers all over the world. Famous names from Mungo Park to... More
Westminster Cathedral
42 Francis Street, Westminster, London SW1P | 19 minutes walk from Diesel
Not to be confused with Westminster Abbey, the nearby Westminster Cathedral in Victoria is London's only example of neo-Byzantine architecture, described by the poet John... More
Kensington Gore, South Kensington, London SW7 | 20 minutes walk from Diesel
The Royal College of Art is one of London's most prestigious art colleges and the world's only wholly postgraduate university of art and design. Students... More
Near Diesel All London hotels
From cheap budget hotels to luxury 5 star hotels see our deals for Diesel hotels, including Holiday Inn London Bloomsbury from 52% off.
Hotels near Royal Exhibition Building, Australia
Hotels near Eulachhallen Winterthur, Switzerland
Our favourite new product. | {
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The Timeless Formula of 'Mystery Science Theater 3000' Goes Live
New host Jonah Ray discusses tour, honorable riffs, and nerd fan acceptance
By Seth Sommerfeld • November 6, 2018 3:30 pm
Tags: comedy, film, Q&A
Jonah Ray (yellow) joins Crow, Servo, and original host Joel Hodgson on the 'Mystery Science Theater 3000' live tour. Photo courtesy MST3K
The toxicity of nerd culture these days often leads to a this is why we can't have nice things result. If projects touching on any semblance of nerd nostalgia don't align with rigid expectations (often totally misguided ones), then fans attempt to stage online revolts. Thankfully, somehow the KickStarter-to-Netflix reboot of Mystery Science Theater 3000 was able to overcome any initial backlash to recapture the original's riffing-with-robot-puppets-over-B-movies magic while garnering universal acclaim (seriously, you can't top 100 percent on Rotten Tomatoes). With MST3K creator and original host Joel Hodgson overseeing things, a fresh comedic cast led by Jonah Ray as new host Jonah Heston unleashed an unrelenting barrage of geeky jokes that made it feel like the show had never left.
Mystery Science Theater now heads out on tour to celebrate the show's 30th anniversary. For the live shows, Hodgson joins Ray and the bots on stage for riffing mayhem. The tour swings into town on Sunday, Nov. 11, with the double feature of The Brain (matinee) and Deathstalker II (night screening) at The Moore.
We caught up with Jonah Ray to discuss the tour, honorable riffs, and nerd fan acceptance.
What about the Mystery Science Theater 3000 formula makes it timeless in a way that people still enjoy it, but flexible enough to change the cast and not miss a beat?
Joel has kind of felt that way about the show: that it would always be a revolving set of characters in the same world—that kind of Dr. Who thing, where you can change up everything, but it's still the same spirit of the show. It's a comedy/variety show: it's SNL, it's Your Show of Shows. The idea and the jokes that people like are still there.
People might like certain eras better. When I was 12 to 14, SNL was Phil Hartman and Chris Farley and Mike Myers and stuff like that, so that's why I'm like, "Oh, that was the best era!" But it's only because that's my era. And it just proves that shows like this can just kind of have this life and this renewal. It's just time-honored tradition of people making fun of other people's art.
How does preparing a MST3K live show differ from putting together an episode?
The nature of the show, the way it's made, it's so kind of live-to-tape that there's no real difference. But the once we start doing the show, that's when it starts to take another [life]. You start to hear what's working. You're like, "Oh, these jokes are a little too close together," because this riff happens and people laugh, but then they're laughing over the next line in the movie, so they're not gonna hear the set-up for the joke that comes after. So we just take out the joke that comes after. You're also like, "Oh, that joke's not working, but we need something here," and then you start rewriting and punching up. So the show has more of a live show frenetic energy during the sketches.
You toured MST3K when the reboot first came out, but how has this tour been different with the addition of Joel being onstage?
The way we set it up, me and the bots come out, and within the first scene, Joel is introduced and runs out. And hearing how excited the audience is to see him, and see him next to the bots, and see him in the jumpsuit, I get excited. Because I would've been screaming in the audience as well.
Also, just having another human to goof off with [is great]. The bots are fun, but someone who can move around with me onstage is kinda nice, you know?
If rights weren't an issue, do you have a dream movie to do for MST3K?
Joel's go-to is always Happy Feet. He hates that movie so much. [Laughs] I really pushed for Maximum Overdrive. I think it'd just be so fun, and it'd work so well right now because we're kind of in a Stephen King renaissance.
I'm trying to think of a movie that I really just hate. But I'm such a sucker for movies that I don't really hate that many movies. I always try to find something I enjoy about any of them.
It really would be something like Dawn of the Dead, where I know it and love it so much that I would really take the time to make it an honorable riff.
Just hanging with friends, a lot of the times the best riffing happens with movies that everyone knows, like a Star Wars. People are less upset about a movie being joked over when they are familiar with where the plot is going, like I'm pretty sure they're gonna try to blow up the Death Star.
That's the thing about riffing: to be able to sustain jokes that long, you have to let the movie show itself and let the characters show themselves, so you have stuff to riff off of. You'll see it—especially with the live shows—where when you get toward the end of the movie, some of the jokes aren't crazy-solid jokes, but they're character-based, because everyone knows the characters now. You can make subtler jokes that people really connect with and laugh hard at. So it's really important to let the movie reveal itself and not get in the way too much.
One of my favorite MST3K joke forms is when a character has been established just making up dumb lines or replies for y'all to say as them.
Yeah, that's one of my favorite things too. It's bestowing added character traits that's based off the character that's already there.
How many times do you have to watch a film when putting together a MST3K episode?
It's hard to say, because the way you do it, you break it into 12-minute [chunks] a day. That's the level before you break into insane fits of rage. That takes a good amount of your day doing 12 minutes. So you sit and write your jokes, and then the next day you bring those jokes to the [writers'] room. And then you watch it with the room and pitch your jokes. Then me and head writer Elliott Kalan—or whoever is riff-producing—will sit down and we have a spreadsheet with all the timecodes and we start to put in jokes that work. This is where it starts getting weird. You don't know how many times you see the entire movie, but you see certain parts of the movie over and over and over again because you're trying to figure out what to do in that moment. Sometimes you're like, "We need something here. No one wrote anything for this section because it was kind of boring, no one was talking." Everybody dropped the ball. So then it becomes the job of the riff producers to go, "OK, well what can we do here?" And that's where the hard work happens. "OK, rewind it. Let's look at it again." There are certain aspects of certain movies that you've seen 30 times to try to get it right.
How has the overall fan reaction been to you taking over hosting duties? How has it compared to what you expected?
When Joel picked me and was getting ready to announce it, I was dreading it. I was really, really dreading it. I know the wrath of nerd culture, and I know how I'd feel if someone just got announced as the new host of this show that I cared so much about. So I was really ready to just kind of stay offline to protect my heart.
I was announced, and it was a little bit of everything. I just started getting all these tweets saying, "Hey, you're going to ruin my favorite show!" "I can't believe they got a hipster!" "You know who they should've got?" Stuff like that. And I would respond here and there. To people who were like "You're going to ruin my favorite show," I'd be like, "Well, I'm going to try not to, because it's my favorite show." Why would I do that? It's not like I wasn't a fan, and wasn't an outward fan. I was very vocal about my love for the show. I mean, I have two comedy records that were named after lines from Mystery Science Theater 3000: The Movie.
But there was this thing that happened with the guy who was running the KickStarter, Ivan Askwith. He was like, "Hey, I see you responding to some of the negative people." And that's the Internet for you, that's your gut reaction — to defend. And he was like, "Try this trick: I see a lot of people responding kindly to you, and you're not responding to any of them. So what you should do is respond to those people. And then once you do three of those, feel free to respond to a negative person." And what I realized is because I had just been positive three times in a row, I could respond to anyone being negative in a kinder, less defensive, more forgiving way. And I felt a change. It felt like maybe I showed people that I wasn't just some dick.
There was also this writeup on Birth Movies Death, where this guy kind of said, "Hey, I know some people are complaining about this guy, but here's why I think he's a good fit." And that really changed people's opinions.
Long story long, I was scared and people were very hesitant, but I understand it completely, because I would've been too.
But since it's come out, I've really, for the most part, have only noticed positive things. And also just seeing people coming to the live shows dressing up in the yellow jumpsuit with the Heston name tag and going to comicons and seeing people dressed up as my character, that feels good. I'm not gonna be a lot of people's favorite, but if I did anything to the Mystery Science Theater world, I finally united the Joel versus Mike crew.
Anything else you'd like to add about the live show?
It's a big fun live comedy show. It goes off the rails a lot because Joel and I get goofy with each other. We're also introducing a character that's in the next season on these live shows. It's a character called Dr. Donna St. Phibes, she's a B-movie monster conservationist, and it's played by Deanna Rooney. It's kind of a sneak peak into the next season if you come and see the show.
Mystery Science Theater 3000 Live
Sunday, Nov. 11, at 3 and 7 p.m | The Moore | $37–$50 | stgpresents.org
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For USAID
Water@Wilson: SWP's John Parker on Transboundary Water Cooperation
Water is essential to human life. But as growing risks such as climate change and demographic shifts alter the realities of water resource management and WASH service provision, new challenges and opportunities arise. On November 28, experts gathered at the Wilson Center in Washington, D.C., to discuss the challenges of water insecurity that stand in the way of building healthy, prosperous and peaceful communities.The event helped mark the Wilson Center's 50thanniversary and was designed to take stock of the first year of the United States' first global water strategy and to explore new research and practice on water, peace and conflict.
"As we think about the future of water peace, a lot can be learned by looking at the institutional policy and planning developments in the Mara Basin, as these characterize in my opinion a strong enabling environment for water cooperation," said John Parker, deputy director of Winrock's Sustainable Water Partnership (SWP), who spoke at the conference. Parker described SWP's work improving water cooperation in East Africa's transboundary Mara region — a success story in which governments and stakeholders have come together to cooperate on the management of a critical shared resource.
The day opened with a brief introduction from the Hon. Jane Harman, director, president and CEO of the Wilson Center, followed by a trio of keynote speakers who introduced the main themes of the day. One of the speakers, USAID's Acting Global Water Coordinator James Peters, discussed the importance of water security in a nation's ability to graduate from donor assistance and achieve self-reliance, a key USAID goal. In the 1960s, he said, South Korea had no sewer system and only 20 percent of its citizens had access to piped water. But a multisector drive for economic development that included water and sanitation reforms launched the country toward a more water-secure and prosperous future. Now, South Korea has the 12thlargest economy in the world with universal access to piped water and sanitation.
"Since its graduation from the U.S. development system in 1980, South Korea has gone from an aid recipient to a global aid donor and America's eighth largest trading partner," Peters said. "The example of South Korea shows just how important water and sanitation can be in helping a country become self-reliant and solve its own development challenges."
Peters and the U.S. Department of State's Aaron Salzberg discussed the four core objectives of the U.S. global water strategy: promoting sustainable access to drinking water and sanitation and adopting key hygiene behaviors; encouraging sound water resource management; reducing conflict by promoting resolution on shared water; and strengthening governance, financing and institutions.
In three panel sessions throughout the day, experts discussed the new face of water conflicts, ways in which countries and local entities are cooperating on water issues, and the future of water peace. During breaks, attendees could peruse a gallery of photos from Winrock water projects in Cambodia, Nepal and the Mara River basin.
There are several important institutional, policy and planning developments in the Mara that allowed it to create a strong enabling environment for water cooperation, Parker said in his presentation. These include a memorandum of understanding between Kenya and Tanzania for the joint management of the Mara River Basin; the creation of national water policies and water allocation planning guidelines for water cooperation; and support for governance institutions at the local level, including the Water Resources User Associations (WRUAs) in Kenya and Water User Associations (WUAs) in Tanzania.
"Progress on transboundary water cooperation requires sustained engagement," Parker said. "As we've heard throughout the day, this is incredibly important work, but success does take time. It's important to take a long perspective on these issues."
These words were echoed by others throughout the day. "The world has made major progress since 50 years ago, when we didn't even have a global mechanism to track water access data," Peters said. "But we still have a long way to go in reaching a world where all governments recognize and invest in the importance of water security for health and economic growth."
Accessibility Privacy Policy
This website and its contents are made possible by the generous support of the American people through the United States Agency for International Development (USAID).The contents are the responsibility of Winrock International and do not necessarily reflect the views of USAID or the United States Government. | {
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Taraji P. Henson joins a group of gorgeous celebs in Allure magazine's Look Better Naked issue. The Oscar-nominated actress bares all in the photo and shows how fabulous she looks at 41!
Taraji P. Henson is currently in the CBS show, Person of Interest and stars in the up-coming Steve Harvey film, "Think Like A Man" opening in theaters April 20.
Previous ArticleHappy Birthday Martin...You So Crazy!
Next ArticleSoul2Soul...RayCornelius with ATL Soul Music Stars! | {
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This necklace is so lovely and divine, it is just like a beautiful royal romance. A princess is born at around the same time as a prince; in two different families, towns next to one another, they grew up together, with the same morals and principles, have always been great friends. One beautiful day they fall madly in love and have the most amazing happily ever after, ruling the towns together. With pearls and stunning Kunzite. 18K Yellow Gold form the pendant and hook the pure white pearls together. | {
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Sewing can be a fun, relatively inexpensive, enjoyable leisure time pasttime.
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You can come up with a schedule for the sewing classes anytime you like, all year long, 6 days a week. Because the top regular sewing session supplier inside Somers, MT, our own knowledgeable coaches you will need to give your classes at your house or the instructor's place, which ever is most convenient to suit your needs. Once you apply, you'll receive a contact listing of accessible Somers trainers in addition to their places to choose from in relation to what is most convenient to suit your needs.
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Regular sewing additionally assists the psychological conditioning. Being a sewer, you will experience improved self-confidence when you workout psychological manage. Sewing improves the self-esteem once you display the creativity.
Whether or not an individual sew by yourself, with pals, or perhaps along with your entire family, sewing offers you an exciting and effective life-long activity. Your own regular sewing training lessons will teach you every little thing, through making and restore sweaters to making a quilt having an electric sew machine.
Crucial sewing strategies, such as exactly what is a French hem and the way to build it.
Assistance in determining the scope of your ability and assisting you reach the regular sewing full potential.
Children are capable of taking sewing courses and find out about not only the relevant skills involved, but in addition grow their attentiveness, while increasing their self-confidence.
Your own specialist teacher has a minimum of fifteen years of sewing experience. Thus, an individual benefit from a mix of personal experience and specialist expertise. Your own teacher will be certified, supplying you with the peace of mind they have passed a high instructing standards examination.
Enroll through enrolling about the type provided beneath.
Both individual and group instruction is offered. Group instruction is less costly and supply a chance to gain knowledge from the activities involving fellow course members. Additionally, getting instruction with other people offers a social exposure to those who share a pursuit with you – regular sewing. Individual coaching provides a brand new or perhaps skilled sewer on-on-one instruction with fast, personalized comments.
can start $47.55 per lesson in Troy, MT.
can be found in programs offering all of the fundamentals.
fit your capability stage, if you are a beginner or perhaps desire to improve your regular sewing capability.
You can come up with a schedule for the sewing lessons anytime, all through the year, seven days per week. As the leading regular sewing training provider in Troy, MT, our expert instructors will be ready to provide your lessons at your house or the instructor's location, whichever is actually most convenient to suit your needs. Whenever you fill out an application, you will receive a contact set of obtainable Troy teachers in addition to their places to choose from based upon what exactly is most convenient to suit your needs.
Learning to sew can help you lower your emotional tension and express creativeness. That doesn't issue your actual age or if perhaps you're not used to regular sewing. We now have courses of instruction for all age and talent amounts. Create lessons now and give sewing an opportunity. Anyone won't be sorry!
Additionally, stitching is wonderful for an individual, physically and mentally.
Stitching actually decreases your own heart and circulation rates, lowering tension and encouraging slow breathing.
Stitching additionally assists your own mental fitness. Like a sewer, you may experience improved self-confidence as you exercise mental handle. Sewing improves your own self-esteem when you display your own creativity.
Whether or not an individual sew all alone, with pals, or along with your entire family, sewing provides you an enjoyable and effective life-long endeavor. Your own stitching training may coach you on everything, coming from steps to make and mend knit tops to steps to make any quilt with an electric machine.
Help when choosing the right equipment plus products.
Essential stitching advice, for example what is a French hem and the way to create one.
Capacity to repair modify outfits and thus save money.
Assistance in figuring out the particular level of the capacity and assisting you achieve your own stitching full potential.
Children are able to take stitching classes and understand not merely the relevant skills involved, but in addition enhance their attentiveness, while increasing their own self-confidence.
In reality, just about anyone of nearly every age may figure out how to sew.
Training from a specialist supply the information and course needed to make certain stitching begins and remains an enjoyable experience.
Your own specialist teacher has no less than fifteen years of stitching experience. Therefore, an individual benefit from a combination of personal experience and specialist experience. Your own teacher is licensed, providing you with the reassurance they have passed a higher instructing specifications examination.
Signup through signing up around the type provided down below.
Both 1 on 1 and group lessons are offered. Group lessons are more affordable and provide a way to gain knowledge from the experiences connected with fellow course people. In addition, getting coaching with other people provides a social knowledge about individuals who discuss a pastime together with you – stitching. Private training can offer a fresh or knowledgeable sewer on-on-one instruction along with quick, tailored feed-back.
start at $47.75 for each training in Rexford, MT.
fit your capability level, whether you are a newcomer or need to enhance your stitching capability.
You are able to schedule your own sewing lessons at your convenience, throughout the year, 7 days a week. As the top stitching lesson provider within Rexford, MT, the experienced coaches are ready to lengthy lessons at your house or perhaps the instructor's spot, whichever will be most convenient to suit your needs. When you sign up, you may receive a contact listing of available Rexford instructors as well as their places to choose from in relation to what's most convenient to suit your needs.
Learning how to sew makes it possible to lower your worry and exhibit creativeness. That doesn't matter how old you are or if perhaps you're not used to stitching. We now have courses of instruction for almost all age and talent levels. Create instruction right now and provide sewing the opportunity. You won't be sorry!
Regular sewing actually minimizes the heart and blood flow rates, lowering anxiety and encouraging proper breathing.
Whenever you decrease and concentrate around the task at hand, you can forget the challenges you will ever have and take it easy.
Regular sewing also assists the psychological conditioning. As a sewer, you may experience improved self-confidence while you physical exercise psychological handle. Sewing boosts the self-esteem once you show the creativeness.
Whether or not an individual sew alone, with pals, or even together with your whole family, sewing offers you a fun and productive life-long pastime. Your own stitching sessions will educate you on every little thing, from how to make and fix sweaters to how to make the cover with an electrical machine.
Capacity to repair and alter garments and thus spend less.
Assistance in determining the particular level of the ability and helping you attain the stitching full potential.
Simple the need for stitches and selection regarding tiny needles for specific duties.
Children are capable of taking stitching sessions and learn about not merely the skills included, but also enhance their focus, and increase their own self-confidence.
Training from your professional supply the info and path needed to ensure stitching begins and remains a fun experience.
Your own professional trainer offers at least many years of stitching experience. Thus, an individual take advantage of a mix of personal experience and professional expertise. Your own trainer happens to be certified, providing you with the assurance they have passed a top training specifications examination.
Register simply by enrolling around the kind provided beneath.
Each individual and group lessons are readily available. Class lessons are less costly and provide a chance to learn from the experiences connected with other class people. Additionally, getting lessons online websites offers a interpersonal experience with those who talk about a pastime with you — stitching. Private training can offer a new or even expert sewer on-on-one instruction together with quick, personalized advice.
can start $47.75 per training in Proctor, Montana.
match your ability level, regardless if you are a beginner or even need to improve your stitching ability.
priced dependent on the quantity of lessons you determine to receive.
It is possible to come up with a schedule for the sewing training anytime you like, all year long, 5 days a week. As the leading stitching session supplier inside Proctor, MT, our own seasoned course instructors are ready to provide your training at your home or the instructor's place, whatever is most convenient for you. Whenever you submit an application, you may be given a contact set of obtainable Proctor teachers as well as their locations from which to choose based on what is most convenient for you.
Learning to sew helps you lower your emotional stress and show the creativity. That doesn't matter your actual age or if you're new to stitching. We've classes for all age group and skill amounts. Create the classes right now and give sewing a chance. You actually won't regret it!
Sewing is really a fun, relatively inexpensive, enjoyable free time pasttime.
Even though you are sitting down, it minimizes your own heart and blood circulation rates, reducing stress and encouraging slow breathing.
Regular sewing furthermore aids your own emotional fitness. Being a sewer, you'll experience greater self-confidence when you workout emotional control. Sewing improves your own self-esteem whenever you demonstrate your own imagination.
Whether or not a person sew by yourself, with the help of buddies, or with your whole family, sewing gives you an enjoyable and effective life-long activity. The sewing lessons will certainly educate you on every thing, coming from how to make and fix knitted garments in order to how to make the quilt by having an electric sewing machine.
Assistance in figuring out the particular level of the ability and assisting you reach your own sewing potential.
Assistance in selecting the correct products and also supplies.
Youngsters are able to take sewing training and learn not merely the skills concerned, but additionally boost their focus, and increase their own self-confidence.
Actually, any of us of all ages may learn how to sew.
Training from the specialist give you the information and direction necessary to make certain sewing begins and remains an enjoyable experience.
The specialist instructor has at least 15 years of sewing experience. Hence, a person take advantage of a combination of personal expertise and specialist experience. The instructor is certified, giving you the reassurance they have passed a top teaching standards check.
Equally individual and group instruction is available. Group instruction is less costly and provide a way to learn from the activities connected with fellow course participants. Plus, taking coaching online websites offers a interpersonal experience with individuals who talk about a pastime along with you : sewing. Personal lessons provides a brand new or expert sewer on-on-one training along with immediate, individualized advice.
begin at $47.75 each lesson in Polebridge, Montana.
match your ability level, whether you are a beginner or desire to enhance your sewing ability.
You can come up with a schedule for your own instruction anytime you like, all through the year, 6 days per week. As the leading sewing lesson provider in Polebridge, MT, our knowledgeable teachers will be ready to provide your instruction at your house or even the instructor's location, whatever will be most convenient for you personally. Once you fill out an application, you'll get a contact set of obtainable Polebridge instructors as well as their places to select from based upon what's most convenient for you personally.
Learning to sew makes it possible to lessen your worry and express the creativity. It doesn't make a difference your actual age or if you're a new comer to sewing. We now have courses of instruction for all age group and skill levels. Create the classes right now and give sewing a chance. You won't regret it!
Even though you are sitting down, it decreases your coronary heart and blood flow rates, reducing tension as well as promoting slow breathing.
Learning to sew decreases the challenges you will ever have as well as relax.
Sewing additionally helps your emotional health. As a sewer, you will experience greater self-confidence when you exercise emotional control. Sewing boosts your self-esteem once you demonstrate your imagination.
Whether or not an individual sew alone, together with friends, or even with your entire family, sewing provides you an enjoyable as well as productive life-long endeavor. The regular sewing coaching will certainly coach you on every little thing, coming from steps to make as well as repair sweaters in order to steps to make a duvet having an electric powered sew machine.
Help when choosing the correct gear and materials.
Basic the need for stitches and selection associated with fine needles for particular jobs.
Important stitching strategies, including exactly what is a French hem and the way to create one.
Guidance in determining the actual level of your ability as well as assisting you to achieve your regular sewing capabilities.
Youngsters are capable of taking stitching classes as well as find out about not only the relevant skills included, but in addition enhance their focus, and increase their self-confidence.
The professional trainer offers at least 15 years of sewing experience. Hence, an individual benefit from a variety of personal experience as well as professional expertise. The trainer happens to be licensed, providing you with the assurance that they have passed a top teaching requirements examination.
Register simply by enrolling on the kind offered below.
Equally 1 on 1 as well as group lessons are offered. Class lessons are less expensive and supply an opportunity to gain knowledge from the experiences of other class people. Plus, taking classes with others provides a social experience with individuals who discuss a pursuit with you – regular sewing. Individual sessions can provide a new or even knowledgeable sewer on-on-one teaching together with speedy, personalised suggestions.
can start $47.75 per training in Kila, MT.
match your capacity stage, regardless if you are a novice or even need to increase your regular sewing capacity.
You are able to schedule your training anytime, all year long, 6 days each week. Because the top regular sewing session supplier inside Kila, MT, our own knowledgeable teachers are ready to provide your training at your home or perhaps the instructor's set, whatever is most convenient for you. Once you submit an application, you will be given a get in touch with list of available Kila trainers in addition to their locations to select from in relation to what exactly is most convenient for you.
Learning to sew helps you lower your anxiety as well as show your own ingenuity. That doesn't issue your actual age or if you're a new comer to regular sewing. We have courses of instruction for all grow older and talent amounts. Create your own lessons right away and give sewing an opportunity. Anyone won't be sorry! | {
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Initiative is 'gaining incredible momentum'
2017-05-15 - By ANDREW MOODY and CHEN YINGQUN Contact the writers at andrewmood[email protected]
The Belt and Road Initiative is the only current significant engine for global economic growth, the head of a leading think tank says.
Helga Zepp-LaRouche, founder of the Schiller Institute, an international political and economic think tank in Washington, said the initiative is already a remarkable achievement.
"This is a new perspective for the future. I think it is a new dynamic that is really gaining incredible momentum.
"The people who said the Belt and Road Initiative would collapse have been proved quickly wrong because the statistics now show it has become the new engine of growth for the world economy — in fact, the only one — and it will continue to be like that."
Zepp-LaRouche, who was speaking on the opening day of the Belt and Road Forum for International Cooperation in Beijing, said the initiative now has a clear shape.
"In my mind it is pretty clear how it is developing Helga Zepp-LaRouche, founder of the Schiller Institute, a Washington think tank because China has had an unbelievable economic miracle in the last 30 years, and in a certain sense what the Belt and Road Initiative does is allow China to export that economic miracle."
The German-born Zepp-LaRouche, 68, said greater connectivity would aid development in some of the world's most troubled areas, particularly in the Middle East.
"The initiative has changed the dynamic around many of the crisis spots already. Hopefully, we can enter a new era of mankind so we can stop having senseless wars with people suffering."
Zepp-LaRouche said her own institute, founded in 1984, was an early advocate of the underlying ideas of the Belt and Road.
Where China could make a difference is in its commitment to high-speed rail, she said.
"China has become a leader in fast-train building. By 2020 it will have 40,000 kilometers of fast rail, compared to none at all in the United States. If the United States wanted to do the same thing with much of its infrastructure in a terrible condition, it would have to ask the Chinese for their expertise."
She hoped the US would eventually join in and fully support the initiative.
"I think there were positive signs of this when President Xi met with President Trump in his Mar-a-Lago private residence in Florida. There has been good communication between the two, and while Mr Trump may not be at the forum, an early trip is planned to China."
Denis Depoux, Asia deputy president and senior partner of Roland Berger, a global consultancy, said the initiative could also be a boon to European companies.
"Many of the European infrastructure, industry equipment and services giants have a chance to leverage their experience in these regions, partner with their Chinese counterparts and develop a new, more inclusive, joint development approach."
The Belt and Road could remove many of the major barriers to development in many parts of the world, he said.
"Financing challenges, and first and foremost insufficient infrastructure, have hindered development. China's initiative brings structure, financing and political impetus, while the strong focus on infrastructure will swiftly enable easier trade and investment."
China has had an unbelievable economic miracle in the last 30 years, and in a certain sense what the Belt and Road Initiative does is allow China to export that economic miracle."
Newspapers from Hong Kong | {
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Anderson .Paak & The Free Nationals
One of the best and most flexible live performers of today. Energetic, heartfelt, engaging and clever, always danceable with lots of help from his uber-talented band The Free Nationals. A few years ago singer, rapper and drummer Anderson .Paak emerged out of California as a fully and spectacularly formed artist, sort of discovered and nurtured by the one and only Dr. Dre. Since then we've learned to have heightened expectations on every new Anderson .Paak album, but he never fails to deliver what we want and, even more, what we didn't know we wanted.
On his four albums Anderson .Paak has told us about different Los Angeles beach suburbs (Venice, Malibu, Oxnard, Ventura) and his life. The songs are bright and warm, sometimes goofy, other times deadly serious. "This is the age of awakening," he The Guardian. "It's no longer that we're just here to be entertainment. We see what's going on and we're not going to be numb to it any more." His 70s funky hip-hop soul with dizzy jazz-drums and traces of psychedelia is sung with that glorious sandpaper voice and played with a genre-defying versatility. No wonder he won a Grammy 2019 for Bubblin' in the Best Rap Performance category. | {
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From adding new functionality and improving performance , to fixing a major bug. Find out how to make your computer faster by running our Free Performance Scan. During this period Intel became the dominant supplier of microprocessors for PCs, and was known for aggressive and anti-competitive tactics in defense of its market position, particularly against Advanced Micro Devices AMD , as well as a struggle with Microsoft for control over the direction of the PC industry. Try a free diagnostic now Introducing Driver Matic. Prior to Driver Matic, all drivers had to be installed differently and required significant user involvement.
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Only at PC Pitstop. It is the inventor of the x86 series of microprocessors, the processors found in most personal computers.
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Prior to Driver Matic, all interfsce had to be installed differently and required significant user involvement. Tips from the PitCrew If a intel r 82801db lpc interface controller 24c0 device isn't functioning properly, or if a program or game that you're installing states that it requires newer drivers, a driver update will be in order.
Find controllerr how to make your computer faster by running our Free Performance Scan. Only download this driver. Try a free diagnostic now Introducing Driver Matic. Please support our project by allowing our site to show ads. A driver update may also improve stability and performance, or may fix issues with games, programs and power management.
From adding new functionality and improving performanceto fixing a major bug. Over the years, over million scans have been runand all that data has been compiled to create fontroller driver libraries. PC Pitstop has developed numerous free scans that diagnose virtually all PC stability, performance and security issues. Intel Corporation better known as Intelstylized as intel is an American multinational technology company headquartered intel r 82801db lpc interface controller 24c0 Santa Clara, California.
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Intel Corporation was founded inteeface July 18,by semiconductor pioneers Robert Noyce and Gordon Moore and widely associated with the executive leadership and vision of Andrew Grove, Intel combines advanced chip design capability with a leading-edge manufacturing capability. During this period Intel became the dominant supplier of microprocessors for PCs, and was known for aggressive and anti-competitive tactics in defense of its market position, particularly against Advanced Micro Devices AMDas well as a struggle with Microsoft for control over the direction of the PC industry.
Intel also makes motherboard chipsets, network interface controllers and integrated circuits, flash memory, graphics chips, embedded processors and other devices intel r 82801db lpc interface controller 24c0 to communications and computing. If a hardware device isn't functioning properly, or if a program or game that you're installing states that it requires newer drivers, a driver update will be in order. | {
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Batman: Gotham by Gaslight is the latest DC animated film to adapt a popular graphic novel for the big screen. The original graphic novel came out of the minds of Brian Augustyn and Mike Mignola, who is the creator of his own superhero, Hellboy. It sets the Dark Knight at the turn of the 20th century, in a borderline steampunk world where he has to face Jack the Ripper, In Gotham.
Batman is voiced by Bruce Greenwood, a perfect choice who gets the more world-weary version of Batman just right. It's not as effective when he voices Bruce Wayne, as he is portrayed as a young aristocrat. Jennifer Carpenter plays Selina Kyle (Catwoman) and Scott Patterson is excellent as James Gordon, who isn't the James Gordon we all know. The rest of the voice cast is all the usual talent who pretty much are locked into the DC animation studios all day long and forced to do funny voices… just kidding.
I haven't read the original source graphic novel, so I can't comment on how faithful the adaptation is to the story. I assume relatively so, based on the nature of the others, but from the panels I've seen online, the animation style is radically different from the graphic novel. They decided to go with an aesthetic that is closer to The Batman cartoon series. These films are obviously done on an almost conveyor-belt system—they do about five a year, and wherever the animators are slaving away they will stick with the same style. It's slightly more televisual in style, while the comic is more like Mignola's own work and visually darker.
The world is obviously in the US despite the Jack the Ripper storyline. It's therefore not for the kids, with some grisly moments, though they could have gone a lot further in that direction than they actually did. It's an interesting alternative origin story for Batman, and definitely better than the usual direct-to-video features. DC Entertainment have in recent years really stepped up the game with the Dark Knight franchise's live-action movies, with adaptations of The Dark Knight Returns, The Killing Joke, Batman '66. However, the way the DC Cinematic Universe is going, I'd much rather watch one of the new animated films at this point than the new live-action Batman films.
The disc has a lot of extras, including a featurette about the comic book, which Mignola is surprisingly absent from, and commentary by the executive producer, director and writer; plus a sneak peek of the next Suicide Squad DC Universe movie. Perhaps the neatest special feature is two archival episodes, with one from the much-loved Batman animated series and one from the more recent series, Batman: The Brave and the Bold. | {
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Sauté 1 tablespoon of oil in saucepan with onion and curry powder for 1 minute over moderate heat.
Add rice and sauté for 2 minutes.
Add stock and bring to a boil. Reduce heat and simmer covered for 15 minutes.
Add prawns and simmer, cover for an additional 4 minutes.
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Couple donates land to school
Published On: October 30, 2017 01:45 AM NPT By: Republica | @RepublicaNepal
PARBAT, Oct 30: A couple of Modi Rural Municipality-4, Kyang has donated seven ropanis of land worth Rs 700,000 to a local school in Parbat district on Sunday. The land has been donated for the construction of school building and playground.
Kiran Pun and Yug Maya Pun donated the land to Bajung Basic School of the same rural municipality. "The school was unable to construct the building and playground due to the financial crisis. But the problem has been solved after getting the land as donation," stated chairman of the school management committee, Cham Bahadur Pun, adding, "We are very grateful and delighted for their help and support."
According to the chairman of the management committee, the couple had bought the land last year and handed over the land owner certificate to the school principal Am Bahadur Pun this year amid a function.
"Last year, we had bought the land for the school but due to some reasons we were unable to donate it," said Kiran with a cheerful smile, adding, "Now, we have donated the land to the school and hope this could make things easier."
Similarly, the couple has raised a fund of Rs 2,05,000 for scholarships to the marginalized students.
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A gay couple was allegedly asked to give up their seats to accommodate a straight couple during an Alaska Airlines...
Khadka family donates land and cash for school's building construction
BABIYACHAUR (Myagdi), Feb 26: A family has donated a huge amount for infrastructure construction of the Muktimarg Secondary School located...
'Over 600,000 school age children still out of school'
KATHMANDU, Nov 4: Some 600,000 children of school-going age are still out of school, it has been claimed. However, the... | {
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We all have our once in a time bad moments like 'Sometimes getting up late in the morning', putting too much salt in our kid's foods'. Upon realization, we often go into guilt mode and blame ourselves for the smallest of things. If we come to think of it, we would never treat the other person like that. So the whole point is that as mothers we should also stop treating ourselves like that.Continue Reading. | {
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SubTopic SAN technology and arrays
Tech Accelerator What is a SAN? Ultimate storage area network guide
Evaluate Weigh the pros and cons of technologies, products and projects you are considering.
Fibre Channel vs. iSCSI: 5 factors to consider
Discover how Fibre Channel and iSCSI compare when it comes to meeting the SAN performance, ease of use, manageability, total package and TCO requirements of SMBs.
Stacey Peterson, Senior Site Editor
Marc Staimer, Dragon Slayer Consulting
It's the battle of the century. In one corner, promoted by every major server and storage vendor, is Fibre Channel....
In the other corner, promoted primarily by NAS vendors, startups and users, is iSCSI. Have you had enough of the hype?
These two SAN technologies have been positioned as fierce competitors. However, major server and storage vendors don't necessarily see it as Fibre Channel vs. iSCSI; most popular SAN arrays support both FC and Ethernet instead of being designated as FC SANs or iSCSI SANs.
Both iSCSI and FC technologies solve the same technical problem of networking block storage. The differences between the two configurations are in the details. There are five areas to consider when picking a SAN technology:
performance and reliability
complexity and ease of use
total storage SAN solution
What follows is a look at the Fibre Channel vs. iSCSI debate, how each technology works and how they compare in the five areas outlined above.
Fibre Channel explained
FC is a high-speed networking technology. It typically has throughput speeds of 8 Gbps, 16 Gbps and 32 Gbps but can go up to 128 Gbps by combining four 32 Gb lanes. It was originally designed for use in SANs as a more reliable, scalable and lower-latency protocol than SCSI. Today, its use is driven by the increasing data volumes businesses generate through the use of analytics, AI and machine learning technologies, as well as the growing use of SSDs and NVMe-oF to improve application and network performance.
Connecting servers with shared storage and providing connectivity between storage controllers and drives are the main ways FC is used. It's often used to transmit data among data centers, servers, storage and switches. Point-to-point, switched and loop interfaces deliver lossless, in-order, raw block data. FC networks are designed to interoperate with SCSI, IP and other protocols.
Because of its high level of reliability, FC is preferred for mission-critical workloads on high-capacity SANs. However, FC requires specialized adapters and switches, as well as extensive technical knowledge and skills to deploy the technology. In addition, businesses generally need two networks when using an FC SAN: the FC network for storage traffic and an Ethernet network for other communication and bandwidth.
ISCSI explained
ISCSI is an Ethernet-based protocol designed to transport SCSI packets over a TCP/IP network. Because it uses standard Ethernet network interface cards and switches, network admins don't need to buy the specialized adapters and network cards that add to the expense and complexity of FC SAN technology. ISCSI can run over an existing Ethernet network, also making it less expensive and easier to deploy than FC.
This article is part of
What is a SAN? Ultimate storage area network guide
Which also includes:
Advantages and disadvantages of using a SAN
7 leading storage area network products and vendors
Make remote SAN management work in the age of coronavirus
Download this entire guide for FREE now!
Both iSCSI and FC technologies solve the same technical problem of networking block storage. The differences between the two configurations are in the details.
An iSCSI network can run at speeds up to 100 Gbps. It transports block-level data between servers and storage arrays or other storage devices. The protocol encapsulates SCSI commands, assembles the data in packets for the TCP/IP layer and sends packets over the network using a point-to-point connection. Once at their destination, the packets are disassembled, and the storage appears to the OS as if it is a locally connected SCSI device.
Fibre Channel vs. iSCSI performance
Fibre Channel is a layer 2 switching technology or cut through, with the protocol handled entirely in hardware. The iSCSI protocol (SCSI mapped to TCP/IP) running on Ethernet is a layer 3 switching technology with the protocol handled in software, hardware or some combination of the two.
FC is often touted as the high-performance, more reliable SAN technology. Early in iSCSI development, that was true, but that's not the case anymore.
Today, performance bottlenecks are far more likely to be the result of the target storage (interface, controller queue depth, controller clustering, number of disks, disk type, etc.), the physical server or the SAN fabric oversubscription rate (number of server initiators to number of storage target ports) than the SAN technology.
So, which technology is the better performer? All things being equal, FC should be marginally better in IOPS (because of lower latency) and throughput (because of lower overhead).
Complexity/ease of use
Because the iSCSI SAN is based on the well-known TCP/IP and Ethernet, it's far simpler and less complex than FC. The learning curve and expertise requirement for FC is measurably higher. FC tends to be significantly more manually intensive vs. iSCSI, which has a lot more built-in automation. As a result, FC technology usually requires more training, a greater knowledge base and ultimately higher costs with both.
When it comes to Fibre Channel vs. iSCSI, hands down, iSCSI SANs are far easier to implement, operate and manage than FC. ISCSI uses the vast capabilities of TCP/IP and Ethernet and is much less expensive. Most moves and changes are performed online and aren't disruptive to applications.
Although FC has come a long way in manageability, the majority of moves and changes are application-disruptive. This means they must be scheduled and performed offline. The alternative is to live with the application disruptions and, in some cases, deal with potential data loss.
Total SAN solution and TCO
When considering the total SAN approach in the Fibre Channel vs. iSCSI debate, the assessment must involve the complete end-to-end package, including the storage system, the storage software (snapshot, mirroring, thin provisioning, etc.) and the types of drives (solid-state flash vs. HDDs).
When assessing TCO, make sure to include the acquisition, installation, professional services (if any), additions and upgrade, management, operational, maintenance, subscription, power, cooling and real estate costs. These costs apply to the storage system, the SAN and the storage software.
FC vendors have done a good job in reducing the costs of their products. But these products have a considerably higher TCO than the iSCSI equivalents. The adapters, switches -- especially the data center class switches called directors -- and software all have considerably higher TCO than their iSCSI equivalents.
Bottom line: How do you make the Fibre Channel vs. iSCSI decision for your SAN? The answer is: It all depends. Choose the technology that best meets your requirements for performance, ease of use, manageability, total package and TCO.
What you need to know about SAN zoning schemas
Find out how HCI, NAS and SAN compare
A look at the SAN vs. NAS differences
Dig Deeper on SAN technology and arrays
iSCSI (Internet Small Computer System Interface)
IP SAN (Internet Protocol storage area network)
SMB SAN solutions: Storage networking options
By: Eric Slack
Storage area network basics you need to know before you buy a SAN
By: Pierre Dorion
Why SMR Drives Should Be in Your Plans Now –Western Digital
Zoned Storage Takes On the Zettabyte Age –Western Digital
SCSI vs. iSCSI -- features, functionality and ... – SearchStorage
iSCSI storage vs. Fibre Channel storage: A SAN ... – SearchITChannel
The anatomy of a SAN: Fibre Channel SAN explained – SearchStorage | {
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One piece that stays missing from the puzzle when it comes to dream-building is programming. There is no doubt that this is the case, especially in our era, where the entire world is reachable via the worldwide web. Where we are our own first audience, it is still essential en-route 'turning a dream into reality', that we have a virtual sandbox, one in-where we can rehearse our dreams into fruition; an interface that represents our vision and intention. Such interface usually constitutes of a piece of code.
When such sandbox comes with mirrors in the form of a "community of reputable great minds", then, that is luxury. In our era, we have this luxury.
In some locations, dreaming and the whole process of dreaming is dead-harder. The odds are just mountain-large. A sandbox can only hold sway for some time. Instead of such sandbox playing its original goal of inciting creativity, innovation etc, it now becomes mostly a tool, to sustain inspiration, a tool to keep one dreams alive in dream-bits. In these locations, 'inspiration' may be just everything.
In general, dream-building and the art of 'turning dreams into reality' isn't very easy. It's a puzzle with pieces and one ever-missing piece can slack or even crash the race or marathon.
As mentioned earlier, in many cases, this ever-missing piece is 'coding'. Being able to code at least, a piece of code.
Well, what i am trying to say is, "this missing-piece should not be so "ever-missing", especially in this era.
Everyone should be able to 'code with swag' or at the very least 'understand code' or at the very least 'be able to code a measure of code'.
Don't mind my jargon; hahaha, I am adding in code.
In deep truth, everyone codes. If you speak a language, you code. If you can tell bingo to sit and it sits, you code. If you can tell Johnny to bring you 'that red file' from a filled-shelf, you code. If someone from another location can simply not understand your language, it is because you have coded. If you can't understand my jargon here, that is perhaps because, i have added some code therein.
And no the tech-geeks can't simplify coding or maybe they can but hey, leave that to the layman.
And no, Bill Gates' Microsoft can't simplify coding or who knows he can but hey, leave it to Macrohard.
One way to keep your dreams alive in dream-bits, is thru coding. Forget the world for a start. In the face of mountainous odds, code your intentions however draft-like, then look at this particular UI on your browser each day and be made to marvel by what your intentions represents; then, use the inspiration from marveling at what your intention can represent, to further evolve your dreams towards levels of spanlessness and go from there.
Each person regardless of levels of literacy, location, age, gender i.e 'anyeveryone', should be able to code a measure of code.
@macrohard's intention? 'everyanyone' should be able to code a measure of code, with SWAG. | {
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Turn heads with striking earrings and necklaces crafted from Texas leather, turquoise gems and vibrant sponge coral.
Looking to inject some color into your spring wardrobe? Make a statement with bold jewelry from J.Forks Designs. The Southern-inspired line features statement pieces made with semi precious stones and unique charms. Striking earrings and necklaces are crafted from Texas leather, turquoise gems and vibrant sponge coral.
I received a beautiful piece of turquoise and leather earrings that are SO perfect for spring. I am obsessed with turquoise and coral so there isn't much of the line that doesn't fit the bill for me! | {
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Jonah helps farmers, fishers, cooks and food producers to form co-ops and networks that grow a prosperous, equitable economy in Maine and the Northeast.
Jonah Fertig-Burd is Director of Cooperative Food Systems at the Cooperative Development Institute. He helps farmers, fishers, cooks and food producers to form co-ops in Maine and the Northeast. He co-founded Local Sprouts Cooperative, Maine Farm & Sea Cooperative, Greater Portland Community Land Trust, Mayor's Initiative for a Healthy and Sustainable Food System, Cooperative Design Lab and People's Free Space. He works closely with the Somali Bantu community of Lewiston-Auburn, Maine and has supported the development of New Roots Cooperative Farm and the Isuken Co-op. He's currently on the board of Cooperative Fund of New England, Cooperative Maine Business Alliance, Good Food Council of Lewiston-Auburn, Maine Farm & Sea Cooperative and Maine Food Strategy. He co-owns Celebration Tree Farm & Yoga, an organic farm. He is a gardener, cook, artist, and musician.
Jonah graduated from NYU in 1999 with a BA in Art and Cultural Studies. He was a 2016 Democracy at Work Institute Worker Co-op Developer Fellow, 2017 USFWC/DAWI Chapter Network Fellow and a graduate of the Food Solutions New England Leadership Institute and Sustainable Food Systems Leadership Institute in Maine. Born in upstate NY, he moved to ME when he was 7 and now lives with his wife and two kids in Durham, ME. | {
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In Germany psychotherapy follows a certain formal pattern: We will make an appointment and you will come to one to three sessions of consultation (Sprechstunde), each lasting about 50 minutes. In these sessions we get to know each other, you tell me about your problem, and we try to find out, what an adequate help or treatment might be.
If behavior or trauma therapy is an adequate treatment in your case we will have 2-4 so called probatory sessions of 50 minutes each, where you tell me more about your problems and your life. We will try to find out, why you are not feeling well and how your problem is connected with your life history and your behavior. We also put the emphasis on your skills and ressources. These sessions also give us the opportunity to find out whether we can work with each other and whether you feel safe working with me. If we both feel comfortable with each other you have to see a medical doctor to get a physical (as a psychologist I don't have sufficient knowledge of somatic disorders). Following this we will file a request for psychotherapy with your medical insurance, either as a short term therapy with up to 24 sessions or a long term therapy with 60 sessions, each 50 minutes. If we need more time we can request more sessions. Up to 80 sessions are paid by the insurance companies.
If it turns out in the consultation sessions that you need psychotherapy very urgently we can start right away with an acute treatment of 12 sessions. | {
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Cascade, ID, population 972, is located in Idaho's Valley county, about 63.0 miles from Boise and 227.3 miles from Spokane.
Through the 90's Cascade's population has grown by about 14%. It is estimated that in the first 5 years of the past decade the population of Cascade has grown by about 1%. Since 2005 Cascade's population has declined by about 1%.
Cascade's property crime levels tend to be lower than Idaho's average level. The same data shows violent crime levels in Cascade tend to be about the same as Idaho's average level. | {
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I have been busy sewing but not posting as I should be 🙁 I know I always promise to do better — well I will do and not talk about it but be about it.
This is a cute plaid top that I created from 100% cotton fabric I obtained at Fabricmart 100% cotton and it was a very easy sew! From lay-out, to cutting, to sewing probably took about two hours.
This top is Simplicity 2255 I plan on wearing it with a pair of drawstring jeans I created from New Look 6351. | {
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Northeastern University–Toronto is the latest addition to our global network and our first international campus. With hundreds of Northeastern alumni who live and work in Toronto, we're dedicated to serving the needs of the city and offering working professionals a clear path to advancing their careers.
Northeastern brings the full resources of a top-tier, globally focused private research university to the region—along with a network of corporate and research partners—expanding opportunities for human capital development and advancing business recruitment and retention.
From project management and information assurance to regulatory affairs for drugs, biologics, and medical devices, Northeastern University's Toronto program is uniquely aligned with the region's economic development and workforce needs.
Here, students benefit from the university's local employer partners through co-ops, Northeastern's distinctive approach to integrating rigorous classroom study with practical experience.
Students benefit from Toronto's close proximity to top industry leaders and booming job opportunities. Whether you earn your graduate degree solely online, on-campus, or both, you can never underestimate the importance of having access to the people and resources of a physical, regional campus hub. | {
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Home - NationalHome Slider FeatureNational
OSLO, Norway (AP) — The prestigious Nobel Peace Prize will be handed out Friday with plenty of speculation about possible winners but no hints from the Nobel committee, which doesn't reveal the names of candidates or nominations for 50 years.
Names flying around include 16-year-old Swedish climate activist Greta Thunberg; Prime Minister Abiy Ahmed of Ethiopia; German Chancellor Angela Merkel; and activists in Hong Kong.
The Norwegian Nobel Institute could also choose to acknowledge United Nations' World Food Program, or the joint leadership of two prime ministers — Greece's Alexis Tsipras and North Macedonia's Zoran Zaev — who brought an end to 30 years of acrimony between their nations.
Outsiders include Davi Kopenawa, a spokesman for the rights of a Brazilian indigenous tribe, and U.S. President Donald Trump.
Since 1901, 99 Nobel Peace Prizes have been handed out, to individuals and 24 organizations. While the other prizes are announced in Stockholm, the peace prize is awarded in the Norwegian capital, Oslo.
So far this week, 11 Nobel laureates have been named, of whom 10 are men.
Two literature prizes were awarded Thursday: One for 2018 that went to Polish novelist Olga Tokarczuk and one for 2019 that was given to Austrian author Peter Handke.
The chemistry prize went to three scientists for their work leading to the development of lithium-ion batteries; the physics award was given to a Canadian-American and two Swiss for exploring the evolution of the universe and discovering a new kind of planet; and the physiology or medicine award went to two Americans and one British scientist for discovering details of how the body's cells sense and react to low oxygen levels.
In his will, Alfred Nobel, the Swedish industrialist and inventor of dynamite, decided the peace prize should be awarded in Oslo. His exact reasons for having an institution in Norway handing out that prize is unclear, but during his lifetime Sweden and Norway were joined in a union, which was dissolved in 1905.
The economics prize wasn't created by Nobel, but by Sweden's central bank in 1968. It is awarded Monday.
With the glory comes a 9-million kronor ($918,000) cash award, a gold medal and a diploma. Even though the peace prize is awarded in Norway, the amount is denominated in Swedish kronor.
The laureates receive them at elegant ceremonies on Dec. 10 — the anniversary of Nobel's death in 1896 — in Stockholm and Oslo.
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Google axes 12,000 jobs as layoffs spread across tech sector
Police: Man killed in Missouri after aiming gun at officers
Tweets by 550KTRS | {
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Two release delays and some serious director drama typically isn't a good sign, but the first trailer for 47 Ronin actually isn't all that bad. A number of vivid and highly impressive visuals are enough to sustain the film's first promo, but the display does raise concern that the final film won't offer enough attention to story details. Regardless of where this one ends up, for now, 47 Ronin is nowhere near worthy of the Best Stuff, but keeps clear of the Worst, too.
1. Gravity: The "Drifting" trailer is an unnerving and heartwrenching display of isolation, but this honor goes to the "Detached" edition thanks to having that plus an absolutely incredible amount of suspense, too. On top of that, it's tough to imagine Alfonso Cuarón spoiling one of the more riveting scenes in the film, so if he's willing to unleash this as part of the promotional effort, just imagine the horror that's to come in the full feature.
2. A Single Shot: Even though it's tough to completely ignore the mixed reviews that came out of A Single Shot's festival run, this new trailer is still effective enough to make you want to pass judgment for yourself. The opening sequence is an attention grabber, the material to follow is riveting, it all takes place in a bleak yet fascinating world, and it comes at you with an increasingly unsettling pace thanks to that effective background beat.
3. The Hunger Games: Catching Fire: If this theatrical trailer is any representation of the quality and intensity of the full film, Catching Fire could match, if not surpass its predecessor. There is a perfect amount of story in this trailer, as the piece is a powerful tease but also functions as a comprehensive and satisfying watch. It doesn't just leave you with that must-see feeling courtesy of a clever cliffhanger. Rather, it makes you desperate to see what comes next because it offers up a clear and poignant representation of the characters, world and situation. The performances seem to be on point yet again, Francis Lawrence's visuals are captivating and often absolutely gorgeous, and there's an exceptional amount of suspense suggesting Catching Fire could go on to be another monumental success, and a truly worthy one at that.
1. Snowpiercer: I've said it before and I'll say it again: what is going on in the Snowpiercer marketing department? Early reviews are in and they're primarily positive, so clearly Joon-ho Bong has something here, but whatever it is, it's not coming through in the film's promotional campaign in the least. This one seems to be an attempt at a character piece, but without a clear sense of who Chris Evans' character is and what he's fighting for, it's tough to care.
2. Cold Comes the Night: Incessant cuts and fades to black, slow motion and other editing tricks are never a good sign. The new trailer for the Alice Eve-starrer Cold Comes the Night flies by, but only because it's overloaded with flashy editing techniques and has an especially short running time, both suggesting that the final film can't even sustain an appealing promo. For the sake of keeping the blurb brief, let's just leave Bryan Cranston's accent out of this.
3. Metallica Through the Never: This one isn't necessarily a bad trailer, but it should be better. If you're aware of Metallica Through the Never, you know that it's an IMAX concert movie and narrative mash-up. However, yet again, the marketing team delivers a promo that runs the risk of isolating those not interested in seeing a big-screen concert and also turning off folks who just want a Metallica show, due to the lack of clarity. But even more disappointing is the absence of creativity in a trailer for a project like this. There just has to be a more exciting and innovative way to sell this film that doesn't involve the overuse of cheesy text pleas. | {
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Articling
Recent Changes to Pour Over Rules
Articles July 17, 2019
The British Columbia Court of Appeal has held that a clause in a will directing estate property to be transferred to a trust that was created before death is invalid. We are writing to alert you to this decision so that you can review your will and determine whether changes are required.
The decision in Quinn Estate, 2019 BCCA 91, relates to the estate of Pat Quinn, the well-known hockey player, coach and general manager. Mr. Quinn included a clause in his will gifting the residue of his estate to the Quinn Family Trust, a trust which he and his wife Sandra had established prior to making the will. The Quinn Family Trust was capable of being revoked or amended by Mr. and Mrs. Quinn. The Court of Appeal found that the clause leaving part of the estate to the Quinn Family Trust was invalid and could not be validated. The issue is that a will must be executed following formal legal requirements, including the need to have two witnesses present, which a pre-existing trust does not meet. A will can incorporate a pre-existing document by reference, but only if certain strict criteria are met, including that the document is already in existence when the will is made. The Court held that the gift to the Quinn Family Trust did not satisfy the criteria to result in a valid incorporation by reference, and that the court did not have the legal authority to save the gift.
A number of prior court decisions regarding pour-over clauses, including the prior decision of the Supreme Court in Quinn, 2018 BCSC 365, and the 2013 decision of the Supreme Court in Kellogg Estate, 2013 BCSC 2292, could be read as suggesting that such a clause would be invalid only if the inter vivos trust was actually amended after the will was made. The Court of Appeal in Quinn has clarified that the mere fact that a trust may be amended or revoked invalidates a pour-over clause in favour of that trust. Further, some portions of the court's decision call into question whether a pour-over clause even to a trust which cannot be amended would be valid.
In light of the Quinn decision, we recommend that all wills with pour-over clauses be amended or replaced. One possible solution would be to have the will create a testamentary trust (a trust created as a result of death) having terms similar to the inter vivos trust that was the intended recipient of the gift. The trustees of the testamentary trust may be given powers under the will that permit them to transfer the property of the testamentary trust to other trusts for the benefit of the same beneficiaries. The will-maker could then leave a non-binding letter of wishes requesting that the trustees exercise this power by merging the property of the testamentary trust into the inter vivos trust.
Richard Weiland, TEP
> Email
Stay current on business and legal news, topics and trends
A refresher on resulting and constructive trusts
Discussion on resulting and constructive trusts and a recent decision: Borkenhagen v. Kessler.
Articles April 5, 2012
Marc Nadon Appointed to the Supreme Court of Canada (SCC)
Articles October 31, 2013
When should a trust for a child vest?
Discussion on when a trust set up for a child should vest
View a complete list of subjects and related content
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© Clark Wilson LLP | {
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Q: Get native video resolution of a video file I'm currently writing some custom EVR for a Media Foundation player.
So far everything work, but i'm in need of finding the native resolution of the video file i'm rendering.
I try to use the IBasicFilter2 Interface to use the getVideoSize, get_VideoHeight or other get_SourceWidth etc... but it always return me a E_NOINTERFACE...
So do someone have an esay way of getting resolution of a video file? Even if it's with a nice light library...just the size nothing else...Windows manage to find it inside the file browser, but i'm totally unable to get it from code...
Thanks!
A: You can use IMediaDet in DirectShow to get information on the streams in a media file including the resolution of video streams.
There are come caveats though so you might want a backup method.
You need suitable DirectShow filters registered which understand the media file being examined. It's possible that you may have a filter installed that gives wrong results - e.g. an audio only filter is registered for a media type that ignores any video streams in the file.
It's currently deprecated with no indication on the MSDN reference page of what is replacing this functionality. It can also be a pain to build as the headers have been removed from the Windows SDK.
Here's one case in point where that method doesn't work...
Get MP4 stream lengths
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10 Clever April Fools' Campaigns Every Brand Can Learn From
Normally, brands need to be authentic and clear in their messaging. Consumers need to be certain about who you are, what you do, and what you stand for. There's one time a year, however, when marketers have the freedom to break the rules, unleash their creativity, and engage in a little harmless deception about their products, services, and ideas: April Fools' Day.
Of course, it's still important to strike the right note to make sure that you amuse and entertain your audience rather than annoy and confuse them.
A successful April Fools' Day campaign must contain these elements:
It takes the message in a clever and unexpected direction while still being on-brand.
It features the brand's products or services in an over-the-top fashion while ensuring that the audience in is on the joke and that the brand is portrayed in a positive light.
It shows that the brand has a sense of humor about itself.
It's executed in a way that looks realistic to the consumer.
In their recent blog post, 10 Great On-Brand April Fools' Campaigns, the marketing experts at MDG Advertising revealed 10 major brands that nailed the art of the April Fools' Day campaign and provide lessons that every marketer can learn for their own brand.
10 Great On-Brand April Fools' Campaigns
While the freedom to engage in April Fools' Day trickery can spark creativity, it can also be a headache for marketers. Brands have to be careful with their stunts, finding ways to humor audiences while ensuring that everyone is in on the joke.
In MDG Advertising's new article, 10 Great On-Brand April Fools' Campaigns, readers will learn how their brand can indulge in some fun without causing confusion and/or provoking a backlash. | {
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Read Chapters 1 through 10. Write down 4 things you learned or found interesting from each chapter (so that is 40 items total). Write down the PAGE NUMBER where you found EACH fact or topic of interest – and include the page numbers next to each item, when you write up your report.
When typing your Report it is fine to simply list the 10 Chapters – and then number (and describe) the four items you learned from reading each Chapter. | {
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After the success of team GB in the recent London Olympics and the success of Bradley Wiggins in the Tour de France the country has gone cycling mad. So let's all get fit!
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To discuss your cycle needs, call us on the number at the top of the screen or come and see us in store today!
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To discuss your cycle equipment and accessory needs, please feel free to contact us today. You can call us on the number above to talk to a member of staff, or alternatively call in to our store and speak to us in person. We look forward to hearing from you. | {
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They Lost Money When Tornado Cash Got Banned. Now Coinbase Is Helping Them Sue the Government
Coinbase has announced that it is funding a lawsuit brought against the U.S. Treasury Department over its decision to sanction Tornado Cash.
Photo: Michael Short/Bloomberg
Coinbase is funding a lawsuit against the U.S. Treasury Department over its decision to sanction Tornado Cash.
The exchange's CEO Brian Armstrong wrote in a blog post that the Treasury had "exceeded its authority" and was harming law-abiding U.S. citizens.
The lawsuit is brought by six individuals who previously used Tornado Cash for legitimate purposes.
Six people who used Tornado Cash for legitimate reasons had their funds frozen after the U.S. Treasury sanctioned the protocol. They're now filing a lawsuit, and Coinbase is funding them.
Coinbase Funds Lawsuit Over Tornado Cash Ban
Coinbase is leading the crypto community's fight against the U.S. Treasury's Tornado Cash sanctions.
The top U.S. cryptocurrency exchange published a note penned by CEO Brian Armstrong Thursday, stating that it would be funding a lawsuit brought by six people challenging the Treasury's decision to blacklist Tornado Cash.
Armstrong argued that the Treasury had "exceeded its authority" granted by Congress when it opted to sanction a piece of open-source software, and that it had ignored the technology's legitimate use cases.
The Treasury added the popular privacy protocol Tornado Cash to its sanctions list on August 8 citing its popularity among cybercriminals like Lazarus Group. It claimed that it had become a vehicle for money laundering and blamed the team for failing to prevent illicit activity. The decision had wide-ranging implications for the crypto space and was met with outcry across the community. Several entities such as Circle and Infura immediately blacklisted Ethereum addresses that had interacted with the protocol, and many prominent industry figures spoke out against the ban. Tornado Cash developer Alexey Pertsev was then arrested in Amsterdam by Netherlands' Fiscal Information and Investigation Service on August 10; he's still sitting in jail despite having received no formal charges.
In his letter, Armstrong highlighted three instances of people using Tornado Cash for legitimate purposes prior to the ban. One had used it to anonymously donate money to Ukraine (something Vitalik Buterin separately admitted to following the ban). Another with a large online presence used the protocol to avoid being targeted by cybercriminals. Another used it to protect his Ethereum staking business. All three have had their funds frozen due to the sanctions; they constitute half of the plaintiffs in the lawsuit Coinbase is bankrolling.
Armstrong likened the Treasury's decision to "permanently shutting down a highway because robbers used it to flee a crime scene," arguing that the decision punished innocent people. He added that it would have a stifling effect on innovation, as open-source developers would live in fear of being held responsible for something they have no control over.
Disclaimer: At the time of writing, the author of this piece owned ETH and several other cryptocurrencies.
"A Major Policy Issue": Circle CEO Criticizes Tornado Cash Sanctio...
News Aug. 9, 2022
Circle quickly complied with the U.S. Treasury's decision to sanction Tornado Cash, but its CEO is calling on industry leaders to establish a privacy-enabling policy framework. Circle CEO Comments on...
U.S. Lawmaker Questions Treasury Over Tornado Cash Sanctions
The U.S. Treasury's decision to sanction a piece of software presents a "divergence from previous OFAC precedent," claims Rep. Tom Emmer (R-MN). Sanctions Questioned A U.S. lawmaker is questioning the...
Kraken CEO Criticizes Tornado Cash Sanctions
Kraken CEO Jesse Powell has objected to recent U.S. sanctions against addresses tied to the Tornado Cash coin mixer. Kraken Leader Defends Tornado Cash Jesse Powell has criticized sanctions against... | {
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Count on the Noon News Roundup for a curated list of top stories, columns, weather updates and more Count on the Noon News Roundup for a list of top stories, columns, weather updates and more Sign up now>
Share this Story: Revelation Biosciences Inc. Appoints Joseph A. Bellanti, M.D. to Scientific Advisory Board
Revelation Biosciences Inc. Appoints Joseph A. Bellanti, M.D. to Scientific Advisory Board
– Dr. Bellanti is Director of the International Center for Interdisciplinary Studies of Immunology and Professor of Pediatrics and Microbiology and Immunology at Georgetown University
SAN DIEGO, Dec. 06, 2021 (GLOBE NEWSWIRE) — Revelation Biosciences Inc. (Revelation), a clinical-stage life sciences company that is focused on the development of immunologic‑based therapies for the prevention and treatment of disease, today announced it has appointed Joseph A. Bellanti, M.D. to its scientific advisory board.
Revelation Biosciences Inc. Appoints Joseph A. Bellanti, M.D. to Scientific Advisory Board Back to video
Dr. Bellanti is a Professor of Pediatrics and Microbiology and Immunology and Director of the International Center for Interdisciplinary Studies of Immunology (ICISI) at Georgetown University Medical Center. Dr. Bellanti's investigative efforts have focused on antimicrobial research, evaluation of new vaccine strategies and developmental immunology. This work resulted in a succession of seminal research contributions including the characterization of the IgM response of the newborn, the identification of the antiviral role of secretory IgA in respiratory secretions and the cellular immune responses to viral infections following immunization or natural infection.
Dr. Bellanti is the recipient of numerous awards and honors, including the prestigious E. Mead Johnson Award for Research in Pediatrics for outstanding scientific contributions, the Humanitarian Award from the American College of Allergists for "excellence and service and teaching of clinical immunology", the Distinguished Medical Alumnus Award from the State University of Buffalo, New York and the Founder's Day Award of Georgetown University School of Medicine. He is also the recipient of Honoris Causa degrees from the University of Palermo, Italy, Georgetown University and recently, the CEA Universidad San Pablo, Madrid, Spain.
"Over the past several decades, my work has centered around generating new knowledge in immunology and translating it to clinical use," said Dr. Bellanti. "We have seen so many advancements and innovations in this area, but still have a long way to go. The work Revelation Biosciences is doing could change the way we look at, prevent and treat stubborn and recurring infections, like influenza and COVID-19. I look forward to working with the team to develop new prevention and treatment options for the infections that impact so many people around the world each and every year."
During the 2019-2020 season, the CDC estimates that influenza was associated with 38 million illnesses, 18 million medical visits, 405,000 hospitalizations, and 22,000 deaths. Globally, COVID-19 is responsible for more than 5 million deaths , with thousands of people dying every day.
"Dr. Bellanti represents the 'triple threat' academician; he's proficient in teaching, research, and patient care," said James Rolke, Chief Executive Officer of Revelation. "He has had a tremendous impact on our understanding of immunology and will be an invaluable voice as we work to build on the foundation he has laid."
Dr. Bellanti has published more than 500 scientific articles and abstracts, as well as numerous textbook chapters and his widely acclaimed textbook in immunology, " Immunology IV: Clinical Applications in Health and Disease ."
For more information on Revelation, please visit www.RevBiosciences.com .
About Revelation Biosciences Inc.
Revelation Biosciences, Inc. is a clinical-stage life sciences company focused on the development of immunologic-based therapies for the prevention and treatment of disease. Revelation has several product candidates in development. REVTx-99, the lead therapeutic candidate, is an intranasal immunomodulator to prevent or treat infections caused by various respiratory viruses such as SARS-CoV-2, including its variants, influenza A and B, parainfluenza, rhinovirus, and RSV. REVTx-99 is also being developed for other indications such as: allergic rhinitis and chronic nasal congestion. REVTx-200 is an intranasal immunomodulator adjunct to be used in combination with an intramuscular vaccination for more complete immunity. REVTx-200 is based on the same technology used in REVTx-99. In addition to Revelation's therapeutic pipeline, Revelation is also developing REVDx-501, a rapid home use diagnostic that can be used to detect any respiratory viral infection, regardless of virus type or strain, without the need for specialized instrumentation.
Revelation recently announced that it has entered into a definitive merger agreement (Merger Agreement) with Petra Acquisition, Inc. (NASDAQ: PAICU, PAIC, & PAICW), a special purpose acquisition company, for a business combination that will result in Revelation becoming a publicly traded company (Business Combination). After the close of the merger the combined company will be listed on NASDAQ under the ticker symbol "REVB."
About Petra Acquisition, Inc.
Petra Acquisition, Inc. (NASDAQ: PAICU, PAIC, & PAICW) is a blank check company organized for the purpose of effecting a merger, share exchange, asset acquisition, stock purchase, recapitalization, reorganization or other similar business combination with one or more businesses or entities, with an initial focus on target businesses in the healthcare or a healthcare-related industry.
This press release contains forward-looking statements as defined in the Private Securities Litigation Reform Act of 1995, as amended, including statements regarding the anticipated benefits of the transaction, the anticipated timing of the transaction, the future business and financial condition of the company post-closing and expected financial impacts of the transaction, the satisfaction of closing conditions to the transaction, the level of redemptions of Petra's public stockholders; the market opportunities for Revelation's product candidates; and the potential for regulatory approval for Revelation's product candidates. These forward-looking statements are generally identified by the words "anticipate", "believe", "expect", "estimate", "plan", "outlook", and "project" and other similar expressions. Forward-looking statements are statements that are not historical facts. We caution investors that forward-looking statements are based on management's expectations and are subject to various risks and uncertainties. As a result, caution must be exercised in relying on forward-looking statements, which speak only as of the date they were made. The following factors, among others, could cause actual results to differ materially from those described in these forward-looking statements: risks relating to the successful completion of RVL-CLR01 clinical study; the risk that we may not fully enroll our RVL-CLR01 clinical study or enrollment will take longer than expected; risks relating to the occurrence of adverse safety events and/or unexpected concerns that may arise from data or analysis from our RVL-CLR01 clinical study; the occurrence of any event, change or other circumstances that could give rise to an amendment or termination of the Merger Agreement and the proposed transaction contemplated thereby; the inability to complete the transactions contemplated by the Merger Agreement due to the failure to obtain approval of the stockholders of Petra or Revelation or other conditions to closing in the Merger Agreement; the inability to project with any certainty the amount of cash proceeds remaining in the Petra trust account at the closing of the transaction; the uncertainty relative to the cash made available to Revelation at the closing as a result of redemption requests be made by the Petra stockholders; the inability of the company post-closing to obtain or maintain the listing of its securities on Nasdaq following the Business Combination; the amount of costs related to the Business Combination; Revelation's ability to yield sufficient cash proceeds from the transaction to support its short-term operations and research and development efforts since the Merger Agreement requires no minimum level of funding in the trust fund to close the transaction; the outcome of any legal proceedings that may be instituted against the parties following the announcement of the Business Combination; changes in applicable laws or regulations; the ability of Revelation to meet its post-closing financial and strategic goals, due to, among other things, competition; the ability of the company post-closing to grow and manage growth profitability and retain its key employees; the possibility that the company post-closing may be adversely affected by other economic, business, and/or competitive factors; risks relating to the successful development of Revelation's product candidates; the clinical utility of an increase in intranasal cytokine levels as a biomarker of viral infections; the ability to complete planned clinical studies of REVTx-99; expected initiation of the clinical studies, the timing of clinical data; the outcome of the clinical data, including whether the results of such study is positive or whether it can be replicated; the outcome of data collected, including whether the results of such data and/or correlation can be replicated; the timing, costs, conduct and outcome of our other clinical studies; the anticipated treatment of future clinical data by the FDA, the EMA or other regulatory authorities, including whether such data will be sufficient for approval; the success of future development activities for REVTx-99 and expanded indications, REVTx-200, REVDx-501, or any other product candidates; potential indications for which product candidates may be developed; the potential impact that COVID-19 may have on Revelation's suppliers, vendors, regulatory agencies, employees and the global economy as a whole; the expected duration over which Revelation's balances will fund its operations; and other risks and uncertainties described herein, as well as those risks and uncertainties discussed from time to time in other reports and other public filings with the SEC by Petra.
This press release shall not constitute an offer to sell or the solicitation of an offer to buy any securities, nor shall there be any sale of securities in any states or jurisdictions in which such offer, solicitation, or sale would be unlawful prior to registration or qualification under the securities laws of any such jurisdiction. No offering of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act, or an exemption therefrom.
In connection with the proposed Business Combination described herein, Petra has filed relevant materials with the SEC, including a Registration Statement on Form S-4, that includes a preliminary proxy statement/prospectus, and when available, will file a definitive proxy statement and final prospectus. Promptly after filing its definitive proxy statement with the SEC, Petra will mail the definitive proxy statement and a proxy card to each stockholder entitled to vote at the Special Meeting relating to the transaction. INVESTORS AND STOCKHOLDERS OF PETRA ARE URGED TO READ THESE MATERIALS (INCLUDING ANY AMENDMENTS OR SUPPLEMENTS THERETO) AND ANY OTHER RELEVANT DOCUMENTS IN CONNECTION WITH THE TRANSACTION THAT PETRA WILL FILE WITH THE SEC WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT PETRA, REVELATION AND THE BUSINESS COMBINATION. The definitive proxy statement, the preliminary proxy statement and other relevant materials in connection with the transaction (when they become available), and any other documents filed by Petra with the SEC, may be obtained free of charge at the SEC's website (www.sec.gov).
Petra and its directors and executive officers may be deemed participants in the solicitation of proxies from Petra's stockholders with respect to the Business Combination. A list of the names of those directors and executive officers and a description of their interests in Petra will be included in the proxy statement for the proposed Business Combination and be available at www.sec.gov. Additional information regarding the interests of such participants will be contained in the proxy statement for the proposed Business Combination when available. Information about Petra's directors and executive officers and their ownership of Petra common stock is set forth in Petra's prospectus, dated October 7, 2020, as modified or supplemented by any Form 3 or Form 4 filed with the SEC since the date of such filing. Other information regarding the interests of the participants in the proxy solicitation will be included in the proxy statement pertaining to the proposed Business Combination when it becomes available. These documents can be obtained free of charge at the SEC's website (www.sec.gov).
Revelation and its directors and executive officers may also be deemed to be participants in the solicitation of proxies from the stockholders of Petra in connection with the proposed Business Combination. A list of the names of such directors and executive officers and information regarding their interests in the proposed Business Combination will be included in the proxy statement for the proposed Business Combination.
Sandra Vedrick
Vice President, Investor Relations & Human Resources
Revelation Biosciences Inc.
Email: [email protected]
Chester Zygmont, III
Email: [email protected]
Kristin Faulder
[email protected]
News Near Kingston | {
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Oingo Boingo
Red Carpet Interview
Oingo Boingo /ˈɔɪŋɡoʊ ˈbɔɪŋɡoʊ/ was a rock band from the United States, best known for their hits "Dead Man's Party" and "Weird Science". They are also known for their soundtrack contributions, their high energy Halloween concerts, and for their unique mixture of styles including ska, punk, new wave, funk, and other world music genres. The band was founded in 1972 as The Mystic Knights of the Oingo Boingo, a performance art group. The band was led by songwriter/vocalist Danny Elfman, who has since achieved success as a composer for film and television.
The group's format changed twice. In 1979, it reshaped from a semi-theatrical music and comedy troupe into a ska-influenced new wave octet and shortened their name to Oingo Boingo. Towards the end of the 1980s, the band began shifting to a more guitar-oriented rock sound, and away from the use of horns and synthesizers. The band retired after a sold-out farewell concert on Halloween 1995. | {
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Aston Martin Vulcan makes dynamic debut in the Middle East
connoisseur November 8, 2015 0
Aston Martin has stunned guests and enthusiasts of the British marque in Dubai, with the Middle East dynamic debut of the limited edition, track-only 7.0-litre V12 supercar, Aston Martin Vulcan, the luxury brand's most intense and exhilarating creation to date.
300 special guests witnessed Aston Martin Middle East and North Africa ambassador, Ahmad Al Harthy get behind the wheel of the 800-plus bhp, all-carbon fibre, Aston Martin Vulcan. Al Harthy, who drives a V12 Vantage GT3 in the British GT championship, demonstrated the supercar's full potential along a closed Emaar Boulevard in downtown Dubai, in the shadow of the world's tallest building, the Burj Khalifa.
Neil Slade, General Manager of Aston Martin Middle East and North Africa, says "This special event in Dubai is very important for the brand globally, as well as in the Middle East. It was a natural choice to select Ahmad to drive and showcase the Aston Martin Vulcan due to his racing experience and strong links with our brand."
The 7.0-litre V12 petrol engine , powered by the most potent iteration yet of the company's naturally-aspirated, eveloped in conjunction with Aston Martin Racing the Aston Martin Vulcan is predicted to be capable of sprinting from rest to 60 mph in under 3.0 seconds, and achieving a top speed of over 200mph.
Aston Martin Ambassador, Ahmad Al Harthy says "I am incredibly proud to have been chosen to drive the Aston Martin Vulcan during this very special demonstration in Dubai, it really is a huge honour. To be entrusted with the Vulcan is very humbling for me, very few people have had the opportunity to get behind the wheel of this amazingnew supercar."
TAGS » Aston Martin, Automobiles
POSTED IN » Automobiles, Luxury Cars
About the author: connoisseur View all posts by connoisseur
LAND ROVER IS MAKING ALL-TERRAIN AUTONOMY A REALITY
Jaguar F PACE with an enhanced chassis and aerodynamics
Cadillac unveiled the first-ever XT4,
Audi, Italdesign and Airbus combine self-driving car and passenger drone | {
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'Furious 7' Is Officially Bigger Than 'Frozen'
Crystal Bell, MTV.com
"Furious 7" can't be stopped.
The seventh installment of the "Fast & Furious" franchise has officially sped past "Frozen" — yes, one of the biggest cultural phenomenons ever — to become the fifth-highest grossing film of all time, according to Box Office Mojo. Sorry Elsa and Olaf, but you've got nothing on Dominic Toretto and his family.
After crossing the $1 billion mark just 17 days after its release, the Vin Diesel-fronted film has grossed a cool $1.32 billion at the worldwide box office, surpassing the Disney animated flick's measly $1.27 billion.
After four furious weeks atop the North American box office, "Furious 7″ should enjoy its final box office victory lap while it still can. Diesel and co. will undoubtedly be knocked off their throne with the May 1 opening of "Avengers: Age of Ultron," which is estimated to make $200 million during its opening weekend. Still, after passing $1 billion internationally, "Furious 7″ could certainly continue its reign overseas.
With the tremendous success of "Furious 7," the "Fast & Furious" franchise has grossed $3.7 billion worldwide. Not too shabby for a gang of Corona-loving street racers.
Somewhere, Vin Diesel can be heard singing "Let It Go" to himself… in the shower, probably.
Meanwhile, Elsa gently croons "See You Again" under her breath — because "Frozen 2″ is happening, which means there will be another chance at eternal, top-five glory. Then again, so is "Fast and Furious 8." So… maybe Dom and Elsa should just race for the title?
OMG, someone please invite Elsa to Race Wars. She has a driver's license, right? | {
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Q: How to use Bitwise shift on ULONG_MAX in C I am writing a small C program to count the number of bits which need to be flipped to make one number equal to another.
The program works very fine but i observe abnormal behaviour (Program hangs) when i pass ULONG_MAX as an argument. Why is this happening? See code below
#include <stdio.h>
#include <limits.h>
#include <stddef.h>
/**
* flip_bits - Count the number of bits to flip to equalize two numbers
* @n: First number
* @m: Second number
*
* Return: the number of bits to flip
*/
unsigned int flip_bits(unsigned long int n, unsigned long int m)
{
unsigned long int diff, count;
int i;
diff = n ^ m;
count = 0;
i = 0;
while (diff >> i)
{
if (diff >> i & 1)
count++;
i++;
}
return (count);
}
/**
* main - check the code
*
* Return: Always 0.
*/
int main(void)
{
unsigned int n;
n = flip_bits(1024, 1);
printf("%u\n", n);
n = flip_bits(402, 98);
printf("%u\n", n);
n = flip_bits(1024, 3);
printf("%u\n", n);
n = flip_bits(ULONG_MAX, 0);
printf("%u\n", n);
return (0);
}
A: Be explicit with signedness and size of all relevant types involved. Don't use bitwise arithmetic on signed numbers. You can simplify this whole code quite a bit by using a readable for loop instead:
#include <stdint.h>
uint32_t count_diff32 (uint32_t x, uint32_t y)
{
uint32_t diff = x ^ y;
uint32_t count = 0;
for(size_t i=0; i<32; i++)
{
if (diff & (1u<<i))
{
count++;
}
}
return count;
}
| {
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Overwatch beta attracts 9.7 million players - Blizzard's biggest ever
The company invited players to try its new hero-shooter, and try it they did: 9.7 million players leapt into Overwatch across PC, PlayStation 4, and Xbox One.
Blizzard invited players to try its new hero-shooter in beta before its official release, and try it they did: 9.7 million players leapt into Overwatch across PC, PlayStation 4, and Xbox One, according to the publisher. Participants played more than 37 million matches of the game during the beta period.
That makes this the biggest beta in the company's history.
In fact, it's even bigger than the audience for Ubisoft's The Division, at 9.5 million -- and that's the best-launched game in that publisher's history. Of course, it's not an exactly apples-to-apples comparison, as the Overwatch beta was free and The Division is a paid product.
Blizzard's game was free to play from May 5th through May 9th. It releases for purchase on May 24th.
Want to better understand the game? Gamasutra recently took a look at the rise of the hero shooter genre, which includes Overwatch. | {
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Checking off legal definition of checking off
https://legal-dictionary.thefreedictionary.com/checking+off
(redirected from checking off)
A written order instructing a bank to pay upon its presentation to the person designated in it, or to the person possessing it, a certain sum of money from the account of the person who draws it.
A check must contain the phrase "pay to the order of." A check differs from a draft in that a check is always drawn on a bank, while a draft is an order for payment drawn on anyone, including a bank, a person, or a trading account with a company.
A blank check is one that the drawer signs but omits filling in the space for the name of the payee, the person in whose favor a check is drawn, or neglects to fill in the space for the amount to be paid.
A cashier's check is one that the bank draws on itself and is signed by an authorized bank official. The bank lends its credit to the purchaser of the check in order to facilitate its immediate use in commercial transactions. It is a direct obligation of the bank.
A personal check is one that the individual draws on his or her own account.
A postdated check is one that bears a date after its date of issuance, and is payable on the stated date.
A traveler's check is one purchased from a bank, express company, or other financial institution in various denominations, and is signed immediately by the purchaser in order to establish the form of his or her signature. The check cannot be treated as cash because of this first signature, but it is treated as cash upon the purchaser's second signature when he or she uses it. The genuineness of the second signature is established by comparing it to the initial signature. A traveler's check is similar to a cashier's check of the issuer.
n. a draft upon a particular account in a bank, in which the drawer or maker (the person who has the account and signs the check) directs the bank to pay a certain amount to the payee (which may include the drawer, "cash," or someone else.) Other checks include cashier's checks issued by the bank for a sum paid to the bank, and certified checks in which the bank sets aside an amount from the maker's bank account and then guarantees the check can be cashed immediately. (See: cashier's check, certified check, negotiable instrument)
CHECK, contracts. A written order or request, addressed to a bank or persons carrying on the banking business, and drawn upon them by a party having money in their hands, requesting them to pay on presentment to a person therein named or to bearer, a named sum of money.
2. It is said that checks are uniformly payable to bearer Chit. on Bills, 411; but that is not so in practice in the United States. they are generally payable to bearer, but sometimes they are payable to order.
3. Cheeks are negotiable instruments, as bills of exchange; though, strictly speaking, they are due before payment has been demanded, i$n which respect they differ from promissory notes and bills of exchange payable on a particular day. 7 T. R. 430.
4. The differences between a common check and a bill of exchange, are, First, that a check may be taken after it is overdue, and still the holder is not subject to the equities which may exist between the drawer and the party 'from whom he receives it; in the case of bills of exchange, the holder is subject to such equity. 3 John. Cas. 5, 9; 9 B. & Cr. 388. Secondly, the drawer of a bill of exchange is liable only on the condition that it be presented in due time, and, if it be dishonored, that he has had notice; but such is not the case with a check, no delay will excuse the drawer of it, unless he has suffered some loss or injury on that account, and then only pro tanto. 3 Kent, Com. 104 n. 5th ed.; 8 John. Cas. 2; Story, Prom. Notes, Sec. 492.
5. There is a kind of check known by the name of memorandum cheeks; these are given in general with an understanding that they are not to be presented at the bank on which they are drawn for payment; and, as between the parties, they have no other effect than an IOU, or common due bill; but third persons who become the holders of them, for a valuable consideration, without notice, have all the rights which the holders of ordinary cheeks can lawfully claim. Story, Prom. Notes, Sec. 499.
6. Giving a creditor a cheek on a bank does not constitute payment of a debt. 1 Hall, 56, 78; 7 S. & R. 116; 2 Pick. 204; 4 John. 296. See 3 Rand. 481. But a tender was held good when made by a check contained in a letter, requesting a receipt in return, which the plaintiff sent back, demanding a larger sum, without objecting to the nature of the tender. 3 Bouv. Inst. n. 2436.
7. A cheek delivered by a testator in his lifetime to a person as a gift, and not presented till after his death, was considered as a part of his will, and allowed to be proved as such. 3 Curt. Ecc. R. 650. Vide, generally,4 John. R. 304; 7 John. R. 26; 2 Ves. jr. 111; Yelv. 4, b, note; 7 Serg. & Rawle, 116; 3 John. Cas. 5, 259; 6 Wend. R. 445; 2 N. & M. 251; 1 Blackf. R. 104; 1 Litt. R. 194; 2 Litt. R. 299; 6 Cowen, R. 484; 4 Har. & J. 276; 13 Wend. R. 133; 10 Wend. R. 304; 7 Har. & J. 381; 1 Hall, R. 78; 15 Mass. R. 74; 4 Yerg. R. 210; 9 S. & R. 125; 2 Story, R. 502; 4 Whart. R. 252.
Accused of having gun
Administrative Law and Procedure
allograph
Arrest for obstructing justice and resisting arrest
Arrested for trying to cash stolen check
Attempted forgery, expunction
bank error regarding funds in account
Blank Endorsement
car tax deductions
cashier's check
cashiers check fraud, scams
Check cashed illegally
"The tremendous advantage is that it would solve the October renewal problem, because you have to send it on June 1st with the old renewal numbers, checking off a box that says it will change, and then the change has to be explained to the tenant.
Division of Housing and Community Renewal
Imagine Radio lets Web surfers create their own stations, with a process that includes checking off as many as 11 musical genres for the station to play.
Station to Station
"You can do it all by checking off the box on the enclosed form and joining our new automatic renewal program."
Customer loyalty paves way to automatic renewals
We write it down and follow it closely, checking off each special team or situation as it is covered.
Ghost games: the real thing in game preparation!
Charre of lead
Charta chyrograpihata vel communis
Charta de non ente non valet
Charta de una parte
charter company
Chartered ship
Charter-land
charterparty
Charter-party
Chartis reddendis
Chase, Salmon Portland
Chase, Samuel
chattel
Chattel Paper
Chattels
Chávez, César Estrada
Check book
check cashing business, jail
checking off
Checkoff
checks cashed, who is liable
Chemistry med
Cherokee Cases
Chessman, Caryl
Chevisance
Chicago Eight
Chicago Jury Project
Chief clerk of the department of state
chief justice
Chief justiciary
child and parent insurance issue
child forced to attend school
child support officer
checking against
Checking and Measurement Devices
Checking Compulsion
checking floor hinge
Checking for Protocol Violations
checking her blood pressure
checking her off
checking her out
checking her skeef
checking him off
checking him out
checking him skeef
checking his blood pressure
checking into
checking it off
checking it skeef
checking me off
checking me out
checking me skeef
checking my blood pressure
checking on
checking on her
checking on him
checking on it
checking on me
checking on one
checking on them
checking on us
checking on you
checking one off
checking one out
checking one skeef
checking our blood pressure
checking our blood pressures
checking out from
checking out of
checking out the plumbing
checking over
checking program | {
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The Question and Answer section for Infinity Ring: Divide and Conquer is a great resource to ask questions, find answers, and discuss the novel.
Infinity Ring: Divide and Conquer study guide contains a biography of Carrie Ryan, literature essays, quiz questions, major themes, characters, and a full summary and analysis.
Infinity Ring: Divide and Conquer essays are academic essays for citation. These papers were written primarily by students and provide critical analysis of Infinity Ring: Divide and Conquer by Carrie Ryan. | {
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Paul McCartney says suing The Beatles was the "only way" to save their music
August 5, 2020 August 5, 2020 Admin Music News
"I also knew that, if I managed to save it, I would be saving it for them"
– McCartney
Read the original article HERE: https://www.nme.com/news/music/paul-mccartney-says-suing-the-beatles-was-the-only-way-to-save-their-music-2721087
Paul McCartney has opened up about the time he sued The Beatles in order to "save" their music and company, Apple.
Read More: The Big Read – Paul McCartney: "The Beatles were brothers arguing, that's what families do"
In a new interview with GQ, McCartney elaborated on what he described as one of the biggest "misconceptions" of The Beatles split saying that he had no option but to sue the band in order to protect their music.
McCartney officially announced his departure from the band in April 1970 and later that year, filed a law suit which called for the group's formal dissolution.Advertisement
After years of further legal battles, he eventually won the rights to the band's music from EMI and music publisher Allen Klein. Klein took over The Beatles business affairs in 1969, following the death of their manager, Brian Epstein.
"Because I had to do that, I think I was thought to be the guy who broke The Beatles up and the bastard who sued his mates," McCartney told GQ.
The Beatles in 1967 CREDIT: Jeff Hochberg/Getty Images
He also revealed that if he hadn't have taken such action, The Beatles would have lost the rights to their music.
McCartney continued: "If I hadn't done that, it would have all belonged to Allen Klein. The only way I was given to get us out of that was to do what I did. I said, 'Well, I'll sue Allen Klein,' and I was told I couldn't because he wasn't party to it. 'You've got to sue The Beatles.'Advertisement
"…As you can imagine, that was horrendous and it gave me some terrible times. I drank way too much and did too much of everything. And it was crazy, but I knew that was the only thing to do, because there was no way I was going to save it for me, because there was no way I was going to work that hard for all my life and see it all vanish in a puff of smoke.
"I also knew that, if I managed to save it, I would be saving it for them too. Because they were about to give it away. They loved this guy Klein. And I was saying, 'He's a fucking idiot.'"
McCartney said the dispute led to one of the biggest "misconceptions" of The Beatles' split. "I suppose that when The Beatles broke up, perhaps there was a misconception that we all sort of hated each other. What I realise now is that, because it was a family, because it was a gang, families argue. And families have disputes," he added.
Last week, McCartney released a previously unheard, acoustic version of 'Calico Skies'.
The original 'Calico Skies' featured on McCartney's 1997 album 'Flaming Pie' – his second-highest-charting album of the last 25 years.
The 'Calico Skies ['In The World Tonight' Campfire Acoustic]' version features on a new boxset containing unreleased demos, outtakes, and rehearsal tapes from the album's recording sessions. Also containing a newly remastered version of the album, the boxset was released last week (July 31).Advertisement
Tagged 60s apple George Harrison John Lennon NME Paul McCartney Ringo Starr The Beatles
Michael Eavis fears Glastonbury won't return until 2022
Taylor Swift makes history with with double debuts at number one | {
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