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https://www.usgs.gov/center-news/volcano-watch-east-laeapuki-bench-keeps-giving
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# Volcano Watch — East Laeapuki: The bench that keeps on giving
Release Date:
Last November, 13.8 hectares (34 acres) of newly formed land and 4 hectares (10 acres) of former coastline at East Laeapuki plunged into the ocean without warning. After this record-breaking collapse, a new bench has formed that is even larger than the last.
Left: East Laeapuki, 4 days after the November 28, 2005, bench collapse.
Right: The current bench at East Laeapuki.
(Public domain.)
The continuous flow of lava into the ocean has created one of the largest benches in the history of this 23-year-long eruption. This gigantic bench is currently about 1,015 m (1,110 yards) long and 317 m (347 yards) wide, covering an area of about 13.8 hectares (44 acres), or roughly 40 football fields.
So why do these benches collapse? The bench is building out over a steep submarine slope of lava flows, fragmented lava, and black sand that forms by the explosive interaction of lava and the sea. As you can imagine, such a slope is very unstable and prone to submarine landslides.
In recent months, the bench had developed major cracks, parallel to the coastline, that ran nearly its entire length. Several weeks ago, as we observed the bench from a helicopter, we were surprised to see that most of the cracks contain water.
Near the center of the bench, the cracks are about 1 m (1.1 yards) wide, and the level of the water is about 3 m (3.3 yards) below the bench surface. This means the lava tube that carries lava across the bench to the ocean must be at least 4 to 5 m (4.4-5.5 yards) below the surface.
Two weeks ago, breakouts at the tip of the bench resurfaced the front of the bench. Many of the cracks have subsequently been buried by the new lava flows, giving the bench a smooth, inviting look.
The bench may look sound, but don't let its appearance belie its dangers. The presence of cracks on the bench, though now buried, indicate that the bench remains very unstable. Walking on or near the bench is extremely hazardous and, thus, the area around the ocean entry has been closed by the National Park Service.
Despite the closures and warnings, people continue to enter the closed area in the evening, sometimes even venturing out onto the bench. There have already been four deaths associated with active benches. The ocean entry was first closed because of concern for a collapse, such as the one in November, and it remains closed because the growth-and-collapse cycle is likely to be repeated. These collapses can occur without warning, so anyone unfortunate enough to be on or near the bench when it collapses risks being hit with a barrage of rocks and spatter, scalding waves, or, worse yet, plunging into the ocean along with the land that once appeared to be stable.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
This past week, activity levels at the summit of Kīlauea Volcano have remained at background levels. The number of earthquakes located in the summit area is low (usually less than 10 per day). Extension of the summit caldera, indicating inflation, appears to have resumed after pausing earlier in April.
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater. Lava continues to flow through the PKK lava tube from its source on the flank of Puu Oo to the ocean, with frequent surface flows breaking out of the tube near the 2,300-ft elevation, and a persistent flow, known as the "March 1 breakout," active on the coastal plain.
Lava continues to enter the ocean at East Laeapuki, in Hawaii Volcanoes National Park. The active lava bench continues to grow following the major collapse of November 28 and is now approximately 1,000 m (3,300 ft) long by 315 m (1,000 ft) wide, with a total area of 17 ha (42 acres).
On April 24, the March 1 breakout reached the ocean about 175 m (575 ft) east of East Laeapuki. A small volume of lava continued to enter the ocean at this location through at least the morning of April 29 but has been inactive since.
Access to the ocean entries and the surrounding area remains closed, due to significant hazards. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
There was one earthquake beneath Hawaii Island reported felt within the past week. A magnitude-2.2 earthquake occurred at 8:58 p.m. H.s.t. on Sunday, April 30, and was located 5 km (3 miles) northeast of Kapoho at a depth of 2 km (1 mile).
Mauna Loa is not erupting. During the past week, earthquake activity remained low beneath the volcano's summit (nine earthquakes were located, six of which were deep and long period in nature). Extension of lengths between locations spanning the summit, indicating inflation, continues at slow rates.
| 2020-12-04T18:05:05 |
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|
http://www-pcmdi.llnl.gov/ipcc/abstract.php?ipcc_publication_id=397
|
UCRL-WEB-152471 Privacy & Legal Notice Thanks to Our Sponsors:
PCMDI > WCRP CMIP3 Model Output > Diagnostic Subprojects Printer Friendly Version
<< Back to WCRP CMIP3 Subproject Publications Ollinger, S.V., C. L. Goodale, K. Hayhoe and J. P. Jenkins, 2008: Potential effects of climate change and rising CO2 on ecosystem processes in northeastern U.S. forests. Mitigation and Adaptation Strategies for Global Change, doi: 10.1007/s11027-007-9128-z. In press. Forest ecosystems represent the dominant form of land cover in the northeastern United States and are heavily relied upon by the region’s residents as a source of fuel, fiber, structural materials, clean water, economic vitality, and recreational opportunities. Although predicted changes in climate have important implications for a number of ecosystem processes, our present understanding of their long-term effects is poor. In this study, we used the PnET-CN model of forest carbon (C), nitrogen (N) and water cycling to evaluate the effects of predicted changes in climate and atmospheric carbon dioxide (CO2) on forest growth, C exchange, water runoff, and nitrate ($${\text{NO}}^{ - }_{3}$$) leaching at five forest research sites across the northeastern U.S. We used four sets of statistically downscaled climate predictions from two general circulation models (the Hadley Centre Coupled Model, version 3 and the Parallel Climate Model) and two scenarios of future CO2 concentrations. A series of model experiments was conducted to examine the effects of future temperature, precipitation, CO2, and various assumptions regarding the physiological response of forests to these changes. Results indicate a wide range of predicted future growth rates. Increased growth was predicted across deciduous sites under most future conditions, while growth declines were predicted for spruce forests under the warmest scenarios and in some deciduous forests when CO2 fertilization effects were absent. Both climate and rising CO2 contributed to predicted changes, but their relative importance shifted from CO2-dominated to climate-dominated from the first to second half of the twenty-first century. Predicted runoff ranged from no change to a slight decrease, depending on future precipitation and assumptions about stomatal response to CO2. Nitrate leaching exhibited variable responses, but was highest under conditions that imposed plant stress with no physiological effects of CO2. Although there are considerable uncertainties surrounding predicted responses to climate change, these results provide a range of possible outcomes and highlight interactions among processes that are likely to be important. Such information can be useful to scientists and land managers as they plan on means of examining and responding to the effects of climate change. Last Updated: 2007-12-20 << Back to WCRP CMIP3 Subproject Publications
| 2017-03-29T22:55:19 |
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https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Lehmann%E2%80%93Scheff%C3%A9_theorem.html
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Lehmann–Scheffé theorem
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation.[1] The theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. The Lehmann–Scheffé theorem is named after Erich Leo Lehmann and Henry Scheffé, given their two early papers.[2][3]
If T is a complete sufficient statistic for θ and E(g(T)) = τ(θ) then g(T) is the uniformly minimum-variance unbiased estimator (UMVUE) of τ(θ).
Statement
Let be a random sample from a distribution that has p.d.f (or p.m.f in the discrete case) where is a parameter in the parameter space. Suppose is a sufficient statistic for θ, and let be a complete family. If then is the unique MVUE of θ.
Proof
By the Rao–Blackwell theorem, if is an unbiased estimator of θ then defines an unbiased estimator of θ with the property that its variance is not greater than that of .
Now we show that this function is unique. Suppose is another candidate MVUE estimator of θ. Then again defines an unbiased estimator of θ with the property that its variance is not greater than that of . Then
Since is a complete family
and therefore the function is the unique function of Y with variance not greater than that of any other unbiased estimator. We conclude that is the MVUE.
Example for when using a non-complete minimal sufficient statistic
An example of an improvable Rao–Blackwell improvement, when using a minimal sufficient statistic that is not complete, was provided by Galili and Meilijson in 2016.[4] Let be a random sample from a scale-uniform distribution with unknown mean and known design parameter . In the search for "best" possible unbiased estimators for , it is natural to consider as an initial (crude) unbiased estimator for and then try to improve it. Since is not a function of , the minimal sufficient statistic for (where and ), it may be improved using the Rao-Blackwell theorem as follows:
However, the following unbiased estimator can be shown to have lower variance:
And in fact, it could be even further improved when using the following estimator:
References
1. Casella, George (2001). Statistical Inference. Duxbury Press. p. 369. ISBN 0-534-24312-6.
2. Lehmann, E. L.; Scheffé, H. (1950). "Completeness, similar regions, and unbiased estimation. I.". Sankhyā. 10 (4): 305–340. JSTOR 25048038. MR 39201.
3. Lehmann, E.L.; Scheffé, H. (1955). "Completeness, similar regions, and unbiased estimation. II.". Sankhyā. 15 (3): 219–236. JSTOR 25048243. MR 72410.
4. Tal Galili & Isaac Meilijson (31 Mar 2016). "An Example of an Improvable Rao–Blackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator". The American Statistician. 70 (1): 108–113. doi:10.1080/00031305.2015.1100683.
This article is issued from Wikipedia - version of the 8/22/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.
| 2022-01-23T08:23:20 |
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https://indico.fnal.gov/event/9718/
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# Spring 2015 EPICS Collaboration Meeting
May 18 – 22, 2015
1200 Molecular Plant Science Building, Michigan State University
EST5EDT timezone
Registration and Abstract Submission Now Open!
### Support
The Spring 2015 EPICS Collaboration meeting is hosted by the Facility for Rare Isotope Beams (FRIB) and the National Superconducting Cyclotron Laboratory (NSCL) and takes place at Michigan State University (MSU) from 18-22 May 2015.
The collaboration meeting will consist of one day pre-meeting sessions on Monday, 18 May 2015 (held at FRIB/NSCL in Conference Room 1221B) followed by the main EPICS meeting on Tuesday-Thursday, 19-20 May 2015 (held at the Molecular Plant Sciences Building, Rm. 1200) and post-meeting sessions on Friday, 22 May 2015 (held at FRIB/NSCL in Conference Room 1221B). Please enter through the main lobby of FRIB/NSCL and the receptionist will direct you to 1221B. In addition, a Code-A-Thon is being organized for Monday-Friday, 11-15 May 2015 (NSCL/FRIB).
EPICS (Experimental Physics and Industrial Control System) is a set of open source software tools, libraries and applications developed collaboratively and used worldwide to create distributed soft real-time control systems for scientific instruments such as particle accelerators, telescopes, and large scientific experiments.
These collaboration meetings provide a chance for developers and managers from the various different sites to come together and discuss their work and progress, and make plans for the future. They give a chance to see what is being done at other laboratories, and to review the specifications for new tools or enhancements to existing ones in order to maximize their usefulness to the whole community and avoid duplication of effort.
Venue:
The Spring 2015 EPICS Collaboration meeting will take place in the Molecular Plant Sciences Building located on the campus on Michigan State University in Rm 1200. All pre- and post- meeting sessions will be held at FRIB/NSCL on the campus of MSU.
Interactive MSU Campus Map
Parking Map - Wharton Center Parking Ramp is recommended for parking.
640 S. Shaw Lane
East Lansing, MI 48824
Molecular Plant Sciences (Rm. 1200) (Tues - Thurs)
1066 Bogue St
East Lansing, MI 48824
Registration:
Please see "Registration Form" at the left to register for the meeting.
Morning and afternoon breaks will be included in the registration.
Meals:
Lunch tickets are no longer available for purchase at the special rate of $6.00ea which can be used at most of the MSU Dining Halls. You can still purchase lunch each day at the dining hall with cash or credit card. A dinner is being organized for Wednesday, 20 May 2015. Join us for a casual evening at HopCat. Price will be$20.00 per person and drinks will be available for purchase.
http://hopcat.com/east-lansing
Follow the link below to purchase dinner tickets before May 14th, 2015. (Dinner tickets can also be purchased at registration on Tuesday with cash or certified check (payable to Michigan State University, Attn: EPICS, 640 South Shaw Lane, East Lansing, MI 48824, USA):
Dinner tickets
| 2023-03-23T23:00:25 |
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https://www.anl.gov/article/argonne-to-lead-8-doe-grid-modernization-projects
|
Skip to main content
# Argonne National Laboratory .st0{fill:none;} .st1{fill:#007934;} .st2{fill:#0082CA;} .st3{fill:#101E8E;} .st4{fill:#FFFFFF;} .st5{fill:#A22A2E;} .st6{fill:#D9272E;} .st7{fill:#82BC00;} Argonne National Laboratory
Press Release | Argonne National Laboratory
# Argonne to lead 8DOE Grid Modernization Projects
The U.S. Department of Energy’s (DOE’s) Argonne National Laboratory will receive about $19 million in funding and will lead eight projects as part of the Grid Modernization Laboratory Consortium (GMLC) announced earlier today by DOE. Argonne will participate as a partner in 23 other GMLC projects. DOE announced that it plans to award up to$220 million over three years, subject to congressional appropriations, to DOE’s national laboratories and partners to support critical research and development in advanced storage systems, clean energy integration, standards and test procedures, and a number of other key grid modernization areas.
Modernizing the U.S. electrical grid is essential to reducing carbon emissions, creating safeguards against attacks on our infrastructure, and keeping the lights on,” said Secretary Moniz. Our Quadrennial Energy Review and Quadrennial Technology Review identified needs and opportunities to invest in the grid. This public-private partnership between our National Laboratories, industry, academia, and state and local government agencies will help us further strengthen our ongoing efforts to improve our electrical infrastructure so that it is prepared to respond to the nation’s energy needs for decades to come.”
The Grid Modernization Initiative represents a comprehensive DOE effort to help shape the future of our nation’s grid and solve the challenges of integrating conventional and renewable sources with energy storage and smart buildings, while ensuring that the grid is resilient and secure to withstand growing cyber security and climate challenges. Today’s announcements fall under the Grid Modernization Initiative’s framework.
Argonne researchers are pleased to bring their long history and expertise in power grid research and development to this concerted effort to modernize the nation’s aging grid,” said Argonne Director Peter B. Littlewood, who has provided Senate testimony on the importance of the future grid. This is a massive and essential effort, and partnering with industry will enable Argonne and our sister DOE national laboratories to methodically address and achieve each of the goals outlined in the DOE’s new grid modernization plan.”
The GMLC initiative represents a truly new way of organizing capabilities across DOE to address a complex challenge, said Guenter Conzelmann, Director of Argonne’s Center for Energy, Environmental, and Economic Systems Analysis. This initiative gives us an opportunity to make a difference and help move the nation’s grid into the 21st century,” Conzelmann said. Our scientists will make critical contributions from foundational research in grid architecture, interoperability, sensing and measurement, advanced mathematical algorithms, and grid service valuation to developing new innovative tools for grid planning and operations. We are excited to work with the GMLC and our project partners at other labs and in industry and academia on these key strategic grid research topics.”
Some of Argonne’s projects will address issues with integrating large shares of solar and wind power into the grid and identify solutions to operating cost-effective and reliable electricity markets with large penetration of renewables, Conzelmann said. Other awards will allow Argonne to expand on and advance existing lab research and lab-developed technologies that will have a direct impact on the reliability and resilience of our grid.
For example, Argonne research will build upon a grid modeling, simulation, analysis and visualization tool called TS3ph to help utility planners more thoroughly understand cascading grid failures that may lead to large blackouts. Under a complementary project, researchers will develop a tool that will help utilities prepare for major disasters by improving and speeding up the power restoration after events such as winter storms or hurricanes.
Below is a complete list of Argonne led-projects under the GMLC.
• Computational Science for Grid Management
Address increasing computational complexity and reduced time-to-solution requirements for grid planning
Funding award: $1.5 million over three years Partners: PNNL, NREL, SNL, LLNL, LANL, PJM, and ISO-New England • Integrated Tool for Improving Grid Performance and Reliability of Combined Transmission-Distribution with High Solar Penetration Develop a software tool suite, comprising of three tools, for improving grid reliability and performance of combined transmission-distribution systems under high solar penetration Funding award:$2.8 million over three years
Partners: NREL, Electrocon International Inc., McCoy Energy, and IIT
• WindView: An Open Platform for Wind Energy Forecast Visualization
Provide solutions to maintain situational awareness in the control room as more wind generation is integrated in power systems
Funding award: $1.8 million over three years Partners: NREL, FERC, and EPRI • Measurement-Based Hierarchical Framework for Time Varying Stochastic Load Modeling Leverage practical AMI, SCADA, PMA and laboratory experimental data to develop static, dynamic as well as customer behavior-driven and demand response-enabled load/DG models at component, customer, feeder and substation levels Funding award:$2.7 million over three years
Partners: Siemens, Eaton, ComEd, Alliant Energy, Midamerican Energy, ERCOT, PJM, Cedar Falls Utilities, City of Ames, Iowa Energy Center, and ISU
• Protection and Dynamic Modeling, Simulation, Analysis and Visualization of Cascading Failures
Develop and validate a dynamics and protection simulation platform to enable utility planning, operations, and protection engineers to better understand and mitigate cascading blackouts involving protection
Funding award: $2.48 million over three years Partners: Electrocon International Inc., McCoy Energy, Altalink, ComEd, SPP, ISU, and IIT • Improved Forecasts of Electric Outages From Tropical Cyclones Improve forecasts of electric outages for tropical cyclone events affecting U.S. territory in the Caribbean, Atlantic seaboard and Gulf of Mexico regions Funding award:$800,000 over two years
Partners: Meade Electric, Georgia Power/Southern Company
• A Closed-Loop Distribution System Restoration Tool for Natural Disaster Recovery
Develop a distribution restoration decision support tool that will help utilities restore distribution after extreme weather events in an optimal and efficient manner
Funding award: $1.95 million over three years Partners: BNL and ISU • Cybersecurity for Renewables, Distributed Energy Resources, and Smart Inverters Develop a holistic attack-resilient architecture and layered cyber-physical solution portfolio to protect critical power grid infrastructure Funding award:$1.8 million over three years
Partners: EPRI and WSU
In addition to the projects it will lead, Argonne will be a participant in many other multi-laboratory GMLC research efforts. Included in these are projects related to how electric vehicles interact with the grid that will total more than \$1.5 million in funding.
These projects relate to vehicle-grid interoperability and interconnection, as well as standards and test procedures for grid services. Other projects are funded by DOE’s Vehicle Technologies Office and include technology development for connecting vehicles to buildings, as well as system-level vehicle-grid integration, analysis and cyber security.
Find more information on the Grid Modernization Initiative and the selected National Lab partnership projects at www.energy.gov/.
Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the Office of Science website.
| 2019-11-13T22:37:36 |
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https://www.itl.nist.gov/div898/handbook/eda/section3/eda35h1.htm
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1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.5. Quantitative Techniques
1.3.5.17. Detection of Outliers
## Grubbs' Test for Outliers
Purpose:
Detection of Outliers
Grubbs' test (Grubbs 1969 and Stefansky 1972) is used to detect a single outlier in a univariate data set that follows an approximately normal distribution.
If you suspect more than one outlier may be present, it is recommended that you use either the Tietjen-Moore test or the generalized extreme studentized deviate test instead of the Grubbs' test.
Grubbs' test is also known as the maximum normed residual test.
Definition Grubbs' test is defined for the hypothesis:
H0: There are no outliers in the data set Ha: There is exactly one outlier in the data set Test Statistic: The Grubbs' test statistic is defined as: $$G = \frac{\max{|Y_{i} - \bar{Y}|}} {s}$$ with $$\bar{Y}$$ and s denoting the sample mean and standard deviation, respectively. The Grubbs' test statistic is the largest absolute deviation from the sample mean in units of the sample standard deviation. This is the two-sided version of the test. The Grubbs' test can also be defined as one of the following one-sided tests: test whether the minimum value is an outlier $$G = \frac{\bar{Y} - Y_{min}} {s}$$ with Ymin denoting the minimum value. test whether the maximum value is an outlier $$G = \frac{Y_{max} - \bar{Y}} {s}$$ with Ymax denoting the maximum value. Significance Level: α Critical Region: For the two-sided test, the hypothesis of no outliers is rejected if $$G > \frac{(N-1)} {\sqrt{N}} \sqrt{\frac{(t_{\alpha/(2N),N-2})^2} {N-2+(t_{\alpha/(2N),N-2})^2}}$$ with $$t_{\alpha/(2N),N-2}$$ denoting the critical value of the t distribution with (N-2) degrees of freedom and a significance level of α/(2N). For one-sided tests, we use a significance level of level of α/N.
Grubbs' Test Example
The Tietjen and Moore paper gives the following set of 8 mass spectrometer measurements on a uranium isotope:
199.31 199.53 200.19 200.82 201.92 201.95 202.18 245.57
As a first step, a normal probability plot was generated
This plot indicates that the normality assumption is reasonable with the exception of the maximum value. We therefore compute Grubbs' test for the case that the maximum value, 245.57, is an outlier.
H0: there are no outliers in the data
Ha: the maximum value is an outlier
Test statistic: G = 2.4687
Significance level: α = 0.05
Critical value for an upper one-tailed test: 2.032
Critical region: Reject H0 if G > 2.032
For this data set, we reject the null hypothesis and conclude that the maximum value is in fact an outlier at the 0.05 significance level.
Questions Grubbs' test can be used to answer the following questions:
1. Is the maximum value an outlier?
2. Is the minimum value an outlier?
Importance Many statistical techniques are sensitive to the presence of outliers. For example, simple calculations of the mean and standard deviation may be distorted by a single grossly inaccurate data point.
Checking for outliers should be a routine part of any data analysis. Potential outliers should be examined to see if they are possibly erroneous. If the data point is in error, it should be corrected if possible and deleted if it is not possible. If there is no reason to believe that the outlying point is in error, it should not be deleted without careful consideration. However, the use of more robust techniques may be warranted. Robust techniques will often downweight the effect of outlying points without deleting them.
Related Techniques Several graphical techniques can, and should, be used to help detect outliers. A simple normal probability plot, run sequence plot, a box plot, or a histogram should show any obviously outlying points. In addition to showing potential outliers, several of these graphics also help assess whether the data follow an approximately normal distribution.
Case Study Heat flow meter data.
Software Some general purpose statistical software programs support the Grubbs' test. Both Dataplot code and R code can be used to generate the analyses in this section.
| 2018-07-19T07:57:48 |
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|
https://www.usgs.gov/publications/calculating-weighted-estimates-peak-streamflow-statistics
|
# Calculating weighted estimates of peak streamflow statistics
March 27, 2012
According to the Federal guidelines for flood-frequency estimation, the uncertainty of peak streamflow statistics, such as the 1-percent annual exceedance probability (AEP) flow at a streamgage, can be reduced by combining the at-site estimate with the regional regression estimate to obtain a weighted estimate of the flow statistic. The procedure assumes the estimates are independent, which is reasonable in most practical situations. The purpose of this publication is to describe and make available a method for calculating a weighted estimate from the uncertainty or variance of the two independent estimates.
## Citation Information
Publication Year 2012 Calculating weighted estimates of peak streamflow statistics 10.3133/fs20123038 Timothy A. Cohn, Charles Berenbrock, Julie E. Kiang, Robert R. Mason, Report USGS Numbered Series Fact Sheet 2012-3038 fs20123038 USGS Publications Warehouse National Center
| 2022-07-06T17:59:32 |
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|
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Book%3A_Elementary_Number_Theory_(Raji)/7%3A_Introduction_to_Analytic_Number_Theory/7.1%3A_Introduct_to_Analytic_Number_Theory
|
# 7.1: Introduct to Analytic Number Theory
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
It is well known that the harmonic series $$\sum_{n=1}^{\infty}\frac{1}{n}$$ diverges. We therefore determine some asymptotic formulas that determines the growth of the $$\sum_{n\leq x}\frac{1}{n}$$. We start by introducing Euler’s summation formula that will help us determine the asymptotic formula.
We might ask the following question. What if the sum is taken over all the primes. In this section, we show that the sum over the primes diverges as well. We also show that an interesting product will also diverge. From the following theorem, we can actually deduce that there are infinitely many primes.
Definition: Euler’s Summation Formula
If $$f$$ has a continuous derivative on an interval $$[a,b]$$ where $$a> 0$$, then $\sum_{a<n\leq b}f(n)=\int_{a}^bf(t)dt+\int_{a}^b(\{t\})f'(t)dt+f(b)(\{b\})-f(a)(\{a\}).$ where $$\{t\}$$ denotes the fractional part of $$t$$.
Proof
For the proof of Euler’s summation formula see .
If $$x\geq 1$$, we have that: $\sum_{n\leq x}\frac{1}{n}=\log x+\gamma+O\left(\frac{1}{x}\right)$
We use Euler’s summation formula by taking $$f(t)=1/t$$. We then get
\begin{aligned} \sum_{n\leq x}\frac{1}{n}&=&\int_{1}^x\frac{1}{t}dt-\int_1^x\frac{\{t\}}{t^2}dt+1+O\left(\frac{1}{x}\right)\\ &=& \log x+1-\int_1^{\infty}\frac{\{t\}}{t^2}dt+\int_x^{\infty}\frac{\{t\}}{t^2}dt+O\left(\frac{1}{x}\right)\end{aligned}
Notice now that $$\{t\}\leq t$$ and hence the two improper integrals exist since they are dominated by integrals that converge. We therefore have
$0\leq \int_x^\infty\frac{\{t\}}{t^2}dt\leq \frac{1}{x},$
we also let
$\gamma=1-\int_1^{\infty}\frac{\{t\}}{t^2}dt$
and we get the asymptotic formula.
Notice that $$\gamma$$ is called Euler’s constant. Notice also that similar steps can be followed to find an asymptotic formulas for other sums involving powers of $$n$$.
We now proceed to show that if we sum over the primes instead, we still get a divergent series.
Both $$\sum_p\frac{1}{p}$$ and $$\prod_p(1-\frac{1}{p})$$ diverge.
Let $$x \geq 2$$ and put $P(x)=\prod_{p\leq x}\left(1-\frac{1}{p}\right)^{-1}, \ \ \ S(x)=\sum_{p\leq x}\frac{1}{p}$ Let $$0<u<1$$ and $$m\in \mathbb{Z}$$, we have
$\frac{1}{1-u}>\frac{1-u^{m+1}}{1-u}=1+u+...+u^m.$
Now taking $$u=\frac{1}{p}$$, we get
$\frac{1}{1-\frac{1}{p}}>1+\frac{1}{p}+...+\left(\frac{1}{p}\right)^m$ As a result, we have that $P(x)>\prod_{p\leq x}\left(1+\frac{1}{p}+...+\frac{1}{p^m}\right)$
Choose $$m>0 \in \mathbb{Z}$$ such that $$2^{m-1}\leq x\leq 2^m$$. Observe also that
$\prod_{p\leq x}\left(1+\frac{1}{p}+...+\frac{1}{p^m}\right)=1+\sum_{p_i\leq x}\frac{1}{p_1^{m_1}p_2^{m_2}...}$
where $$1\leq m_i\leq m$$. As a result, we get every $$\frac{1}{n}, n\in \mathbb{Z^+}$$ where each prime factor of $$n$$ is less than or equal to $$x$$(Exercise). Thus we have
$\prod_{p\leq x}\left(1+\frac{1}{p}+...+\frac{1}{p^m}\right)>\sum_{n=1}^{2^{m-1}}\frac{1}{n}>\sum_{n=1}^{[x/2]}\frac{1}{n}$
Taking the limit as $$x$$ approaches infinity, we conclude that $$P(x)$$ diverges.
We proceed now to prove that $$S(x)$$ diverges. Notice that if $$u>0$$, then
$\log(1/u-1)<u+\frac{1}{2}(u^2+u^3+...).$
Thus we have
$\log(1/u-1)<u+\frac{u^2}{2}(1/1-u), \ \ \ 0<u<1.$
We now let $$u=1/p$$ for each $$p\leq x$$, then $\log\left(\frac{1}{1-1/p}\right)-\frac{1}{p}<\frac{1}{2p(p-1)}$ Thus $\log P(x)=\sum_{p\leq x}log(1/1-p).$ Thus we have $\log P(x)-S(x)<\frac{1}{2}\sum_{p\leq x}\frac{1}{p(p-1)}<\frac{1}{2}\sum_{n=1}^{\infty}\frac{1}{n(n-1)}$ This implies that $S(x)>\log P(x)-\frac{1}{2}$ And thus $$S(x)$$ diverges as $$x$$ approaches infinity.
[1] For any arithmetic function $$f(n)$$, we let $A(x)=\sum_{n\leq x}f(n)$ where $$A(x)=0$$ for $$x<1$$. Assume also that $$g$$ has a continuous derivative on the interval $$[y,x]$$, where $$0<y<x$$. Then we have
$\sum_{y<n\leq x}f(n)g(n)=A(x)g(x)-A(y)g(y)-\int_y^xA(t)g'(t)dt.$
The proof of this theorem can be found in .
### Exercises
1. Show that one gets every $$\frac{1}{n}, n\in \mathbb{Z^+}$$ where each prime factor of $$n$$ is less than or equal to $$x$$ in the proof of Theorem 1.
2. Write down the proof of Abel’s summation formula in details.
### Contributors
• Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution (CC BY) license.
| 2019-05-22T23:53:19 |
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|
https://par.nsf.gov/biblio/10364632-measuring-mass-black-widow-psr-j1555
|
Measuring the mass of the black widow PSR J1555-2908
ABSTRACT
Accurate measurements of the masses of neutron stars are necessary to test binary evolution models, and to constrain the neutron star equation of state. In pulsar binaries with no measurable post-Keplerian parameters, this requires an accurate estimate of the binary system’s inclination and the radial velocity of the companion star by other means than pulsar timing. In this paper, we present the results of a new method for measuring this radial velocity using the binary synthesis code Icarus. This method relies on constructing a model spectrum of a tidally distorted, irradiated star as viewed for a given binary configuration. This method is applied to optical spectra of the newly discovered black widow PSR J1555–2908. By modeling the optical spectroscopy alongside optical photometry, we find that the radial velocity of the companion star is 397 ± 4 km s−1 (errors quoted at 95 per cent confidence interval), as well as a binary inclination of >75°. Combined with γ-ray pulsation timing information, this gives a neutron star mass of 1.67$^{+0.15}_{-0.09}$ M⊙ and a companion mass of 0.060$^{+0.005}_{-0.003}$ M⊙, placing PSR J1555–2908 at the observed upper limit of what is considered a black widow system.
Authors:
; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10364632
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
512
Issue:
2
Page Range or eLocation-ID:
p. 3001-3014
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. ABSTRACT
Black widows are extreme millisecond pulsar binaries where the pulsar wind ablates their low-mass companion stars. In the optical range, their light curves vary periodically due to the high irradiation and tidal distortion of the companion, which allows us to infer the binary parameters. We present simultaneous multiband observations obtained with the HIPERCAM instrument at the 10.4-m GTC telescope for six of these systems. The combination of this five-band (us,gs, rs, is, zs) fast photometer with the world’s largest optical telescope enables us to inspect the light curve range near minima. We present the first light curve for PSR J1641+8049, as well as attain a significant increase in signal to noise and cadence compared with previous publications for the remaining five targets: PSR J0023+0923, PSR J0251+2606, PSR J0636+5129, PSR J0952−0607, and PSR J1544+4937. We report on the results of the light-curve modelling with the Icarus code for all six systems, which reveals some of the hottest and densest companion stars known. We compare the parameters derived with the limited but steadily growing black widow population for which optical modelling is available. We find some expected correlations, such as that between the companion star mean density and the orbital period of the system, which can be attributedmore »
2. Abstract
We present timing solutions for 12 pulsars discovered in the Green Bank North Celestial Cap 350 MHz pulsar survey, including six millisecond pulsars (MSPs), a double neutron star (DNS) system, and a pulsar orbiting a massive white dwarf companion. Timing solutions presented here include 350 and 820 MHz Green Bank Telescope data from initial confirmation and follow-up, as well as a dedicated timing campaign spanning 1 ryr PSR J1122−3546 is an isolated MSP, PSRs J1221−0633 and J1317−0157 are MSPs in black widow systems and regularly exhibit eclipses, and PSRs J2022+2534 and J2039−3616 are MSPs that can be timed with high precision and have been included in pulsar timing array experiments seeking to detect low-frequency gravitational waves. PSRs J1221−0633 and J2039−3616 have Fermi Large Area Telescope gamma-ray counterparts and also exhibit significant gamma-ray pulsations. We measure proper motions for three of the MSPs in this sample and estimate their space velocities, which are typical compared to those of other MSPs. We have detected the advance of periastron for PSR J1018−1523 and therefore measure the total mass of the DNS system,mtot= 2.3 ± 0.3M. Long-term pulsar timing with data spanning more than 1 yr is critical for classifying recycled pulsars, carryingmore »
3. ABSTRACT The Fermi Large Area Telescope gamma-ray source 3FGL J2039.6–5618 contains a periodic optical and X-ray source that was predicted to be a ‘redback’ millisecond pulsar (MSP) binary system. However, the conclusive identification required the detection of pulsations from the putative MSP. To better constrain the orbital parameters for a directed search for gamma-ray pulsations, we obtained new optical light curves in 2017 and 2018, which revealed long-term variability from the companion star. The resulting orbital parameter constraints were used to perform a targeted gamma-ray pulsation search using the Einstein@Home-distributed volunteer computing system. This search discovered pulsations with a period of 2.65 ms, confirming the source as a binary MSP now known as PSR J2039–5617. Optical light-curve modelling is complicated, and likely biased, by asymmetric heating on the companion star and long-term variability, but we find an inclination i ≳ 60°, for a low pulsar mass between $1.1\, \mathrm{M}_{\odot } \lt M_{\rm psr} \lt$ 1.6 M⊙, and a companion mass of 0.15–$0.22\, \mathrm{M}_{\odot }$, confirming the redback classification. Timing the gamma-ray pulsations also revealed significant variability in the orbital period, which we find to be consistent with quadrupole moment variations in the companion star, suggestive of convective activity. We also find thatmore »
4. Abstract
AQ Col (EC 05217-3914) is one of the first detected pulsating subdwarf B (sdB) stars and has been considered to be a single star. Photometric monitoring of AQ Col reveals a pulsation timing variation with a period of 486 days, interpreted as time delay due to reflex motion in a wide binary formed with an unseen companion with expected mass larger than 1.05M. The optical spectra and color–magnitude diagram of the system suggested that the companion is not a main-sequence star but a white dwarf or neutron star. The pulsation timing variation also shows that the system has an eccentricity of 0.424, which is much larger than any known sdB long period binary system. That might be due to the existence of another short period companion to the sdB star. Two optical spectra obtained on 1996 December 5 show a radial velocity change of 49.1 km s−1in 46.1 minutes, which suggests the hot subdwarf in the wide binary is itself a close binary formed with another unseen white dwarf or neutron star companion; if further observations show this interpretation to be correct, AQ Col is an interesting triple system worthy of further study.
5. Abstract We present new discoveries and results from long-term timing of 72 pulsars discovered in the Pulsar Arecibo L -band Feed Array (PALFA) survey, including precise determination of astrometric and spin parameters, and flux density and scatter broadening measurements at 1.4 GHz. Notable discoveries include two young pulsars (characteristic ages ∼30 kyr) with no apparent supernova remnant associations, three mode-changing, 12 nulling and two intermittent pulsars. We detected eight glitches in five pulsars. Among them is PSR J1939+2609, an apparently old pulsar (characteristic age ∼1 Gy), and PSR J1954+2529, which likely belongs to a newly emerging class of binary pulsars. The latter is the only pulsar among the 72 that is clearly not isolated: a nonrecycled neutron star with a 931 ms spin period in an eccentric ( e = 0.114) wide ( P b = 82.7 days) orbit with a companion of undetermined nature having a minimum mass of ∼0.6 M ⊙ . Since operations at Arecibo ceased in 2020 August, we give a final tally of PALFA sky coverage, and compare its 207 pulsar discoveries to the known population. On average, they are 50% more distant than other Galactic plane radio pulsars; PALFA millisecond pulsars (MSPs) have twicemore »
| 2023-03-29T22:05:16 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M021W&home=MXXX020
|
# ${{\boldsymbol K}{(1460)}}$ WIDTH INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$335.60$ $\pm6.20$ $\pm8.65$ 894k
2018 AI
LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{\mp}}$2 ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$
$\sim{}\text{ 260}$ 63
1981 C
CNTR - ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}}{{\mathit p}}$
$\sim{}\text{ 250}$ 15 1
1976 B
ASPK $\pm{}$ ${{\mathit K}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}$2 ${{\mathit \pi}}{{\mathit p}}$
1 Coupled mainly to ${{\mathit K}}{{\mathit f}_{{0}}{(1370)}}$ . Decay into ${{\mathit K}^{*}{(892)}}{{\mathit \pi}}$ seen.
References:
AAIJ 2018AI
EPJ C78 443 Studies of the resonance structure in $D^{0} \rightarrow K^\mp \pi ^\pm \pi ^\pm \pi ^\mp$ decays
DAUM 1981C
NP B187 1 Diffractive Production of Strange Mesons at 63 GeV
BRANDENBURG 1976B
PRL 36 1239 Evidence for a New Strangeness One Pseudoscalar Meson
| 2020-10-22T12:18:37 |
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|
https://par.nsf.gov/biblio/10369279-dust-masses-large-sample-core-collapse-supernovae-from-optical-emission-line-asymmetries-dust-formation-year-time-scales
|
Dust masses for a large sample of core-collapse supernovae from optical emission line asymmetries: dust formation on 30-year time-scales
ABSTRACT
Modelling the red–blue asymmetries seen in the broad emission lines of core-collapse supernovae (CCSNe) is a powerful technique to quantify total dust mass formed in the ejecta at late times (>5 yr after outburst) when ejecta dust temperatures become too low to be detected by mid-infrared (IR) instruments. Following our success in using the Monte Carlo radiative transfer code damocles to measure the dust mass evolution in SN 1987A and other CCSNe, we present the most comprehensive sample of dust mass measurements yet made with damocles, for CCSNe aged between 4 and 60 yr after outburst. Our sample comprises multi-epoch late-time optical spectra taken with the Gemini/Gemini Multi-Object Spectrographs (GMOS) and Very Large Telescope (VLT) X-Shooter spectrographs, supplemented by archival spectra. For the 14 CCSNe that we have modelled, we confirm a dust mass growth with time that can be fit by a sigmoid curve that is found to saturate beyond an age of ∼30 yr, at a mass of 0.23$^{+0.17}_{-0.12}$ M⊙. For an expanded sample including dust masses found in the literature for a further 11 CCSNe and six CCSN remnants, the dust mass at saturation is found to be 0.42$^{+0.09}_{-0.05}$ M⊙. Uncertainty limits for our dust masses were determined from a Bayesian analysis more »
Authors:
; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10369279
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
515
Issue:
3
Page Range or eLocation-ID:
p. 4302-4343
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. Abstract
The detailed observations of GW170817 proved for the first time directly that neutron star mergers are a major production site of heavy elements. The observations could be fit by a number of simulations that qualitatively agree, but can quantitatively differ (e.g., in total r-process mass) by an order of magnitude. We categorize kilonova ejecta into several typical morphologies motivated by numerical simulations, and apply a radiative transfer Monte Carlo code to study how the geometric distribution of the ejecta shapes the emitted radiation. We find major impacts on both spectra and light curves. The peak bolometric luminosity can vary by two orders of magnitude and the timing of its peak by a factor of five. These findings provide the crucial implication that the ejecta masses inferred from observations around the peak brightness are uncertain by at least an order of magnitude. Mixed two-component models with lanthanide-rich ejecta are particularly sensitive to geometric distribution. A subset of mixed models shows very strong viewing angle dependence due to lanthanide “curtaining,” which persists even if the relative mass of lanthanide-rich component is small. The angular dependence is weak in the rest of our models, but different geometric combinations of the two componentsmore »
2. ABSTRACT
We present multi-instrument observations of the disc around the Herbig Ae star, HD 145718, employing geometric and Monte Carlo radiative transfer models to explore the disc orientation, the vertical and radial extent of the near-infrared (NIR) scattering surface, and the properties of the dust in the disc surface and sublimation rim. The disc appears inclined at 67–71°, with position angle, PA = −1.0 to 0.6°, consistent with previous estimates. The NIR scattering surface extends out to ${\sim}75\,$ au and we infer an aspect ratio, hscat(r)/r ∼ 0.24 in J band; ∼0.22 in H band. Our Gemini Planet Imager images and VLTI + CHARA NIR interferometry suggest that the disc surface layers are populated by grains ≳λ/2π in size, indicating these grains are aerodynamically supported against settling and/or the density of smaller grains is relatively low. We demonstrate that our geometric analysis provides a reasonable assessment of the height of the NIR scattering surface at the outer edge of the disc and, if the inclination can be independently constrained, has the potential to probe the flaring exponent of the scattering surface in similarly inclined (i ≳ 70°) discs. In re-evaluating HD 145718’s stellar properties, we found that the object’s dimming events – previously characterized as UX Ormore »
3. Abstract In recent years, many Type IIn supernovae have been found to share striking similarities with the peculiar SN 2009ip, whose true nature is still under debate. Here, we present 10 yr of observations of SN 2011fh, an interacting transient with spectroscopic and photometric similarities to SN 2009ip. SN 2011fh had an M r ∼ −16 mag brightening event, followed by a brighter M r ∼ −18 mag luminous outburst in 2011 August. The spectra of SN 2011fh are dominated by narrow to intermediate Balmer emission lines throughout its evolution, with P Cygni profiles indicating fast-moving material at ∼6400 km s −1 . HST/WFC3 observations from 2016 October revealed a bright source with M F814W ≈ −13.3 mag, indicating that we are seeing the ongoing interaction of the ejecta with the circumstellar material or that the star might be going through an eruptive phase five years after the luminous outburst of 2011. Using HST photometry of the stellar cluster around SN 2011fh, we estimated an age of ∼4.5 Myr for the progenitor, which implies a stellar mass of ∼60 M ⊙ , using single-star evolution models, or a mass range of 35–80 M ⊙ , considering a binary system. Wemore »
4. ABSTRACT
The observed diversity in Type Ia supernovae (SNe Ia) – the thermonuclear explosions of carbon–oxygen white dwarf stars used as cosmological standard candles – is currently met with a variety of explosion models and progenitor scenarios. To help improve our understanding of whether and how often different models contribute to the occurrence of SNe Ia and their assorted properties, we present a comprehensive analysis of seven nearby SNe Ia. We obtained one to two epochs of optical spectra with Gemini Observatory during the nebular phase (>200 d past peak) for each of these events, all of which had time series of photometry and spectroscopy at early times (the first ∼8 weeks after explosion). We use the combination of early- and late-time observations to assess the predictions of various models for the explosion (e.g. double-detonation, off-centre detonation, stellar collisions), progenitor star (e.g. ejecta mass, metallicity), and binary companion (e.g. another white dwarf or a non-degenerate star). Overall, we find general consistency in our observations with spherically symmetric models for SN Ia explosions, and with scenarios in which the binary companion is another degenerate star. We also present an in-depth analysis of SN 2017fzw, a member of the subgroup of SNe Ia which appear to be transitional betweenmore »
5. Cometary activity is a manifestation of sublimation-driven processes at the surface of nuclei. However, cometary outbursts may arise from other processes that are not necessarily driven by volatiles. In order to fully understand nuclear surfaces and their evolution, we must identify the causes of cometary outbursts. In that context, we present a study of mini-outbursts of comet 46P/Wirtanen. Six events are found in our long-term lightcurve of the comet around its perihelion passage in 2018. The apparent strengths range from −0.2 to −1.6 mag in a 5" radius aperture, and correspond to dust masses between ∼104 to 106 kg, but with large uncertainties due to the unknown grain size distributions. However, the nominal mass estimates are the same order of magnitude as the mini-outbursts at comet 9P/Tempel 1 and 67P/Churyumov-Gerasimenko, events which were notably lacking at comet 103P/Hartley 2. We compare the frequency of outbursts at the four comets, and suggest that the surface of 46P has large-scale (∼10-100 m) roughness that is intermediate to that of 67P and 103P, if not similar to the latter. The strength of the outbursts appear to be correlated with time since the last event, but a physical interpretation with respect to solar insolationmore »
| 2023-03-30T11:51:48 |
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|
https://par.nsf.gov/biblio/10378835-simulations-black-hole-fueling-isolated-merging-galaxies-explicit-multiphase-ism
|
Simulations of black hole fueling in isolated and merging galaxies with an explicit, multiphase ISM
ABSTRACT
We study gas inflows on to supermassive black holes using hydrodynamics simulations of isolated galaxies and idealized galaxy mergers with an explicit, multiphase interstellar medium (ISM). Our simulations use the recently developed ISM and stellar evolution model called Stars and MUltiphase Gas in GaLaxiEs (SMUGGLE). We implement a novel super-Lagrangian refinement scheme that increases the gas mass resolution in the immediate neighbourhood of the black holes (BHs) to accurately resolve gas accretion. We do not include black hole feedback in our simulations. We find that the complex and turbulent nature of the SMUGGLE ISM leads to highly variable BH accretion. BH growth in SMUGGLE converges at gas mass resolutions ≲3 × 103 M⊙. We show that the low resolution simulations combined with the super-Lagrangian refinement scheme are able to produce central gas dynamics and BH accretion rates very similar to that of the uniform high resolution simulations. We further explore BH fueling by simulating galaxy mergers. The interaction between the galaxies causes an inflow of gas towards the galactic centres and results in elevated and bursty star formation. The peak gas densities near the BHs increase by orders of magnitude resulting in enhanced accretion. Our results support the idea that galaxy mergers more »
Authors:
; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10378835
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
517
Issue:
4
Page Range or eLocation-ID:
p. 4752-4767
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. ABSTRACT
Formation of supermassive black holes (BHs) remains a theoretical challenge. In many models, especially beginning from stellar relic ‘seeds,’ this requires sustained super-Eddington accretion. While studies have shown BHs can violate the Eddington limit on accretion disc scales given sufficient ‘fuelling’ from larger scales, what remains unclear is whether or not BHs can actually capture sufficient gas from their surrounding interstellar medium (ISM). We explore this in a suite of multiphysics high-resolution simulations of BH growth in magnetized, star-forming dense gas complexes including dynamical stellar feedback from radiation, stellar mass-loss, and supernovae, exploring populations of seeds with masses $\sim 1\!-\!10^{4}\, \mathrm{M}_{\odot }$. In this initial study, we neglect feedback from the BHs: so this sets a strong upper limit to the accretion rates seeds can sustain. We show that stellar feedback plays a key role. Complexes with gravitational pressure/surface density below $\sim 10^{3}\, \mathrm{M}_{\odot }\, {\rm pc^{-2}}$ are disrupted with low star formation efficiencies so provide poor environments for BH growth. But in denser cloud complexes, early stellar feedback does not rapidly destroy the clouds but does generate strong shocks and dense clumps, allowing $\sim 1{{\ \rm per\ cent}}$ of randomly initialized seeds to encounter a dense clump withmore »
2. Abstract
We explore the effect of dust on the growth of seed black holes (BHs) in the early universe. Previous 1D radiation-hydrodynamic (RHD) simulations show that increased radiation pressure on dust further suppresses the accretion rate than the case for the chemically pristine gas. Using the Enzo+Moray code, we perform a suite of 3D RHD simulations of accreting BHs in a dusty interstellar medium (ISM). We use the modified Grackle cooling library to consider dust physics in its nonequilibrium chemistry. The BH goes through an early evolutionary phase, where ionizing BH radiation creates an oscillating Hiiregion as it cycles between accretion and feedback. As the simulations proceed, dense cold gas accumulates outside the ionized region where inflow from the neutral medium meets the outflow driven by radiation pressure. In the late phase, high-density gas streams develop and break the quasi-spherical symmetry of the ionized region, rapidly boosting the accretion rate. The late phase is characterized by the coexistence of strong ionized outflows and fueling high-density gas inflows. The mean accretion rate increases with metallicity reaching a peak atZ∼ 0.01–0.1Z, one order of magnitude higher than the one for pristine gas. However, as the metallicity approaches the solar abundance, the meanmore »
3. ABSTRACT
We explore implications of a range of black hole (BH) seeding prescriptions on the formation of the brightest $z$ ≳ 6 quasars in cosmological hydrodynamic simulations. The underlying galaxy formation model is the same as in the IllustrisTNG simulations. Using constrained initial conditions, we study the growth of BHs in rare overdense regions (forming $\gtrsim 10^{12}\, {\rm M}_{\odot }\,h^{-1}$ haloes by $z$ = 7) using a (9 Mpc h−1)3 simulated volume. BH growth is maximal within haloes that are compact and have a low tidal field. For these haloes, we consider an array of gas-based seeding prescriptions wherein $M_{\mathrm{seed}}=10^4\!-\!10^6\, {\rm M}_{\odot }\,h^{-1}$ seeds are inserted in haloes above critical thresholds for halo mass and dense, metal-poor gas mass (defined as $\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, in units of Mseed). We find that a seed model with $\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfully produces a $z$ ∼ 6 quasar with $\sim 10^9\, {\rm M}_{\odot }$ mass and ∼1047 erg s−1 luminosity. BH mergers play a crucial role at $z$ ≳ 9, causing an early boost in BH mass at a time when accretion-driven BH growth is negligible. With more stringent seeding conditions (e.g. $\tilde{M}_{\mathrm{sf,mp}}=1000$), the relative paucity of BH seeds results in a much lower merger rate. In this case, $z$more »
4. ABSTRACT
Direct collapse black holes (BHs) are promising candidates for producing massive z ≳ 6 quasars, but their formation requires fine-tuned conditions. In this work, we use cosmological zoom simulations to study systematically the impact of requiring: (1) low gas angular momentum (spin), and (2) a minimum incident Lyman–Werner (LW) flux in order to form BH seeds. We probe the formation of seeds (with initial masses of $M_{\rm seed} \sim 10^4\!-\!10^6\, \mathrm{M}_{\odot }\, h^{-1})$ in haloes with a total mass >3000 × Mseed and a dense, metal-poor gas mass >5 × Mseed. Within this framework, we find that the seed-forming haloes have a prior history of star formation and metal enrichment, but they also contain pockets of dense, metal-poor gas. When seeding is further restricted to haloes with low gas spins, the number of seeds formed is suppressed by factors of ∼6 compared to the baseline model, regardless of the seed mass. Seed formation is much more strongly impacted if the dense, metal-poor gas is required to have a critical LW flux (Jcrit). Even for Jcrit values as low as 50J21, no $8\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$ seeds are formed. While lower mass ($1.25\times 10^{4},1\times 10^{5}~\mathrm{M}_{\odot }\, h^{-1}$) seeds do form, they are strongly suppressed (by factors of ∼10–100) comparedmore »
5. Abstract Accreting black holes can drive fast and energetic nuclear winds that may be an important feedback mechanism associated with active galactic nuclei (AGN). In this paper, we implement a scheme for capturing feedback from these fast nuclear winds and examine their impact in simulations of isolated disk galaxies. Stellar feedback is modeled using the FIRE physics and produces a realistic multiphase interstellar medium (ISM). We find that AGN winds drive the formation of a low-density, high-temperature central gas cavity that is broadly consistent with analytic model expectations. The effects of AGN feedback on the host galaxy are a strong function of the wind kinetic power and momentum. Low and moderate luminosity AGN do not have a significant effect on their host galaxy: the AGN winds inefficiently couple to the ambient ISM and instead a significant fraction of their energy vents in the polar direction. For such massive black holes, accretion near the Eddington limit can have a dramatic impact on the host galaxy ISM: if AGN wind feedback acts for ≳ 20 − 30 Myr, the inner ∼1 − 10 kpc of the ISM is disrupted and the global galaxy star formation rate is significantly reduced. We quantify the properties ofmore »
| 2023-02-03T19:40:39 |
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|
https://pdglive.lbl.gov/Particle.action?init=0&node=B053&home=BXXX025
|
${{\boldsymbol \Sigma}}$ BARYONS($\boldsymbol S$ = $-1$, $\boldsymbol I$ = 1) ${{\mathit \Sigma}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$ INSPIRE search
# ${{\boldsymbol \Sigma}{(2455)}}$ Bumps $I(J^P)$ = $1(?^{?})$
There is also some slight evidence for ${{\mathit Y}^{*}}$ states in this mass region from the reaction ${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit X}}$ $-$ see GREENBERG 1968 .
${{\mathit \Sigma}{(2455)}}$ MASS $\approx2455$ MeV
${{\mathit \Sigma}{(2455)}}$ WIDTH
| 2020-09-20T01:21:00 |
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https://pdglive.lbl.gov/DataBlock.action?node=S020D&home=sumtabB
|
#### ${\mathit m}_{{{\mathit \Sigma}^{-}}}–{\mathit m}_{{{\mathit \Sigma}^{+}}}$
VALUE (MeV) EVTS DOCUMENT ID TECN
$\bf{ 8.08 \pm0.08}$ OUR FIT Error includes scale factor of 1.9.
$\bf{ 8.09 \pm0.16}$ OUR AVERAGE
$7.91$ $\pm0.23$ 86
1972
EMUL
$8.25$ $\pm0.25$ 2500
1965
HBC
$8.25$ $\pm0.40$ 87
1963
EMUL
References:
BOHM 1972
NP B48 1 Determination of the Masses of the Charged ${{\mathit \Sigma}}$ Hyperons
Also
IIHE-73.2 Nov A Determination of the Masses of the Charged ${{\mathit \Sigma}}$ Hyperons $−$ a Reevaluation
DOSCH 1965
PL 14 239 The Mass Difference of the ${{\mathit \Sigma}}$ Hyperons
Also
PR 151 1081 ${{\mathit \Sigma}^{\pm}}$ Lifetime and the Branching Ratio Br(${{\mathit \Sigma}^{+}}$) = ( ${{\mathit \Sigma}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit n}}$ )/( ${{\mathit \Sigma}^{+}}$ $\rightarrow$ )
BARKAS 1963
PRL 11 26 Resolution of the ${{\mathit \Sigma}^{-}}$-Mass Anomaly
Also
Thesis UCRL 9450 Charged ${{\mathit \Sigma}}$-Hyperon Production and Decay: Energetics, Lifetimes, and Branching Ratios
| 2022-09-26T09:58:17 |
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https://zbmath.org/authors/billingsley.patrick
|
## Billingsley, Patrick Paul
Compute Distance To:
Author ID: billingsley.patrick Published as: Billingsley, Patrick; Billingsley, P. External Links: MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 37 Publications since 1956, including 15 Books Co-Authors: 7 Co-Authors with 9 Joint Publications 36 Co-Co-Authors
all top 5
### Co-Authors
28 single-authored 5 Huntsberger, David V. 2 Croft, D. James 1 Baum, Leonard E. 1 Henningsen, Inge 1 Topsøe, Flemming 1 Watson, Collin J. 1 Wichura, Michael J.
all top 5
### Serials
5 Annals of Mathematical Statistics 3 American Mathematical Monthly 3 The Annals of Probability 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 Wiley Series in Probability and Mathematical Statistics 2 Illinois Journal of Mathematics 1 Periodica Mathematica Hungarica 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Roczniki Polskiego Towarzystwa Matematycznego. Seria II. Wiadomości Matematyczne 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Wiley Series in Probability and Statistics
all top 5
### Fields
13 Probability theory and stochastic processes (60-XX) 8 Measure and integration (28-XX) 6 Number theory (11-XX) 6 Statistics (62-XX) 2 Information and communication theory, circuits (94-XX) 1 Real functions (26-XX)
### Citations contained in zbMATH Open
30 Publications have been cited 9,645 times in 9,197 Documents Cited by Year
Convergence of probability measures. Zbl 0172.21201
Billingsley, P.
1968
Probability and measure. 3rd ed. Zbl 0822.60002
Billingsley, Patrick
1995
Convergence of probability measures. 2nd ed. Zbl 0944.60003
Billingsley, Patrick
1999
Probability and measure. 2nd ed. Zbl 0649.60001
Billingsley, Patrick
1986
Ergodic theory and information. Zbl 0141.16702
Billingsley, P.
1965
Probability and measure. Zbl 0411.60001
Billingsley, Patrick
1979
The Lindeberg-Levy theorem for martingales. Zbl 0129.10701
Billingsley, P.
1961
Statistical inference for Markov processes. (Statistical Research Monographs. Vol. 2). Zbl 0106.34201
Billingsley, Patrick
1961
Weak convergence of measures: Applications in probability. Zbl 0271.60009
Billingsley, Patrick
1971
Statistical methods in Markov chains. Zbl 0104.12802
Billingsley, Patrick
1961
Probability and measure. Anniversary edition. Zbl 1236.60001
Billingsley, Patrick
2012
Ergodic theory and information. (Ергодическая Теория и Информация.) Zbl 0184.43301
Billingsley, Patrick
1969
Hausdorff dimension in probability theory. I, II. Zbl 0098.10602
Billingsley, Patrick
1960
Uniformity in weak convergence. Zbl 0147.15701
Billingsley, P.; Topsoe, F.
1967
On the distribution of large prime divisors. Zbl 0242.10033
Billingsley, P.
1972
The probability theory of additive arithmetic functions. Zbl 0327.10055
Billingsley, Patrick
1974
Convergence of types in $$k$$-space. Zbl 0152.17102
Billingsley, P.
1966
The invariance principle for dependent random variables. Zbl 0075.13703
Billingsley, Patrick
1956
Van der Waerden’s continuous nowhere differentiable function. Zbl 0598.26014
Billingsley, Patrick
1982
Asymptotic distributions for the coupon collector’s problem. Zbl 0227.62010
Baum, Leonard E.; Billingsley, Patrick
1965
On the central limit theorem for the prime divisor function. Zbl 0182.07401
Billingsley, P.
1969
Prime numbers and Brownian motion. Zbl 0275.10029
Billingsley, Patrick
1973
Limit theorems for randomly selected partial sums. Zbl 0113.12402
Billingsley, P.
1962
Conditional distributions and tightness. Zbl 0286.60003
Billingsley, Patrick
1974
Maxima of partial sums. Zbl 0181.44303
Billingsley, P.
1969
Hausdorff dimension of some continued-fraction sets. Zbl 0287.10042
Billingsley, Patrick; Henningsen, Inge
1975
Asymptotic distributions of two goodness of fit criteria. Zbl 0073.35605
Billingsley, Patrick
1956
On the coding theorem for the noiseless channel. Zbl 0114.33903
Billingsley, P.
1961
An application of Prohorov’s theorem to probabilistic number theory. Zbl 0128.04302
Billingsley, Patrick
1964
Elements of statistical inference. 4th ed. Zbl 0371.62001
Huntsberger, David V.; Billingsley, Patrick
1977
Probability and measure. Anniversary edition. Zbl 1236.60001
Billingsley, Patrick
2012
Convergence of probability measures. 2nd ed. Zbl 0944.60003
Billingsley, Patrick
1999
Probability and measure. 3rd ed. Zbl 0822.60002
Billingsley, Patrick
1995
Probability and measure. 2nd ed. Zbl 0649.60001
Billingsley, Patrick
1986
Van der Waerden’s continuous nowhere differentiable function. Zbl 0598.26014
Billingsley, Patrick
1982
Probability and measure. Zbl 0411.60001
Billingsley, Patrick
1979
Elements of statistical inference. 4th ed. Zbl 0371.62001
Huntsberger, David V.; Billingsley, Patrick
1977
Hausdorff dimension of some continued-fraction sets. Zbl 0287.10042
Billingsley, Patrick; Henningsen, Inge
1975
The probability theory of additive arithmetic functions. Zbl 0327.10055
Billingsley, Patrick
1974
Conditional distributions and tightness. Zbl 0286.60003
Billingsley, Patrick
1974
Prime numbers and Brownian motion. Zbl 0275.10029
Billingsley, Patrick
1973
On the distribution of large prime divisors. Zbl 0242.10033
Billingsley, P.
1972
Weak convergence of measures: Applications in probability. Zbl 0271.60009
Billingsley, Patrick
1971
Ergodic theory and information. (Ергодическая Теория и Информация.) Zbl 0184.43301
Billingsley, Patrick
1969
On the central limit theorem for the prime divisor function. Zbl 0182.07401
Billingsley, P.
1969
Maxima of partial sums. Zbl 0181.44303
Billingsley, P.
1969
Convergence of probability measures. Zbl 0172.21201
Billingsley, P.
1968
Uniformity in weak convergence. Zbl 0147.15701
Billingsley, P.; Topsoe, F.
1967
Convergence of types in $$k$$-space. Zbl 0152.17102
Billingsley, P.
1966
Ergodic theory and information. Zbl 0141.16702
Billingsley, P.
1965
Asymptotic distributions for the coupon collector’s problem. Zbl 0227.62010
Baum, Leonard E.; Billingsley, Patrick
1965
An application of Prohorov’s theorem to probabilistic number theory. Zbl 0128.04302
Billingsley, Patrick
1964
Limit theorems for randomly selected partial sums. Zbl 0113.12402
Billingsley, P.
1962
The Lindeberg-Levy theorem for martingales. Zbl 0129.10701
Billingsley, P.
1961
Statistical inference for Markov processes. (Statistical Research Monographs. Vol. 2). Zbl 0106.34201
Billingsley, Patrick
1961
Statistical methods in Markov chains. Zbl 0104.12802
Billingsley, Patrick
1961
On the coding theorem for the noiseless channel. Zbl 0114.33903
Billingsley, P.
1961
Hausdorff dimension in probability theory. I, II. Zbl 0098.10602
Billingsley, Patrick
1960
The invariance principle for dependent random variables. Zbl 0075.13703
Billingsley, Patrick
1956
Asymptotic distributions of two goodness of fit criteria. Zbl 0073.35605
Billingsley, Patrick
1956
all top 5
### Cited by 9,392 Authors
109 Laurinčikas, Antanas 43 Horváth, Lajos 39 Lee, Sangyeol 39 Whitt, Ward 38 Peligrad, Magda 37 Janson, Svante 33 Resnick, Sidney Ira 32 Berkes, István 32 Yin, Gang George 28 Macaitienė, Renata 28 Samorodnitsky, Gennady Pinkhosovich 25 Iksanov, Aleksander M. 24 Mikosch, Thomas 22 Glynn, Peter W. 22 Taqqu, Murad S. 21 Kushner, Harold J. 21 Šiaučiūnas, Darius 21 Wang, Dehui 20 Basawa, Ishwar V. 20 Francq, Christian 19 Kabluchko, Zakhar A. 19 Meerschaert, Mark Marvin 19 Minkevičius, Saulius 19 Pang, Guodong 19 Pardoux, Etienne 18 Fernández-Sánchez, Juan 18 Ling, Shiqing 18 Sen, Pranab Kumar 17 Artstein, Zvi 17 Harel, Michel 17 Hušková, Marie 17 Kokoszka, Piotr S. 17 Puri, Madan Lal 17 Sun, Yeneng 17 Surgailis, Donatas 17 Zhang, Li-Xin 16 Bouzebda, Salim 16 Komorowski, Tomasz 15 Bai, Zhi-Dong 15 Kifer, Yuri 15 Koul, Hira Lal 15 Volný, Dalibor 15 Yang, Kai 15 Zakoïan, Jean-Michel 14 Ferger, Dietmar 14 López-Díaz, Miguel 14 Louchard, Guy 14 Prakasa Rao, B. L. S. 13 Atar, Rami 13 Dette, Holger 13 Díaz-García, José Antonio 13 Hidalgo, Javier 13 Limnios, Nikolaos 13 Merlevède, Florence 13 Philipp, Walter 13 Račkauskas, Alfredas Yurgevich 13 Soulier, Philippe 13 Stute, Winfried 12 Albeverio, Sergio A. 12 Borkar, Vivek Shripad 12 Davis, Richard A. 12 Dehling, Herold G. 12 Denker, Manfred 12 Diaz Carrillo, Manuel 12 Mahmoud, Hosam M. 12 Pap, Gyula 12 Paulauskas, Vygantas Ionovič 12 Phillips, Peter Charles Bonest 12 van der Hofstad, Remco W. 12 Wu, Wei Biao 12 Zhang, Qing 11 Balan, Raluca M. 11 Bingham, Nicholas Hugh 11 De Amo, Enrique 11 Dedecker, Jérôme 11 Dombry, Clément 11 El Barmi, Hammou 11 Faggionato, Alessandra 11 Goldsman, David M. 11 Goldstein, Sheldon 11 Gorostiza, Luis G. 11 Grübel, Rudolf 11 Guillou, Armelle 11 Kallenberg, Olav 11 Liu, Wen 11 Marynych, Alexander V. 11 Nualart, David 11 Penrose, Mathew D. 11 Rachev, Svetlozar T. 11 Rahimov, Ibrahim 11 Shao, Xiaofeng 11 Talarczyk, Anna 11 Wang, Leyi 11 Woodroofe, Michael Barrett 11 Yoshihara, Ken-ichi 11 Zwart, Bert P. 10 Afanas’ev, Valeriĭ Ivanovich 10 Aki, Sigeo 10 Aue, Alexander 10 Balbus, Łukasz ...and 9,292 more Authors
all top 5
### Cited in 703 Serials
518 Stochastic Processes and their Applications 394 Statistics & Probability Letters 258 Journal of Statistical Planning and Inference 214 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 204 The Annals of Applied Probability 197 Journal of Econometrics 184 Probability Theory and Related Fields 166 The Annals of Probability 164 Communications in Statistics. Theory and Methods 163 Journal of Multivariate Analysis 157 Journal of Statistical Physics 146 Journal of Mathematical Analysis and Applications 146 The Annals of Statistics 139 Journal of Theoretical Probability 131 Bernoulli 127 Lithuanian Mathematical Journal 116 Journal of Applied Probability 114 Queueing Systems 112 Journal of Economic Theory 109 Annals of the Institute of Statistical Mathematics 98 Communications in Mathematical Physics 83 Transactions of the American Mathematical Society 81 Journal of Mathematical Economics 76 Advances in Applied Probability 70 Stochastic Analysis and Applications 70 Electronic Journal of Statistics 67 Metrika 64 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 64 Computational Statistics and Data Analysis 63 Statistics 59 Electronic Journal of Probability 54 Journal of Nonparametric Statistics 51 Theoretical Computer Science 50 Proceedings of the American Mathematical Society 47 Journal of Mathematical Sciences (New York) 46 Journal of Time Series Analysis 45 Advances in Mathematics 45 Econometric Theory 43 Economic Theory 42 Kybernetika 40 Fuzzy Sets and Systems 40 Journal of Soviet Mathematics 39 Stochastics 39 Statistical Papers 39 Probability in the Engineering and Informational Sciences 38 Israel Journal of Mathematics 37 Monatshefte für Mathematik 37 Journal of Statistical Computation and Simulation 37 Extremes 37 Methodology and Computing in Applied Probability 36 Games and Economic Behavior 35 Journal of Differential Equations 35 Test 34 Econometric Reviews 33 Journal of Mathematical Biology 33 Journal of Functional Analysis 33 Random Structures & Algorithms 33 European Journal of Operational Research 32 Operations Research Letters 32 Physica D 31 Mathematical Notes 31 Ukrainian Mathematical Journal 30 Annals of Operations Research 30 Economics Letters 30 Mathematical Programming. Series A. Series B 29 Scandinavian Journal of Statistics 29 Insurance Mathematics & Economics 29 Statistical Inference for Stochastic Processes 28 Applied Mathematics and Optimization 28 Journal of Computational and Applied Mathematics 27 Journal of Optimization Theory and Applications 27 Mathematical Methods of Statistics 27 Stochastic Models 27 Stochastics and Dynamics 26 Journal of Number Theory 25 SIAM Journal on Control and Optimization 25 Sequential Analysis 25 Electronic Communications in Probability 25 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 25 Comptes Rendus. Mathématique. Académie des Sciences, Paris 24 Mathematische Nachrichten 24 Communications in Statistics. Simulation and Computation 23 Mathematische Zeitschrift 23 Acta Mathematica Sinica. English Series 22 Acta Mathematica Hungarica 22 Journal of Economic Dynamics & Control 22 Stochastics 22 ALEA. Latin American Journal of Probability and Mathematical Statistics 21 The Canadian Journal of Statistics 21 Chaos, Solitons and Fractals 21 Theory of Probability and its Applications 21 Systems & Control Letters 21 Theory of Probability and Mathematical Statistics 21 Annales Henri Poincaré 21 Journal of the Korean Statistical Society 20 Journal of Mathematical Physics 20 Physica A 20 Automatica 20 Mathematical Social Sciences 19 Mathematical Proceedings of the Cambridge Philosophical Society ...and 603 more Serials
all top 5
### Cited in 61 Fields
5,080 Probability theory and stochastic processes (60-XX) 3,063 Statistics (62-XX) 840 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 528 Operations research, mathematical programming (90-XX) 502 Measure and integration (28-XX) 449 Numerical analysis (65-XX) 439 Statistical mechanics, structure of matter (82-XX) 426 Dynamical systems and ergodic theory (37-XX) 410 Number theory (11-XX) 399 Computer science (68-XX) 319 Partial differential equations (35-XX) 298 Systems theory; control (93-XX) 265 Biology and other natural sciences (92-XX) 262 Combinatorics (05-XX) 157 Functional analysis (46-XX) 152 Calculus of variations and optimal control; optimization (49-XX) 143 Information and communication theory, circuits (94-XX) 131 Operator theory (47-XX) 119 Ordinary differential equations (34-XX) 113 Quantum theory (81-XX) 110 Real functions (26-XX) 102 General topology (54-XX) 101 Linear and multilinear algebra; matrix theory (15-XX) 86 Fluid mechanics (76-XX) 79 Mathematical logic and foundations (03-XX) 73 Functions of a complex variable (30-XX) 65 Harmonic analysis on Euclidean spaces (42-XX) 49 Approximations and expansions (41-XX) 40 Special functions (33-XX) 36 Convex and discrete geometry (52-XX) 35 Global analysis, analysis on manifolds (58-XX) 34 Group theory and generalizations (20-XX) 34 Differential geometry (53-XX) 28 Integral transforms, operational calculus (44-XX) 27 Difference and functional equations (39-XX) 26 Mechanics of particles and systems (70-XX) 24 Potential theory (31-XX) 24 Abstract harmonic analysis (43-XX) 20 Integral equations (45-XX) 19 Sequences, series, summability (40-XX) 18 Order, lattices, ordered algebraic structures (06-XX) 18 Topological groups, Lie groups (22-XX) 18 Manifolds and cell complexes (57-XX) 18 Geophysics (86-XX) 17 Algebraic geometry (14-XX) 16 Algebraic topology (55-XX) 13 History and biography (01-XX) 13 Mechanics of deformable solids (74-XX) 8 General and overarching topics; collections (00-XX) 7 Category theory; homological algebra (18-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Optics, electromagnetic theory (78-XX) 5 Astronomy and astrophysics (85-XX) 5 Mathematics education (97-XX) 4 Commutative algebra (13-XX) 3 Relativity and gravitational theory (83-XX) 2 Nonassociative rings and algebras (17-XX) 2 Geometry (51-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2023-01-31T06:44:12 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S067CP2
|
(C) Other neutrino mixing results
The LSND collaboration reported in AGUILAR 2001 a signal which is consistent with ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillations. In a three neutrino framework, this would be a measurement of $\theta _{12}$ and $\Delta \mathit m{}^{2}_{21}$. This does not appear to be consistent with most of the other neutrino data. The following listings include results from ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ , ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ appearance and ${{\mathit \nu}_{{\mu}}}$, ${{\overline{\mathit \nu}}_{{\mu}}}$, ${{\mathit \nu}_{{e}}}$, and ${{\overline{\mathit \nu}}_{{e}}}$ disappearance experiments, and searches for $\mathit CPT$ violation.
$\langle \Delta {{\boldsymbol m}^{2}}_{\mathrm {32}}−\Delta {{\overline{\boldsymbol m}}}{}^{2}_{32}\rangle$ INSPIRE search
VALUE ($10^{-3}$ eV${}^{2}$) CL% DOCUMENT ID TECN COMMENT
$-0.12$ ${}^{+0.26}_{-0.24}$ 1
2013 B
MINS beam and atmosperic
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.6$ ${}^{+2.4}_{-0.8}$ 90 2
2012 B
MINS MINOS atmospheric
1 ADAMSON 2013B quotes this difference as a negative of our convention.
2 The quoted result is the single-parameter 90$\%$ C.L. interval determined from the 90$\%$ C.L. contour in the ($\Delta \mathit m{}^{2}$, $\Delta \bar m{}^{2}$) plane, which is obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters.
Conservation Laws:
$\mathit CPT$ INVARIANCE
References:
| 2020-07-03T13:58:22 |
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|
https://www.nist.gov/publications/ipogipog-d-efficient-test-generation-multi-way-combinatorial-testing?pub_id=50964
|
# IPOG/IPOG-D: Efficient Test Generation for Multi-way Combinatorial Testing
Published: November 29, 2007
### Author(s)
Yu Lei, Raghu N. Kacker, David R. Kuhn, Vadim Okun, James F. Lawrence
### Abstract
We present two strategies for multi-way testing (i.e., t-way testing with t > 2). The first strategy generalizes an existing strategy, called In-Parameter-Order, from pairwise testing to multi-way testing. This strategy requires all t-way combinations to be explicitly enumerated. When the number of t-way combinations is large, however, explicit enumeration can be prohibitive both in terms of the space for storing these combinations and the time needed to enumerate them. To alleviate this problem, the second strategy combines the first strategy with a recursive construction procedure to reduce the number of t-way combinations that have to be enumerated. Both strategies are deterministic, i.e., they always produce the same test set for the same system configuration. We describe a t-way testing tool called FireEye and provide both analytic and experimental evaluation of the two strategies.
Citation: Software Testing Verification & Reliability
Volume: 18
Issue: 3
Pub Type: Journals
| 2018-03-24T00:44:17 |
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|
http://cs.lbl.gov/news-media/intheloop-recent-issues/intheloop-historical-archive/2011/intheloop-09-19-2011/
|
# InTheLoop | 09.19.2011
September 19, 2011
## Kathy Yelick Appointed to National Academies’ Computer Science and Telecommunications Board
Associate Laboratory Director for Computing Sciences Kathy Yelick has been appointed to the Computer Science and Telecommunications Board (CSTB) of the National Academies, which include the National Academy of Sciences, National Academy of Engineering, Institute of Medicine, and National Research Council. CSTB is composed of nationally recognized experts from across the information technology fields and complementary fields germane to the Board's interests in IT and society. Board members are appointed by the National Academies following a rigorous vetting process, and they serve staggered terms of three to five years.
CSTB was established in 1986 to provide independent advice to the federal government on technical and public policy issues relating to computing and communications. CSTB conducts studies of critical national issues that recommend actions or changes in actions by government, industry, academic researchers, and the larger nonprofit sector. CSTB also provides a neutral meeting ground for consideration of complex issues where resolution and action may be premature. It convenes invitational discussion sessions that bring together principals from the public and private sectors to share perspectives on all sides of an issue.
Yelick was previously a member of the CSTB’s Committee on Sustaining Growth in Computing Performance, which published the report The Future of Computing Performance: Game Over or Next Level? earlier this year.
## The Path to Interoperability Passes through Rio
Last week (Sept. 13–14), Inder Monga represented ESnet at the 11th Annual Global LambdaGrid Workshop, held at the Museum of Modern Art, Rio de Janeiro, Brazil. ESnet participated in a Network Services Interface (NSI) protocol “plugfest” with OSCARS, its award-winning On-Demand Secure Circuits and Advance Reservation System software, testing it against other bandwidth reservation software to determine its level of interoperability and find any issues with specifications. Monga also gave a talk titled “Networks & Power—ESnet’s Initiatives towards Green.” Read more.
## Export Control Training Session on Sept. 27
Are you in compliance with export control regulations? Do you:
• Transfer information including technical data to persons and entities outside the US?
• Make verbal, written, electronic, or visual disclosures to foreign nationals of controlled scientific and technical information either internationally or within the US?
• Travel to certain sanctioned or embargoed countries for purposes of teaching or performing research?
• Ship physical items such as scientific equipment from the US to a foreign country?
If you are a PI or administrator involved in international collaboration and projects, you need to know what it takes to be in compliance with export control regulations in order to avoid civil or criminal liability for LBNL or for an individual researcher. A training session will be held Tuesday, Sept. 27, from 9:00 to 10:30 am in the Bldg. 66 auditorium. If you have any questions, email Deb Troxell or call x7026.
## Correction: Optometrist Is On Site Every Thursday
A Lab Health Services optometrist is on site every Thursday, not every Wednesday as reported in last week’s InTheLoop. Free glasses for eye protection or assistance with computer viewing are available to all Lab employees. Eye exams are performed by appointment only. Call Health Services at x6266.
## This Week’s Computing Sciences Seminars
Laser Interferometer Gravitational Wave Observatory (LIGO) Analysis on the Open Science Grid (OSG)
Monday, Sept. 19, 9:30–10:30 am, OSF room 236
Britta Daudert, Caltech
Homology Search vs Supercomputing
Monday, Sept. 19, 2:00–3:00 pm, OSF room 236
Al Shpuntoff, AFS Informatics
Phase Transitions of AMP Algorithms in Compressed Sensing: Net/Comm/DSP Seminar
Monday, Sept. 19, 2:00–3:00 pm, 521 Cory Hall (Hogan Room), UC Berkeley
David Donoho, Stanford University
Approximate Message Passing (AMP) algorithms for compressed sensing can be generalized to employ denoising operators besides the traditional scalar shrinkers underlying the original derivation (soft thresholding, positive soft thresholding and capping). This talk gives several examples including scalar shrinkers not derivable from convex optimization — the firm shrinkage nonlinearity and the the minimax nonlinearity — and also nonscalar denoisers — block thresholding (both block soft and James-Stein), monotone regression, and total variation minimization.
We give a general formula showing precisely when such algorithms guarantee recovery of objects obeying (generalized) sparsity constraints. Let the variables $\epsilon = k/N$ and $\delta = n/N$ denote the generalized sparsity and undersampling fractions for sampling a k-generalized-sparse $N$-vector $x_0$ according to $y = Ax_0$ with entries of the $n \times N$ matrix $A$ iid standard Gaussian. The formula states that the phase transition curve $\delta = \delta(\epsilon)$ separating successful from unsuccessful reconstruction of $x_0$ by AMP is given by:
$\delta = M(\epsilon|Denoiser)$,
where $M(\epsilon|Denoiser) denotes the per-coordinate minimax mean squared error of the specified, optimally-tuned denoiser in the directly observed problem$y = x + z\$. In short, the phase transition of successful reconstruction in a noiseless undersampling problem is identical to the minimax MSE in a denoising problem.
We view this as a “precise undersampling theorem” covering a wide range of signal types and reconstructions methods.
Matrix Computations and Scientific Computing Seminar: Numerical Algorithms for the Electronic Structure Analysis
Wednesday, Sept. 21, 12:10–1:00 pm, 380 Soda Hall, UC Berkeley
Lin Lin, LBNL/CRD
Kohn-Sham density functional theory (KSDFT) is by far the most widely used electronic structure theory for condensed matter systems. The computational time of KSDFT increases as O(N^3) with respect to the number of electrons (N), which hinders its practical application to systems of large size. We have developed an accurate and efficient algorithm to solve KSDFT which is uniformly applicable to insulating and metallic systems. Our method directly uses the property that the electron density and the electron energy are fully characterized by the diagonal elements and the nearest off diagonal elements of the single particle density matrix. This property is not reflected in the current O(N^3) scaling methods. Our new method achieves O(N) scaling for quasi-1D systems, O(N^1.5) scaling for quasi-2D systems, and O(N^2) scaling for 3D bulk systems.
EECS Colloquium: Looking Around Corners: New Opportunities in Femto-Photography
Wednesday, Sept. 21, 4:00–5:00 pm, 306 Soda Hall (HP Auditorium), UC Berkeley
Can we look around corners beyond the line of sight? Our goal is to exploit the finite speed of light to improve image capture and scene understanding. New theoretical analysis coupled with emerging ultra-high-speed imaging techniques can lead to a new source of computational visual perception. We are developing the theoretical foundation for sensing and reasoning using femto-photography and transient light transport, and experimenting with scenarios in which transient reasoning exposes scene properties that are beyond the reach of traditional computer vision. (Joint work with a large team, see http://raskar.info/femto)
## Link of the Week: Where Is Everybody? Doing the Maths on Extraterrestrial Life
CRD’s Complex Systems Group Leader David Bailey and his frequent collaborator Jon Borwein are now writing a regular monthly math column for The Conversation. Their latest article, “Where Is Everybody? Doing the Maths on Extraterrestrial Life,” begins with a question posed by physicist Enrico Fermi:
Since there are likely many other technological civilizations in the Milky Way galaxy, and since in a few tens of thousands of years at most they could have explored or even colonized many distant planets, why don’t we see any evidence of even a single extraterrestrial civilization?
Mathematically speaking, Fermi seems to be right — so where are the aliens? Read more.
About Computing Sciences at Berkeley Lab
The Lawrence Berkeley National Laboratory (Berkeley Lab) Computing Sciences organization provides the computing and networking resources and expertise critical to advancing the Department of Energy's research missions: developing new energy sources, improving energy efficiency, developing new materials and increasing our understanding of ourselves, our world and our universe.
ESnet, the Energy Sciences Network, provides the high-bandwidth, reliable connections that link scientists at 40 DOE research sites to each other and to experimental facilities and supercomputing centers around the country. The National Energy Research Scientific Computing Center (NERSC) powers the discoveries of 6,000 scientists at national laboratories and universities, including those at Berkeley Lab's Computational Research Division (CRD). CRD conducts research and development in mathematical modeling and simulation, algorithm design, data storage, management and analysis, computer system architecture and high-performance software implementation. NERSC and ESnet are DOE Office of Science User Facilities.
Lawrence Berkeley National Laboratory addresses the world's most urgent scientific challenges by advancing sustainable energy, protecting human health, creating new materials, and revealing the origin and fate of the universe. Founded in 1931, Berkeley Lab's scientific expertise has been recognized with 13 Nobel prizes. The University of California manages Berkeley Lab for the DOE’s Office of Science.
DOE’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States, and is working to address some of the most pressing challenges of our time. For more information, please visit science.energy.gov.
| 2018-03-18T21:20:32 |
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|
https://mooseframework.inl.gov/help/modules_issues.html
|
## Modules
Modules allow users to control what libraries and binaries are being made available within that terminal session. It is worth mentioning that module commands, only affect the terminal they are in. It is not global. This is why we routinely ask users to operate in a single terminal while troubleshooting issues.
Users who have installed one of our moose-environment packages, will have access to modules. Please familiarize yourself with some commonly used module commands:
CommandCommand ArgUsage
moduleavailList available modules
To begin working with modules manually, it is best to start clean (especially for the duration of this FAQ). You can do so by purging any current modules loaded:
module purge
• Linux:
• module load moose-dev-gcc moose-tools
• Macintosh:
• module load moose-dev-clang moose-tools
Loading these two modules will in-turn load other necessary modules. The correct modules that should be loaded will approximately resemble the following list:
• Linux:
module list
1) moose/.gcc-7.3.1 5) moose/.cppunit-__CPPUNIT___gcc-7.3.1
2) moose/.mpich-__MPICH___gcc-7.3.1 6) moose-dev-gcc
3) moose/.petsc-__PETSC_DEFAULT___mpich-3.2_gcc-7.3.1-opt 7) miniconda
4) moose/.tbb-2018_U3 8) moose-tools
• Macintosh:
module list
1) moose/.gcc-7.3.1 6) moose/.cppunit-__CPPUNIT___clang-6.0.1
2) moose/.clang-6.0.1 7) moose-dev-clang
3) moose/.mpich-__MPICH___clang-6.0.1 8) miniconda
4) moose/.petsc-__PETSC_DEFAULT___mpich-__MPICH___clang-6.0.1-opt 9) moose-tools
5) moose/.tbb-2018_U3
If your terminal mirrors the above (version numbers may vary slightly), then you have a proper environment. Please return from whence you came, and continue troubleshooting.
note:Ughh! None of this is working!
If you find yourself looping through our troubleshooting guide, unable to solve your issue, there is still another attempt you can perform. Start over. But this time, perform the following before starting over:
env -i bash
export PATH=/usr/bin:/usr/sbin:/sbin
source /opt/moose/Modules/3.2.10/init/bash
These three commands will start a new command interpreter without any of your default environment. This is important because for most errors we end up solving, it was due to something in the users environment.
Do note, if this ends up solving your issue, then there is something in one of possibly many bash profiles getting in the way. At this point, you will want to reach out to our mailing list and ask for help tracking this down. Keep in mind, depending on the situation you may be asked to contact the administrators of the machine in which you are operating on (HPC clusters for example are beyound our control).
note
The modules contained in the moose-environment package are built in a hierarchal directory structure (some modules may not be visible until other modules are loaded).
| 2019-01-23T16:24:53 |
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https://zbmath.org/authors/?q=ai%3Awolfowitz.jacob
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## Wolfowitz, Jacob
Compute Distance To:
Author ID: wolfowitz.jacob Published as: Wolfowitz, Jacob; Wolfowitz, J. External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 139 Publications since 1939, including 6 Books 2 Contributions as Editor Biographic References: 3 Publications Co-Authors: 16 Co-Authors with 74 Joint Publications 272 Co-Co-Authors
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### Co-Authors
67 single-authored 22 Kiefer, Jack Carl 20 Wald, Abraham 19 Weiss, Lionel I. 11 Dvoretzky, Aryeh 6 Ahlswede, Rudolf 2 Behara, Minaketan 2 Krickeberg, Klaus 1 Augustin, Udo 1 Berger, Toby 1 Chung, Kai Lai 1 Hoeffding, Wassily 1 Housewright, Kim B. 1 Kac, Mark 1 Levene, Howard 1 Omura, Jim K. 1 Teicher, H. 1 Tung, Suiyin
all top 5
### Serials
45 Annals of Mathematical Statistics 11 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 7 Information and Control 6 Proceedings of the National Academy of Sciences of the United States of America 5 Annals of the Institute of Statistical Mathematics 4 Econometrica 4 Illinois Journal of Mathematics 3 Theory of Probability and its Applications 3 Proceedings of the American Mathematical Society 3 Annals of Mathematics. Second Series 3 Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Lecture Notes in Mathematics 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Journal of Combinatorics, Information & System Sciences 2 Transactions of the American Mathematical Society 1 Advances in Applied Probability 1 Archive for Rational Mechanics and Analysis 1 IEEE Transactions on Information Theory 1 The Annals of Statistics 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Journal of Applied Probability 1 Pacific Journal of Mathematics 1 Quarterly of Applied Mathematics 1 Sankhyā. Series A. Methods and Techniques 1 Journal of the Royal Statistical Society. Series B 1 Bulletin of the American Mathematical Society 1 Bulletin de l’Institut International de Statistique 1 Operations-Research-Verfahren 1 Skandinavisk Aktuarietidskrift 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae
all top 5
### Fields
24 Information and communication theory, circuits (94-XX) 21 Statistics (62-XX) 4 Probability theory and stochastic processes (60-XX) 3 History and biography (01-XX) 2 General and overarching topics; collections (00-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 General topology (54-XX)
### Citations contained in zbMATH Open
108 Publications have been cited 2,522 times in 2,193 Documents Cited by Year
Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Zbl 0073.14701
Kiefer, J.; Wolfowitz, Jacob
1956
Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Zbl 0073.14603
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1956
The equivalence of two extremum problems. Zbl 0093.15602
Kiefer, J.; Wolfowitz, Jacob
1960
Stochastic estimation of the maximum of a regression function. Zbl 0049.36601
Kiefer, J.; Wolfowitz, Jacob
1952
Optimum designs in regression problems. Zbl 0090.11404
Kiefer, J.; Wolfowitz, Jacob
1959
Optimum character of the sequential probability ratio test. Zbl 0032.17302
Wald, A.; Wolfowitz, Jacob
1948
Products of indecomposable, aperiodic, stochastic matrices. Zbl 0116.35001
Wolfowitz, Jacob
1963
Relations among certain ranges of vector measures. Zbl 0044.15002
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1951
The minimum distance method. Zbl 0086.35403
Wolfowitz, Jacob
1957
On the theory of queues with many servers. Zbl 0064.13303
Kiefer, J.; Wolfowitz, Jacob
1955
On tests of normality and other tests of goodness of fit based on distance methods. Zbl 0066.12301
Kac, M.; Kiefer, J.; Wolfowitz, Jacob
1955
Statistical tests based on permutations of the observations. Zbl 0063.08124
Wald, A.; Wolfowitz, Jacob
1944
The characteristics of the general queueing process, with applications to random walk. Zbl 0070.36602
Kiefer, J.; Wolfowitz, Jacob
1956
Asymptotically minimax estimation of concave and convex distribution functions. Zbl 0354.62035
Kiefer, J.; Wolfowitz, Jacob
1976
On a test whether two samples are from the same population. Zbl 0023.24802
Wald, A.; Wolfowitz, Jacob
1940
Elimination of randomization in certain statistical decision procedures and zero-sum two-person games. Zbl 0044.15003
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1951
On a test whether two samples are from the same population. JFM 66.0645.01
Wald, A.; Wolfowitz, J.
1940
An exact test for randomness in the non-parametric case based on serial correlation. Zbl 0060.30206
Wald, A.; Wolfowitz, Jacob
1943
On the deviations of the empiric distribution function of vector chance variables. Zbl 0088.11305
Kiefer, J.; Wolfowitz, Jacob
1958
Sequential decision problems for processes with continuous time parameter. Testing hypotheses. Zbl 0050.14803
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
Coding theorems of information theory. 2nd ed. Zbl 0132.39704
Wolfowitz, Jacob
1964
Distinguishability of sets of distributions. Zbl 0135.19404
Hoeffding, Wassily; Wolfowitz, Jacob
1958
Tolerance limits for a normal distribution. Zbl 0063.08130
Wald, A.; Wolfowitz, Jacob
1946
Estimation by the minimum distance method. Zbl 0051.37004
Wolfowitz, Jacob
1953
The efficiency of sequential estimates and Wald’s equation for sequential processes. Zbl 0032.04203
Wolfowitz, Jacob
1947
Maximum probability estimators and related topics. Zbl 0297.62015
Weiss, Lionel; Wolfowitz, Jacob
1974
Generalized maximum likelihood estimators. Zbl 0183.21202
Weiss, L.; Wolfowitz, Jacob
1966
On the theory of runs with some applications to quality control. Zbl 0063.08308
Wolfowitz, Jacob
1943
Maximum probability estimators. Zbl 0183.21203
Weiss, L.; Wolfowitz, Jacob
1967
Asymptotic efficiency of the maximum likelihood estimator. Zbl 0142.15402
Wolfowitz, Jacob
1965
Sequential decision problems for processes with continuous time parameter. Problems of estimation. Zbl 0051.36606
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
Optimum extrapolation and interpolation designs. I, II. Zbl 0137.13104
Kiefer, J.; Wolfowitz, Jacob
1964
Bayes solutions of sequential decision problems. Zbl 0036.09502
Wald, A.; Wolfowitz, Jacob
1950
Asymptotic distribution of runs up and down. Zbl 0063.08310
Wolfowitz, Jacob
1944
Coding theorems of information theory. Zbl 0102.34501
Wolfowitz, Jacob
1961
On a theorem of Hoel and Levine on extrapolation designs. Zbl 0138.14002
Kiefer, J.; Wolfowitz, Jacob
1965
The inventory problem. I. Case of known distributions of demand. Zbl 0046.37603
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1952
Coding theorems of information theory. 3rd ed. Zbl 0373.94012
Wolfowitz, Jacob
1978
On Wald’s proof of the consistency of the maximum likelihood estimate. Zbl 0034.22903
Wolfowitz, Jacob
1949
The inventory problem. II. Case of unknown distributions of demand. Zbl 0048.37101
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1952
Asymptotically efficient non-parametric estimators of location and scale parameters. Zbl 0193.47501
Weiss, L.; Wolfowitz, Jacob
1970
The covariance matrix of runs up and down. Zbl 0063.03502
Levene, Howard; Wolfowitz, Jacob
1944
Channels with arbitrarily varying channel probability functions. Zbl 0107.34503
Kiefer, J.; Wolfowitz, Jacob
1962
Sums of random integers reduced modulo $$m$$. Zbl 0043.33904
Dvoretzky, A.; Wolfowitz, Jacob
1951
Generalization of the theorem of Glivenko-Cantelli. Zbl 0055.36505
Wolfowitz, Jacob
1954
Estimation of a density function at a point. Zbl 0162.50003
Weiss, L.; Wolfowitz, Jacob
1967
Elimination of randomization in certain problems of statistics and of the theory of games. Zbl 0041.45902
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1950
Two methods of randomization in statistics and the theory of games. Zbl 0042.38401
Wald, A.; Wolfowitz, Jacob
1951
On the stochastic approximation method of Robbins and Monro. Zbl 0049.36505
Wolfowitz, Jacob
1952
Additive partition functions and a class of statistical hypotheses. Zbl 0060.30205
Wolfowitz, Jacob
1942
The coding of messages subject to chance errors. Zbl 0078.32503
Wolfowitz, Jacob
1957
Simultaneous channels. Zbl 0111.32405
Wolfowitz, Jacob
1960
Elimination of randomization in certain problems of statistics and of the theory of games. Zbl 0044.15001
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1950
On sequential binomial estimation. Zbl 0063.08312
Wolfowitz, Jacob
1946
On the optimal character of the $$(s, S)$$ policy in inventory theory. Zbl 0053.27904
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
Note on runs of consecutive elements. Zbl 0063.08309
Wolfowitz, Jacob
1944
Generalized maximum likelihood estimators in a particular case. Zbl 0169.21303
Weiss, L.; Wolfowitz, Jacob
1968
Maximum probability estimators with a general loss function. Zbl 0188.50001
Weiss, L.; Wolfowitz, Jacob
1969
The capacity of channels with arbitrarily varying channel probability functions and binary output alphabet. Zbl 0198.24003
Ahlswede, Rudolf; Wolfowitz, Jacob
1970
Consistent estimators of the parameters of a linear structural relation. Zbl 0048.36903
Wolfowitz, Jacob
1952
Confidence limits for continuous distribution functions. JFM 65.0585.02
Wald, A.; Wolfowitz, J.
1939
Maximum probability estimators and asymptotic sufficiency. Zbl 0218.62035
Weiss, L.; Wolfowitz, Jacob
1970
Confidence limits for continuous distribution functions. Zbl 0021.42405
Wald, A.; Wolfowitz, Jacob
1939
On stochastic approximation methods. Zbl 0074.35501
Wolfowitz, Jacob
1956
On channels without a capacity. Zbl 0113.12005
Wolfowitz, Jacob
1963
Correlated decoding for channels with arbitrarily varying channel probability functions. Zbl 0179.49004
Ahlswede, Rudolf; Wolfowitz, Jacob
1969
Asymptotically minimax tests of composite hypotheses. Zbl 0184.42804
Weiss, L.; Wolfowitz, Jacob
1969
Remarks on the notion of recurrence. Zbl 0040.05005
Wolfowitz, Jacob
1949
Minimax estimates of the mean of a normal distribution with known variance. Zbl 0038.09801
Wolfowitz, Jacob
1950
On a limit theorem in renewal theory. Zbl 0047.12402
Chung, K. L.; Wolfowitz, Jacob
1952
The method of maximum likelihood and the Wald theory of decision functions. Zbl 0051.37003
Wolfowitz, Jacob
1953
Estimation by the minimum distance method in nonparametric stochastic difference equations. Zbl 0055.37602
Wolfowitz, Jacob
1954
Asymptotically efficient non-parametric estimators of location and scale parameters. II. Zbl 0276.62049
Wolfowitz, Jacob
1974
Existence of optimal stopping rules for linear and quadratic rewards. Zbl 0295.60033
Teicher, H.; Wolfowitz, Jacob
1966
Strong converse of the coding theorem for semicontinuous channels. Zbl 0089.33904
Wolfowitz, Jacob
1959
Two methods of randomization in statistics and the theory of games. Zbl 0040.36501
Wald, A.; Wolfowitz, Jacob
1951
Maximum likelihood estimation of a translation parameter of a truncated distribution. Zbl 0271.62043
Weiss, L.; Wolfowitz, Jacob
1973
Bayesian inference and axioms of consistent decision. Zbl 0129.32002
Wolfowitz, Jacob
1962
Abraham Wald, 1902-1950. Zbl 0046.00313
Wolfowitz, Jacob
1952
Sampling inspection plans for continuous production which insure a prescribed limit on the outgoing quality. Zbl 0060.30107
Wald, A.; Wolfowitz, Jacob
1945
Confidence limits for the fraction of a normal population which lies between two given limits. Zbl 0063.08311
Wolfowitz, Jacob
1946
Asymptotically minimax estimation of concave and convex distribution functions. II. Zbl 0418.62031
Kiefer, J.; Wolfowitz, Jacob
1977
An upper bound on the rate distortion function for source coding with partial side information at the decoder. Zbl 0427.94010
Berger, Toby; Housewright, Kim B.; Omura, Jim K.; Tung, Suiyin; Wolfowitz, Jacob
1979
Optimal, fixed length, nonparametric sequential confidence limits for a translation parameter. Zbl 0248.62037
Weiss, L.; Wolfowitz, Jacob
1972
Asymptotic minimax character of the sample distribution function for vector chance variables. Zbl 0093.15603
Kiefer, J.; Wolfowitz, Jacob
1959
Notes on a general strong converse. Zbl 0176.49503
Wolfowitz, Jacob
1968
Note on confidence limits for continuous distribution functions. Zbl 0024.42701
Wald, A.; Wolfowitz, Jacob
1941
Consistency of sequential binomial estimates. Zbl 0032.42002
Wolfowitz, Jacob
1947
Characterization of the minimal complete class of decision functions when the number of distributions and decisions is finite. Zbl 0044.14903
Wald, A.; Wolfowitz, Jacob
1951
Estimation of the components of stochastic structures. Zbl 0055.37601
Wolfowitz, Jacob
1954
Note on confidence limits for continuous distribution functions. JFM 67.0482.02
Wald, A.; Wolfowitz, J.
1941
The rate distortion function for source coding with side information at the decoder. Zbl 0422.94018
Wolfowitz, Jacob
1979
On list codes. Zbl 0427.94008
Wolfowitz, Jacob
1979
The structure of capacity functions for compound channels. Zbl 0199.54501
Ahlswede, Rudolf; Wolfowitz, Jacob
1969
Asymptotically efficient non-parametric estimators of location and scale parameters. Zbl 0207.49802
Weiss, L.; Wolfowitz, Jacob
1970
Reflections on the future of mathematical statistics. Zbl 0225.62002
Wolfowitz, Jacob
1970
Approximation with a fidelity criterion. Zbl 0242.94017
Wolfowitz, Jacob
1967
The moments of recurrence time. Zbl 0283.28011
Wolfowitz, Jacob
1967
An upper bound on the rate of transmission of messages. Zbl 0081.36903
Wolfowitz, Jacob
1958
The maximum achievable length of an error correcting code. Zbl 0081.36904
Wolfowitz, Jacob
1958
An upper bound on the rate distortion function for source coding with partial side information at the decoder. II. Zbl 0545.94007
Wolfowitz, Jacob
1981
An upper bound on the rate distortion function for source coding with partial side information at the decoder. Zbl 0427.94010
Berger, Toby; Housewright, Kim B.; Omura, Jim K.; Tung, Suiyin; Wolfowitz, Jacob
1979
The rate distortion function for source coding with side information at the decoder. Zbl 0422.94018
Wolfowitz, Jacob
1979
On list codes. Zbl 0427.94008
Wolfowitz, Jacob
1979
Coding theorems of information theory. 3rd ed. Zbl 0373.94012
Wolfowitz, Jacob
1978
Asymptotically minimax estimation of concave and convex distribution functions. II. Zbl 0418.62031
Kiefer, J.; Wolfowitz, Jacob
1977
Asymptotically minimax estimation of concave and convex distribution functions. Zbl 0354.62035
Kiefer, J.; Wolfowitz, Jacob
1976
Maximum probability estimators in the classical case and in the ’almost smooth’ case. Zbl 0338.62017
Wolfowitz, Jacob
1975
Maximum probability estimators and related topics. Zbl 0297.62015
Weiss, Lionel; Wolfowitz, Jacob
1974
Asymptotically efficient non-parametric estimators of location and scale parameters. II. Zbl 0276.62049
Wolfowitz, Jacob
1974
Maximum likelihood estimation of a translation parameter of a truncated distribution. Zbl 0271.62043
Weiss, L.; Wolfowitz, Jacob
1973
Optimal, fixed length, nonparametric sequential confidence limits for a translation parameter. Zbl 0248.62037
Weiss, L.; Wolfowitz, Jacob
1972
Asymptotically efficient non-parametric estimators of location and scale parameters. Zbl 0193.47501
Weiss, L.; Wolfowitz, Jacob
1970
The capacity of channels with arbitrarily varying channel probability functions and binary output alphabet. Zbl 0198.24003
Ahlswede, Rudolf; Wolfowitz, Jacob
1970
Maximum probability estimators and asymptotic sufficiency. Zbl 0218.62035
Weiss, L.; Wolfowitz, Jacob
1970
Asymptotically efficient non-parametric estimators of location and scale parameters. Zbl 0207.49802
Weiss, L.; Wolfowitz, Jacob
1970
Reflections on the future of mathematical statistics. Zbl 0225.62002
Wolfowitz, Jacob
1970
Maximum probability estimators with a general loss function. Zbl 0188.50001
Weiss, L.; Wolfowitz, Jacob
1969
Correlated decoding for channels with arbitrarily varying channel probability functions. Zbl 0179.49004
Ahlswede, Rudolf; Wolfowitz, Jacob
1969
Asymptotically minimax tests of composite hypotheses. Zbl 0184.42804
Weiss, L.; Wolfowitz, Jacob
1969
The structure of capacity functions for compound channels. Zbl 0199.54501
Ahlswede, Rudolf; Wolfowitz, Jacob
1969
The structure of capacity functions for compound channels. Zbl 0188.24002
Ahlswede, Rudolf; Wolfowitz, Jacob
1969
Maximum probability estimators with a general loss function. Zbl 0188.49901
Weiss, L.; Wolfowitz, Jacob
1969
Generalized maximum likelihood estimators in a particular case. Zbl 0169.21303
Weiss, L.; Wolfowitz, Jacob
1968
Notes on a general strong converse. Zbl 0176.49503
Wolfowitz, Jacob
1968
Maximum probability estimators. Zbl 0183.21203
Weiss, L.; Wolfowitz, Jacob
1967
Estimation of a density function at a point. Zbl 0162.50003
Weiss, L.; Wolfowitz, Jacob
1967
Approximation with a fidelity criterion. Zbl 0242.94017
Wolfowitz, Jacob
1967
The moments of recurrence time. Zbl 0283.28011
Wolfowitz, Jacob
1967
Generalized maximum likelihood estimators. Zbl 0183.21202
Weiss, L.; Wolfowitz, Jacob
1966
Existence of optimal stopping rules for linear and quadratic rewards. Zbl 0295.60033
Teicher, H.; Wolfowitz, Jacob
1966
Remark on the optimum character of the sequential probability ratio test. Zbl 0144.40802
Wolfowitz, Jacob
1966
Asymptotic efficiency of the maximum likelihood estimator. Zbl 0142.15402
Wolfowitz, Jacob
1965
On a theorem of Hoel and Levine on extrapolation designs. Zbl 0138.14002
Kiefer, J.; Wolfowitz, Jacob
1965
Coding theorems of information theory. 2nd ed. Zbl 0132.39704
Wolfowitz, Jacob
1964
Optimum extrapolation and interpolation designs. I, II. Zbl 0137.13104
Kiefer, J.; Wolfowitz, Jacob
1964
Products of indecomposable, aperiodic, stochastic matrices. Zbl 0116.35001
Wolfowitz, Jacob
1963
On channels without a capacity. Zbl 0113.12005
Wolfowitz, Jacob
1963
Channels with arbitrarily varying channel probability functions. Zbl 0107.34503
Kiefer, J.; Wolfowitz, Jacob
1962
Bayesian inference and axioms of consistent decision. Zbl 0129.32002
Wolfowitz, Jacob
1962
Coding theorems of information theory. Zbl 0102.34501
Wolfowitz, Jacob
1961
The equivalence of two extremum problems. Zbl 0093.15602
Kiefer, J.; Wolfowitz, Jacob
1960
Simultaneous channels. Zbl 0111.32405
Wolfowitz, Jacob
1960
Covergence of the empiric distribution function on half-spaces. Zbl 0094.33102
Wolfowitz, Jacob
1960
Optimum designs in regression problems. Zbl 0090.11404
Kiefer, J.; Wolfowitz, Jacob
1959
Strong converse of the coding theorem for semicontinuous channels. Zbl 0089.33904
Wolfowitz, Jacob
1959
Asymptotic minimax character of the sample distribution function for vector chance variables. Zbl 0093.15603
Kiefer, J.; Wolfowitz, Jacob
1959
On the deviations of the empiric distribution function of vector chance variables. Zbl 0088.11305
Kiefer, J.; Wolfowitz, Jacob
1958
Distinguishability of sets of distributions. Zbl 0135.19404
Hoeffding, Wassily; Wolfowitz, Jacob
1958
An upper bound on the rate of transmission of messages. Zbl 0081.36903
Wolfowitz, Jacob
1958
The maximum achievable length of an error correcting code. Zbl 0081.36904
Wolfowitz, Jacob
1958
Information theory for mathematicians. Zbl 0088.10601
Wolfowitz, Jacob
1958
The minimum distance method. Zbl 0086.35403
Wolfowitz, Jacob
1957
The coding of messages subject to chance errors. Zbl 0078.32503
Wolfowitz, Jacob
1957
Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Zbl 0073.14701
Kiefer, J.; Wolfowitz, Jacob
1956
Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Zbl 0073.14603
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1956
The characteristics of the general queueing process, with applications to random walk. Zbl 0070.36602
Kiefer, J.; Wolfowitz, Jacob
1956
On stochastic approximation methods. Zbl 0074.35501
Wolfowitz, Jacob
1956
On the theory of queues with many servers. Zbl 0064.13303
Kiefer, J.; Wolfowitz, Jacob
1955
On tests of normality and other tests of goodness of fit based on distance methods. Zbl 0066.12301
Kac, M.; Kiefer, J.; Wolfowitz, Jacob
1955
Generalization of the theorem of Glivenko-Cantelli. Zbl 0055.36505
Wolfowitz, Jacob
1954
Estimation by the minimum distance method in nonparametric stochastic difference equations. Zbl 0055.37602
Wolfowitz, Jacob
1954
Estimation of the components of stochastic structures. Zbl 0055.37601
Wolfowitz, Jacob
1954
Sequential decision problems for processes with continuous time parameter. Testing hypotheses. Zbl 0050.14803
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
Estimation by the minimum distance method. Zbl 0051.37004
Wolfowitz, Jacob
1953
Sequential decision problems for processes with continuous time parameter. Problems of estimation. Zbl 0051.36606
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
On the optimal character of the $$(s, S)$$ policy in inventory theory. Zbl 0053.27904
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1953
The method of maximum likelihood and the Wald theory of decision functions. Zbl 0051.37003
Wolfowitz, Jacob
1953
Stochastic estimation of the maximum of a regression function. Zbl 0049.36601
Kiefer, J.; Wolfowitz, Jacob
1952
The inventory problem. I. Case of known distributions of demand. Zbl 0046.37603
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1952
The inventory problem. II. Case of unknown distributions of demand. Zbl 0048.37101
Dvoretzky, A.; Kiefer, J.; Wolfowitz, Jacob
1952
On the stochastic approximation method of Robbins and Monro. Zbl 0049.36505
Wolfowitz, Jacob
1952
Consistent estimators of the parameters of a linear structural relation. Zbl 0048.36903
Wolfowitz, Jacob
1952
On a limit theorem in renewal theory. Zbl 0047.12402
Chung, K. L.; Wolfowitz, Jacob
1952
Abraham Wald, 1902-1950. Zbl 0046.00313
Wolfowitz, Jacob
1952
Relations among certain ranges of vector measures. Zbl 0044.15002
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1951
Elimination of randomization in certain statistical decision procedures and zero-sum two-person games. Zbl 0044.15003
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1951
Sums of random integers reduced modulo $$m$$. Zbl 0043.33904
Dvoretzky, A.; Wolfowitz, Jacob
1951
Two methods of randomization in statistics and the theory of games. Zbl 0042.38401
Wald, A.; Wolfowitz, Jacob
1951
Two methods of randomization in statistics and the theory of games. Zbl 0040.36501
Wald, A.; Wolfowitz, Jacob
1951
Characterization of the minimal complete class of decision functions when the number of distributions and decisions is finite. Zbl 0044.14903
Wald, A.; Wolfowitz, Jacob
1951
Bayes solutions of sequential decision problems. Zbl 0036.09502
Wald, A.; Wolfowitz, Jacob
1950
Elimination of randomization in certain problems of statistics and of the theory of games. Zbl 0041.45902
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1950
Elimination of randomization in certain problems of statistics and of the theory of games. Zbl 0044.15001
Dvoretzky, A.; Wald, A.; Wolfowitz, Jacob
1950
Minimax estimates of the mean of a normal distribution with known variance. Zbl 0038.09801
Wolfowitz, Jacob
1950
On Wald’s proof of the consistency of the maximum likelihood estimate. Zbl 0034.22903
Wolfowitz, Jacob
1949
Remarks on the notion of recurrence. Zbl 0040.05005
Wolfowitz, Jacob
1949
Bayes solutions of sequential decision problems. Zbl 0032.17401
Wald, A.; Wolfowitz, Jacob
1949
Optimum character of the sequential probability ratio test. Zbl 0032.17302
Wald, A.; Wolfowitz, Jacob
1948
The efficiency of sequential estimates and Wald’s equation for sequential processes. Zbl 0032.04203
Wolfowitz, Jacob
1947
Consistency of sequential binomial estimates. Zbl 0032.42002
Wolfowitz, Jacob
1947
Tolerance limits for a normal distribution. Zbl 0063.08130
Wald, A.; Wolfowitz, Jacob
1946
On sequential binomial estimation. Zbl 0063.08312
Wolfowitz, Jacob
1946
Confidence limits for the fraction of a normal population which lies between two given limits. Zbl 0063.08311
Wolfowitz, Jacob
1946
Sampling inspection plans for continuous production which insure a prescribed limit on the outgoing quality. Zbl 0060.30107
Wald, A.; Wolfowitz, Jacob
1945
Statistical tests based on permutations of the observations. Zbl 0063.08124
Wald, A.; Wolfowitz, Jacob
1944
Asymptotic distribution of runs up and down. Zbl 0063.08310
Wolfowitz, Jacob
1944
The covariance matrix of runs up and down. Zbl 0063.03502
Levene, Howard; Wolfowitz, Jacob
1944
Note on runs of consecutive elements. Zbl 0063.08309
Wolfowitz, Jacob
1944
An exact test for randomness in the non-parametric case based on serial correlation. Zbl 0060.30206
Wald, A.; Wolfowitz, Jacob
1943
...and 8 more Documents
all top 5
### Cited by 2,885 Authors
24 Dette, Holger 20 Wolfowitz, Jacob 19 Pronzato, Luc 15 Schwabe, Rainer 13 Wong, Wengkee 12 Weiss, Lionel I. 10 Atkinson, Anthony C. 9 Ahlswede, Rudolf 9 Boche, Holger 9 Kiefer, Jack Carl 9 Lai, Tze Leung 9 Yu, Qiqing 8 Akahira, Masafumi 8 Chang, Fu-Chuen 8 Fang, Zhide 8 Graßhoff, Ulrike 8 Horváth, Lajos 8 Mokkadem, Abdelkader 8 Pelletier, Mariane 8 Stute, Winfried 7 Haines, Linda M. 7 Hallin, Marc 7 Holling, Heinz 7 Irle, Albrecht 7 Koutras, Markos V. 7 Legut, Jerzy 7 Lindsay, Bruce G. 7 Pepelyshev, Andrey 7 Sagara, Nobusumi 7 Xu, Xingzhong 6 Bickel, Peter John 6 Chen, Jiahua 6 Csörgő, Miklós 6 Durot, Cécile 6 Eryılmaz, Serkan N. 6 Fu, James C. 6 Großmann, Heiko 6 Jokiel-Rokita, Alicja 6 Lopuhaä, Hendrik P. 6 Magiera, Ryszard 6 Mukhopadhyay, Nitis 6 Novikov, Andreĭ Alekseevich 6 Roussas, George Gregory 6 Seo, Byungtae 6 Sinha, Bikas Kumar 6 Van der Vaart, Adrianus Willem 6 Yatracos, Yannis G. 6 Zhigljavsky, Anatoly A. 5 Ahmad, Ibrahim A. 5 Bogacz, Rafal 5 Bouzebda, Salim 5 Chan, Lingyau 5 Chen, Louis Hsiao-Yun 5 Cheng, Fuxia 5 Devroye, Luc P. J. A. 5 Ding, Xiaobo 5 Flournoy, Nancy 5 Harman, Radoslav 5 Henze, Norbert 5 Herzberg, Agnes Margaret 5 Holmes, Philip J. 5 Jaśkiewicz, Anna 5 Jiang, Wenhua 5 Khan, Mohammed Ali 5 Mandal, Nripes Kumar 5 Mays, D’Arcy Paul III 5 Melas, Viatcheslav B. 5 Myers, Raymond H. 5 Nowak, Andrzej S. 5 Pázman, Andrej 5 Rosenberger, William F. 5 Sen, Pranab Kumar 5 Sigman, Karl 5 Wellner, Jon August 5 Wiens, Douglas P. 5 Wynn, Henry P. 4 Balder, Erik J. 4 Banerjee, Moulinath 4 Bhatnagar, Shalabh 4 Bjelaković, Igor 4 Blanchet, Jose H. 4 Bos, Len P. 4 Brown, Lawrence David 4 Chen, Yao 4 Daley, Daryl John 4 Dayanik, Savas 4 Di Mari, Roberto 4 Duarte, Belmiro P. M. 4 Dufour, Jean-Marie 4 El Barmi, Hammou 4 Fabian, Václav 4 Fëdorov, Valeriĭ V. 4 Gaivoronski, Alexei A. 4 Gattone, Stefano Antonio 4 Glynn, Peter W. 4 Granichin, Oleg N. 4 Johnson, Brad C. 4 Josić, Krešimir 4 Kilpatrick, Zachary P. 4 Koenker, Roger W. ...and 2,785 more Authors
all top 5
### Cited in 348 Serials
161 Journal of Statistical Planning and Inference 99 Communications in Statistics. Theory and Methods 85 Statistics & Probability Letters 76 The Annals of Statistics 73 Annals of the Institute of Statistical Mathematics 61 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 52 Sequential Analysis 49 Computational Statistics and Data Analysis 48 Journal of Multivariate Analysis 43 Metrika 37 Stochastic Processes and their Applications 34 Statistics 34 Communications in Statistics. Simulation and Computation 33 The Canadian Journal of Statistics 33 Automatica 31 Kybernetika 28 Journal of Statistical Computation and Simulation 27 Statistical Science 25 European Journal of Operational Research 22 Journal of Optimization Theory and Applications 22 Journal of Nonparametric Statistics 21 Psychometrika 21 Journal of Econometrics 20 Proceedings of the American Mathematical Society 19 Queueing Systems 19 Bernoulli 19 Electronic Journal of Statistics 18 Journal of Mathematical Analysis and Applications 16 Statistical Papers 16 Statistics and Computing 14 Linear Algebra and its Applications 13 Journal of Mathematical Psychology 13 Transactions of the American Mathematical Society 12 Journal of Soviet Mathematics 12 Probability Theory and Related Fields 12 Annals of Operations Research 12 Neural Computation 12 Automation and Remote Control 12 Test 12 Mathematical Methods of Statistics 11 Biometrics 11 Journal of Statistical Theory and Practice 10 The Annals of Applied Probability 9 Journal of Economic Theory 9 Journal of Mathematical Economics 9 Operations Research 9 SIAM Journal on Control and Optimization 9 Statistica Neerlandica 9 Journal of Applied Statistics 8 International Journal of Systems Science 8 Journal of Applied Probability 8 Trabajos de Estadistica y de Investigacion Operativa 8 Mathematical Programming. Series A. Series B 8 SIAM Journal on Optimization 7 Journal of the Franklin Institute 7 Information Sciences 7 Mathematics of Operations Research 7 Computational Optimization and Applications 7 Journal of Mathematical Sciences (New York) 6 Communications in Mathematical Physics 6 International Journal of Control 6 Mathematical Biosciences 6 International Journal of Game Theory 6 Journal of the American Statistical Association 6 Journal of Computational and Applied Mathematics 6 Econometric Reviews 6 Machine Learning 6 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 6 Journal of Biopharmaceutical Statistics 6 Economic Theory 6 Econometric Theory 6 Bulletin of the American Mathematical Society 6 Kodai Mathematical Seminar Reports 6 Advances in Data Analysis and Classification. ADAC 5 Advances in Applied Probability 5 Computers & Mathematics with Applications 5 Israel Journal of Mathematics 5 Mathematics and Computers in Simulation 5 Cybernetics 5 American Journal of Mathematical and Management Sciences 5 Journal of Complexity 5 Journal of Theoretical Probability 5 Neural Networks 5 Computational Statistics 5 International Journal of Robust and Nonlinear Control 5 Probability in the Engineering and Informational Sciences 5 Methodology and Computing in Applied Probability 5 Journal of the Korean Statistical Society 4 Discrete Mathematics 4 Inverse Problems 4 Journal of Mathematical Physics 4 Periodica Mathematica Hungarica 4 Arkiv för Matematik 4 The Annals of Probability 4 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 4 Computing 4 Journal of Approximation Theory 4 Siberian Mathematical Journal 4 Advances in Applied Mathematics 4 Stochastic Analysis and Applications ...and 248 more Serials
all top 5
### Cited in 45 Fields
1,449 Statistics (62-XX) 437 Probability theory and stochastic processes (60-XX) 248 Operations research, mathematical programming (90-XX) 200 Numerical analysis (65-XX) 151 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 111 Computer science (68-XX) 105 Systems theory; control (93-XX) 65 Information and communication theory, circuits (94-XX) 52 Biology and other natural sciences (92-XX) 35 Measure and integration (28-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 29 Combinatorics (05-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 22 History and biography (01-XX) 18 Functional analysis (46-XX) 15 Approximations and expansions (41-XX) 14 Quantum theory (81-XX) 13 Ordinary differential equations (34-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Partial differential equations (35-XX) 10 Operator theory (47-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Convex and discrete geometry (52-XX) 6 Mathematical logic and foundations (03-XX) 6 Special functions (33-XX) 6 Geophysics (86-XX) 4 Number theory (11-XX) 4 Real functions (26-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Mechanics of deformable solids (74-XX) 3 Potential theory (31-XX) 3 General topology (54-XX) 3 Fluid mechanics (76-XX) 3 Astronomy and astrophysics (85-XX) 2 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-10-06T01:04:25 |
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https://runescape.fandom.com/wiki/Talk:Divine_location
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## FANDOM
44,132 Pages
This talk page is for discussing the Divine location page.
## Friends Chat?
Can someone create fc so people can deploy divine locations on same world and spot? I mean i deploy divine mithril rock every day and i mine it by myself.... if others help me, i get noted mith ore in my invent, witch is extra profit for me, and free mith ore for them.... so we all benefit.... some times i also do divne hunter location with my friend and i have to tell u loot is very good :)
-- 14:48, October 9, 2013 (UTC)
I'm sure there already are fcs, but I mostly see people dropping them at the SW-GE in W2... just say which location you're dropping, and mostly people will come and join in (if they have enough time to react). . . . Yours, Enquidou Talk . . 17:33, October 9, 2013 (UTC)
It's not 100% free for them since there is a daily cap and there are people that want to maximise the profit from their cap. I am currently trying to research what the best daily profit is. 03:01, October 11, 2013 (UTC)
Darn capialists... only care for moneys! ... *quickly takes a look :3* . . . Yours, Enquidou Talk . . 05:55, October 11, 2013 (UTC)
if you check this revision http://runescape.wikia.com/wiki/Divine_location?oldid=16446514 there is already a price per resource, but apparently this revision removed it:"(cur | prev) 05:39, April 19, 2016 Iiii I I I (Talk | contribs) . . (12,654 bytes) (-8,724) . . (way too much clutter) (undo)"--77.171.100.56 23:39, October 6, 2016 (UTC)
## Daily gathering limit
The daily gathering limited is listed as (level/50)*5 ... surely it should just be level/10 ? 86.17.207.165 09:53, October 19, 2013 (UTC)
The limit is listed as $floor(level/50)*5$. This is not equal to $level/10$. For example, with $level = 2423$, the first is equal to 240, while the second is equal to 242.3. IP83.101.44.209 (talk) 10:10, October 19, 2013 (UTC)
Furthermore I now have reason to suspect there is an additional maximum of 250. 00:02, October 21, 2013 (UTC)
$floor(level/50)*5$ is not correct though. It's clearly $floor(level/10)$. I'm 2488 total, I max out at 248 items. Obviously if the only resource you harvest are Box Traps, I can understand why someone would make that mistake since the game prevents you from harvesting from a location if harvesting would put you past your limit. Old Smithy (talk) 00:25, October 29, 2013 (UTC)
I used coal to check for any remaining resources. But if you get 248 (or even 250) at level 2488 then the formula is indeed in need of tweaking. Please check my research page for existing data and add data if you have any new information. 14:16, November 4, 2013 (UTC)
Whatever the equation is, it's not what it is on the page as of right now. Calculating says I get 258 resources (2582 total level), but the game only allows me to collect 250 resources. I usually get 248 from divine herb patch III's daily then get the 'your daily limit won't allow you to gather from this location' message; then I'm able to get 2 more from either 2 logs from a divine yew tree, or 1 log from a divine magic tree which gives me the 'you have reached your limit from gathering from divine locations message'.)72.71.151.183 03:26, February 4, 2014 (UTC)
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-04-02T01:22:23 |
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https://www.usgs.gov/programs/national-water-quality-program/prior-budget-justifications
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# Prior Budget Justifications
A summary of the budget process for the National Water Quality Program (NWQP) is provided below for the three most recent fiscal years. To supplement each summary, a more detailed reference document for the Water Resources Mission Area (WMA) showing the reports released with each congressional mark, links to the USGS and WMA President’s Budget Request, and associated details is also provided
### Fiscal Year 2020
Final Enacted Bill
On December 20, 2019, the Consolidated Appropriations Act, 2020 (Public Law 116-94) was enacted. The bill funded the WMA at \$234.1 million, including \$92.5 million for the NWQP. Within this amount, the bill included an increase of \$529,000 and \$273,000 to Cooperative Matching Funds for harmful algal blooms work and the Urban Waters Federal Partnership respectively.
A table summarizing the 2019 Enacted, 2020 President’s Budget Request, and 2020 changes proposed in House and Senate Marks, then enacted in the final bill, is provided below.
For more information on the entire 2020 budget process for the WMA, please use this reference document
### Fiscal Year 2019
Final Enacted Bill
On February 15, 2019, the Consolidated Appropriations Act, 2019 (Public Law 116-6) was enacted. The bill funded the WMA at \$226.3 million, including \$91.6 million for the NWQP. Within this amount, the bill included a \$819,000 increase to Cooperative Matching Funds for harmful algal blooms work. A table summarizing the 2018 Enacted, 2019 President’s Budget Request, and 2019 changes proposed in House and Senate Marks, then enacted in the final bill, is provided below. *Harmful Algal Blooms funding increase in the 2019 PB is Non-CMF Funding. For more information on the entire 2019 budget process for the WMA, please use this reference document. ### Fiscal Year 2018 Final Enacted Bill On March 23, 2018, the Consolidated Appropriations Act, 2018 (Public Law 115-141) was enacted. The bill funded the WMA at \$217.6 million, including \$90.8 million for the NWQP. Within this amount, the bill included a \$300,000 increase for groundwater research in shallow and fractured bedrock terrain.
A table summarizing the 2017 Enacted, the 2018 President’s Budget Request, and the 2018 changes proposed in House and Senate Marks, then enacted in the final bill, is provided below.
For more information on the entire 2018 budget process for the WMA, please use this reference document.
### Funding History
Below, a five-year funding history has been provided for the major NWQP activities:
| 2022-01-17T03:19:07 |
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https://par.nsf.gov/biblio/10361378-jets-jet-substructure-future-colliders
|
This content will become publicly available on June 22, 2023
Jets and Jet Substructure at Future Colliders
Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the motivation for and design of future energy Frontier colliders. In particular, we discuss the need for a vibrant theory and experimental research and development program to extend jet substructure physics into the new regimes probed by future colliders. Jet substructure has organically evolved with a close connection between theorists and experimentalists and has catalyzed exciting innovations in both communities. We expect such developments will play an important role in the future energy Frontier physics program.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10361378
Journal Name:
Frontiers in Physics
Volume:
10
ISSN:
2296-424X
4. A bstract The ALICE Collaboration reports the first fully-corrected measurements of the N -subjettiness observable for track-based jets in heavy-ion collisions. This study is performed using data recorded in pp and Pb-Pb collisions at centre-of-mass energies of $$\sqrt{s}$$ s = 7 TeV and $$\sqrt{s_{\mathrm{NN}}}$$ s NN = 2 . 76 TeV, respectively. In particular the ratio of 2-subjettiness to 1-subjettiness, τ 2 /τ 1 , which is sensitive to the rate of two-pronged jet substructure, is presented. Energy loss of jets traversing the strongly interacting medium in heavy-ion collisions is expected to change the rate of two-pronged substructure relative to vacuum. The results are presented for jets with a resolution parameter of R = 0 . 4 and charged jet transverse momentum of 40 ≤ p T , jet ≤ 60 GeV/ c , which constitute a larger jet resolution and lower jet transverse momentum interval than previous measurements in heavy-ion collisions. This has been achieved by utilising a semi-inclusive hadron-jet coincidence technique to suppress the larger jet combinatorial background in this kinematic region. No significant modification of the τ 2 /τ 1 observable for track-based jets in Pb-Pb collisions is observed relative to vacuum PYTHIA6more »
| 2023-01-27T10:53:45 |
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https://mooseframework.inl.gov/modules/porous_flow/
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Porous Flow
The PorousFlow module is a library of physics for fluid and heat flow in porous media. It is formulated in an extremely general manner, so is capable of solving problems with an arbitrary number of phases and fluid components.
By simply adding pieces of physics together in an input file, the PorousFlow module enables the user to model problems with any combination of fluid, heat and geomechanics.
Other sources of information
This documentation is based on earlier latex documentation, and we are still in the process of transferring the latex into the online format. You may find the latex documentation and its associated PDF files at porous_flow/doc/theory, porous_flow/doc/tests and in the porous_flow/test/tests directories.
Theoretical foundation
The equations governing motion of fluid and heat in porous media that are implemented in Kernels in the PorousFlow module.
Available models
Several different flow models are available in PorousFlow.
General formulations for the following cases are possible:
Specialised formulations for miscible two-phase flow are also provided, that use a persistent set of primary variables and a compositional flash to calculate the partitioning of fluid components amongst fluid phases:
Material laws
Material laws implemented in PorousFlow.
Fluid equation of states
PorousFlow uses formulations contained in the Fluid Properties module to calculate fluid properties such as density or viscosity.
Boundary conditions
Several boundary conditions useful for many simulations are provided.
Point and line sources and sinks
A number of fluid and/or heat sources/sinks are available for use in PorousFlow.
The Dictator
The PorousFlowDictator is a UserObject that holds information about the nonlinear variables used in the PorousFlow module, as well as the number of fluid phases and fluid components in each simulation.
Other PorousFlow objects, such as Kernels or Materials query the PorousFlowDictator to make sure that only valid fluid components or phases are used.
note
A PorousFlowDictator must be present in all simulations!
Examples
We are currently in the process of building a few key examples of PorousFlow.
The following AuxKernels can be used to save properties and data to AuxVariables, which can then be used as input for other MOOSE objects, or saved to output files and used to visualise results.
A number of Postprocessors are available:
| 2019-02-20T07:31:43 |
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http://researchprofiles.herts.ac.uk/portal/en/publications/ska-studies-of-nearby-galaxies(2d05c439-22f2-4ba4-b9ed-d00c06100511).html
|
# University of Hertfordshire
## SKA studies of nearby galaxies: star-formation, accretion processes and molecular gas across all environments
Research output: Contribution to journalArticle
### Documents
• pdf
Final published version, 4.95 MB, PDF document
• R. J. Beswick
• E. Brinks
• M. A. Perez-Torres
• A. M. S. Richards
• S. Aalto
• A. Alberdi
• M.K. Argo
• I. van Bemmel
• J. E. Conway
• C. Dickinson
• D. M. Fenech
• M.D. Gray
• H-R Klockner
• E. J. Murphy
• T.W.B. Muxlow
• M. Peel
• A. P. Rushton
• E. Schinnerer
Original language English 070 23 Proceedings of Science 215 https://doi.org/10.22323/1.215.0070 Published - 29 May 2015 Advancing Astrophysics with the Square Kilometre Array - Giardini Naxos, ItalyDuration: 8 Jun 2014 → 13 Jun 2014
### Abstract
The SKA will be a transformational instrument in the study of our local Universe. In particular, by virtue of its high sensitivity (both to point sources and diffuse low surface brightness emission), angular resolution and the frequency ranges covered, the SKA will undertake a very wide range of astrophysical research in the field of nearby galaxies. By surveying vast numbers of nearby galaxies of all types with $\mu$Jy sensitivity and sub-arcsecond angular resolutions at radio wavelengths, the SKA will provide the cornerstone of our understanding of star-formation and accretion activity in the local Universe. In this chapter we outline the key continuum and molecular line science areas where the SKA, both during phase-1 and when it becomes the full SKA, will have a significant scientific impact.
### Notes
Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence
ID: 8243009
| 2020-01-20T23:19:45 |
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https://par.nsf.gov/biblio/10350066-cosmic-ultraviolet-baryon-survey-cubs-iv-complex-multiphase-circumgalactic-medium-revealed-partial-lyman-limit-systems
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The Cosmic Ultraviolet Baryon Survey (CUBS) – IV. The complex multiphase circumgalactic medium as revealed by partial Lyman limit systems
ABSTRACT We present a detailed study of two partial Lyman limit systems (pLLSs) of neutral hydrogen column density $N_\mathrm{H\, I}\approx (1-3)\times 10^{16}\, \mathrm{cm}^{-2}$ discovered at $z$ = 0.5 in the Cosmic Ultraviolet Baryon Survey (CUBS). Available far-ultraviolet spectra from the Hubble Space Telescope Cosmic Origins Spectrograph and optical echelle spectra from MIKE on the Magellan Telescopes enable a comprehensive ionization analysis of diffuse circumgalactic gas based on resolved kinematics and abundance ratios of atomic species spanning five different ionization stages. These data provide unambiguous evidence of kinematically aligned multiphase gas that masquerades as a single-phase structure and can only be resolved by simultaneous accounting of the full range of observed ionic species. Both systems are resolved into multiple components with inferred α-element abundance varying from [α/H] ≈−0.8 to near solar and densities spanning over two decades from log nH/cm−3 ≈ −2.2 to <−4.3. Available deep galaxy survey data from the CUBS program taken with VLT/MUSE, Magellan/LDSS3-C and Magellan/IMACS reveal that the $z$ = 0.47 system is located 55 kpc from a star-forming galaxy with prominent Balmer absorption of stellar mass ${{M_{\rm star}}}\approx 2\times 10^{10}\, {{M_{\odot}}}$, while the $z$ = 0.54 system resides in an overdense environment of 11 galaxies within 750 kpc in projected distance, with more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10350066
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
508
Issue:
3
Page Range or eLocation-ID:
4359 to 4384
ISSN:
0035-8711
1. ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the cosmic ultraviolet baryon survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicitymore »
2. ABSTRACT We present initial results from the Cosmic Ultraviolet Baryon Survey (CUBS). CUBS is designed to map diffuse baryonic structures at redshift z ≲ 1 using absorption-line spectroscopy of 15 UV-bright QSOs with matching deep galaxy survey data. CUBS QSOs are selected based on their NUV brightness to avoid biases against the presence of intervening Lyman limit systems (LLSs) at zabs < 1. We report five new LLSs of $\log \, N({\mathrm{ H} \,{\small I}})/{{\rm cm^{-2}}}\gtrsim 17.2$ over a total redshift survey path-length of $\Delta \, z_{\mathrm{ LL}}=9.3$, and a number density of $n(z)=0.43_{-0.18}^{+0.26}$. Considering all absorbers with $\log \, N({{\mathrm{ H} \,{\small I}}})/{{\rm cm^{-2}}}\gt 16.5$ leads to $n(z)=1.08_{-0.25}^{+0.31}$ at zabs < 1. All LLSs exhibit a multicomponent structure and associated metal transitions from multiple ionization states such as C ii, C iii, Mg ii, Si ii, Si iii, and O vi absorption. Differential chemical enrichment levels as well as ionization states are directly observed across individual components in three LLSs. We present deep galaxy survey data obtained using the VLT-MUSE integral field spectrograph and the Magellan Telescopes, reaching sensitivities necessary for detecting galaxies fainter than $0.1\, L_*$ at d ≲ 300 physical kpc (pkpc) in all five fields. A diverse range of galaxy properties ismore »
3. ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$, $M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore »
Hydrogen emission lines can provide extensive information about star-forming galaxies in both the local and high-redshift Universe. We present a detailed Lyman continuum (LyC), Lyman-α (Lyα), and Balmer line (Hα and Hβ) radiative transfer study of a high-resolution isolated Milky Way simulation using the state-of-the-art Arepo-RT radiation hydrodynamics code with the SMUGGLE galaxy formation model. The realistic framework includes stellar feedback, non-equilibrium thermochemistry accounting for molecular hydrogen, and dust grain evolution in the interstellar medium (ISM). We extend our publicly available Cosmic Lyα Transfer (COLT) code with photoionization equilibrium Monte Carlo radiative transfer and various methodology improvements for self-consistent end-to-end (non-)resonant line predictions. Accurate LyC reprocessing to recombination emission requires modelling pre-absorption by dust ($f_\text{abs} \approx 27.5\,\rm{per\,\,cent}$), helium ionization ($f_\text{He} \approx 8.7\,\rm{per\,\,cent}$), and anisotropic escape fractions ($f_\text{esc} \approx 7.9\,\rm{per\,\,cent}$), as these reduce the available budget for hydrogen line emission ($f_\text{H} \approx 55.9\,\rm{per\,\,cent}$). We investigate the role of the multiphase dusty ISM, disc geometry, gas kinematics, and star formation activity in governing the physics of emission and escape, focusing on the time variability, gas-phase structure, and spatial spectral, and viewing angle dependence of the emergent photons. Isolated disc simulations are well-suited for comprehensive observational comparisons with local Hα surveys, butmore »
5. ABSTRACT We revisit the question of ‘hot mode’ versus ‘cold mode’ accretion on to galaxies using steady-state cooling flow solutions and idealized 3D hydrodynamic simulations. We demonstrate that for the hot accretion mode to exist, the cooling time is required to be longer than the free-fall time near the radius where the gas is rotationally supported, Rcirc, i.e. the existence of the hot mode depends on physical conditions at the galaxy scale rather than on physical conditions at the halo scale. When allowing for the depletion of the halo baryon fraction relative to the cosmic mean, the longer cooling times imply that a virialized gaseous halo may form in halo masses below the threshold of $\sim 10^{12}\, {\rm M_{\odot }}$ derived for baryon-complete haloes. We show that for any halo mass there is a maximum accretion rate for which the gas is virialized throughout the halo and can accrete via the hot mode of ${\dot{M}}_{\rm crit}\approx 0.7(v_{\rm c}/100\, \rm km\ s^{-1})^{5.4}(R_{\rm circ}/10\, {\rm kpc})(Z/\, {\rm Z_{\odot }})^{-0.9}\, {\rm M_{\odot }}\, {\rm yr}^{-1}$, where Z and vc are the metallicity and circular velocity measured at Rcirc. For accretion rates $\gtrsim {\dot{M}}_{\rm crit}$ the volume-filling gas phase can in principle be ‘transonic’ –more »
| 2022-12-04T08:57:38 |
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https://pos.sissa.it/354/078/
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Volume 354 - High Energy Phenomena in Relativistic Outflows VII (HEPRO VII) - Poster Session
Stability analysis of magnetized astrophysical relativistic jets without current sheets
S. Charalampos, N. Vlahakis*
*corresponding author
Full text: pdf
Published on: 2020 February 25
Abstract
Astrophysical jets are observed as stable structures, extending in lengths several times their radii. The role of various instabilities and how they affect the observed jet properties has not been fully understood. Using the ideal relativistic MHD equations to describe jet dynamics we aim to study the stability properties through linear analysis.
In this work we probe stability properties of jets without current sheets and low magnetizations, moving with mildly relativistic Lorentz factors. In particular we find the dispersion relation for kink $(m = \pm 1)$ and pinch $(m=0)$ modes. In the former we find that a wide range of wavelengths $\sim$ 1 - 1000 jet radii equally contributes to the instability with growth rates $\sim$ a few $10^{-3}c/r_j$, while in the latter the large wavelengths are more unstable, giving similar growth rates. Evaluating the eigenfunctions of the instability we see that they attain their highest values near the jet boundary, indicating that the instabilities are most likely of a Kelvin-Helmholtz type rather than current driven.
DOI: https://doi.org/10.22323/1.354.0078
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2020-03-29T15:51:02 |
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https://par.nsf.gov/biblio/10147672-adaptive-partitioned-methods-time-accurate-approximation-evolutionary-stokesdarcy-system
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Adaptive partitioned methods for the time-accurate approximation of the evolutionary Stokes–Darcy system
This paper develops, analyzes and tests a time-accurate partitioned method for the Stokes-Darcy equations. The method combines a time filter and Backward Euler scheme, is second order accurate and provide, at no extra complexity, an estimated the temporal error. This approach post-processes the solutions of Backward Euler scheme by adding three lines to original codes to increase the time accuracy from first order to second order. We prove long time stability and error estimates of Backward Euler plus time filter with constant time stepsize. Moreover, we extend the approach to variable time stepsize and construct adaptive algorithms. Numerical tests show convergence of our method and support the theoretical analysis.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10147672
Journal Name:
Computer methods in applied mechanics and engineering
Volume:
364
ISSN:
1879-2138
3. In this paper, we discuss the stability and error estimates of the fully discrete schemes for linear conservation laws, which consists of an arbitrary Lagrangian–Eulerian discontinuous Galerkin method in space and explicit total variation diminishing Runge–Kutta (TVD-RK) methods up to third order accuracy in time. The scaling arguments and the standard energy analysis are the key techniques used in our work. We present a rigorous proof to obtain stability for the three fully discrete schemes under suitable CFL conditions. With the help of the reference cell, the error equations are easy to establish and we derive the quasi-optimal error estimates in space and optimal convergence rates in time. For the Euler-forward scheme with piecewise constant elements, the second order TVD-RK method with piecewise linear elements and the third order TVD-RK scheme with polynomials of any order, the usual CFL condition is required, while for other cases, stronger time step restrictions are needed for the results to hold true. More precisely, the Euler-forward scheme needs τ ≤ ρh 2 and the second order TVD-RK scheme needs $\tau \le \rho {h}^{\frac{4}{3}}$ for higher order polynomials in space, where τ and h are the time and maximum space step, respectively, and ρmore »
4. The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase space that includes the independent variables of time, space, and velocity. In order to reduce the dimensionality of the phase space, classical approaches such as the P$_N$ (spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H$^T_N$) approximation to the radiative thermal transfer equations. This approach acquires desirable properties of both P$_N$ and S$_N$, and indeed reduces to each of these approximations in various limits: H$^1_N$ $\equiv$ P$_N$ and H$^T_0$ $\equiv$ S$_T$. We prove that H$^T_N$ results in a system of hyperbolic partial differential equations for all $T\ge 1$ and $N\ge 0$. Another challenge in solving the TRT system is the inherent stiffness due to the large timescale separation between propagation and collisions, especially in the diffusive (i.e., highly collisional) regime. This stiffness challenge can be partially overcome via implicit time integration, although fully implicit methods may become computationally expensivemore »
| 2022-12-01T23:15:06 |
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https://www.zbmath.org/authors/?q=ai%3Aamyari.maryam
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# zbMATH — the first resource for mathematics
## Amyari, Maryam
Compute Distance To:
Author ID: amyari.maryam Published as: Amyari, M.; Amyari, Maryam External Links: MGP · Wikidata
Documents Indexed: 31 Publications since 2002 Reviewing Activity: 224 Reviews
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#### Co-Authors
3 single-authored 4 Chakoshi, Mahnaz 4 Hassani, Mahmoud 4 Moslehian, Mohammad Sal 4 Niknam, Assadollah 3 Khanehgir, Mahnaz 2 Gohari, Mahdi Mohammadi 2 Hassanniah, Reyhaneh 2 Karizaki, Mehdi Mohammadzadeh 2 Khibary, M. Moradian 2 Mehrazin, Marzieh 2 Sadeghi, Ghadir 1 Keyhani, Eqbal 1 Khosravi, Maryam 1 Majidi, Alireza 1 Mirzavaziri, Majdid 1 Moradian Khibary, Marzieh 1 Omidvar, Mohsen Erfanian 1 Park, Choonkil 1 Rahbarnia, Freydoon 1 Saraei, Ateyeh 1 Zamani, Ali
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#### Serials
2 Journal of Mathematical Analysis and Applications 2 Bulletin of the Iranian Mathematical Society 1 Letters in Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Colloquium Mathematicum 1 Mathematica Slovaca 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Journal of Operator Theory 1 Aequationes Mathematicae 1 The Journal of Analysis 1 Turkish Journal of Mathematics 1 Filomat 1 Mathematical Communications 1 Taiwanese Journal of Mathematics 1 Tamsui Oxford Journal of Mathematical Sciences 1 Communications of the Korean Mathematical Society 1 Journal of the Korean Society of Mathematical Education. Series B. The Pure and Applied Mathematics 1 Acta Mathematica Academiae Paedagogicae Nyíregyháziensis. New Series 1 Nonlinear Functional Analysis and Applications 1 International Mathematical Journal 1 Kragujevac Journal of Mathematics 1 Mathematical Reports 1 The Australian Journal of Mathematical Analysis and Applications 1 Kochi Journal of Mathematics 1 Tbilisi Mathematical Journal 1 International Journal of Nonlinear Analysis and Applications
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#### Fields
25 Functional analysis (46-XX) 11 Operator theory (47-XX) 7 Difference and functional equations (39-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX)
#### Citations contained in zbMATH
15 Publications have been cited 77 times in 65 Documents Cited by Year
Approximate homomorphisms of ternary semigroups. Zbl 1112.39021
Amyari, M.; Moslehian, M. S.
2006
Nearly ternary derivations. Zbl 1141.39024
Amyari, Maryam; Baak, Choonkil; Moslehian, Mohammad Sal
2007
Some results on stability of extended derivations. Zbl 1153.39308
Amyari, M.; Rahbarnia, F.; Sadeghi, Gh.
2007
Operator matrix of Moore-Penrose inverse operators on Hilbert $$C^*$$-modules. Zbl 1342.46054
2015
Moore-Penrose inverse of product operators in Hilbert $$C^*$$-modules. Zbl 06749978
2016
Hyers-Ulam-Rassias stability of derivations on Hilbert $$C^*$$-modules. Zbl 1121.39028
2007
Quasi-representations of Finsler modules over $$C^*$$-algebras. Zbl 1299.46062
Amyari, Maryam; Chakoshi, Mahnaz; Moslehian, Mohammad Sal
2013
A note on Finsler modules. Zbl 1063.46045
Amyari, M.; Niknam, A.
2003
Isometrics in non-Archimedean strictly convex and strictly 2-convex 2-normed spaces. Zbl 1198.46055
2010
Stability of $$C^{*}$$-inner products. Zbl 1125.46047
Amyari, Maryam
2006
On homomorphisms of Finsler modules. Zbl 1193.46037
Amyari, M.; Niknam, A.
2003
Numerical radius parallelism of Hilbert space operators. Zbl 07220174
Mehrazin, Marzieh; Amyari, Maryam; Zamani, Ali
2020
Maps preserving quasi-isometries on Hilbert $$C^*$$-modules. Zbl 1408.46055
Majidi, Alireza; Amyari, Maryam
2018
Imprimitivity Finsler $$C^*$$-bimodules. Zbl 1325.46061
Hassanniah, R.; Amyari, M.; Hassani, M.
2014
Inner products on a Hilbert $$C^{\ast}$$-module. Zbl 1030.46072
Amyari, M.; Niknam, A.
2002
Numerical radius parallelism of Hilbert space operators. Zbl 07220174
Mehrazin, Marzieh; Amyari, Maryam; Zamani, Ali
2020
Maps preserving quasi-isometries on Hilbert $$C^*$$-modules. Zbl 1408.46055
Majidi, Alireza; Amyari, Maryam
2018
Moore-Penrose inverse of product operators in Hilbert $$C^*$$-modules. Zbl 06749978
2016
Operator matrix of Moore-Penrose inverse operators on Hilbert $$C^*$$-modules. Zbl 1342.46054
2015
Imprimitivity Finsler $$C^*$$-bimodules. Zbl 1325.46061
Hassanniah, R.; Amyari, M.; Hassani, M.
2014
Quasi-representations of Finsler modules over $$C^*$$-algebras. Zbl 1299.46062
Amyari, Maryam; Chakoshi, Mahnaz; Moslehian, Mohammad Sal
2013
Isometrics in non-Archimedean strictly convex and strictly 2-convex 2-normed spaces. Zbl 1198.46055
2010
Nearly ternary derivations. Zbl 1141.39024
Amyari, Maryam; Baak, Choonkil; Moslehian, Mohammad Sal
2007
Some results on stability of extended derivations. Zbl 1153.39308
Amyari, M.; Rahbarnia, F.; Sadeghi, Gh.
2007
Hyers-Ulam-Rassias stability of derivations on Hilbert $$C^*$$-modules. Zbl 1121.39028
2007
Approximate homomorphisms of ternary semigroups. Zbl 1112.39021
Amyari, M.; Moslehian, M. S.
2006
Stability of $$C^{*}$$-inner products. Zbl 1125.46047
Amyari, Maryam
2006
A note on Finsler modules. Zbl 1063.46045
Amyari, M.; Niknam, A.
2003
On homomorphisms of Finsler modules. Zbl 1193.46037
Amyari, M.; Niknam, A.
2003
Inner products on a Hilbert $$C^{\ast}$$-module. Zbl 1030.46072
Amyari, M.; Niknam, A.
2002
all top 5
all top 5
#### Cited in 31 Serials
6 Journal of Mathematical Physics 5 Journal of Mathematical Analysis and Applications 5 Abstract and Applied Analysis 5 Journal of Inequalities and Applications 4 Advances in Difference Equations 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Banach Journal of Mathematical Analysis 2 Fuzzy Sets and Systems 2 Applied Mathematics Letters 2 Functional Analysis, Approximation and Computation 2 Mathematics 2 Journal of Linear and Topological Algebra 2 Journal of Function Spaces 2 Sahand Communications in Mathematical Analysis 1 Linear and Multilinear Algebra 1 Glasgow Mathematical Journal 1 Acta Applicandae Mathematicae 1 Aequationes Mathematicae 1 Indagationes Mathematicae. New Series 1 Journal of Difference Equations and Applications 1 Positivity 1 Communications of the Korean Mathematical Society 1 Bulletin of the Brazilian Mathematical Society. New Series 1 International Journal of Geometric Methods in Modern Physics 1 Mediterranean Journal of Mathematics 1 Journal of Fixed Point Theory and Applications 1 Complex Analysis and Operator Theory 1 Journal of Nonlinear Science and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Advances in Operator Theory 1 Korean Journal of Mathematics
all top 5
#### Cited in 20 Fields
47 Functional analysis (46-XX) 42 Difference and functional equations (39-XX) 29 Operator theory (47-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Nonassociative rings and algebras (17-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-03-03T21:52:37 |
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https://www.usgs.gov/center-news/slow-earthquake-study-relies-fast-digital-data
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# Slow earthquake study relies on fast digital data
Release Date:
Several weeks ago, we reported on the anticipated Kīlauea slow earthquake - a very interesting and recently recognized component of our volcano's evolution. Unfortunately, the slow earthquake did not comply with our expectations, and we continue to wait for it with both our permanent monitoring networks and the temporary instruments that we deployed in February.
Anticipated Kīlauea volcano's "slow earthquake" location.
Image courtesy of NASA.
(Public domain.)
Studies like our Kīlauea slow earthquake project provide terrific opportunities to work somewhat differently than in our routine volcano and earthquake monitoring mode. In this case, we were able to borrow and deploy a type of seismometer that we hope to add to our Hawaiian Volcano Observatory's (HVO) permanent seismic monitoring tool kit.
Our current earthquake monitoring network is made up of sensors whose signals are radioed to HVO in analog form, then digitized on two computers. These newer seismometers are designed to produce their data in digital form right at the sensor. As with digital music and television, this reduces the possibility of loss of data quality in the sometimes long radio trip back to HVO.
With additional electronics at the remote stations, the digital seismometers can be configured to record a wider range of seismic frequencies and increase the range of earthquake magnitudes that we can analyze. Our permanent network affords a very narrow view (black and white) into the wide range of seismic signals that earthquakes generate (full color).
Because the data from the newer instruments is digital in form, it can be brought back to HVO via several technologies, including the Internet and digital radio. If successful, we can view and analyze the data continuously and in real time. If communication links fail, the data are stored on site. When communication is restored, we can retrieve the data that would otherwise have been lost.
In the case of our slow earthquake chase along Kīlauea's south flank, we are not sending anything to HVO and must manually retrieve the data. Not a problem. As visitors to Hawaii Volcanoes National Park can attest, this is done by hiking on wonderful trails in one of the world's most incredibly scenic settings. The data can be downloaded on site and/or data cards can be swapped.
Following the December 2004 Sumatra and 2006 Kiholo Bay earthquakes, we are working with our Pacific Tsunami Warning Center (PTWC) and U. S. Geological Survey (USGS) National Strong Motion Project (NSMP) monitoring partners to upgrade our seismic networks in Hawaii to include a much larger number of real-time digital seismic sensors.
Along with the new instruments being installed around the islands, it is also important that we improve and expand upon our collection of analytical tools to take advantage of the improved data quality.
The PTWC is striving to compute reliable earthquake magnitudes and report them within 90 seconds of the earthquake. Likewise, the USGS is committed to rapid and reliable earthquake analysis and reporting. In addition, the USGS is committed to posting information relating to earthquake damage and earthquake hazards, like the ShakeMap and Community Internet Intensity Maps (CIIM) that we have mentioned in earlier Volcano Watch reports. We would also like to compute more detailed faulting and slip models of large earthquakes.
We greatly appreciate the community interest that allows the posting of Hawaii CIIM. The Kiholo Bay ShakeMap was posted almost a day after the earthquake. We are hoping to be able to automatically compute and post a ShakeMap, minutes after an earthquake. Recent and planned upgrades to PTWC and USGS stations in Hawaii are critical to meeting our performance goals. In the meantime, while waiting for our slow earthquake, we?re able to get better acquainted with the seismic tools of our future.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
This past week, activity levels at the summit of Kīlauea Volcano have remained at background levels. The summit caldera has been expanding, indicating inflation, since the beginning of 2007. The number of earthquakes located in the summit area is at low levels (usually fewer than 10 per day are large enough to locate). There have been local concentrations of earthquakes beneath the summit area.
Eruptive activity at Puu Oo continues, though the level of activity seems somewhat subdued compared to the last few years. On clear nights, glow is visible from three vents within the eastern half of the crater. Lava is still flowing through the PKK lava tube, and unusual activity along the uppermost portion of the tube has built new hornitos there. The PKK tube continues to carry some lava to the top of Pulama pali, where a small breakout has been active for weeks. Most of the lava, however, is going into the Campout tube that branches off from the PKK tube about 1 km south of Puu Oo. The Campout tube carries lava to the ocean at Kamokuna located inside Hawaii Volcanoes National Park.
For the past week on the flow field, streams of lava from the Campout flow have been seen daily descending Pulama pali. Scattered breakouts also remain active from near the base of the Royal Gardens subdivision to within several hundred meters of the coast. The laze plume created by the ocean entry at Kamokuna remains small, suggesting that little lava is entering the water.
Access to the sea cliff near the ocean entries is closed, due to significant hazards. The surrounding area, however, is open. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
No earthquakes beneath Hawaii Island were reported felt within the past week.
Mauna Loa is not erupting. Two earthquakes were located beneath the summit. Extension of distances between locations spanning the summit, indicating inflation, continues at steady, slow rates.
| 2020-01-28T07:27:47 |
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https://zbmath.org/authors/?q=ai%3Ayager.ronald-r
|
zbMATH — the first resource for mathematics
Yager, Ronald R.
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Author ID: yager.ronald-r Published as: Jager, R.; Yager, R.; Yager, R. R.; Yager, Ronald; Yager, Ronald R. Homepage: http://www.panix.com/~yager/HP/rry.html External Links: Wikidata · dblp · GND
Documents Indexed: 391 Publications since 1977, including 37 Books Biographic References: 1 Publication
all top 5
all top 5
Serials
48 Information Sciences 46 Fuzzy Sets and Systems 32 International Journal of General Systems 26 International Journal of Intelligent Systems 22 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18 International Journal of Approximate Reasoning 18 Fuzzy Optimization and Decision Making 13 Kybernetes 12 International Journal of Man-Machine Studies 11 IEEE Transactions on Systems, Man, and Cybernetics 11 Studies in Fuzziness and Soft Computing 9 Soft Computing 9 Communications in Computer and Information Science 6 Cybernetics and Systems 4 Lecture Notes in Computer Science 3 Journal of Information & Optimization Sciences 3 European Journal of Operational Research 2 Information and Control 2 Stochastica 2 Applied Intelligence 2 Journal of Cybernetics 1 Artificial Intelligence 1 International Journal of Systems Science 1 Journal of Mathematical Analysis and Applications 1 Cybernetica 1 Control and Cybernetics 1 International Journal of Computer & Information Sciences 1 Theory and Decision 1 Large Scale Systems 1 Bulletin pour les Sous Ensembles Flous et Leurs Applications 1 Mathematical Modelling 1 Annals of Operations Research 1 Mathware & Soft Computing 1 Notes on Intuitionistic Fuzzy Sets 1 Annals of Mathematics and Artificial Intelligence 1 International Transactions in Operational Research 1 Mathematical Problems in Engineering 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 International Journal of Applied Mathematics and Computer Science 1 1 Journal of Intelligent and Fuzzy Systems 1 Iranian Journal of Fuzzy Systems 1 The Kluwer International Series in Engineering and Computer Science 1 Advances in Fuzzy Systems – Applications and Theory 1 Studies in Computational Intelligence 1 1 Applied and Computational Mathematics
all top 5
Fields
203 Computer science (68-XX) 120 Mathematical logic and foundations (03-XX) 78 Information and communication theory, circuits (94-XX) 77 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 38 Operations research, mathematical programming (90-XX) 34 General and overarching topics; collections (00-XX) 23 Systems theory; control (93-XX) 20 Statistics (62-XX) 15 Measure and integration (28-XX) 15 Probability theory and stochastic processes (60-XX) 5 Biology and other natural sciences (92-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 2 Functional analysis (46-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX)
Citations contained in zbMATH
284 Publications have been cited 5,556 times in 3,158 Documents Cited by Year
On ordered weighted averaging aggregation operators in multicriteria decisionmaking. Zbl 0637.90057
Yager, Ronald R.
1988
A procedure for ordering fuzzy subsets of the unit interval. Zbl 0459.04004
Yager, Ronald R.
1981
Uninorm aggregation operators. Zbl 0871.04007
Yager, Ronald R.; Rybalov, Alexander
1996
Structure of uninorms. Zbl 1232.03015
Fodor, János C.; Yager, Ronald R.; Rybalov, Alexander
1997
Some geometric aggregation operators based on intuitionistic fuzzy sets. Zbl 1113.54003
Xu, Zeshui; Yager, Ronald R.
2006
Families of OWA operators. Zbl 0790.94004
Yager, Ronald R.
1993
On a general class of fuzzy connectives. Zbl 0443.04008
Yager, Ronald R.
1980
Defuzzification under constrains and forbidden zones. Zbl 1002.93530
Yager, Ronald R.; Filev, Dimitar P.
1994
Entropy and specificity in a mathematical theory of evidence. Zbl 0521.94008
Yager, Ronald R.
1983
On the measure of fuzziness and negation. I. Membership in the unit interval. Zbl 0429.04007
Yager, Ronald R.
1979
The ordered weighted averaging operators. Zbl 0948.68532
Yager, Ronald R. (ed.); Kacprzyk, Janusz (ed.)
1997
Generalized OWA aggregation operators. Zbl 1057.90032
Yager, Ronald R.
2004
On the Dempster-Shafer framework and new combination rules. Zbl 0629.68092
Yager, Ronald R.
1987
Dynamic intuitionistic fuzzy multi-attribute decision making. Zbl 1185.91073
Xu, Zeshui; Yager, Ronald R.
2008
On some new classes of implication operators and their role in approximate reasoning. Zbl 1095.68119
Yager, Ronald R.
2004
Aggregation operators and fuzzy systems modeling. Zbl 0845.93047
Yager, Ronald R.
1994
Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Zbl 1386.91051
Atanassov, Krassimir; Pasi, Gabriella; Yager, Ronald
2005
An approach to ordinal decision making. Zbl 0870.68137
Yager, Ronald R.
1995
Fuzzy decision making including unequal objectives. Zbl 0378.90011
Yager, Ronald R.
1978
Induced aggregation operators. Zbl 1056.68146
Yager, Ronald R.
2003
Multiple objective decision-making using fuzzy sets. Zbl 0371.90005
Yager, R. R.
1977
Uninorms in fuzzy systems modeling. Zbl 0978.93007
Yager, Ronald R.
2001
Connectives and quantifiers in fuzzy sets. Zbl 0725.03033
Yager, Ronald R.
1991
On choosing between fuzzy subsets. Zbl 0428.03050
Yager, R. R.
1980
A characterization of the extension principle. Zbl 0628.04005
Yager, Ronald R.
1986
Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Zbl 1183.91038
Xu, Zeshui; Yager, Ronald R.
2009
Advances in the Dempster-Shafer theory of evidence. Zbl 0816.68110
Yager, Ronald R. (ed.); Kacprzyk, Janusz (ed.); Fedrizzi, Mario (ed.)
1994
Analytic properties of maximum entropy OWA operators. Zbl 0870.90004
Filev, Dimitar; Yager, Ronald R.
1995
On generalized Bonferroni mean operators for multi-criteria aggregation. Zbl 1186.91076
Yager, Ronald R.
2009
On the specificity of a possibility distribution. Zbl 0783.94035
Yager, Ronald R.
1992
A generalized defuzzification method via bad distributions. Zbl 0752.93040
Filev, Dimitar P.; Yager, Ronald R.
1991
Classic works on the Dempster-Shafer theory of belief functions. Zbl 1135.68051
Yager, Ronald R. (ed.); Liu, Liping (ed.)
2008
Measuring tranquility and anxiety in decision making: An application of fuzzy sets. Zbl 0487.90007
Yager, Ronald R.
1982
On the measure of fuzziness and negation. II. Lattices. Zbl 0429.04008
Yager, Ronald R.
1980
Generalized probabilities of fuzzy events from fuzzy belief structures. Zbl 0525.60006
Yager, Ronald R.
1982
Decision making under Dempster-Shafer uncertainties. Zbl 0756.90005
Yager, Ronald R.
1992
The entailment principle for Dempster-Shafer granules. Zbl 0643.94054
Yager, Ronald R.
1986
On the issue of defuzzification and selection based on a fuzzy set. Zbl 0785.93060
Yager, Ronald R.; Filev, Dimitar
1993
Prioritized aggregation operators. Zbl 1184.68526
Yager, Ronald R.
2008
Approximate reasoning as a basis for rule-based expert systems. Zbl 0555.68066
Yager, Ronald R.
1984
Generalized Bonferroni mean operators in multi-criteria aggregation. Zbl 1207.68381
Beliakov, Gleb; James, Simon; Mordelová, Juliana; Rückschlossová, Tatiana; Yager, Ronald R.
2010
Some properties of overlap and grouping functions and their application to image thresholding. Zbl 1284.68549
Jurio, A.; Bustince, H.; Pagola, M.; Pradera, A.; Yager, R. R.
2013
A new approach to the summarization of data. Zbl 0517.94027
Yager, Ronald R.
1982
A foundation for a theory of possibility. Zbl 0438.94042
Yager, Ronald R.
1980
The continuous ordered weighted geometric operator and its application to decision making. Zbl 1132.91385
Yager, Ronald R.; Xu, Zeshui
2006
Centered OWA operators. Zbl 1113.68106
Yager, R. R.
2007
A new class of fuzzy implications. Axioms of fuzzy implication revisited. Zbl 0939.03030
Türkşen, I. Burhan; Kreinovich, Vladik; Yager, Ronald R.
1998
On ranking fuzzy numbers using valuations. Zbl 0937.68115
Yager, Ronald R.; Filev, Dimitar
1999
Quantified propositions in a linguistic logic. Zbl 0522.03013
Yager, Ronald R.
1983
Merging fuzzy information. Zbl 0951.94028
Dubois, Didier; Prade, Henri; Yager, Ronald
1999
Arithmetic and other operations on Dempster-Shafer structures. Zbl 0653.68106
Yager, Ronald R.
1987
A note on probabilities of fuzzy events. Zbl 0438.60006
Yager, Ronald R.
1979
Fuzzy set-theoretic operators and quantifiers. Zbl 0973.03072
Fodor, János; Yager, Ronald R.
2000
Defending against strategic manipulation in uninorm-based multi-agent decision making. Zbl 0998.90046
Yager, Ronald R.
2002
Ranking fuzzy numbers using $$\alpha$$-weighted valuations. Zbl 1113.68512
Detyniecki, Marcin; Yager, Ronald R.
2000
Decision making under interval probabilities. Zbl 1041.91500
1999
Neural network implementation of fuzzy logic. Zbl 0744.68125
Keller, James M.; Yager, Ronald R.; Tahani, Hossein
1992
Cardinality of fuzzy sets via bags. Zbl 0625.04007
Yager, R. R.
1987
Using approximate reasoning to represent default knowledge. Zbl 0624.68083
Yager, Ronald R.
1987
Modeling the concept of majority opinion in group decision making. Zbl 1126.91016
Pasi, Gabriella; Yager, Ronald R.
2006
Universal approximation theorem for uninorm-based fuzzy systems modeling. Zbl 1040.93043
2003
On the analytic representation of the Leximin ordering and its application to flexible constraint propagation. Zbl 0948.90112
Yager, Ronald R.
1997
Understanding the median as a fusion operator. Zbl 0980.68502
Yager, Ronald R.; Rybalov, Alexander
1997
On weighted median aggregation. Zbl 1232.68150
Yager, Ronald R.
1994
General multiple-objective decision functions and linguistically quantified statements. Zbl 0563.94032
Yager, Ronald R.
1984
Quantifiers in the formulation of multiple objective decision functions. Zbl 0551.90084
Yager, Ronald R.
1983
Some aspects of intuitionistic fuzzy sets. Zbl 1179.03054
Yager, Ronald R.
2009
Fusion of ordinal information using weighted median aggregation. Zbl 0942.68043
Yager, Ronald R.
1998
Interpreting linguistically quantified propositions. Zbl 0807.68069
Yager, Ronald R.
1994
Fuzzy set and possibility theory. Recent developments. Papers presented at the Symposium held in Acapulco (Mexico), December 1980. Zbl 0568.94036
Yager, Ronald R. (ed.)
1982
Some procedures for selecting fuzzy set-theoretic operators. Zbl 0488.04005
Yager, Ronald R.
1982
On the dispersion measure of OWA operators. Zbl 1183.68622
Yager, Ronald R.
2009
Prioritized OWA aggregation. Zbl 1173.90540
Yager, Ronald R.
2009
Using trapezoids for representing granular objects: applications to learning and OWA aggregation. Zbl 1128.68104
Yager, Ronald R.
2008
A context-dependent method for ordering fuzzy numbers using probabilities. Zbl 0996.03511
Yager, Ronald R.; Detyniecki, Marcin; Bouchon-Meunier, Bernadette
2001
A class of fuzzy measures generated from a Dempster-Shafer belief structure. Zbl 0937.68119
Yager, Ronald R.
1999
An introduction to fuzzy logic applications in intelligent systems. Zbl 0755.68018
Yager, Ronald R. (ed.); Zadeh, Lotfi A. (ed.)
1992
Toward a general theory of reasoning with uncertainty. I: Nonspecificity and fuzziness. Zbl 0641.68154
Yager, Ronald R.
1986
On the lack of inverses in fuzzy arithmetic. Zbl 0433.03033
Yager, Ronald R.
1980
Modeling holistic fuzzy implication using co-copulas. Zbl 1127.03324
Yager, Ronald R.
2006
On the cardinality index and attitudinal character of fuzzy measures. Zbl 1025.28014
Yager, Ronald R.
2002
On the normalization of fuzzy belief structures. Zbl 0935.03036
Yager, Ronald R.
1996
Set-based representations of conjunctive and disjunctive knowledge. Zbl 0626.68073
Yager, Ronald R.
1987
OWA aggregation of intuitionistic fuzzy sets. Zbl 1187.68615
Yager, Ronald R.
2009
Choquet aggregation using order inducing variables. Zbl 1074.68074
Yager, Ronald R.
2004
Noncommutative self-identity aggregation. Zbl 0903.04005
Yager, Ronald R.; Rybalov, Alexander
1997
On the concept of immediate probabilities. Zbl 0846.62007
Yager, Ronald R.; Engemann, Kurt J.; Filev, Dimitar P.
1995
Default knowledge and measures of specificity. Zbl 0738.68075
Yager, Ronald R.
1992
Fuzzy prediction based on regression models. Zbl 0509.62087
Yager, Ronald R.
1982
A measurement-informational discussion of fuzzy union and intersection. Zbl 0403.03044
Yager, Ronald R.
1979
Generalized moving averages, distance measures and OWA operators. Zbl 1323.68506
Merigó, José M.; Yager, Ronald R.
2013
Aggregation of ordinal information. Zbl 1153.68496
Yager, Ronald R.
2007
Heavy OWA operators. Zbl 1091.91506
Yager, Ronald R.
2002
On the valuation of alternatives for decision-making under uncertainty. Zbl 1016.68108
Yager, Ronald R.
2002
Linguistic summaries of data using fuzzy logic. Zbl 1001.68039
Kacprzyk, Janusz; Yager, Ronald R.
2001
On global requirements for implication operators in fuzzy modus ponens. Zbl 0931.68117
Yager, Ronald R.
1999
Measures of entropy and fuzziness related to aggregation operators. Zbl 0871.94009
Yager, Ronald R.
1995
On the implication operator in fuzzy logic. Zbl 0557.03015
Yager, Ronald R.
1983
Bipolar aggregation using the uninorms. Zbl 1304.91068
Yager, Ronald R.; Rybalov, Alexander
2011
Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures. Zbl 1154.68530
Yager, Ronald R.
2008
Extremal symmetrization of aggregation functions. Zbl 1434.91029
Mesiar, Radko; Stupňanová, Andrea; Yager, Ronald R.
2018
Belief structures, weight generating functions and decision-making. Zbl 1428.68292
Yager, Ronald R.
2017
Properties and applications of Pythagorean fuzzy sets. Zbl 1370.03074
Yager, Ronald R.
2016
On the measure based formulation of multi-criteria decision functions. Zbl 1428.68304
Yager, Ronald R.; Alajlan, Naif
2016
Recursively spreadable and reductible measures of specificity. Zbl 1391.94953
Garmendia, Luis; González-del-Campo, Ramón; Yager, Ronald R.
2016
On the consistency of fuzzy measures in multi-criteria aggregation. Zbl 1429.91140
Yager, Ronald R.; Alajlan, Naif
2015
Combining uncertain information of differing modalities. Zbl 1390.68673
Petry, Fred; Elmore, Paul; Yager, Ronald
2015
Conditional information using copulas with an application to decision making. Zbl 1381.62078
Yager, Ronald R.
2015
Combining various types of belief structures. Zbl 1360.68852
Yager, Ronald R.
2015
On characterizing features of OWA aggregation operators. Zbl 1428.90091
Yager, Ronald R.; Alajlan, Naif
2014
The use of ordered weighted averaging method for decision making under uncertainty. Zbl 1287.91036
Ahn, Byeong Seok; Yager, Ronald R.
2014
A note on mean absolute deviation. Zbl 1355.60023
Yager, Ronald R.; Alajlan, Naif
2014
An intuitionistic view of the Dempster-Shafer belief structure. Zbl 1326.68291
Yager, Ronald R.
2014
Recent developments and new directions in soft computing. Zbl 1298.68035
Zadeh, Lotfi A. (ed.); Abbasov, Ali M. (ed.); Yager, Ronald R. (ed.); Shahbazova, Shahnaz N. (ed.); Reformat, Marek Z. (ed.)
2014
Modeling, querying and mining social relational networks using fuzzy set techniques (survey). Zbl 1414.91310
Yager, Ronald R.
2014
Some properties of overlap and grouping functions and their application to image thresholding. Zbl 1284.68549
Jurio, A.; Bustince, H.; Pagola, M.; Pradera, A.; Yager, R. R.
2013
Generalized moving averages, distance measures and OWA operators. Zbl 1323.68506
Merigó, José M.; Yager, Ronald R.
2013
Joint cumulative distribution functions for Dempster-Shafer belief structures using copulas. Zbl 1397.91156
Yager, Ronald R.
2013
Density-based averaging – a new operator for data fusion. Zbl 1293.62133
Angelov, P.; Yager, R.
2013
Exponential smoothing with credibility weighted observations. Zbl 1321.62116
Yager, Ronald R.
2013
Ranking fuzzy numbers and its extensions. Zbl 1299.00005
Allahviranloo, Tofigh (ed.); Yager, Ronald R. (ed.); Abbasbandy, Saeid (ed.); Ulutagay, Gozde (ed.)
2013
Fairness in selecting multiple objects under diversity requirements. Zbl 1293.91053
Yager, Ronald R.
2013
Norm aggregations and OWA operators. Zbl 1277.90056
Merigó, José M.; Yager, Ronald R.
2013
A new type of simplified fuzzy rule-based system. Zbl 1252.68293
Angelov, Plamen; Yager, Ronald
2012
Measure based representation of uncertain information. Zbl 1258.60008
Yager, Ronald R.; Alajlan, Naif
2012
On a view of Zadeh’s Z-numbers. Zbl 1252.94143
Yager, Ronald R.
2012
Expansible measures of specificity. Zbl 1283.94167
Yager, Ronald R.
2012
Bipolar aggregation using the uninorms. Zbl 1304.91068
Yager, Ronald R.; Rybalov, Alexander
2011
On the fusion of imprecise uncertainty measures using belief structures. Zbl 1216.68297
Yager, Ronald R.
2011
A measure based approach to the fusion of possibilistic and probabilistic uncertainty. Zbl 1213.28009
Yager, Ronald R.
2011
Generalized Bonferroni mean operators in multi-criteria aggregation. Zbl 1207.68381
Beliakov, Gleb; James, Simon; Mordelová, Juliana; Rückschlossová, Tatiana; Yager, Ronald R.
2010
The power average operator for information fusion. Zbl 1209.68608
Yager, Ronald R.
2010
Level sets and the representation theorem for intuitionistic fuzzy sets. Zbl 1188.03041
Yager, Ronald R.
2010
A framework for reasoning with soft information. Zbl 1187.68616
Yager, Ronald R.
2010
Criteria satisfaction under measure based uncertainty. Zbl 1232.91148
Yager, Ronald R.
2010
Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Zbl 1183.91038
Xu, Zeshui; Yager, Ronald R.
2009
On generalized Bonferroni mean operators for multi-criteria aggregation. Zbl 1186.91076
Yager, Ronald R.
2009
Some aspects of intuitionistic fuzzy sets. Zbl 1179.03054
Yager, Ronald R.
2009
On the dispersion measure of OWA operators. Zbl 1183.68622
Yager, Ronald R.
2009
Prioritized OWA aggregation. Zbl 1173.90540
Yager, Ronald R.
2009
OWA aggregation of intuitionistic fuzzy sets. Zbl 1187.68615
Yager, Ronald R.
2009
On the fusion of non-independent belief structures. Zbl 1187.68200
Yager, Ronald R.
2009
Comparing approximate reasoning and probabilistic reasoning using the Dempster-Shafer framework. Zbl 1191.68701
Yager, Ronald R.
2009
Dynamic intuitionistic fuzzy multi-attribute decision making. Zbl 1185.91073
Xu, Zeshui; Yager, Ronald R.
2008
Classic works on the Dempster-Shafer theory of belief functions. Zbl 1135.68051
Yager, Ronald R. (ed.); Liu, Liping (ed.)
2008
Prioritized aggregation operators. Zbl 1184.68526
Yager, Ronald R.
2008
Using trapezoids for representing granular objects: applications to learning and OWA aggregation. Zbl 1128.68104
Yager, Ronald R.
2008
Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures. Zbl 1154.68530
Yager, Ronald R.
2008
Intelligent social network analysis using granular computing. Zbl 1160.68386
Yager, Ronald R.
2008
Building ensemble classifiers using belief functions and OWA operators. Zbl 1133.68406
Reformat, Marek; Yager, Ronald R.
2008
A knowledge-based approach to adversarial decision making. Zbl 1126.68590
Yager, Ronald R.
2008
Measures of specificity over continuous spaces under similarity relations. Zbl 1175.03035
Yager, Ronald R.
2008
Summarizing data using a similarity based mountain method. Zbl 1126.68539
Yager, Ronald R.; Filev, Dimitar P.
2008
Centered OWA operators. Zbl 1113.68106
Yager, R. R.
2007
Aggregation of ordinal information. Zbl 1153.68496
Yager, Ronald R.
2007
Entropy conserving probability transforms and the entailment principle. Zbl 1123.68127
2007
On the soundness of altering granular information. Zbl 1123.68121
Yager, Ronald R.
2007
Some geometric aggregation operators based on intuitionistic fuzzy sets. Zbl 1113.54003
Xu, Zeshui; Yager, Ronald R.
2006
The continuous ordered weighted geometric operator and its application to decision making. Zbl 1132.91385
Yager, Ronald R.; Xu, Zeshui
2006
Modeling the concept of majority opinion in group decision making. Zbl 1126.91016
Pasi, Gabriella; Yager, Ronald R.
2006
Modeling holistic fuzzy implication using co-copulas. Zbl 1127.03324
Yager, Ronald R.
2006
OWA trees and their role in security modeling using attack trees. Zbl 1102.68665
Yager, Ronald R.
2006
Generalizing variance to allow the inclusion of decision attitude in decision making under uncertainty. Zbl 1100.68115
Yager, Ronald R.
2006
Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Zbl 1386.91051
Atanassov, Krassimir; Pasi, Gabriella; Yager, Ronald
2005
Extending multicriteria decision making by mixing $$t$$-norms and OWA operators. Zbl 1159.68579
Yager, Ronald R.
2005
Recursive and iterative OWA operators. Zbl 1085.68172
Troiano, Luigi; Yager, Ronald R.
2005
Mountain clustering on non-uniform grids using $$p$$-trees. Zbl 1078.68722
Rickard, John T.; Yager, Ronald R.; Miller, Wendy
2005
Generalizing Leximin to t-norms and t-conorms: the LexiT and LexiS orderings. Zbl 1112.90356
Yager, Ronald R.; Walker, Carol L.; Walker, Elbert A.
2005
Generalized OWA aggregation operators. Zbl 1057.90032
Yager, Ronald R.
2004
On some new classes of implication operators and their role in approximate reasoning. Zbl 1095.68119
Yager, Ronald R.
2004
Choquet aggregation using order inducing variables. Zbl 1074.68074
Yager, Ronald R.
2004
Weighted triangular norms using generating functions. Zbl 1101.68850
Yager, Ronald R.
2004
Induced aggregation operators. Zbl 1056.68146
Yager, Ronald R.
2003
Universal approximation theorem for uninorm-based fuzzy systems modeling. Zbl 1040.93043
2003
Fuzzy logic methods in recommender systems. Zbl 1024.68100
Yager, Ronald R.
2003
On t-norms based measures of specificity. Zbl 1024.94023
2003
Modeling the concept of fuzzy majority opinion. Zbl 1037.68752
Pasi, Gabriella; Yager, Ronald R.
2003
On the relation between two approaches to combining evidence: ordered abelian groups and uninorms. Zbl 1083.68613
2003
Generalized triangular norm and conorm aggregation operators on ordinal spaces. Zbl 1047.03046
Yager, Ronald R.
2003
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https://wwwn.cdc.gov/nchs/nhanes/tutorials/Module10.aspx
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# Module 10: Logistic Regression
The NHANES Tutorials are currently being reviewed and revised, and are subject to change. Specialized tutorials (e.g. Dietary, etc.) will be included in the future.
Logistic Regression is a statistical method used to assess the likelihood of a disease or health condition as a function of a risk factor (and covariates). There are two kinds of logistic regression, simple and multiple. Both simple and multiple logistic regression, assess the association between independent variable(s) (Xi) — sometimes called exposure or predictor variables — and a dichotomous dependent variable (Y) — sometimes called the outcome or response variable.
Logistic Regression is used to assess the likelihood of a disease or health condition as a function of a risk factor (and covariates). Both simple and multiple logistic regression, assess the association between independent variable(s) (Xi) — sometimes called exposure or predictor variables — and a dichotomous dependent variable (Y) — sometimes called the outcome or response variable. Logistic regression analysis tells you how much an increment in a given exposure variable affects the odds of the outcome.
Simple logistic regression is used to explore associations between one (dichotomous) outcome and one (continuous, ordinal, or categorical) exposure variable. Simple logistic regression lets you answer questions like, "how does gender affect the probability of having hypertension?
Multiple logistic regression is used to explore associations between one (dichotomous) outcome variable and two or more exposure variables (which may be continuous, ordinal or categorical). The purpose of multiple logistic regression is to let you isolate the relationship between the exposure variable and the outcome variable from the effects of one or more other variables (called covariates or confounders). Multiple logistic regression lets you answer the question, "how does gender affect the probability of having hypertension, after accounting for — or unconfounded by — or independent of — age, income, etc.?" This process — accounting for covariates or confounders — is also called adjustment.
Comparing the results of simple and multiple logistic regression can help to answer the question "how much did the covariates in the model alter the relationship between exposure and outcome (i.e., how much confounding was there)?"
Research Question
In this module, you will assess the association between gender (the exposure variable) and the likelihood of having hypertension (the outcome). You will look at both simple logistic regression and then multiple logistic regression. The multiple logistic regression will include the covariates of age, cholesterol, body mass index (BMI) and fasting triglycerides. This analysis will answer the question, what is the effect of gender on the likelihood of having hypertension — after controlling for age, cholesterol, BMI, and fasting triglycerides?
Dependent Variable and Independent Variables
As noted, the dependent variable Yi for a Logistic Regression is dichotomous, which means that it can take on one of two possible values. NHANES includes many questions where people must answer either "yes" or "no", questions like "has the doctor ever told you that you have congestive heart failure?". Or, you can create dichotomous variables by setting a threshold (e.g., "diabetes" = fasting blood sugar > 126); or by combining information from several variables. In this module, you will create a dichotomous variable called "hyper" based on two variables: measured blood pressure and use of blood pressure medications. In SUDAAN, SAS Survey, and Stata, the dependent variable is coded as 1 (for having the outcome) and 0 (for not having the outcome). In this example, for people who have been told they have hypertension or reported use of blood pressure medication, the hypertension variable would have a value of 1, while people who were never told of hypertension or not taking blood pressure medication would have a value of 0.
The independent variables Xj can be dichotomous (e.g. gender ,"high cholesterol"), ordinal (e.g. age groups, BMI categories), or continuous (e.g. fasting triglycerides).
Logit Function
Since you are trying to find associations between risk factors and a condition, you need a formula that will allow you to link these variables. The logit function that you use in logistic regression is also known as the link function because it connects, or links, the values of the independent variables to the probability of occurrence of the event defined by the dependent variable.
Logit Model
In the logit formula above, E(Yi)=pi implies that the Expected Value of (Yi) equals the probability that Yi=1. In this case, ‘Log' indicates natural Log.
Optional: Learn more about odds ratios, linear and logistic regression
Output of Logistic Regression
The statistics of primary interest in logistic regression are the b coefficients ( b1,b2,b3... ), their standard errors, and their p-values. Like other statistics, the standard errors are used to calculate confidence intervals around the beta coefficients.
The interpretation of the beta coefficients for different types of independent variables is as follows:
If Xj is a dichotomous variable with values of 1 or 0, then the b coefficient represents the log odds that an individual will have the event for a person with X j=1 versus a person with Xj=0. In a multivariate model, this b coefficient is the independent effect of variable X j on Yi after adjusting for all other covariates in the model.
If Xj is a continuous variable, then the e b represents the odds that an individual will have the event for a person with Xj=m+1 versus an individual with Xj=m. In other words, for every one unit increase in Xj, the odds of having the event Y i changes by e b , adjusting for all other covariates in a multivariate model.
A summary table about interpretation of beta coefficients is provided below:
Table: What does the b Coefficient Mean?
Independent Variable Type Example Variables The b coefficient in simple logistic regression The b coefficient in multiple logistic regression
Continuous
height, weight, LDL
The change in the log odds of the dependent variable per 1unit change in the independent variable.
The change in the log odds of dependent variable per 1 unit change in the independent variable after controlling for the confounding effects of the covariates in the model.
Categorical (also known as discrete) sex (two subgroups - men and women. This example will use men as the reference group.) The difference in the log odds of the dependent variable for one value of categorical variable vs. the reference group (for example, between women, and the reference group, men). The difference in the log odds of the dependent variable for one value of categorical variable vs. the reference group (for example, between women and the reference group, men), after controlling for the confounding effects of the covariates in the model.
It is easy to transform the b coefficients into a more interpretable format, the odds ratio, as follows:
e b = odds ratio
## IMPORTANT NOTE
Odds and odds ratios are not the same as risk and relative risks.
Odds and probability are two different ways to express the likelihood of an outcome.
Here are their definitions and some examples.
Table of Differences between Odds and Probability
Definition Example: Getting heads in a 1 flip of a coins Example: Getting a 1 in a single roll of a dice
Odds # of times something happens
# of times it does NOT happen
= 1/1 = 1 (or 1:1) = 1/5 = 0.2 (or 1:5)
Probability # of times something happens
# of times it could happen
= 1/2 = .5 (or 50%) = 1/6 = .16 (or 16%)
Few people think in terms of odds. Many people equate odds with probability and thus equate odds ratios with risk ratios. When the outcome of interest is uncommon (i.e. it occurs less than 10% of the time), such confusion makes little difference, since odds ratios and risk ratios are approximately equal. When the outcome is more common, however, the odds ratio increasingly overstates the risk ratio. So, to avoid confusion, when event rates are high, odds ratios should be converted to risk ratios. (Schwartz LM, Woloshin S, Welch HG. Misunderstandings about the effects of race and sex on physicians’ referrals for cardiac catheterization. N Engl J Med 1999;341:279—83) There are simple methods of conversion for both crude and adjusted data. (Zhang J, Yu KF. What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA 1998;280:1690-1691. Davies HT, Crombie IK, Tavakoli M. When can odds ratios mislead? BMJ 1998;316:989-991)
The following formulas demonstrate how you can go between probability and odds.
Probability or Odds
References:
Logistic Regression Using the SAS System
By Paul D. Allison
Epidemiology
By Leon Gordis
Simple logistic regression is used for univariate analyses when there is one dependent variable and one independent variable, while multiple logistic regression model contains one dependent variable and multiple independent variables. To run univariate and mulitple Logistic Regression in SAS-callable SUDAAN, SAS, and Stata, you will need to provide three things:
• Correct weight
• Appropriate procedure, and
• model statement
## IMPORTANT NOTE
Simple logistic regression is used for univariate analyses when there is one dependent variable and one independent variable, while multiple logistic regression model contains one dependent variable and multiple independent variables.
Determine the appropriate weight for the data used
It is always important to check all the variables in the model, and use the weight of the smallest common denominator. In the example of univariate analysis, the 4-year MEC weight is used, because the hypertension variable is from the MEC examination. In the multivariate analysis example, the 4-year MEC morning subsample weight is used, because the fasting triglycerides variable is from the morning fasting subsample from the lab component, which is the smallest common denominator for all variables in the model.
Examples
Simple logistic regressions for gender, age, cholesterol, and BMI:
Because these analyses use 4 years of data and includes variables that come from the household interview and the MEC (e.g. blood pressure, BMI, HDL cholesterol), the MEC 4-year weight - wtmec4yr is the right one.
Simple logistic regression for fasting triglyceride:
Because this analysis uses 4 years of data and fasting triglycerides were only done on the morning subsample, the MEC morning fasting subsample 4-year weight - wtsaf4yr is the right one.
Multiple logistic regression:
Because this analysis uses 4 years of data and includes variables from the household interview, MEC and morning subsample of the MEC, the weight for the smallest group - the morning fasting subsample 4 -year weight - wtsaf4yr is the right one.
• See the Weighting module for more information on weighting and combining weights.
Determine the appropriate procedure
You can run logistic regression with stand-alone SUDAAN, SAS-callable SUDAAN, SAS Survey procedure, or Stata Survey commands. However, note that each version of SUDAAN, SAS-callable SUDAAN, and SAS Survey procedures has its own unique commands for executing logistic regression analysis. You need to use the correct command for the software that you are using. Please also note that different versions of SAS and SUDAAN use slightly different statements to specify categorical variables and reference groups. Make sure that you are using the correct commands for the version of software on your computer.
If you use
• the stand-alone version of SUDAAN, the procedure is logistic
• SAS-callable SUDAAN, the procedure is called rlogist
• SAS survey procedures, the procedure is surveylogistic
Be sure you are using the correct procedure name because SAS also has a procedure logistic , which is used with simple random samples and not complex datasets like NHANES. Using logistic in SAS will yield different results from stand-alone SUDAAN.
Provide a model statement
Remember that when you run logistic regression analyses, you must provide a model statement to specify the dependent variable and independent variable(s), and you can have only one model statement each time you run a logistic regression analysis.
In this module, you will use simple logistic regression to analyze NHANES data to assess the association between gender (riagendr) — the exposure or independent variable — and the likelihood of having hypertension (based on bpxsar, bpxdar) — the outcome or dependent variable, among participants 20 years old and older. You will then use multiple logistic regression to assess the relationship after controlling for selected covariates. The covariates include gender (riagendr), age (ridageyr), cholesterol (lbxtc), body mass index (bmxbmi) and fasting triglycerides (lbxtr).
Step 1: Create dependent dichotomous variable
For continuous variables, you have a choice of using the variable in its original form (continuous) or changing it into a categorical variable (e.g. based on standard cutoffs, quartiles or common practice). The categorical variables should reflect the underlying distribution of the continuous variable and not create categories where there are only a few observations.
For the dependent variable, you will create a dichotomous variable, hyper, which defines people as having (or not having) hypertension. Specifically, a person is said to have hypertension if their systolic blood pressure (measured in the MEC) exceeds 140 or their diastolic blood pressure exceeds 90 or if they are taking blood pressure medication. Remember for logistic regression to work in SUDAAN, this variable needs to be defined as 0 (meaning outcome did not occur, here person does not have hypertension) or 1 (outcome occurs, here person has hypertension). The code to create this variable is below:
if (bpxsar >= 140 or bpxdar >= 90 or bpq050a = 1 ) then Hyper = 1 ;
else if (bpxsar ne . and bpxdar ne .) then Hyper = 0 ;
Step 2: Create independent categorical variables
In addition to creating the dependent dichotomous variable, this example will also create additional independent categorical variables (age, hichol, bmigrp) from the age, cholesterol, and BMI categorical variables to use in this analysis.
Code to generate independent categorical variables
Independent variable Code to generate independent categorical variables
Age
if 20 <=ridageyr< 40 then 1 ;
else if 40 <=ridageyr< 60 then 2 ;
else if 60 then 3 ;
High cholesterol
if (lbxtc>= 240 or bpq100d = 1) then HiChol = 1 ;
else if (lbxtc ne .) then HiChol = 0 ;
BMI category
if 0 <=bmxbmi< 25 then 1 ;
else if 25 <=bmxbmi< 30 then 2 ;
else if 30 then 3 ;
Step 3: Transform highly skewed variables
Because the triglycerides variable (lbxtr) is highly skewed, you will use a log transformation to create new variable to use in this analysis.
logtrig=log(lbxtr);
Step 4: Create eligibility variable
Because not every participant in NHANES responded to every question asked, there may be a different level of item non-response to each variable. To ensure that your analyses are done on the same number of respondents, create a variable called eligible which is 1 for individuals who have a non-blank value for each of the variables used in the analyses, and 0 otherwise. Although this is a univariate analysis using only exam variables, the fasting subsample weight (wtsaf4yr) is included in determining the eligible variable. This is because you will be conducting a multivariate analysis using the triglycerides variable later and will limit the sample to persons included in both analyses. The SAS code defining eligible is:
if hyper ne . and hichol ne . and bmigrp ne . and age ne . and logtrig ne . and wtsaf4yr ne 0 then eligible=1 ;
Step 5: Set up SUDAAN univariate logistic procedure
This step introduces you to the SUDAAN Univariate Logistic Regression procedure (proc rlogist). You can read the explanations in the summary table below.
## IMPORTANT NOTE
These programs use variable formats listed in the Tutorial Formats page. You may need to format the variables in your dataset the same way to reproduce results presented in the tutorial.
SUDAAN Univariate Logistic Procedure
Statements Explanation
proc sort data =analysis_data;
by sdmvstra sdmvpsu;
run ;
Use the proc sort procedure to sort the data by strata and primary sampling units (PSU) before running the procedure.
proc rlogist data=analysis_data;
Use the SUDAAN procedure, proc rlogist, to run logistic regression.
nest sdmvstra sdmvpsu;
Use the nest statement with strata and PSU to account for the design effects.
weight
Use the weight statement to account for the unequal probability of sampling and non-response. In this example, the MEC weight for four years of data is used.
subpopn eligible=1 ;
Use the subpopn statement to limit the sample to the observations included in the final logistic model.
Because only a subpopulation is of interest, use the subpopn statement to select this subgroup. Please note that for accurate estimates, it is preferable to use subpopn in SUDAAN to select a subgroup for analysis, rather than select the study subgroup in the SAS program while preparing the data file.
class riagendr
Use a class statement for categorical variables in version 9.0 and later. In earlier versions, you need a subgroup and levels statement.
reflevel riagendr=2 ;
Use the reflevel statement to choose your reference group for the categorical variables. By default SUDAAN uses the highest category as the reference group.
model hyper=riagendr;
Use the model statement to specify dependent variable and independent variable(s) in your Logistic Regression model.
test waldf satadjf satadjchi;
Use the test statement to produce statistics and P values for the Satterthwaite adjusted CHI square (satadjchi), the Satterthwaite adjusted F (satadjf), and Satterthwaite adjusted degrees of freedom (printed by default). If this statement is omitted, the nominal degrees of freedom, the WALDF and the p-value corresponding to the WALDF and WALDP will be produced.
rformat riagendr sexfmt. ;
rformat hyper bpfmt. ;
Use the rformat statement to read the SAS formats into SUDAAN.
Step 6: Review SUDAAN univariate logistic regression output
In this step, the SUDAAN output is reviewed.
• 1,304 respondents have hypertension and 2,515 do not.
• Men are less likely to have hypertension than women. Their odds of hypertension are 0.89 times the odds of women.
• Assuming a p-value less than 0.05 indicates statistical significance, note that gender is not significantly associated with hypertension based on the p-value for Satterthwaite χ2 or F test, which gives the overall p-value for gender. The Satterthwaite adjusted F gives the most conservative estimate of the test statistics. The p-value of 0.156 indicates that this relationship is not statistically significant.
Step 7: Set up SUDAAN multivariate logistic procedure
The SUDAAN Multivariate Logistic Regression procedure is similar to the univariate procedure explained in the table above. You can follow the steps outlined below to perform a multivariate logistic regression.
## IMPORTANT NOTE
These programs use variable formats listed in the Tutorial Formats page. You may need to format the variables in your dataset the same way to reproduce results presented in the tutorial.
SUDAAN Multivariate Logistic Procedure
Statements Explanation
proc sort data =analysis_data;
by sdmvstra sdmvpsu;
run ;
Use the SAS procedure, proc sort, to sort the data by strata and primary sampling units (PSU) before running the procedure.
proc rlogist data=analysis_data;
Use the SUDAAN procedure, proc rlogist, to run logistic regression.
nest sdmvstra sdmvpsu;
Use the nest statement with strata and primary sampling unit to account for design effects.
weight WTSAF4YR;
Use the fasting subsample weight because the log of fasting triglycerides variable comes from a subsample of the lab data file. Not all respondents were tested on triglycerides.
subpopn eligible=1 ;
Use the subpopn statement to limit the sample to the observations included in the final logistic model.
Please note that for accurate estimates, it is preferable to use subpopn in SUDAAN to select a subgroup for analysis, rather than select the study subgroup in the SAS program while preparing the dataset.
class age riagendr hichol bmigrp;
Use the class statement to specify all categorical variables in the model.
Use a class statement for categorical variables in version 9.0 and later. In earlier versions, you need a subgroup and levels statement.
reflevel age=2 2 ;
Use the reflevel statement to choose your reference group for the categorical variables. By default, SUDAAN uses the highest category as the reference group.
model hyper=age riagendr hichol bmigrp logtrig;
Use the model statement to specify dependent variable and all independent variable(s) in your Logistic Regression model.
test waldf satadjf satadjchi;
Use the test statement to produce statistics and P values for the Satterthwaite adjusted CHI square (satadjchi), the Satterthwaite adjusted F (satadjf), and Satterthwaite adjusted degrees of freedom (printed by default). If this statement is omitted, the nominal degrees of freedom, the WALDF and the p-value corresponding to the WALDF and WALDP will be produced.
Step 8: Review SUDAAN multivariate logistic procedure output
This step reviews the SUDAAN multivariate logistic procedure output.
• 1,304 respondents have hypertension and 2,515 do not.
• All covariates are statistically significant at p-value<0.05, except for gender. The Satterthwaite adjusted F gives the most conservative estimate of the test statistics.
• Odds ratios should be interpreted as adjusted odds ratios because there are multiple covariates in the model. The adjusted odds of hypertension are 1.29 (95% C.I. 1.03-1.61) for each unit increase in the log of triglycerides.
In this module, you will use NHANES data to assess the association between several risk factors and the likelihood of having hypertension for participants 20 years and older. The dependent variable Y is hypertension, and the independent variables Xj, or covariates, are age, gender, high cholesterol, body mass index, and fasting triglycerides. In this task , you will only be reviewing the Multivariate Logistic Procedure.
Step 1: Create Variable to Subset Population
In order to subset the data in SAS Survey Procedures, you will need to create a variable for the population of interest. You should not use a where clause or by-group processing in order to analyze a subpopulation with the SAS Survey Procedures.
In this example, the sel variable is set to 1 if the sample person is 20 years or older, and 2 if the sample person is younger than 20 years. Then this variable is used in the domain statement to specify the population of interest (those 20 years and older).
if ridageyr GE 20 then sel = 1;
else sel = 2;
Step 2: Review SAS Multivariate Logistic Procedure
This step introduces you to the SAS multivariate survey Logistic Regression procedure, proc surveylogistic. There is a summary table of the SAS program below.
## IMPORTANT NOTE
These programs use variable formats listed in the Tutorial Formats page. You may need to format the variables in your dataset the same way to reproduce results presented in the tutorial.
SAS Multivariate Logistic Procedure
Statements Explanation
PROC SURVEYLOGISTIC DATA = Analysis_Data nomcar;
Use the proc surveylogistic procedure to perform multiple logistic regression to assess the association between hypertension and multiple risk factors, including: age, gender, high cholesterol, body mass index, and fasting triglycerides. Use the nomcar option to read all observations.
STRATUM sdmvstra;
Use the stratum statement to specify strata to account for design effects of stratification.
CLUSTER sdmvpsu;
Use the cluster statement to specify primary sampling unit (PSU) to account for design effects of clustering.
WEIGHT wtsafyr;
se the weight statement to account for the unequal probability of sampling and non-response. In this example, the 4-year fasting weight variable is used.
DOMAIN sel;
Use the domain statement to specify the subpopulation of interest.
CLASS age (PARAM=REF REF= '40-59 yrs')
riagendr (PARAM=REF REF='Female')
hichol (PARAM=REF REF='high cholesterol')
bmigrp (PARAM=REF REF='25<=BMI<30');
Use the class statement to specify all categorical variables in the model.
Use the param and ref options to choose your reference group for the categorical variables.
MODEL hyper (desc)=age riagendr hichol bmigrp logtrig/ vadjust=none;
Use the model statement to specify the dependent variable and all independent variable(s) in your Logistic Regression model. The vadjust option specifies whether or not to use variance adjustment.
format age agefmt. riagendr sexfmt. hichol chfmt. bmigrp bmifmt. ; run ;
Use the format statement to read the SAS formats for all formatted variables.
## IMPORTANT NOTE
The SAS Survey Procedure, proc surveylogistic, produces the Wald statistic and its p value. It does not produce the Satterthwaite χ2 or the Satterthwaite F and the corresponding p values recommended for NHANES analyses. For this reason, it is recommended that you use proc rlogist in SUDAAN for logistic regression.
Step 3: Review SAS Multivariate Logistic Regression Output
In this step, the SAS output is reviewed. You can compare your results with the sample output, which you can download from the Sample Code and Datasets page. Or, you can view an animated version of the results with narration by clicking the link below. In the narration, the highlighted elements show that:
• 1,304 respondents have hypertension and 2,515 do not.
• The beta coefficients and odds ratio point estimates are identical to the SUDAAN estimates.
In this module, you will use simple logistic regression to analyze NHANES data to assess the association between gender (riagendr) — the exposure or independent variable — and the likelihood of having hypertension (based on bpxsar, bpxdar) — the outcome or dependent variable, among participants 20 years old and older. You will then use multiple logistic regression to assess the relationship after controlling for selected covariates. The covariates include age (ridageyr), cholesterol (lbxtc), body mass index (bmxbmi) and fasting triglycerides (lbxtr).
## IMPORTANT NOTE
There are several things you should be aware of while analyzing NHANES data with Stata. Please see the Stata Tips page to review them before continuing.
Step 1: Use svyset to define survey design variables
Remember that you need to define the SVYSET before using the SVY series of commands. The general format of this command is below:
svyset [w=weightvar], psu(psuvar) strata(stratavar) vce(linearized)
To define the survey design variables for your cholesterol analysis, use the weight variable for four-yours of MEC data (wtmec4yr), the PSU variable (sdmvpsu), and strata variable (sdmvstra) .The vce option specifies the method for calculating the variance and the default is "linearized" which is Taylor linearization. Here is the svyset command for fur years of MEC data:
svyset [w= wtmec4yr], psu(sdmvpsu) strata(sdmvstra) vce(linearized)
Step 2: Create dependent dichotomous variable
For continuous variables, you have a choice of using the variable in its original form (continuous) or changing it into a categorical variable (e.g. based on standard cutoffs, quartiles or common practice). The categorical variables should reflect the underlying distribution of the continuous variable and not create categories where there are only a few observations.
For the dependent variable, you will create a dichotomous variable, hyper, which defines people as having (or not having) hypertension. Specifically, a person is said to have hypertension if their systolic blood pressure (measured in the MEC) exceeds 140 or their diastolic blood pressure exceeds 90 or if they are taking blood pressure medication. Remember for logistic regression to work in Stata, this variable needs to be defined as 0 (meaning outcome did not occur, here person does not have hypertension) or 1 (outcome occurs, here person has hypertension). The code to create this variable is below:
gen hyper=1 if (bpxsar>=140 & bpxsar<. | bpxdar>=90 & bpxdar<.) | bpq050a==1
replace hyper=0 if hyper !=1 & (bpxsar !=. & bpxdar !=.)
Step 3: Create independent categorical variables
In addition to creating the dichotomous dependent variable, this example will also create additional independent categorical variables (age, hichol, bmigrp) from the age, cholesterol, and BMI categorical variables to use in this analysis.
Code to generate independent categorical variables
Independent variable Code to generate independent categorical variables
Age
gen age=1 if ridageyr >=20 & ridageyr <40
replace age=2 if ridageyr >=40 & ridageyr <60
replace age=3 if ridageyr >=60 abd ridageyr <.
High cholesterol
gen hichol =1 if lbxtc >=240 & lbxtc<. | bpq100d==1
replace hichol =0 if hichol ~=1 & lbxtc !=.
BMI category
gen bmigrp=1 if bmxbmi<25
replace bmigrp=2 if bmxbmi>=25 & bmxbmi <30
replace bmigrp=3 if bmxbmi>=30 & bmxbmi <.
Step 4: Transform highly skewed variables
Because the triglycerides variable (lbxtr) is highly skewed, you will use a log transformation to create new variable to use in this analysis.
gen logtrig = log(lbxtr)
Step 5: Choose reference groups for categorical variables
For all categorical variables, you need to decide which category to use as the reference group. If you do not specify the reference group options, Stata will choose the lowest numbered group by default. You can use the following general command to tell Stata the reference group:
char var [omit] reference_group_value
For your analyses, use the following commands to specify the following reference groups:
Code to specify reference groups
Variable Code to specify reference group Reference group
Gender
char riagendr [omit] 2
Women
Age
char age [omit] 2
40-59 year olds
BMI
char bmigrp [omit] 2
overweight (bmi25-29)
Cholesterol
char hichol [omit] 1
low cholesterol (<240mg/dL)
Step 6: Create eligibility variable
Because not every participant in NHANES responded to every question asked, there may be a different level of item non-response to each variable. To ensure that your analyses are done on the same number of respondents, create a variable called eligible which is 1 for individuals who have a non-blank value for each of the variables used in the analyses, and 0 otherwise. Although this is a univariate analysis using only exam variables, the fasting subsample weight (wtsaf4yr) is included in determining the eligible variable. This is because you will be conducting a multivariate analysis using the triglycerides variable later and will limit the sample to persons included in both analyses. The Stata code defining eligible is:
gen eligible=1 if wtsaf4yr!=. & hyper!=. & riagendr!=. &age!=. & hichol!=. & bmigrp!=. & logtrig~=. &wtsafyr!=0
Step 7: Create simple logistic regression model to understand relationships
The association between the dependent (or outcome) and independent (or exposure) variables is expressed using the svy:logit command. The dependent variable must be a dichotomous variable and the independent variables may be either discrete, ordinal, or continuous.
The general form of the command to get beta coefficients is:
xi: svy, subpop(condition): logit depvar i.indvar
To get odds ratios with the logit command, use the or option:
xi: svy, subpop(condition): logit depvar i.indvar, or
Odds ratios are automatically produced by the logistic command:
xi: svy, subpop(condition): logistic depvar i.indvar
An example command analyzing the relationship between gender and hypertension using the logistic commend is shown below:
xi: svy, subpop(if eligible==1): logistic hyper i.riagendr
In this example, the output for the logistic command is:
Highlights in the output include:
• Men are less likely to have hypertension than women. Their odds of hypertension are 0.89 times the odds of women.
• Assuming a p-value less than 0.05 indicates statistical significance, note that gender is not significantly associated with hypertension based on the p-value. The p-value of 0.156 indicates that this relationship is not statistically significant.
Step 8: Specify multiple logistic regression model
Multiple logistic regression uses the same command structure but now includes other independent variables. If you want to create indicator variables for categorical variables, you will want to use the xi option. However, the general structure remains the same:
xi: svy, subpop(condition): logistic depvar indvar i.indvar
For this example, you will be using these commands to analyze the effects of gender, age, high cholesterol, BMI, and triglycerides on hypertension. Please note that the svyset commands is using the subsample weight, wtsat4yr, because this analysis includes the triglycerides variable that was only collected on a subsample of the survey.
svyset [w=wtsaf4yr], psu(sdmvpsu) strata(sdmvstra)
xi: svy, subpop(if eligible==1): logistic hyper i.riagendr i.age i.hichol i.bmigrp logtrig
In this example, this output is:
Highlights from the output include:
• All covariates are statistically significant at p-value<0.05, except for gender.
• Odds ratios should be interpreted as adjusted odds ratios because there are multiple covariates in the model. The adjusted odds of hypertension are 1.29 (95% C.I. 1.03-1.61) for each unit increase in the log of triglycerides.
Step 9: Compare results of simple and multiple linear regressions
To understand how much adjustment matters, it is helpful to compare the odds ratio from the simple and multiple regression models. The following tables summarize the results.
Table Comparing Differences between Crude Analysis (Simple Logistic Regression) and Adjusted Analysis (Multiple Logistic Regression) - Sex
Sex Crude Analysis
% with hypertension
Crude Analysis
Odds Ratio*
(95% CI)
Adjusted Analysis Odds Ratio*
(95% CI)
Crude Analysis
p value
p value
men 27% 0.89
(0.75 - 1.05)
0.94
(0.76 - 1.16)
0.16 0.55
women 30% Reference Group Reference Group Reference Group Reference Group
Table Comparing Differences between Crude Analysis (Simple Logistic Regression) and Adjusted Analysis (Multiple Logistic Regression) - Age
Age
(years)
Crude Analysis
% with hypertension
Crude Analysis
Odds Ratio*
(95% CI)
Adjusted Analysis Odds Ratio*
(95% CI)
Crude Analysis
p value
p value
20-39 9% 0.25
(0.18-.034)
0.28
(0.21 - .038)
<0.001 <0.001
40-59 28% Reference Group Reference Group Reference Group Reference Group
60+ 66% 4.87
(3.76 - 6.3)
5.27
(4.00 - 6.94)
<0.001 <0.001
Table Comparing Differences between Crude Analysis (Simple Logistic Regression) and Adjusted Analysis (Multiple Logistic Regression) - BMI
BMI Crude Analysis
% with hypertension
Crude Analysis
Odds Ratio*
(95% CI)
Odds Ratio*
(95% CI)
Crude Analysis
p value
p value
underweight/
normal
18% 0.58
(0.46 - 0.72)
0.67
(0.51- 0.87)
<0.001 0.004
overweight 28% Reference Group Reference Group Reference Group Reference Group
obese 42% 1.85
(1.52 - 2.25)
2.18
(1.70 - 2.80)
<0.001 <0.001
Table Comparing Differences between Crude Analysis (Simple Logistic Regression) and Adjusted Analysis (Multiple Logistic Regression) - Cholesterol
Cholesterol Crude Analysis
% with hypertension
Crude Analysis
Coefficient*
(95% CI)
>Coefficient*
(95% CI)
Crude Analysis
p value
p value
High 43% Reference Group Reference Group Reference Group Reference Group
Low/Normal 24% 0.41
(0.34 - 0.49)
0.78
(0.62 - 0.97)
<0.001 0.028
Table Comparing Differences between Crude Analysis (Simple Logistic Regression) and Adjusted Analysis (Multiple Logistic Regression) - Triglycerides
Triglycerides Crude Analysis
% with hypertension
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value
Triglycerides N/A 1.98
(1.65 - 2.37)
1.28
(1.03 - 1.61)
<0.001 0.029
Stata Multivariate Logistic Procedure
Statements Explanation
use "C:\Stata\tutorial\analysis_data.dta", clear
Use the use command to load the Stata-format dataset. Use the clear option to replace any data in memory.
svyset sdmvpsu [pweight=wtsaf4yr], strata(sdmvstra) vce(linearized)
Use the svyset command to declare the survey design for the dataset. Specify the psu variable sdmvpsu. Use the [pweight=] option to account for the unequal probability of sampling and non-response. In this example, the MEC fasting weight for four years of data (wtsaf4yr) is used. Use the strata () option to specify the stratum identifier (sdmvstra). Use the vce( ) option to specific the variance estimation method (linearized) for Taylor linearization.
char age[omit] 2
char riagendr[omit]2
char bmigrp[omit] 2
char hichol[omit]1
Use these options to choose your reference group for the categorical variables. For example, the 2nd age category (age 40-59) is chosen as the reference group.
If you do not specify the reference group options, Stata will choose the lowest numbered group by default.
xi: svy, subpop(if ridageyr >=20) vce(linearized): logit hyper i.age i.riagendr i.hichol i.bmigrp logtrig
Use the xi command to expand terms containing categorical variables (denoted i.varname) into indicator (also called dummy) variable sets. Use the svy: logit command to perform multiple logistic regressions to assess the association between hypertension and multiple risk factors, including: age, gender, high cholesterol, body mass index, and fasting triglycerides. Use the subpop( ) option to select a subpopulation for analysis, rather than select the study population in the Stata program while preparing the data file. (Note: omission of the or option as shown below will yield estimates as coefficients.)
xi: svy, subpop(if ridageyr >=20) vce(linearized): logit hyper i.age i.riagendr i.hichol i.bmigrp logtrig, or
Use the xi command to expand terms containing categorical variables into indicator (also
called dummy) variable sets. Use the svy: logit command to perform multiple logistic regressions to assess the association between hypertension and multiple risk factors, including: age, gender, high cholesterol, body mass index, and fasting triglycerides.
Use the subpop( ) option to select a subpopulation for analysis, rather than select the study population in the Stata program while preparing the data file. Use the or option to produce estimates as odds ratios.
test
*******************************
test _Iage_1 _Iage_3, nosvyadjust
test _Ibmigrp_1 _Ibmigrp_3, nosvyadjust
test logtrig, nosvyadjust
Use the test postestimation command to produce the Wald F statistic and the corresponding p-value. Use the nosvyadjust option to produce the unadjusted Wald F. In the example, the command test is used to test all coefficient together and then all coefficients separately.
## WARNING
The Stata command, svy:logit, produces the adjusted and unadjusted Wald statistic and its p value. It does not produce the Satterthwaite χ2 or the Satterthwaite F and the corresponding p values recommended for NHANES analyses.
Step 10: Post-estimation
You may want to know whether different comparisons (other than the reference categories you specified) are significant. In that case, you can use a post-estimation command (i.e. a command that can only be run after you have run the logit model command). This takes the general form, if you do not want the unadjusted Wald F:
This example will be using this command to test that the youngest age group has a statistically significant different likelihood of having hypertension than the oldest age group:
test _Iage_1 = _Iage_3, nosvyadjust
The results for this example are:
If you ran both the SAS Survey and SUDAAN programs (or reviewed the output provided on the Sample Code and Datasets Page page), you may have noticed slight differences in the output. These differences can be caused by missing data in any paired PSU or how each software program handles degrees of freedom.
• Both programs calculate that 1,304 respondents have hypertension and 2,515 do not.
• The beta coefficient and odds ratio estimates are identical.
• The variance estimates and standard errors are identical if there are no missing data in any paired PSUs (which was the case in this example). They will be different if any one of the paired PSUs contains missing data, as SAS and SUDAAN handle stratum contribution from the missing cells differently.
• The confidence intervals are slightly different since SAS and SUDAAN handles degrees of freedom differently.
Page last reviewed: 8/4/2020
| 2020-10-23T22:00:53 |
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https://zbmath.org/authors/?q=ai%3Agray.john-w
|
# zbMATH — the first resource for mathematics
## Gray, John W.
Compute Distance To:
Author ID: gray.john-w Published as: Gray, John W.; Gray, J. W. Homepage: https://faculty.math.illinois.edu/~gray/ External Links: IdRef · MGP · Wikidata · dblp · GND
Documents Indexed: 31 Publications since 1959, including 4 Books
#### Co-Authors
29 single-authored 1 Mac Lane, Leslie Saunders 1 Scedrov, Andre
all top 5
#### Serials
3 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Journal of Pure and Applied Algebra 2 Bulletin of the American Mathematical Society 2 Contemporary Mathematics 2 Lecture Notes in Mathematics 1 Illinois Journal of Mathematics 1 Pacific Journal of Mathematics 1 Theoretical Computer Science 1 Topology 1 Advances in Applied Mathematics 1 Diagrammes 1 Annals of Mathematics. Second Series
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#### Fields
23 Category theory; homological algebra (18-XX) 7 Computer science (68-XX) 4 Mathematical logic and foundations (03-XX) 4 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 General topology (54-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
22 Publications have been cited 399 times in 359 Documents Cited by Year
Some global properties of contact structures. Zbl 0092.39301
Gray, John W.
1959
Formal category theory: Adjointness for 2-categories. Zbl 0285.18006
Gray, John W.
1974
Fibred and cofibred categories. Zbl 0192.10701
Gray, J. W.
1966
Closed categories, lax limits and homotopy limits. Zbl 0462.55008
Gray, John W.
1980
The categorical comprehension scheme. Zbl 0211.03403
Gray, John W.
1969
Sheaves with values in a category. Zbl 0132.17605
Gray, J. W.
1965
The meeting of the Midwest Category Seminar in Zurich August 24-30, 1970. Zbl 0222.18002
Gray, John W.
1971
Categorical aspects of data type constructors. Zbl 0629.68014
Gray, John W.
1987
The category of sketches as a model for algebraic semantics. Zbl 0688.68077
Gray, John W.
1989
Fragments of the history of sheaf theory. Zbl 0436.55002
Gray, John W.
1979
The existence and construction of lax limits. Zbl 0465.18003
Gray, John W.
1980
Category-valued sheaves. Zbl 0109.25202
Gray, J. W.
1962
The representation of limits, lax limits and homotopy limits as sections. Zbl 0541.18010
Gray, John W.
1984
Quasi-Kan extensions for 2-categories. Zbl 0358.18005
Gray, John W.
1974
Reports of the Midwest category seminar. V. Zbl 0222.18001
Gray, J. W. (ed.); MacLane, S. (ed.)
1971
Order-enriched sketches for typed lambda calculi. Zbl 0782.03004
Gray, John W.
1991
Executable specifications for data-type constructors. Zbl 0792.68101
Gray, John W.
1990
Intrinsic linear programming. Zbl 0594.90094
Gray, John W.
1985
Ascoli’s theorem for topological categories. Zbl 0498.18006
Gray, John W.
1982
Mathematical applications of category theory. (Proceedings of the Special Session on Mathematical Applications of Category Theory, 89th Annual Meeting of the American Mathematical Society, held in Denver, Colorado, January 5-9, 1983). Zbl 0534.00008
Gray, J. W. (ed.)
1984
Coherence for the tensor product of 2-categories, and braid groups. Zbl 0391.18007
Gray, John W.
1976
Extensions of sheaves of algebras. Zbl 0099.02402
Gray, John W.
1961
Order-enriched sketches for typed lambda calculi. Zbl 0782.03004
Gray, John W.
1991
Executable specifications for data-type constructors. Zbl 0792.68101
Gray, John W.
1990
The category of sketches as a model for algebraic semantics. Zbl 0688.68077
Gray, John W.
1989
Categorical aspects of data type constructors. Zbl 0629.68014
Gray, John W.
1987
Intrinsic linear programming. Zbl 0594.90094
Gray, John W.
1985
The representation of limits, lax limits and homotopy limits as sections. Zbl 0541.18010
Gray, John W.
1984
Mathematical applications of category theory. (Proceedings of the Special Session on Mathematical Applications of Category Theory, 89th Annual Meeting of the American Mathematical Society, held in Denver, Colorado, January 5-9, 1983). Zbl 0534.00008
Gray, J. W.
1984
Ascoli’s theorem for topological categories. Zbl 0498.18006
Gray, John W.
1982
Closed categories, lax limits and homotopy limits. Zbl 0462.55008
Gray, John W.
1980
The existence and construction of lax limits. Zbl 0465.18003
Gray, John W.
1980
Fragments of the history of sheaf theory. Zbl 0436.55002
Gray, John W.
1979
Coherence for the tensor product of 2-categories, and braid groups. Zbl 0391.18007
Gray, John W.
1976
Formal category theory: Adjointness for 2-categories. Zbl 0285.18006
Gray, John W.
1974
Quasi-Kan extensions for 2-categories. Zbl 0358.18005
Gray, John W.
1974
The meeting of the Midwest Category Seminar in Zurich August 24-30, 1970. Zbl 0222.18002
Gray, John W.
1971
Reports of the Midwest category seminar. V. Zbl 0222.18001
Gray, J. W.; MacLane, S.
1971
The categorical comprehension scheme. Zbl 0211.03403
Gray, John W.
1969
Fibred and cofibred categories. Zbl 0192.10701
Gray, J. W.
1966
Sheaves with values in a category. Zbl 0132.17605
Gray, J. W.
1965
Category-valued sheaves. Zbl 0109.25202
Gray, J. W.
1962
Extensions of sheaves of algebras. Zbl 0099.02402
Gray, John W.
1961
Some global properties of contact structures. Zbl 0092.39301
Gray, John W.
1959
all top 5
#### Cited by 361 Authors
7 Ehresmann, Andree Charles 7 Gray, John W. 7 Street, Ross H. 6 Banyaga, Augustin 6 Okumura, Masafumi 5 Cordier, Jean-Marc 5 Ehresmann, Charles 5 Eliashberg, Yakov Matveevich 4 Bourke, John 4 Bourn, Dominique 4 Geiges, Hansjörg 4 Guitart, René 4 Paré, Robert 4 Rosebrugh, Robert D. 4 Szyld, Martín 4 Tholen, Walter 3 Böhm, Gabriella 3 Boyer, Charles P. 3 Cegarra, Antonio Martínez 3 Goguen, Joseph Amadee 3 Gurski, Nick 3 Heggie, Murray 3 Lack, Stephen 3 Lindner, Harald 3 MacDonald, John L. 3 Osius, Gerhard 3 Spencer, Christopher B. 3 Thomason, Robert Wayne 3 Wang, Wei 3 Wolff, Harvey 2 Baškienė, Angele Leonovna 2 Brown, Ronald 2 Bullejos, Manuel 2 Cao, Huai-Dong 2 Carqueville, Nils 2 Chang, Shu-Cheng 2 Chen, Chih-Wei 2 Chinea, Domingo 2 Cigoli, Alan S. 2 Colin, Vincent 2 D’Ambra, Giuseppina 2 Datta, Mahuya 2 de la Llave, Rafael 2 Descotte, María Emilia 2 Dubuc, Eduardo J. 2 Elgueta, Josep 2 Epstein, Charles Lawrence 2 Gálvez-Carrillo, Imma 2 Gambino, Nicola 2 Garner, Richard 2 Ginzburg, Viktor L’vovich 2 Gonzalo Pérez, Jesús 2 Grandis, Marco 2 Hatakeyama, Yoji 2 Hilton, Peter John 2 Hurt, Norman E. 2 Ishihara, Shigeru 2 Jay, C. Barry 2 Johnson, Niles 2 Kamishima, Yoshinobu 2 Kapranov, Mikhail M. 2 Kelly, Gregory Maxwell 2 Kirichenko, Vadim Fëdorovich 2 Lee, John M. 2 Lutz, Robert 2 Mac Lane, Leslie Saunders 2 Maehara, Yuki 2 Makkai, Michael 2 Mantovani, Sandra 2 Marmolejo, Francisco 2 Massamba, Fortuné 2 Metere, Giuseppe 2 Miranda, Eva 2 Murfet, Daniel 2 Neumann, Frank 2 Osorno, Angélica Maria 2 Power, John 2 Prasma, Matan 2 Puhle, Christof 2 Schaumann, Gregor 2 Shulman, Michael A. 2 Tanaka, Kohei 2 Thomas, Charles Benedict 2 Tonks, Andrew 2 Tronci, Cesare 2 van den Bril, Luc 2 Vitale, Enrico Maria 2 Wayne, Clarence Eugene 2 Wischnewsky, Manfred Bernd 2 Yano, Kentaro 2 Yilmaz, Hülya Bagdatli 2 Zhitomirskii, Michail 1 Abe, Kinetsu 1 Adachi, Jiro 1 Ageron, Pierre 1 Alekseevskiĭ, Dmitriĭ Vladimirovich 1 Ardizzoni, Alessandro 1 Arnol’d, Vladimir Igorevich 1 Attarchi, Hassan 1 Baez, John C. ...and 261 more Authors
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https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/9%3A_Curves_in_the_Plane/9.1%3A_Conic_Sections
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# 9.1: Conic Sections
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The ancient Greeks recognized that interesting shapes can be formed by intersecting a plane with a double napped cone (i.e., two identical cones placed tip--to--tip as shown in the following figures). As these shapes are formed as sections of conics, they have earned the official name "conic sections.''
The three "most interesting'' conic sections are given in the top row of Figure $$\PageIndex{1}$$. They are the parabola, the ellipse (which includes circles) and the hyperbola. In each of these cases, the plane does not intersect the tips of the cones (usually taken to be the origin).
Figure $$\PageIndex{1}$$: Conic Sections
When the plane does contain the origin, three degenerate sections can be formed as shown the bottom row of Figure $$\PageIndex{1}$$: a point, a line, and crossed lines. We focus here on the nondegenerate cases.
While the above geometric constructs define the conics in an intuitive, visual way, these constructs are not very helpful when trying to analyze the shapes algebraically or consider them as the graph of a function. It can be shown that all conics can be defined by the general second--degree equation
$Ax^2+Bxy+Cy^2+Dx+Ey+F=0.$
While this algebraic definition has its uses, most find another geometric perspective of the conics more beneficial. Each nondegenerate conic can be defined as the locus, or set, of points that satisfy a certain distance property. These distance properties can be used to generate an algebraic formula, allowing us to study each conic as the graph of a function.
### Large Parabolas
Definition 40: parabolas
A parabola is the locus of all points equidistant from a point (called a focus) and a line (called the directrix) that does not contain the focus.
Figure $$\PageIndex{2}$$: Illustrating the definition of the parabola and establishing an algebraic formula.
Figure $$\PageIndex{1}$$ illustrates this definition. The point halfway between the focus and the directrix is the vertex. The line through the focus, perpendicular to the directrix, is the axis of symmetry, as the portion of the parabola on one side of this line is the mirror--image of the portion on the opposite side.
The definition leads us to an algebraic formula for the parabola. Let $$P=(x,y)$$ be a point on a parabola whose focus is at $$F=(0,p)$$ and whose directrix is at $$y=-p$$. (We'll assume for now that the focus lies on the $$y$$- axis; by placing the focus $$p$$ units above the $$x$$- axis and the directrix $$p$$ units below this axis, the vertex will be at $$(0,0)$$.)
We use the Distance Formula to find the distance $$d_1$$ between $$F$$ and $$P$$:
$d_1=\sqrt{(x-0)^2+(y-p)^2}.$
The distance $$d_2$$ from $$P$$ to the directrix is more straightforward:
$d_2=y-(-p) = y+p.$
These two distances are equal. Setting $$d_1=d_2$$, we can solve for $$y$$ in terms of $$x$$:
\begin{align*} d_1&= d_2 \\ \sqrt{x^2+(y-p)^2} &= y+p \\ \text{Now square both sides.}& \\ x^2+(y-p)^2 &= (y+p)^2 \\ x^2+y^2-2yp+p^2 &= y^2+2yp+p^2\\ x^2 &=4yp\\ y&= \frac{1}{4p}x^2. \end{align*}
The geometric definition of the parabola has led us to the familiar quadratic function whose graph is a parabola with vertex at the origin. When we allow the vertex to not be at $$(0,0)$$, we get the following standard form of the parabola.
key idea 33: general equation of a parabola
1. Vertical Axis of Symmetry: The equation of the parabola with vertex at $$(h,k)$$ and directrix $$y=k-p$$ in standard form is $y=\frac{1}{4p}(x-h)^2+k.$ The focus is at $$(h,k+p)$$.
2. Horizontal Axis of Symmetry: The equation of the parabola with vertex at $$(h,k)$$ and directrix $$x=h-p$$ in standard form is $x=\frac{1}{4p}(y-k)^2+h.$ The focus is at $$(h+p,k)$$.
Note: $$p$$ is not necessarily a positive number.
Example $$\PageIndex{1}$$: Finding the equation of a parabola
Give the equation of the parabola with focus at $$(1,2)$$ and directrix at $$y=3$$.
SOLUTION
The vertex is located halfway between the focus and directrix, so $$(h,k) = (1,2.5)$$. This gives $$p=-0.5$$. Using Key Idea 33 we have the equation of the parabola as
$y=\frac{1}{4(-0.5)}(x-1)^2+2.5 = -\frac12(x-1)^2+2.5.$
The parabola is sketched in Figure $$\PageIndex{3}$$.
Figure $$\PageIndex{3}$$: The parabola described in Example 9.1.1
Example $$\PageIndex{2}$$: Finding the focus and directrix of a parabola
Find the focus and directrix of the parabola $$x=\frac18y^2-y+1$$. The point $$(7,12)$$ lies on the graph of this parabola; verify that it is equidistant from the focus and directrix.
SOLUTION
We need to put the equation of the parabola in its general form. This requires us to complete the square:
\begin{align*} x &= \frac18y^2-y+1 \\ &= \frac18\big(y^2-8y+8\big)\\ &= \frac18\big(y^2-8y+16 -16+8\big)\\ &= \frac18\big((y-4)^2 - 8\big)\\ &= \frac18(y-4)^2 -1. \end{align*}
Hence the vertex is located at $$(-1,4)$$. We have $$\frac18=\frac1{4p}$$, so $$p=2$$. We conclude that the focus is located at $$(1,4)$$ and the directrix is $$x=-3$$. The parabola is graphed in Figure $$\PageIndex{4}$$, along with its focus and directrix.
The point $$(7,12)$$ lies on the graph and is $$7-(-3)=10$$ units from the directrix. The distance from $$(7,12)$$ to the focus is:
$\sqrt{(7-1)^2 + (12-4)^2} = \sqrt{100}=10.$
Indeed, the point on the parabola is equidistant from the focus and directrix.
Figure $$\PageIndex{4}$$: The parabola described in Example $$\PageIndex{2}$$. The distances from a point on the parabola to the focus and directrix is given.
### Reflective Property
One of the fascinating things about the nondegenerate conic sections is their reflective properties. Parabolas have the following reflective property:
Any ray emanating from the focus that intersects the parabola reflects off along a line perpendicular to the directrix.
This is illustrated in Figure $$\PageIndex{5}$$. The following theorem states this more rigorously.
Figure $$\PageIndex{5}$$: Illustrating the parabola's reflective property.
THEOREM 79: REFLECTIVE PROPERTY OF THE PARABOLA
Let $$P$$ be a point on a parabola. The tangent line to the parabola at $$P$$ makes equal angles with the following two lines:
1. The line containing $$P$$ and the focus $$F$$, and
2. The line perpendicular to the directrix through $$P$$.
Because of this reflective property, paraboloids (the 3D analogue of parabolas) make for useful flashlight reflectors as the light from the bulb, ideally located at the focus, is reflected along parallel rays. Satellite dishes also have paraboloid shapes. Signals coming from satellites effectively approach the dish along parallel rays. The dish then focuses these rays at the focus, where the sensor is located.
## Ellipses
Definition 41: ellipse
An ellipse is the locus of all points whose sum of distances from two fixed points, each a focus of the ellipse, is constant.
An easy way to visualize this construction of an ellipse is to pin both ends of a string to a board. The pins become the foci. Holding a pencil tight against the string places the pencil on the ellipse; the sum of distances from the pencil to the pins is constant: the length of the string. See Figure $$\PageIndex{6}$$.
Figure $$\PageIndex{6}$$: Illustrating the construction of an ellipse with pins, pencil and string.
We can again find an algebraic equation for an ellipse using this geometric definition. Let the foci be located along the $$x$$- axis, $$c$$ units from the origin. Let these foci be labeled as $$F_1 = (-c,0)$$ and $$F_2=(c,0)$$. Let $$P=(x,y)$$ be a point on the ellipse. The sum of distances from $$F_1$$ to $$P$$ ($$d_1$$) and from $$F_2$$ to $$P$$ ($$d_2$$) is a constant $$d$$. That is, $$d_1+d_2=d$$. Using the Distance Formula, we have
$\sqrt{(x+c)^2+y^2} + \sqrt{(x-c)^2+y^2} = d.$
Using a fair amount of algebra can produce the following equation of an ellipse (note that the equation is an implicitly defined function; it has to be, as an ellipse fails the Vertical Line Test):
$\frac{x^2}{\left(\frac d2\right)^2} + \frac{y^2}{\left(\frac d2\right)^2-c^2} = 1.$
This is not particularly illuminating, but by making the substitution $$a=d/2$$ and $$b=\sqrt{a^2-c^2}$$, we can rewrite the above equation as
$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$
This choice of $$a$$ and $$b$$ is not without reason; as shown in Figure $$\PageIndex{7}$$, the values of $$a$$ and $$b$$ have geometric meaning in the graph of the ellipse.
Figure $$\PageIndex{7}$$: Labeling the significant features of an ellipse.
In general, the two foci of an ellipse lie on the major axis of the ellipse, and the midpoint of the segment joining the two foci is the center. The major axis intersects the ellipse at two points, each of which is a vertex. The line segment through the center and perpendicular to the major axis is the minor axis. The "constant sum of distances'' that defines the ellipse is the length of the major axis, i.e., $$2a$$.
Allowing for the shifting of the ellipse gives the following standard equations.
key idea 34: standard equation of the ellipse
The equation of an ellipse centered at $$(h,k)$$ with major axis of length $$2a$$ and minor axis of length $$2b$$ in standard form is:
1. Horizontal major axis: $$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.$$
2. Vertical major axis: $$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1.$$
The foci lie along the major axis, $$c$$ units from the center, where $$c^2=a^2-b^2$$.
Example $$\PageIndex{3}$$: Finding the equation of an ellipse
Find the general equation of the ellipse graphed in Figure $$\PageIndex{8}$$.
Solution
The center is located at $$(-3,1)$$. The distance from the center to a vertex is 5 units, hence $$a=5$$. The minor axis seems to have length 4, so $$b=2$$. Thus the equation of the ellipse is
$\frac{(x+3)^2}{4}+\frac{(y-1)^2}{25} = 1.$
Figure $$\PageIndex{8}$$: The ellipse used in Example $$\PageIndex{3}$$.
Example $$\PageIndex{4}$$: Graphing an ellipse
Graph the ellipse defined by $$4x^2+9y^2-8x-36y=-4$$.
SOLUTION
It is simple to graph an ellipse once it is in standard form. In order to put the given equation in standard form, we must complete the square with both the $$x$$ and $$y$$ terms. We first rewrite the equation by regrouping:
$4x^2+9y^2-8x-36y=-4 \quad \Rightarrow \quad (4x^2-8x) + (9y^2-36y) = -4.$
Now we complete the squares.
\begin{align*} (4x^2-8x) + (9y^2-36y) &= -4\\ 4(x^2-2x) + 9(y^2-4y) &= -4 \\ 4(x^2-2x +1 - 1) + 9(y^2-4y+4-4) &= - 4\\ 4\big((x-1)^2-1\big) + 9\big((y-2)^2-4\big) &= -4\\ 4(x-1)^2 -4 + 9(y-2)^2-36 &= -4 \\ 4(x-1)^2 + 9(y-2)^2 &= 36 \\ \frac{(x-1)^2}{9} + \frac{(y-2)^2}{4} &= 1. \end{align*}
We see the center of the ellipse is at $$(1,2)$$. We have $$a=3$$ and $$b=2$$; the major axis is horizontal, so the vertices are located at $$(-2,2)$$ and $$(4,2)$$. We find $$c=\sqrt{9-4} = \sqrt{5}\approx 2.24.$$ The foci are located along the major axis, approximately $$2.24$$ units from the center, at $$(1\pm 2.24,2)$$. This is all graphed in Figure $$\PageIndex{9}$$.
Figure $$\PageIndex{9}$$: Graphing the ellipse in Example $$\PageIndex{4}$$.
### Eccentricity
When $$a=b$$, we have a circle. The general equation becomes
$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{a^2} = 1 \quad \Rightarrow (x-h)^2 + (y-k)^2 = a^2,$
the familiar equation of the circle centered at $$(h,k)$$ with radius $$a$$. Since $$a=b$$, $$c = \sqrt{a^2-b^2}=0$$. The circle has "two'' foci, but they lie on the same point, the center of the circle.
Consider Figure $$\PageIndex{1}$$, where several ellipses are graphed with $$a=1$$. In (a), we have $$c=0$$ and the ellipse is a circle. As $$c$$ grows, the resulting ellipses look less and less circular. A measure of this "noncircularness'' is eccentricity.
Figure $$\PageIndex{10}$$: Understanding the eccentricity of an ellipse.
Definition 42: eccentricity of an ellipse
The eccentricity $$e$$ of an ellipse is $$e=\frac{c}{a}$$.
The eccentricity of a circle is 0; that is, a circle has no "noncircularness.'' As $$c$$ approaches $$a$$, $$e$$ approaches 1, giving rise to a very noncircular ellipse, as seen in Figure $$\PageIndex{10d}$$.
It was long assumed that planets had circular orbits. This is known to be incorrect; the orbits are elliptical. Earth has an eccentricity of $$0.0167$$ -- it has a nearly circular orbit. Mercury's orbit is the most eccentric, with $$e=0.2056$$. (Pluto's eccentricity is greater, at $$e=0.248$$, the greatest of all the currently known dwarf planets.) The planet with the most circular orbit is Venus, with $$e=0.0068$$. The Earth's moon has an eccentricity of $$e=0.0549$$, also very circular.
### Reflective Property
The ellipse also possesses an interesting reflective property. Any ray emanating from one focus of an ellipse reflects off the ellipse along a line through the other focus, as illustrated in Figure $$\PageIndex{11}$$. This property is given formally in the following theorem.
Figure $$\PageIndex{11}$$: Illustrating the reflective property of an ellipse.
theorem 80: reflective property of an ellipse
Let $$P$$ be a point on a ellipse with foci $$F_1$$ and $$F_2$$. The tangent line to the ellipse at $$P$$ makes equal angles with the following two lines:
1. The line through $$F_1$$ and $$P$$, and
2. The line through $$F_2$$ and $$P$$.
This reflective property is useful in optics and is the basis of the phenomena experienced in whispering halls.
### Hyperbolas
The definition of a hyperbola is very similar to the definition of an ellipse; we essentially just change the word "sum'' to "difference.''
Definition 43: hyperbola
A hyperbola is the locus of all points where the absolute value of difference of distances from two fixed points, each a focus of the hyperbola, is constant.
We do not have a convenient way of visualizing the construction of a hyperbola as we did for the ellipse. The geometric definition does allow us to find an algebraic expression that describes it. It will be useful to define some terms first.
The two foci lie on the transverse axis of the hyperbola; the midpoint of the line segment joining the foci is the center of the hyperbola. The transverse axis intersects the hyperbola at two points, each a vertex of the hyperbola. The line through the center and perpendicular to the transverse axis is the conjugate axis. This is illustrated in Figure $$\PageIndex{1}$$. It is easy to show that the constant difference of distances used in the definition of the hyperbola is the distance between the vertices, i.e., $$2a$$.
Figure $$\PageIndex{12}$$: Labeling the significant features of a hyperbola.
key idea 35 standard equation of a hyperbola
The equation of a hyperbola centered at $$(h,k)$$ in standard form is:
1. Horizontal Transverse Axis: $$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1.$$
2. Vertical Transverse Axis: $$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2} = 1.$$
The vertices are located $$a$$ units from the center and the foci are located $$c$$ units from the center, where $$c^2 = a^2+b^2$$.
### Graphing Hyperbolas
Consider the hyperbola $$\frac{x^2}9-\frac{y^2}1 = 1$$. Solving for $$y$$, we find $$y=\pm\sqrt{x^2/9-1}$$. As $$x$$ grows large, the "$$- 1$$'' part of the equation for $$y$$ becomes less significant and $$y\approx \pm\sqrt{x^2/9} = \pm x/3$$. That is, as $$x$$ gets large, the graph of the hyperbola looks very much like the lines $$y=\pm x/3$$. These lines are asymptotes of the hyperbola, as shown in Figure $$\PageIndex{13}$$.
Figure $$\PageIndex{13}$$: Graphing the hyperbola $$\frac{x^2}9-\frac{y^2}1 = 1$$ along with its asymptotes, $$y=\pm x/3$$.
This is a valuable tool in sketching. Given the equation of a hyperbola in general form, draw a rectangle centered at $$(h,k)$$ with sides of length $$2a$$ parallel to the transverse axis and sides of length $$2b$$ parallel to the conjugate axis. (See Figure $$\PageIndex{14}$$ for an example with a horizontal transverse axis.) The diagonals of the rectangle lie on the asymptotes.
Figure $$\PageIndex{14}$$:
Using the asymptotes of a hyperbola as a graphing aid.
These lines pass through $$(h,k)$$. When the transverse axis is horizontal, the slopes are $$\pm b/a$$; when the transverse axis is vertical, their slopes are $$\pm a/b$$. This gives equations:
Example $$\PageIndex{5}$$: Graphing a hyperbola
Sketch the hyperbola given by $$\frac{(y-2)^2}{25}-\frac{(x-1)^2}{4}=1.$$
Solution
The hyperbola is centered at $$(1,2)$$; $$a=5$$ and $$b=2$$. In Figure $$\PageIndex{15}$$ we draw the prescribed rectangle centered at $$(1,2)$$ along with the asymptotes defined by its diagonals. The hyperbola has a vertical transverse axis, so the vertices are located at $$(1,7)$$ and $$(1,-3)$$. This is enough to make a good sketch.
Figure $$\PageIndex{15}$$: Graphing the hyperbola in Example $$\PageIndex{5}$$.
We also find the location of the foci: as $$c^2= a^2+b^2$$, we have $$c=\sqrt{29}\approx 5.4$$. Thus the foci are located at $$(1,2\pm 5.4)$$ as shown in Figure $$\PageIndex{15}$$.
Example $$\PageIndex{6}$$: Graphing a hyperbola
Sketch the hyperbola given by $$9x^2-y^2+2y=10.$$
Solution
We must complete the square to put the equation in general form. (We recognize this as a hyperbola since it is a general quadratic equation and the $$x^2$$ and $$y^2$$ terms have opposite signs.)
\begin{align*} 9x^2-y^2+2y &=10\\ 9x^2- (y^2-2y) &= 10\\ 9x^2 - (y^2-2y+1-1) &= 10\\ 9x^2 -\big((y-1)^2-1\big) &= 10\\ 9x^2 - (y-1)^2 &= 9\\ x^2 - \frac{(y-1)^2}{9} &=1 \end{align*}
Figure $$\PageIndex{16}$$: Graphing the hyperbola in Example $$\PageIndex{6}$$.
We see the hyperbola is centered at $$(0,1)$$, with a horizontal transverse axis, where $$a=1$$ and $$b=3$$. The appropriate rectangle is sketched in Figure $$\PageIndex{16}$$ along with the asymptotes of the hyperbola. The vertices are located at $$(\pm 1,1)$$. We have $$c=\sqrt{10}\approx 3.2$$, so the foci are located at $$(\pm 3.2,1)$$ as shown in the figure.
### Eccentricity
Definition 44: ECCENTRICITY OF A HYPERBOLA
The eccentricity of a hyperbola is $$e=\frac ca$$.
Note that this is the definition of eccentricity as used for the ellipse. When $$c$$ is close in value to $$a$$ (i.e., $$e\approx 1$$), the hyperbola is very narrow (looking almost like crossed lines). Figure $$\PageIndex{17}$$ shows hyperbolas centered at the origin with $$a=1$$. The graph in (a) has $$c=1.05$$, giving an eccentricity of $$e=1.05$$, which is close to 1. As $$c$$ grows larger, the hyperbola widens and begins to look like parallel lines, as shown in Figure $$\PageIndex{17d}$$.
Figure $$\PageIndex{17}$$: Understanding the eccentricity of a hyperbola.
### Reflective Property
Hyperbolas share a similar reflective property with ellipses. However, in the case of a hyperbola, a ray emanating from a focus that intersects the hyperbola reflects along a line containing the other focus, but moving away from that focus. This is illustrated in Figure $$\PageIndex{19}$$. Hyperbolic mirrors are commonly used in telescopes because of this reflective property. It is stated formally in the following theorem.
THEOREM 81: REFLECTIVE PROPERTY OF HYPERBOLAS
Let $$P$$ be a point on a hyperbola with foci $$F_1$$ and $$F_2$$. The tangent line to the hyperbola at $$P$$ makes equal angles with the following two lines:
1. The line through $$F_1$$ and $$P$$, and
2. The line through $$F_2$$ and $$P$$.
### Location Determination
Determining the location of a known event has many practical uses (locating the epicenter of an earthquake, an airplane crash site, the position of the person speaking in a large room, etc.).
To determine the location of an earthquake's epicenter, seismologists use trilateration (not to be confused with triangulation). A seismograph allows one to determine how far away the epicenter was; using three separate readings, the location of the epicenter can be approximated.
A key to this method is knowing distances. What if this information is not available? Consider three microphones at positions $$A$$, $$B$$ and $$C$$ which all record a noise (a person's voice, an explosion, etc.) created at unknown location $$D$$. The microphone does not "know'' when the sound was created, only when the sound was detected. How can the location be determined in such a situation?
Figure $$\PageIndex{19}$$: Illustrating the reflective property of a hyperbola.
If each location has a clock set to the same time, hyperbolas can be used to determine the location. Suppose the microphone at position $$A$$ records the sound at exactly 12:00, location $$B$$ records the time exactly 1 second later, and location $$C$$ records the noise exactly 2 seconds after that. We are interested in the difference of times. Since the speed of sound is approximately 340 m/s, we can conclude quickly that the sound was created 340 meters closer to position $$A$$ than position $$B$$. If $$A$$ and $$B$$ are a known distance apart (as shown in Figure $$\PageIndex{1a}$$), then we can determine a hyperbola on which $$D$$ must lie.
The "difference of distances'' is 340; this is also the distance between vertices of the hyperbola. So we know $$2a= 340$$. Positions $$A$$ and $$B$$ lie on the foci, so $$2c=1000$$. From this we can find $$b\approx 470$$ and can sketch the hyperbola, given in Figure $$\PageIndex{19b}$$. We only care about the side closest to $$A$$. (Why?)
We can also find the hyperbola defined by positions $$B$$ and $$C$$. In this case, $$2a = 680$$ as the sound traveled an extra 2 seconds to get to $$C$$. We still have $$2c=1000$$, centering this hyperbola at $$(-500,500)$$. We find $$b\approx 367$$. This hyperbola is sketched in Figure $$\PageIndex{1c}$$. The intersection point of the two graphs is the location of the sound, at approximately $$(188,-222.5)$$.
Figure $$\PageIndex{18}$$: Using hyperbolas in location detection.
This chapter explores curves in the plane, in particular curves that cannot be described by functions of the form $$y=f(x)$$. In this section, we learned of ellipses and hyperbolas that are defined implicitly, not explicitly. In the following sections, we will learn completely new ways of describing curves in the plane, using parametric equations and polar coordinates, then study these curves using calculus techniques.
## Contributors
• Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/
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Author ID: whitehead.john-henry-constantine Published as: Whitehead, J. H. C. External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 133 Publications since 1930, including 3 Books Biographic References: 5 Publications Co-Authors: 14 Co-Authors with 31 Joint Publications 240 Co-Co-Authors
all top 5
### Co-Authors
102 single-authored 6 Spanier, Edwin Henry 5 James, Ioan Mackenzie 4 Newman, Maxwell Herman Alexander 4 Veblen, Oswald 3 Barratt, M. G. 3 Lefschetz, Solomon 1 Chang, Sucheng 1 Hilton, Peter John 1 Mac Lane, Leslie Saunders 1 Milnor, John Willard 1 Penrose, Roger 1 Shapiro, Arnold S. 1 Steenrod, Norman Earl 1 Whitehead, Barbara 1 Williams, B. V. 1 Zeeman, Erik Christopher
all top 5
### Serials
29 Annals of Mathematics. Second Series 21 The Quarterly Journal of Mathematics. Oxford Series 9 Proceedings of the London Mathematical Society. Third Series 9 Proceedings of the National Academy of Sciences of the United States of America 9 Bulletin of the American Mathematical Society 8 Journal of the London Mathematical Society 7 Proceedings of the London Mathematical Society. Second Series 5 The Quarterly Journal of Mathematics. Oxford Second Series 4 Transactions of the American Mathematical Society 4 Proceedings of the Cambridge Philosophical Society 2 Commentarii Mathematici Helvetici 2 Fundamenta Mathematicae 2 Mathematische Zeitschrift 2 Bollettino della Unione Matematica Italiana. Series III 2 Cambridge Tracts in Mathematics and Mathematical Physics 1 The Mathematical Gazette 1 American Journal of Mathematics 1 Colloquium Mathematicum 1 Mathematika 1 Michigan Mathematical Journal 1 Annales de la Société Polonaise de Mathématique 1 Princeton Mathematical Series
all top 5
### Fields
6 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX)
### Citations contained in zbMATH Open
96 Publications have been cited 1,983 times in 1,503 Documents Cited by Year
Combinatorial homotopy. II. Zbl 0040.38801
1949
Combinatorial homotopy. I. Zbl 0040.38704
1949
A certain exact sequence. Zbl 0037.26101
1950
Simplicial spaces, nuclei and m-groups. Zbl 0022.40702
1939
On adding relations to homotopy groups. Zbl 0027.26404
1941
On equivalent sets of elements in a free group. Zbl 0015.24804
1936
On the 3-type of a complex. Zbl 0035.39001
MacLane, Saunders; Whitehead, J. H. C.
1950
On $$C^1$$-complexes. Zbl 0025.09203
1940
Simple homotopy types. Zbl 0040.38901
1950
On certain sets of elements in a free group. Zbl 0013.24801
1936
The homotopy theory of sphere bundles over spheres. I. Zbl 0056.16703
James, I. M.; Whitehead, J. H. C.
1954
On simply connected, 4-dimensional polyhedra. Zbl 0036.12704
1949
Manifolds with transverse fields in euclidean space. Zbl 0096.37802
1961
Note on a previous paper entitled ’On adding relations to homotopy groups’. Zbl 0060.41104
1946
Convex regions in the geometry of paths. Zbl 0004.13102
1932
The foundations of differential geometry. Zbl 0005.21801
Veblen, Oswald; Whitehead, J. H. C.
1932
On the covering of a complete space by the geodesics though a point. Zbl 0012.27802
1935
Simplicial spaces, nuclei and $$m$$-groups. JFM 65.1443.01
1939
A certain open manifold whose group is unity. Zbl 0013.08103
1935
On $$C^1$$-complexes. JFM 66.0955.03
1940
An expression of Hopf’s invariant as an integral. Zbl 0030.07902
1947
The homotopy theory of sphere bundles over spheres. II. Zbl 0067.15901
James, I. M.; Whitehead, J. H. C.
1955
On the asphericity of regions in a 3-sphere. Zbl 0021.16203
1939
Note on a theorem due to Borsuk. Zbl 0041.31901
1948
Duality in homotopy theory. Zbl 0064.17202
Spanier, Edwin H.; Whitehead, J. H. C.
1955
A proof and extension of Dehn’s lemma. Zbl 0084.19104
Shapiro, Arnold; Whitehead, J. H. C.
1958
The representation of projective spaces. Zbl 0002.15201
1931
Imbedding of manifolds in Euclidean space. Zbl 0113.38101
Penrose, Roger; Whitehead, J. H. C.; Zeeman, E. C.
1961
On operators in relative homotopy groups. Zbl 0041.10102
1948
On incidence matrices, nuclei and homotopy types. Zbl 0063.08227
1941
On the homotopy type of ANR’s. Zbl 0041.31902
1948
On 2-spheres in 3-manifolds. Zbl 0084.19103
1958
A certain open manifold whose group is unity. JFM 61.0607.01
1935
On doubled knots. Zbl 0016.04402
1937
On certain theorems of G. W. Whitehead. Zbl 0052.19203
1953
On equivalent sets of elements in a free group. JFM 62.1093.04
1936
On the groups $$\pi_r(V_n,V_m)$$ and sphere bundles. Zbl 0060.41413
1944
On certain sets of elements in a free group. JFM 62.0079.04
1936
The immersion of an open 3-manifold in euclidean 3-space. Zbl 0105.17203
1961
On fibre spaces in which the fibre is contractible. Zbl 0064.41601
Spanier, Edwin H.; Whitehead, J. H. C.
1955
On analytical complexes. Zbl 0006.37006
Lefschetz, Solomon; Whitehead, J. H. C.
1933
On finite cocycles and the sphere theorem. Zbl 0119.38605
1958
Note on the Whitehead product. Zbl 0052.19204
Hilton, Peter J.; Whitehead, J. H. C.
1953
Vector fields on the $$n$$-sphere. Zbl 0054.07104
Steenrod, N. E.; Whitehead, J. H. C.
1951
On a class of projectively flat affine connections. Zbl 0001.16502
1931
On the group of a certain linkage. Zbl 0016.27804
Newman, M. H. A.; Whitehead, J. H. C.
1937
On the realizability of homotopy groups. Zbl 0037.39601
1949
On the theory of obstructions. Zbl 0043.38401
1951
A set of axioms for differential geometry. Zbl 0003.13002
Veblen, O.; Whitehead, J. H. C.
1931
A certain region in Euclidean 3-space. Zbl 0012.03604
1935
On the homotopy type of manifolds. Zbl 0025.09304
1940
A first approximation to homotopy theory. Zbl 0051.14001
Spanier, Edwin H.; Whitehead, J. H. C.
1953
The first non-vanishing group of an (n + 1)-ad. Zbl 0072.18002
Barratt, M. G.; Whitehead, J. H. C.
1956
Duality in relative homotopy theory. Zbl 0092.15701
Spanier, Edwin H.; Whitehead, J. H. C.
1958
On adding relations to homotopy groups. JFM 67.0738.04
1941
Convex regions in the geometry of paths. Addendum. Zbl 0007.36801
1933
The theory of carriers and $$S$$-theory. Zbl 0084.38901
Spanier, Edwin H.; Whitehead, J. H. C.
1957
The $$G$$-dual of a semi-exact couple. Zbl 0052.39801
1953
Note on fibre spaces. Zbl 0056.16702
James, I. M.; Whitehead, J. H. C.
1954
Convex regions in the geometry of paths, addendum. JFM 59.1349.02
1933
A method of obtaining normal representations for projective connection. JFM 56.0625.02
1930
On subdivisions of complexes. Zbl 0011.03603
1935
Obstructions to compression. Zbl 0066.17001
Spanier, Edwin H.; Whitehead, J. H. C.
1955
On the decomposition of an infinitesimal group. JFM 62.0443.05
1936
On the covering of a complete space by geodesics through a point. JFM 61.0788.01
1935
The representation of projective spaces. JFM 57.0909.02
1931
The mathematical works. Edited by I. M. James. Vol I: Differential geometry. With a biographical note by M. H. A. Newman and Barbara Whitehead and a mathematical appreciation by John W. Milnor. Vol. II: Complexes and manifolds. Vol. III: Homotopy theory. Vol. IV: Algebraic and classical topology. Zbl 0108.24101
1962
On the asphericity of regions in a 3-sphere. JFM 65.1442.01
1939
On subdivisions of complexes. JFM 61.0606.01
1935
On linear connections. Zbl 0001.16703
1931
Certain theorems about three-dimensional manifolds. I. Zbl 0010.27504
1934
On the decomposition of an infinitesimal group. Zbl 0014.34701
1936
Certain equations in the algebra of a semi-simple infinitesimal group. Zbl 0017.20002
1937
Note on manifolds. Zbl 0027.09404
1941
On group extensions with operators. Zbl 0037.26002
1950
The homotopy type of a special kind of polyhedron. Zbl 0041.10103
1949
Note on manifolds. JFM 67.0742.02
1941
Certain theorems about three-dimensional manifolds. I. JFM 60.0516.02
1934
Convex regions in the geometry of paths. JFM 58.0763.02
1932
Homology with zero coefficients. Zbl 0086.16002
James, I. M.; Whitehead, J. H. C.
1958
The Weierstrass E-function in differential metric geometry. Zbl 0008.18003
1933
Three- dimensional manifolds (Corrigendum). Zbl 0011.17803
1935
The secondary boundary operator. Zbl 0035.38903
1950
Algebraic homotopy theory. Zbl 0049.24103
1952
On involutions of spheres. Zbl 0080.16101
1957
On the groupe of a certain linkage. JFM 63.0552.04
Newman, M. H. A.; Whitehead, J. H. C.
1937
Certain equations in the algebra of a semisimple infinitesimal group. JFM 63.1001.01
1937
Tree-dimensional manifolds (Corrigendum). JFM 61.0608.01
1935
The foundations of differential geometry. JFM 58.0754.01
Veblen, Oswald; Whitehead, J. H. C.
1932
A set of axioms for differential geometry. JFM 57.0861.01
Veblen, O.; Whitehead, J. H. C.
1931
On linear connections. JFM 57.0908.02
1931
A theorem on linear connections. JFM 56.0629.02
Whitehead, J. H. C.; Williams, B. V.
1930
Note on suspension. Zbl 0035.24802
1950
On the exact couple of a $$CW$$-triad. Zbl 0065.16202
Barratt, M. G.; Whitehead, J. H. C.
1955
Duality in topology. Zbl 0073.39705
1956
Note on the condition $$n$$-colc. Zbl 0077.16403
1957
The mathematical works. Edited by I. M. James. Vol I: Differential geometry. With a biographical note by M. H. A. Newman and Barbara Whitehead and a mathematical appreciation by John W. Milnor. Vol. II: Complexes and manifolds. Vol. III: Homotopy theory. Vol. IV: Algebraic and classical topology. Zbl 0108.24101
1962
Manifolds with transverse fields in euclidean space. Zbl 0096.37802
1961
Imbedding of manifolds in Euclidean space. Zbl 0113.38101
Penrose, Roger; Whitehead, J. H. C.; Zeeman, E. C.
1961
The immersion of an open 3-manifold in euclidean 3-space. Zbl 0105.17203
1961
A proof and extension of Dehn’s lemma. Zbl 0084.19104
Shapiro, Arnold; Whitehead, J. H. C.
1958
On 2-spheres in 3-manifolds. Zbl 0084.19103
1958
On finite cocycles and the sphere theorem. Zbl 0119.38605
1958
Duality in relative homotopy theory. Zbl 0092.15701
Spanier, Edwin H.; Whitehead, J. H. C.
1958
Homology with zero coefficients. Zbl 0086.16002
James, I. M.; Whitehead, J. H. C.
1958
The theory of carriers and $$S$$-theory. Zbl 0084.38901
Spanier, Edwin H.; Whitehead, J. H. C.
1957
On involutions of spheres. Zbl 0080.16101
1957
Note on the condition $$n$$-colc. Zbl 0077.16403
1957
The first non-vanishing group of an (n + 1)-ad. Zbl 0072.18002
Barratt, M. G.; Whitehead, J. H. C.
1956
Duality in topology. Zbl 0073.39705
1956
The homotopy theory of sphere bundles over spheres. II. Zbl 0067.15901
James, I. M.; Whitehead, J. H. C.
1955
Duality in homotopy theory. Zbl 0064.17202
Spanier, Edwin H.; Whitehead, J. H. C.
1955
On fibre spaces in which the fibre is contractible. Zbl 0064.41601
Spanier, Edwin H.; Whitehead, J. H. C.
1955
Obstructions to compression. Zbl 0066.17001
Spanier, Edwin H.; Whitehead, J. H. C.
1955
On the exact couple of a $$CW$$-triad. Zbl 0065.16202
Barratt, M. G.; Whitehead, J. H. C.
1955
The homotopy theory of sphere bundles over spheres. I. Zbl 0056.16703
James, I. M.; Whitehead, J. H. C.
1954
Note on fibre spaces. Zbl 0056.16702
James, I. M.; Whitehead, J. H. C.
1954
On certain theorems of G. W. Whitehead. Zbl 0052.19203
1953
Note on the Whitehead product. Zbl 0052.19204
Hilton, Peter J.; Whitehead, J. H. C.
1953
A first approximation to homotopy theory. Zbl 0051.14001
Spanier, Edwin H.; Whitehead, J. H. C.
1953
The $$G$$-dual of a semi-exact couple. Zbl 0052.39801
1953
Algebraic homotopy theory. Zbl 0049.24103
1952
Vector fields on the $$n$$-sphere. Zbl 0054.07104
Steenrod, N. E.; Whitehead, J. H. C.
1951
On the theory of obstructions. Zbl 0043.38401
1951
A certain exact sequence. Zbl 0037.26101
1950
On the 3-type of a complex. Zbl 0035.39001
MacLane, Saunders; Whitehead, J. H. C.
1950
Simple homotopy types. Zbl 0040.38901
1950
On group extensions with operators. Zbl 0037.26002
1950
The secondary boundary operator. Zbl 0035.38903
1950
Note on suspension. Zbl 0035.24802
1950
Combinatorial homotopy. II. Zbl 0040.38801
1949
Combinatorial homotopy. I. Zbl 0040.38704
1949
On simply connected, 4-dimensional polyhedra. Zbl 0036.12704
1949
On the realizability of homotopy groups. Zbl 0037.39601
1949
The homotopy type of a special kind of polyhedron. Zbl 0041.10103
1949
Note on a theorem due to Borsuk. Zbl 0041.31901
1948
On operators in relative homotopy groups. Zbl 0041.10102
1948
On the homotopy type of ANR’s. Zbl 0041.31902
1948
An expression of Hopf’s invariant as an integral. Zbl 0030.07902
1947
Note on a previous paper entitled ’On adding relations to homotopy groups’. Zbl 0060.41104
1946
On the groups $$\pi_r(V_n,V_m)$$ and sphere bundles. Zbl 0060.41413
1944
On adding relations to homotopy groups. Zbl 0027.26404
1941
On incidence matrices, nuclei and homotopy types. Zbl 0063.08227
1941
On adding relations to homotopy groups. JFM 67.0738.04
1941
Note on manifolds. Zbl 0027.09404
1941
Note on manifolds. JFM 67.0742.02
1941
On $$C^1$$-complexes. Zbl 0025.09203
1940
On $$C^1$$-complexes. JFM 66.0955.03
1940
On the homotopy type of manifolds. Zbl 0025.09304
1940
Simplicial spaces, nuclei and m-groups. Zbl 0022.40702
1939
Simplicial spaces, nuclei and $$m$$-groups. JFM 65.1443.01
1939
On the asphericity of regions in a 3-sphere. Zbl 0021.16203
1939
On the asphericity of regions in a 3-sphere. JFM 65.1442.01
1939
On doubled knots. Zbl 0016.04402
1937
On the group of a certain linkage. Zbl 0016.27804
Newman, M. H. A.; Whitehead, J. H. C.
1937
Certain equations in the algebra of a semi-simple infinitesimal group. Zbl 0017.20002
1937
On the groupe of a certain linkage. JFM 63.0552.04
Newman, M. H. A.; Whitehead, J. H. C.
1937
Certain equations in the algebra of a semisimple infinitesimal group. JFM 63.1001.01
1937
On equivalent sets of elements in a free group. Zbl 0015.24804
1936
On certain sets of elements in a free group. Zbl 0013.24801
1936
On equivalent sets of elements in a free group. JFM 62.1093.04
1936
On certain sets of elements in a free group. JFM 62.0079.04
1936
On the decomposition of an infinitesimal group. JFM 62.0443.05
1936
On the decomposition of an infinitesimal group. Zbl 0014.34701
1936
On the covering of a complete space by the geodesics though a point. Zbl 0012.27802
1935
A certain open manifold whose group is unity. Zbl 0013.08103
1935
A certain open manifold whose group is unity. JFM 61.0607.01
1935
A certain region in Euclidean 3-space. Zbl 0012.03604
1935
On subdivisions of complexes. Zbl 0011.03603
1935
On the covering of a complete space by geodesics through a point. JFM 61.0788.01
1935
On subdivisions of complexes. JFM 61.0606.01
1935
Three- dimensional manifolds (Corrigendum). Zbl 0011.17803
1935
Tree-dimensional manifolds (Corrigendum). JFM 61.0608.01
1935
Certain theorems about three-dimensional manifolds. I. Zbl 0010.27504
1934
Certain theorems about three-dimensional manifolds. I. JFM 60.0516.02
1934
On analytical complexes. Zbl 0006.37006
Lefschetz, Solomon; Whitehead, J. H. C.
1933
Convex regions in the geometry of paths. Addendum. Zbl 0007.36801
1933
Convex regions in the geometry of paths, addendum. JFM 59.1349.02
1933
The Weierstrass E-function in differential metric geometry. Zbl 0008.18003
1933
Convex regions in the geometry of paths. Zbl 0004.13102
1932
The foundations of differential geometry. Zbl 0005.21801
Veblen, Oswald; Whitehead, J. H. C.
1932
Convex regions in the geometry of paths. JFM 58.0763.02
1932
The foundations of differential geometry. JFM 58.0754.01
Veblen, Oswald; Whitehead, J. H. C.
1932
The representation of projective spaces. Zbl 0002.15201
1931
On a class of projectively flat affine connections. Zbl 0001.16502
1931
A set of axioms for differential geometry. Zbl 0003.13002
Veblen, O.; Whitehead, J. H. C.
1931
The representation of projective spaces. JFM 57.0909.02
1931
On linear connections. Zbl 0001.16703
1931
A set of axioms for differential geometry. JFM 57.0861.01
Veblen, O.; Whitehead, J. H. C.
1931
On linear connections. JFM 57.0908.02
1931
A method of obtaining normal representations for projective connection. JFM 56.0625.02
1930
A theorem on linear connections. JFM 56.0629.02
Whitehead, J. H. C.; Williams, B. V.
1930
all top 5
### Cited by 1,512 Authors
18 Brown, Ronald 16 Baues, Hans-Joachim 14 Ellis, Graham J. 14 Ladra González, Manuel 12 Cegarra, Antonio Martínez 10 Şahan, Tunçar 9 Huebschmann, Johannes 9 Mucuk, Osman 9 Ulualan, Erdal 8 Adiprasito, Karim Alexander 8 Benedetti, Bruno 8 Benkhalifa, Mahmoud 8 Casas Miras, José Manuel 8 Gilbert, Nick D. 8 Niroomand, Peyman 8 Repovš, Dušan D. 7 Cárdenas, Manuel 7 Gluck, Herman 7 Higgins, Philip John 7 McMillan, D. R. jun. 7 Michal, Aristotle Demetrius 7 Mikhaĭlov, Roman Valer’evich 7 Minian, Elias Gabriel 7 Ventura Capell, Enric 6 Alp, Murat 6 Conduché, Daniel 6 Datuashvili, Tamar 6 Davvaz, Bijan 6 Hegenbarth, Friedrich 6 Hilton, Peter John 6 Lasheras, Francisco F. 6 Mac Lane, Leslie Saunders 6 Miyazaki, Hiroshi 6 Porter, Timothy 6 Quintero, Antonio 6 R-Grandjeán, Alfredo 6 Temel, Sedat 6 Yamaguchi, Kohhei 5 Baumslag, Gilbert 5 Bertrand, Gilles 5 Bortolotti, Enea 5 Cavicchioli, Alberto 5 Couprie, Michel 5 Curtis, Morton L. 5 Emir, Kadir 5 Goldstein, Richard Z. 5 Gordon, Cameron McA. 5 Hambleton, Ian 5 Hirsch, Morris W. 5 Hlavatý, Václav 5 Inassaridze, Nikoloz 5 Ishimoto, Hiroyasu 5 Ivanov, Sergei Vladimirovich 5 James, Ioan Mackenzie 5 Khmaladze, Emzar 5 Laudenbach, François 5 Lee, Donghi 5 Mikhalëv, Aleksandr Aleksandrovich 5 Milnor, John Willard 5 Muro, Fernando 5 Rosenberger, Gerhard 5 Saunders, David J. 5 Spaggiari, Fulvia 5 Suciu, Alexander I. 5 Whitehead, John Henry Constantine 5 Wu, Jie 5 Zieschang, Heiner 4 Arlettaz, Dominique 4 Avcioǧlu, Osman 4 Bass, Hyman 4 Blanc, David Abraham 4 Boissonnat, Jean-Daniel 4 Bullejos, Manuel 4 Collins, Donald J. 4 Donadze, Guram 4 Dyer, Michael N. 4 Fritsch, Rudolf 4 Garzón, Antonio R. 4 Gersten, Stephen M. 4 Golasiński, Marek 4 Gutierrez, Mauricio A. 4 Heller, Alex 4 Howie, James 4 Hsin, Po-Shen 4 Husch, Laurence S. 4 Hyers, Donald H. 4 Javaloyes, Miguel Angel 4 Kapovich, Ilya 4 Kim, Inkang 4 Kołodziejczyk, Danuta 4 Luft, Erhard 4 Odabaş, Alper 4 Pamuk, Mehmetcik 4 Paoli, Simona 4 Pirashvili, Teimuraz 4 Poénaru, Valentin 4 Siegmund Puppe, Dieter 4 Ratcliffe, John G. 4 Saeedi, Farshid 4 Sánchez Caja, Miguel ...and 1,412 more Authors
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### Cited in 273 Serials
102 Transactions of the American Mathematical Society 85 Topology and its Applications 79 Proceedings of the American Mathematical Society 77 Journal of Pure and Applied Algebra 73 Bulletin of the American Mathematical Society 49 Mathematische Zeitschrift 43 Journal of Algebra 43 Mathematische Annalen 27 Advances in Mathematics 26 Communications in Algebra 26 Archiv der Mathematik 22 Inventiones Mathematicae 22 Algebraic & Geometric Topology 21 Mathematical Proceedings of the Cambridge Philosophical Society 21 Tohoku Mathematical Journal. Second Series 18 Proceedings of the Japan Academy 17 Geometry & Topology 16 Compositio Mathematica 14 Applied Categorical Structures 13 Annali di Matematica Pura ed Applicata. Serie Quarta 12 Journal of Geometry and Physics 12 Cahiers de Topologie et Géométrie Différentielle Catégoriques 12 Kodai Mathematical Journal 12 Manuscripta Mathematica 12 International Journal of Mathematics 12 Journal of Homotopy and Related Structures 11 Geometriae Dedicata 11 Journal of Mathematical Sciences (New York) 10 Journal of Mathematical Physics 10 Publications Mathématiques 10 International Journal of Algebra and Computation 10 Differential Geometry and its Applications 9 Communications in Mathematical Physics 9 Israel Journal of Mathematics 9 Bulletin de la Société Mathématique de France 9 Bulletin of the American Mathematical Society. New Series 9 Journal of Group Theory 8 Annales de l’Institut Fourier 8 Glasgow Mathematical Journal 8 Journal of Soviet Mathematics 8 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Discrete & Computational Geometry 8 Journal of Knot Theory and its Ramifications 8 Journal of High Energy Physics 7 Proceedings of the Edinburgh Mathematical Society. Series II 6 Journal of Mathematical Analysis and Applications 6 Journal of Symbolic Computation 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 Hacettepe Journal of Mathematics and Statistics 6 Journal of Topology 6 Journal of Topology and Analysis 5 Letters in Mathematical Physics 5 Acta Mathematica 5 Duke Mathematical Journal 5 Nagoya Mathematical Journal 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Indagationes Mathematicae. New Series 5 Turkish Journal of Mathematics 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Journal of Algebra and its Applications 4 General Relativity and Gravitation 4 International Journal of Theoretical Physics 4 Arkiv för Matematik 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Journal of the Mathematical Society of Japan 4 Monatshefte für Mathematik 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Quaestiones Mathematicae 4 Annals of Global Analysis and Geometry 4 Journal of the American Mathematical Society 4 Forum Mathematicum 4 Journal of Mathematical Imaging and Vision 4 Georgian Mathematical Journal 4 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics 4 Kodai Mathematical Seminar Reports 4 Rendiconti del Circolo Matematico di Palermo 4 Asian-European Journal of Mathematics 4 Journal of $$K$$-Theory 3 Archive for Rational Mechanics and Analysis 3 Bulletin of the Australian Mathematical Society 3 Classical and Quantum Gravity 3 The Mathematical Intelligencer 3 Czechoslovak Mathematical Journal 3 Illinois Journal of Mathematics 3 Memoirs of the American Mathematical Society 3 Siberian Mathematical Journal 3 Synthese 3 Acta Mathematica Hungarica 3 Acta Applicandae Mathematicae 3 $$K$$-Theory 3 Aequationes Mathematicae 3 Linear Algebra and its Applications 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Applicable Algebra in Engineering, Communication and Computing 3 Calculus of Variations and Partial Differential Equations 3 Theory and Applications of Categories 3 LMS Journal of Computation and Mathematics 3 Acta Mathematica Sinica. English Series 3 Living Reviews in Relativity ...and 173 more Serials
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### Cited in 52 Fields
457 Manifolds and cell complexes (57-XX) 402 Algebraic topology (55-XX) 320 Group theory and generalizations (20-XX) 217 Category theory; homological algebra (18-XX) 145 Differential geometry (53-XX) 76 Global analysis, analysis on manifolds (58-XX) 73 General topology (54-XX) 56 Associative rings and algebras (16-XX) 50 Nonassociative rings and algebras (17-XX) 49 Combinatorics (05-XX) 35 $$K$$-theory (19-XX) 32 Algebraic geometry (14-XX) 32 Quantum theory (81-XX) 29 Dynamical systems and ergodic theory (37-XX) 29 Computer science (68-XX) 28 Several complex variables and analytic spaces (32-XX) 28 Relativity and gravitational theory (83-XX) 27 Topological groups, Lie groups (22-XX) 27 Convex and discrete geometry (52-XX) 24 History and biography (01-XX) 23 Functional analysis (46-XX) 16 Functions of a complex variable (30-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 13 Mathematical logic and foundations (03-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 11 General and overarching topics; collections (00-XX) 11 Commutative algebra (13-XX) 8 Geometry (51-XX) 8 Numerical analysis (65-XX) 7 Operator theory (47-XX) 7 Optics, electromagnetic theory (78-XX) 6 Number theory (11-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Partial differential equations (35-XX) 5 Real functions (26-XX) 5 Difference and functional equations (39-XX) 5 Fluid mechanics (76-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General algebraic systems (08-XX) 4 Field theory and polynomials (12-XX) 4 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Operations research, mathematical programming (90-XX) 2 Measure and integration (28-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Potential theory (31-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-07-05T06:19:31 |
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|
https://par.nsf.gov/biblio/10229888-intensive-disc-reverberation-mapping-fairall9-first-year-swiftand-lco-monitoring
|
Intensive disc-reverberation mapping of Fairall 9: first year of Swift and LCO monitoring
ABSTRACT We present results of time-series analysis of the first year of the Fairall 9 intensive disc-reverberation campaign. We used Swift and the Las Cumbres Observatory global telescope network to continuously monitor Fairall 9 from X-rays to near-infrared at a daily to subdaily cadence. The cross-correlation function between bands provides evidence for a lag spectrum consistent with the τ ∝ λ4/3 scaling expected for an optically thick, geometrically thin blackbody accretion disc. Decomposing the flux into constant and variable components, the variable component’s spectral energy distribution is slightly steeper than the standard accretion disc prediction. We find evidence at the Balmer edge in both the lag and flux spectra for an additional bound-free continuum contribution that may arise from reprocessing in the broad-line region. The inferred driving light curve suggests two distinct components, a rapidly variable (<4 d) component arising from X-ray reprocessing, and a more slowly varying (>100 d) component with an opposite lag to the reverberation signal.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10229888
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
498
Issue:
4
Page Range or eLocation-ID:
5399 to 5416
ISSN:
0035-8711
We report on daily monitoring of the Seyfert galaxy ngc 7469, around 95 and 143 GHz, with the iram (Institut de Radioastronomie Millimetrique) 30- m radio telescope, and with the Swift X-ray and UV/optical telescopes, over an overlapping period of 45 d. The source was observed on 36 d with iram, and the flux density in both mm bands was on average ∼10 mJy, but varied by $\pm 50{{\ \rm per\ cent}}$, and by up to a factor of 2 between days. The present iram variability parameters are consistent with earlier monitoring, which had only 18 data points. The X-ray light curve of ngc 7469 over the same period spans a factor of 5 in flux with small uncertainties. Similar variability in the mm band and in the X-rays lends support to the notion of both sources originating in the same physical component of the active galactic nucleus (AGN), likely the accretion disc corona. Simultaneous monitoring in eight UV/optical bands shows much less variability than the mm and X-rays, implying this light originates from a different AGN component, likely the accretion disc itself. We use a tentative 14-d lag of the X-ray light curve with respect to the 95 GHz light curve to speculate on coronal implications. Moremore »
| 2022-12-06T23:17:40 |
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https://itl.nist.gov/div898/handbook/apr/section2/apr24.htm
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8. Assessing Product Reliability
8.2. Assumptions/Prerequisites
## How do you choose an appropriate physical acceleration model?
Choosing a good acceleration model is part science and part art - but start with a good literature search
Choosing a physical acceleration model is a lot like choosing a life distribution model. First identify the failure mode and what stresses are relevant (i.e., will accelerate the failure mechanism). Then check to see if the literature contains examples of successful applications of a particular model for this mechanism.
If the literature offers little help, try the models described in earlier sections :
All but the last model (the Coffin-Manson) apply to chemical or electronic failure mechanisms, and since temperature is almost always a relevant stress for these mechanisms, the Arrhenius model is nearly always a part of any more general model. The Coffin-Manson model works well for many mechanical fatigue-related mechanisms.
Sometimes models have to be adjusted to include a threshold level for some stresses. In other words, failure might never occur due to a particular mechanism unless a particular stress (temperature, for example) is beyond a threshold value. A model for a temperature-dependent mechanism with a threshold at $$T = T_0$$ might look like $$\mbox{time to fail } = \frac{f(T)}{T - T_0} \, ,$$ for which $$f(T)$$ could be Arrhenius. As the temperature decreases towards $$T_0$$, time to fail increases toward infinity in this (deterministic) acceleration model.
Models derived theoretically have been very successful and are convincing In some cases, a mathematical/physical description of the failure mechanism can lead to an acceleration model. Some of the models above were originally derived that way.
Simple models are often the best In general, use the simplest model (fewest parameters) you can. When you have chosen a model, use visual tests and formal statistical fit tests to confirm the model is consistent with your data. Continue to use the model as long as it gives results that "work," but be quick to look for a new model when it is clear the old one is no longer adequate.
There are some good quotes that apply here:
Quotes from experts on models "All models are wrong, but some are useful." - George Box, and the principle of Occam's Razor (attributed to the 14th century logician William of Occam who said “Entities should not be multiplied unnecessarily” - or something equivalent to that in Latin).
A modern version of Occam's Razor is: If you have two theories that both explain the observed facts then you should use the simplest one until more evidence comes along - also called the Law of Parsimony
Finally, for those who feel the above quotes place too much emphasis on simplicity, there are several appropriate quotes from Albert Einstein:
"Make your theory as simple as possible, but no simpler."
"For every complex question there is a simple and wrong solution."
| 2019-07-18T02:31:50 |
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|
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/16%3A_Electromagnetic_Waves/16.E%3A_Electromagnetic_Waves_(Exercises)
|
$$\require{cancel}$$
# 16.E: Electromagnetic Waves (Exercises)
## Conceptual Questions
### 16.1 Maxwell’s Equations and Electromagnetic Waves
1. Explain how the displacement current maintains the continuity of current in a circuit containing a capacitor.
2. Describe the field lines of the induced magnetic field along the edge of the imaginary horizontal cylinder shown below if the cylinder is in a spatially uniform electric field that is horizontal, pointing to the right, and increasing in magnitude.
3. Why is it much easier to demonstrate in a student lab that a changing magnetic field induces an electric field than it is to demonstrate that a changing electric field produces a magnetic field?
### 16.2 Plane Electromagnetic Waves
4. If the electric field of an electromagnetic wave is oscillating along the z-axis and the magnetic field is oscillating along the x-axis, in what possible direction is the wave traveling?
5. In which situation shown below will the electromagnetic wave be more successful in inducing a current in the wire? Explain.
6. In which situation shown below will the electromagnetic wave be more successful in inducing a current in the loop? Explain.
7. Under what conditions might wires in a circuit where the current flows in only one direction emit electromagnetic waves?
8. Shown below is the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this be used to make a directional antenna system that broadcasts preferentially in certain directions? Explain.
### 16.3 Energy Carried by Electromagnetic Waves
9. When you stand outdoors in the sunlight, why can you feel the energy that the sunlight carries, but not the momentum it carries?
10. How does the intensity of an electromagnetic wave depend on its electric field? How does it depend on its magnetic field?
11. What is the physical significance of the Poynting vector?
12. A 2.0-mW helium-neon laser transmits a continuous beam of red light of cross-sectional area $$\displaystyle 0.25cm^2$$. If the beam does not diverge appreciably, how would its rms electric field vary with distance from the laser? Explain.
### 16.4 Momentum and Radiation Pressure
13. Why is the radiation pressure of an electromagnetic wave on a perfectly reflecting surface twice as large as the pressure on a perfectly absorbing surface?
14. Why did the early Hubble Telescope photos of Comet Ison approaching Earth show it to have merely a fuzzy coma around it, and not the pronounced double tail that developed later (see below)?
(credit: ESA, Hubble)
15. (a) If the electric field and magnetic field in a sinusoidal plane wave were interchanged, in which direction relative to before would the energy propagate?
(b) What if the electric and the magnetic fields were both changed to their negatives?
### 16.5 The Electromagnetic Spectrum
16. Compare the speed, wavelength, and frequency of radio waves and X-rays traveling in a vacuum.
17. Accelerating electric charge emits electromagnetic radiation. How does this apply in each case: (a) radio waves, (b) infrared radiation.
18. Compare and contrast the meaning of the prefix “micro” in the names of SI units in the term microwaves.
19. Part of the light passing through the air is scattered in all directions by the molecules comprising the atmosphere. The wavelengths of visible light are larger than molecular sizes, and the scattering is strongest for wavelengths of light closest to sizes of molecules.
(a) Which of the main colors of light is scattered the most?
(b) Explain why this would give the sky its familiar background color at midday.
20. When a bowl of soup is removed from a microwave oven, the soup is found to be steaming hot, whereas the bowl is only warm to the touch. Discuss the temperature changes that have occurred in terms of energy transfer.
21. Certain orientations of a broadcast television antenna give better reception than others for a particular station. Explain.
22. What property of light corresponds to loudness in sound?
23. Is the visible region a major portion of the electromagnetic spectrum?
24. Can the human body detect electromagnetic radiation that is outside the visible region of the spectrum?
25. Radio waves normally have their E and B fields in specific directions, whereas visible light usually has its E and fields in random and rapidly changing directions that are perpendicular to each other and to the propagation direction. Can you explain why?
26. Give an example of resonance in the reception of electromagnetic waves.
27. Illustrate that the size of details of an object that can be detected with electromagnetic waves is related to their wavelength, by comparing details observable with two different types (for example, radar and visible light).
28. In which part of the electromagnetic spectrum are each of these waves:
(a) $$\displaystyle f = 10.0 kHz$$,
(b) $$\displaystyle f=λ=750nm$$,
(c) $$\displaystyle f=1.25×10^8Hz$$,
(d) $$\displaystyle 0.30 nm$$
29. In what range of electromagnetic radiation are the electromagnetic waves emitted by power lines in a country that uses 50-Hz ac current?
30. If a microwave oven could be modified to merely tune the waves generated to be in the infrared range instead of using microwaves, how would this affect the uneven heating of the oven?
31. A leaky microwave oven in a home can sometimes cause interference with the homeowner’s WiFi system. Why?
32. When a television news anchor in a studio speaks to a reporter in a distant country, there is sometimes a noticeable lag between when the anchor speaks in the studio and when the remote reporter hears it and replies. Explain what causes this delay.
## Problems
### 16.1 Maxwell’s Equations and Electromagnetic Waves
33. Show that the magnetic field at a distance r from the axis of two circular parallel plates, produced by placing charge Q(t) on the plates is
$$\displaystyle B_{ind}=\frac{μ_0}{2πr}\frac{dQ(t)}{dt}$$
34. Express the displacement current in a capacitor in terms of the capacitance and the rate of change of the voltage across the capacitor.
35. A potential difference $$\displaystyle V(t)=V_0sinωt$$ is maintained across a parallel-plate capacitor with capacitance consisting of two circular parallel plates. A thin wire with resistance connects the centers of the two plates, allowing charge to leak between plates while they are charging.
(a) Obtain expressions for the leakage current $$\displaystyle I_{res}(t)$$ in the thin wire. Use these results to obtain an expression for the current $$\displaystyle I_{real}(t)$$ in the wires connected to the capacitor.
(b) Find the displacement current in the space between the plates from the changing electric field between the plates.
(c) Compare $$\displaystyle I_{real}(t)$$ with the sum of the displacement current $$\displaystyle I_d(t)$$ and resistor current $$\displaystyle I_{res}(t)$$ between the plates, and explain why the relationship you observe would be expected.
36. Suppose the parallel-plate capacitor shown below is accumulating charge at a rate of 0.010 C/s. What is the induced magnetic field at a distance of 10 cm from the capacitator?
37. The potential difference V(t) between parallel plates shown above is instantaneously increasing at a rate of $$\displaystyle 10^7V/s$$. What is the displacement current between the plates if the separation of the plates is 1.00 cm and they have an area of $$\displaystyle 0.200m^2$$?
38. A parallel-plate capacitor has a plate area of $$\displaystyle A=0.250m^2$$ and a separation of 0.0100 m. What must be must be the angular frequency $$\displaystyle ω$$ for a voltage $$\displaystyle V(t)=V_0sinωt$$ with $$\displaystyle V_0=100V$$ to produce a maximum displacement induced current of 1.00 A between the plates?
39. The voltage across a parallel-plate capacitor with area $$\displaystyle A=800cm^2$$ and separation $$\displaystyle d=2mm$$ varies sinusoidally as $$\displaystyle V=(15mV)cos(150t)$$, where t is in seconds. Find the displacement current between the plates.
40. The voltage across a parallel-plate capacitor with area A and separation d varies with time t as $$\displaystyle V=at^2$$, where $$\displaystyle a$$ is a constant. Find the displacement current between the plates.
### 16.2 Plane Electromagnetic Waves
41. If the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is $$\displaystyle 1.496×10^{11}m$$ away?
42. What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of $$\displaystyle 5.00×10^{−4}T$$ (about 10 times Earth’s magnetic field)?
43. An electromagnetic wave has a frequency of 12 MHz. What is its wavelength in vacuum?
44. If electric and magnetic field strengths vary sinusoidally in time at frequency 1.00 GHz, being zero at $$\displaystyle t=0$$, then $$\displaystyle E=E_0sin2πft$$ and $$\displaystyle B=B_0sin2πft$$.
(a) When are the field strengths next equal to zero?
(b) When do they reach their most negative value? (c) How much time is needed for them to complete one cycle?
45. The electric field of an electromagnetic wave traveling in vacuum is described by the following wave function:
$$\displaystyle \vec{E} =(5.00V/m)cos[kx−(6.00×10^9s^{−1})t+0.40]\hat{j}$$
where k is the wavenumber in rad/m, x is in m, t is in s.
Find the following quantities:
(a) amplitude
(b) frequency
(c) wavelength
(d) the direction of the travel of the wave
(e) the associated magnetic field wave
46. A plane electromagnetic wave of frequency 20 GHz moves in the positive y-axis direction such that its electric field is pointed along the z-axis. The amplitude of the electric field is 10 V/m. The start of time is chosen so that at $$\displaystyle t=0$$, the electric field has a value 10 V/m at the origin.
(a) Write the wave function that will describe the electric field wave.
(b) Find the wave function that will describe the associated magnetic field wave.
47. The following represents an electromagnetic wave traveling in the direction of the positive y-axis:
$$\displaystyle E_x=0;E_y=E_0cos(kx−ωt);E_z=0$$
$$\displaystyle B_x=0;B_y=0;B_z=B_0cos(kx−ωt)$$
The wave is passing through a wide tube of circular cross-section of radius R whose axis is along the y-axis. Find the expression for the displacement current through the tube.
### 16.3 Energy Carried by Electromagnetic Waves
48. While outdoors on a sunny day, a student holds a large convex lens of radius 4.0 cm above a sheet of paper to produce a bright spot on the paper that is 1.0 cm in radius, rather than a sharp focus. By what factor is the electric field in the bright spot of light related to the electric field of sunlight leaving the side of the lens facing the paper?
49. A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 6.0 V/m and points eastward. What are the magnitude and direction of the magnetic field at this instant?
50. The electric field of an electromagnetic wave is given by
$$\displaystyle E=(6.0×10^{−3}V/m)sin[2π(\frac{x}{18m}−\frac{t}{6.0×10^{−8}s})]\hat{j}$$.
Write the equations for the associated magnetic field and Poynting vector.
51. A radio station broadcasts at a frequency of 760 kHz. At a receiver some distance from the antenna, the maximum magnetic field of the electromagnetic wave detected is $$\displaystyle 2.15×10^{−11}T$$.
(a) What is the maximum electric field?
(b) What is the wavelength of the electromagnetic wave?
52. The filament in a clear incandescent light bulb radiates visible light at a power of 5.00 W. Model the glass part of the bulb as a sphere of radius $$\displaystyle r_0=3.00cm$$ and calculate the amount of electromagnetic energy from visible light inside the bulb.
53. At what distance does a 100-W lightbulb produce the same intensity of light as a 75-W lightbulb produces 10 m away? (Assume both have the same efficiency for converting electrical energy in the circuit into emitted electromagnetic energy.)
54. An incandescent light bulb emits only 2.6 W of its power as visible light. What is the rms electric field of the emitted light at a distance of 3.0 m from the bulb?
55. A 150-W lightbulb emits 5% of its energy as electromagnetic radiation. What is the magnitude of the average Poynting vector 10 m from the bulb?
56. A small helium-neon laser has a power output of 2.5 mW. What is the electromagnetic energy in a 1.0-m length of the beam?
57. At the top of Earth’s atmosphere, the time-averaged Poynting vector associated with sunlight has a magnitude of about $$\displaystyle 1.4kW/m^2$$.
(a) What are the maximum values of the electric and magnetic fields for a wave of this intensity?
(b) What is the total power radiated by the sun? Assume that the Earth is $$\displaystyle 1.5×10^{11}m$$ from the Sun and that sunlight is composed of electromagnetic plane waves.
58. The magnetic field of a plane electromagnetic wave moving along the z axis is given by
$$\displaystyle \vec{B} =B_0(coskz+ωt)\hat{j}$$, where $$\displaystyle B_0=5.00×10^{−10}T$$ and $$\displaystyle k=3.14×10^{−2}m^{−1}.$$
(a) Write an expression for the electric field associated with the wave.
(b) What are the frequency and the wavelength of the wave?
(c) What is its average Poynting vector?
59. What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?
60. Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.500 mW.
(a) If such a laser beam is projected onto a circular spot 1.00 mm in diameter, what is its intensity?
(b) Find the peak magnetic field strength.
(c) Find the peak electric field strength.
61. An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions. (a) Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 30.0 km away? (Hint: Half the power will be spread over the area of a hemisphere.) (b) What is the maximum electric field strength at this distance?
62. Suppose the maximum safe intensity of microwaves for human exposure is taken to be $$\displaystyle 1.00W/m^2$$.
(a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection.
(b) What is the maximum electric field strength at the safe intensity? (Note that early radar units leaked more than modern ones do. This caused identifiable health problems, such as cataracts, for people who worked near them.)
63. A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of 7.50μV/m (see below). (a) What is the intensity of this wave? (b) What is the power received by the antenna? (c) If the orbiting satellite broadcasts uniformly over an area of $$\displaystyle 1.50×10^{13}m^2$$ (a large fraction of North America), how much power does it radiate?
64. Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to initiate nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of $$\displaystyle 1.00×10^{11}V/m$$ for a time of 1.00 ns.
(a) What is the maximum magnetic field strength in the wave?
(b) What is the intensity of the beam?
(c) What energy does it deliver on an $$\displaystyle 1.00-mm^2$$ area?
### 16.4 Momentum and Radiation Pressure
65. A 150-W lightbulb emits 5% of its energy as electromagnetic radiation. What is the radiation pressure on an absorbing sphere of radius 10 m that surrounds the bulb?
66. What pressure does light emitted uniformly in all directions from a 100-W incandescent light bulb exert on a mirror at a distance of 3.0 m, if 2.6 W of the power is emitted as visible light?
67. A microscopic spherical dust particle of radius 2μm and mass 10μg is moving in outer space at a constant speed of 30 cm/sec. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Assuming the particle decelerates uniformly to zero speed in one second, what is the average electric field amplitude in the light?
68. A Styrofoam spherical ball of radius 2 mm and mass 20μg is to be suspended by the radiation pressure in a vacuum tube in a lab. How much intensity will be required if the light is completely absorbed the ball?
69. Suppose that $$\displaystyle \vec{S}_{avg}$$ for sunlight at a point on the surface of Earth is $$\displaystyle 900W/m^2$$.
(a) If sunlight falls perpendicularly on a kite with a reflecting surface of area 0.75m20.75m2, what is the average force on the kite due to radiation pressure?
(b) How is your answer affected if the kite material is black and absorbs all sunlight?
70. Sunlight reaches the ground with an intensity of about $$\displaystyle 1.0kW/m^2$$. A sunbather has a body surface area of 0.8m20.8m2 facing the sun while reclining on a beach chair on a clear day.
(a) how much energy from direct sunlight reaches the sunbather’s skin per second?
(b) What pressure does the sunlight exert if it is absorbed?
71. Suppose a spherical particle of mass m and radius R in space absorbs light of intensity I for time t.
(a) How much work does the radiation pressure do to accelerate the particle from rest in the given time it absorbs the light?
(b) How much energy carried by the electromagnetic waves is absorbed by the particle over this time based on the radiant energy incident on the particle?
### 16.5 The Electromagnetic Spectrum
72. How many helium atoms, each with a radius of about 31 pm, must be placed end to end to have a length equal to one wavelength of 470 nm blue light?
(a) What is its frequency?
(b) What type of electromagnetic radiation might this be?
74. Find the frequency range of visible light, given that it encompasses wavelengths from 380 to 760 nm.
75. (a) Calculate the wavelength range for AM radio given its frequency range is 540 to 1600 kHz.
(b) Do the same for the FM frequency range of 88.0 to 108 MHz.
76. Radio station WWVB, operated by the National Institute of Standards and Technology (NIST) from Fort Collins, Colorado, at a low frequency of 60 kHz, broadcasts a time synchronization signal whose range covers the entire continental US. The timing of the synchronization signal is controlled by a set of atomic clocks to an accuracy of $$\displaystyle 1×10^{−12}s$$, and repeats every 1 minute. The signal is used for devices, such as radio-controlled watches, that automatically synchronize with it at preset local times. WWVB’s long wavelength signal tends to propagate close to the ground.
(a) Calculate the wavelength of the radio waves from WWVB.
(b) Estimate the error that the travel time of the signal causes in synchronizing a radio controlled watch in Norfolk, Virginia, which is 1570 mi (2527 km) from Fort Collins, Colorado.
77. An outdoor WiFi unit for a picnic area has a 100-mW output and a range of about 30 m. What output power would reduce its range to 12 m for use with the same devices as before? Assume there are no obstacles in the way and that microwaves into the ground are simply absorbed.
78. The prefix “mega” (M) and “kilo” (k), when referring to amounts of computer data, refer to factors of 1024 or 210210rather than 1000 for the prefix kilo, and $$\displaystyle 1024^2=2^{20}$$ rather than 1,000,000 for the prefix Mega (M). If a wireless (WiFi) router transfers 150 Mbps of data, how many bits per second is that in decimal arithmetic?
79. A computer user finds that his wireless router transmits data at a rate of 75 Mbps (megabits per second). Compare the average time to transmit one bit of data with the time difference between the wifi signal reaching an observer’s cell phone directly and by bouncing back to the observer from a wall 8.00 m past the observer.
80. (a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength (λ/4) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band?
(b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.
81. What are the wavelengths of (a) X-rays of frequency $$\displaystyle 2.0×10^{17}Hz$$?
(b) Yellow light of frequency $$\displaystyle 5.1×10^{14}Hz$$?
(c) Gamma rays of frequency $$\displaystyle 1.0×10^{23}Hz$$?
82. For red light of λ=660nm, what are $$\displaystyle f, ω$$ and $$\displaystyle k$$?
83. A radio transmitter broadcasts plane electromagnetic waves whose maximum electric field at a particular location is $$\displaystyle 1.55×10^{−3}V/m$$. What is the maximum magnitude of the oscillating magnetic field at that location? How does it compare with Earth’s magnetic field?
84. (a) Two microwave frequencies authorized for use in microwave ovens are: 915 and 2450 MHz. Calculate the wavelength of each.
(b) Which frequency would produce smaller hot spots in foods due to interference effects?
85. During normal beating, the heart creates a maximum 4.00-mV potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave.
(a) What is the maximum electric field strength created?
(b) What is the corresponding maximum magnetic field strength in the electromagnetic wave?
(c) What is the wavelength of the electromagnetic wave?
86. Distances in space are often quoted in units of light-years, the distance light travels in 1 year.
(a) How many meters is a light-year?
(b) How many meters is it to Andromeda, the nearest large galaxy, given that it is $$\displaystyle 2.54×10^6$$ ly away?
(c) The most distant galaxy yet discovered is $$\displaystyle 13.4×10^9$$ ly away. How far is this in meters?
87. A certain 60.0-Hz ac power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m.
(a) What is the wavelength of this very-low-frequency electromagnetic wave?
(b) What type of electromagnetic radiation is this wave
(c) What is its maximum magnetic field strength?
88. (a) What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this electromagnetic radiation can ablate (reshape) the cornea is directly proportional to wavelength, how much more accurate can this UV radiation be than the shortest visible wavelength of light?
89. In a region of space, the electric field is pointed along the x-axis, but its magnitude changes as described by
$$\displaystyle E_x=(10N/C)sin(20x−500t)$$
$$\displaystyle E_y=E_z=0$$
where is in nanoseconds and x is in cm. Find the displacement current through a circle of radius 3 cm in the $$\displaystyle x=0$$ plane at $$\displaystyle t=0$$.
90. A microwave oven uses electromagnetic waves of frequency $$\displaystyle f=2.45×10^9Hz$$ to heat foods. The waves reflect from the inside walls of the oven to produce an interference pattern of standing waves whose antinodes are hot spots that can leave observable pit marks in some foods. The pit marks are measured to be 6.0 cm apart. Use the method employed by Heinrich Hertz to calculate the speed of electromagnetic waves this implies.
Use the Appendix D for the next two exercises
91. Galileo proposed measuring the speed of light by uncovering a lantern and having an assistant a known distance away uncover his lantern when he saw the light from Galileo’s lantern, and timing the delay. How far away must the assistant be for the delay to equal the human reaction time of about 0.25 s?
92. Show that the wave equation in one dimension
$$\displaystyle \frac{∂^2f}{∂x^2}=\frac{1}{v^2}\frac{∂^2f}{∂t^2}$$
is satisfied by any doubly differentiable function of either the form $$\displaystyle f(x−vt)$$ or $$\displaystyle f(x+vt)$$.
93. On its highest power setting, a microwave oven increases the temperature of 0.400 kg of spaghetti by 45.0°C in 120 s.
(a) What was the rate of energy absorption by the spaghetti, given that its specific heat is $$\displaystyle 3.76×10^3J/kg⋅°C$$? Assume the spaghetti is perfectly absorbing.
(b) Find the average intensity of the microwaves, given that they are absorbed over a circular area 20.0 cm in diameter.
(c) What is the peak electric field strength of the microwave?
(d) What is its peak magnetic field strength?
94. A certain microwave oven projects 1.00 kW of microwaves onto a 30-cm-by-40-cm area.
(a) What is its intensity in $$\displaystyle W/m^2$$?
(b) Calculate the maximum electric field strength $$\displaystyle E_0$$ in these waves.
(c) What is the maximum magnetic field strength $$\displaystyle B_0$$ ?
95. Electromagnetic radiation from a 5.00-mW laser is concentrated on a $$\displaystyle 1.00-mm^2$$ area.
(a) What is the intensity in $$\displaystyle W/m^2$$?
(b) Suppose a 2.00-nC electric charge is in the beam. What is the maximum electric force it experiences?
(c) If the electric charge moves at 400 m/s, what maximum magnetic force can it feel?
96. A 200-turn flat coil of wire 30.0 cm in diameter acts as an antenna for FM radio at a frequency of 100 MHz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of $$\displaystyle 1.00×10^{−12}T$$.
(a) What power is incident on the coil?
(b) What average emf is induced in the coil over one-fourth of a cycle?
(c) If the radio receiver has an inductance of 2.50μH, what capacitance must it have to resonate at 100 MHz?
97. Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects.
(a) Show that the intensity is inversely proportional to $$\displaystyle r^2$$, the distance from the source squared.
(b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r.
98. A radio station broadcasts its radio waves with a power of 50,000 W. What would be the intensity of this signal if it is received on a planet orbiting Proxima Centuri, the closest star to our Sun, at 4.243 ly away?
99. The Poynting vector describes a flow of energy whenever electric and magnetic fields are present. Consider a long cylindrical wire of radius r with a current I in the wire, with resistance R and voltage V. From the expressions for the electric field along the wire and the magnetic field around the wire, obtain the magnitude and direction of the Poynting vector at the surface. Show that it accounts for an energy flow into the wire from the fields around it that accounts for the Ohmic heating of the wire.
100. The Sun’s energy strikes Earth at an intensity of $$\displaystyle 1.37kW/m^2$$. Assume as a model approximation that all of the light is absorbed. (Actually, about 30% of the light intensity is reflected out into space.)
(a) Calculate the total force that the Sun’s radiation exerts on Earth.
(b) Compare this to the force of gravity between the Sun and Earth.
Note: Earth’s mass is $$\displaystyle 5.972×10^{24}kg$$.
101. If a Lightsail spacecraft were sent on a Mars mission, by what fraction would its propulsion force be reduced when it reached Mars?
102. Lunar astronauts placed a reflector on the Moon’s surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time.
(a) To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns?
(b) What percent accuracy is this, given the average distance to the Moon is 384,400 km?
103. Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object.
(a) How far away is the planet Venus if the echo time is 1000 s?
(b) What is the echo time for a car 75.0 m from a highway police radar unit?
(c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 10.0 m?
104. Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm. (Note that the ratio of highest to lowest frequencies the ear can hear is 1000.)
105. How does the wavelength of radio waves for an AM radio station broadcasting at 1030 KHz compare with the wavelength of the lowest audible sound waves (of 20 Hz). The speed of sound in air at 20°C is about 343 m/s.
## Challenge Problems
106. A parallel-plate capacitor with plate separation d is connected to a source of emf that places a time-dependent voltage V(t) across its circular plates of radius $$\displaystyle r_0$$ and area $$\displaystyle A=πr^2_0$$ (see below).
(a) Write an expression for the time rate of change of energy inside the capacitor in terms of V(t) and dV(t)/dt.
(b) Assuming that V(t) is increasing with time, identify the directions of the electric field lines inside the capacitor and of the magnetic field lines at the edge of the region between the plates, and then the direction of the Poynting vector $$\displaystyle \vec{S}$$ at this location.
(c) Obtain expressions for the time dependence of E(t), for B(t) from the displacement current, and for the magnitude of the Poynting vector at the edge of the region between the plates.
(d) From $$\displaystyle \vec{S}$$, obtain an expression in terms of V(t) and dV(t)/dt for the rate at which electromagnetic field energy enters the region between the plates.
(e) Compare the results of parts (a) and (d) and explain the relationship between them.
107. A particle of cosmic dust has a density $$\displaystyle ρ=2.0g/cm^3$$.
(a) Assuming the dust particles are spherical and light absorbing, and are at the same distance as Earth from the Sun, determine the particle size for which radiation pressure from sunlight is equal to the Sun’s force of gravity on the dust particle.
(b) Explain how the forces compare if the particle radius is smaller.
(c) Explain what this implies about the sizes of dust particle likely to be present in the inner solar system compared with outside the Oort cloud.
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-04-20T13:05:48 |
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|
http://dlmf.nist.gov/13.9
|
# §13.9(i) Zeros of $\mathop{M\/}\nolimits\!\left(a,b,z\right)$
If $a$ and $b-a\neq 0,-1,-2,\dots$, then $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ has infinitely many $z$-zeros in $\Complex$. When $a,b\in\Real$ the number of real zeros is finite. Let $p(a,b)$ be the number of positive zeros. Then
13.9.1 $\displaystyle p(a,b)$ $\displaystyle=\left\lceil-a\right\rceil,$ $a<0$, $b\geq 0$, 13.9.2 $\displaystyle p(a,b)$ $\displaystyle=0,$ $a\geq 0$, $b\geq 0$, Symbols: $p(a,b)$: number of positive zeros Permalink: http://dlmf.nist.gov/13.9.E2 Encodings: TeX, pMML, png 13.9.3 $\displaystyle p(a,b)$ $\displaystyle=1,$ $a\geq 0$, $-1, Symbols: $p(a,b)$: number of positive zeros Permalink: http://dlmf.nist.gov/13.9.E3 Encodings: TeX, pMML, png
13.9.4 $p(a,b)=\left\lfloor-\tfrac{1}{2}b\right\rfloor-\left\lfloor-\tfrac{1}{2}(b+1)% \right\rfloor,$ $a\geq 0$, $b\leq-1$.
13.9.5 $p(a,b)=\left\lceil-a\right\rceil-\left\lceil-b\right\rceil,$ $\left\lceil-a\right\rceil\geq\left\lceil-b\right\rceil$, $a<0$, $b<0$,
13.9.6 $p(a,b)=\left\lfloor\tfrac{1}{2}\left(\left\lceil-b\right\rceil-\left\lceil-a% \right\rceil+1\right)\right\rfloor-\left\lfloor\tfrac{1}{2}\left(\left\lceil-b% \right\rceil-\left\lceil-a\right\rceil\right)\right\rfloor,$ $\left\lceil-b\right\rceil>\left\lceil-a\right\rceil>0$.
The number of negative real zeros $n(a,b)$ is given by
13.9.7 $n(a,b)=p(b-a,b).$ Symbols: $p(a,b)$: number of positive zeros and $n(a,b)$: number of negative real zeros Permalink: http://dlmf.nist.gov/13.9.E7 Encodings: TeX, pMML, png
When $a<0$ and $b>0$ let $\phi_{r}$, $r=1,2,3,\dots$, be the positive zeros of $\mathop{M\/}\nolimits\!\left(a,b,x\right)$ arranged in increasing order of magnitude, and let $j_{b-1,r}$ be the $r$th positive zero of the Bessel function $\mathop{J_{b-1}\/}\nolimits\!\left(x\right)$10.21(i)). Then
13.9.8 $\phi_{r}=\frac{j_{b-1,r}^{2}}{2b-4a}\left(1+\frac{2b(b-2)+j_{b-1,r}^{2}}{3(2b-% 4a)^{2}}\right)+\mathop{O\/}\nolimits\!\left(\frac{1}{a^{5}}\right),$
as $a\to-\infty$ with $r$ fixed.
Inequalities for $\phi_{r}$ are given in Gatteschi (1990), and identities involving infinite series of all of the complex zeros of $\mathop{M\/}\nolimits\!\left(a,b,x\right)$ are given in Ahmed and Muldoon (1980).
For fixed $a,b\in\Complex$ the large $z$-zeros of $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ satisfy
13.9.9 $z=\pm(2n+a)\pi i+\mathop{\ln\/}\nolimits\!\left(-\frac{\mathop{\Gamma\/}% \nolimits\!\left(a\right)}{\mathop{\Gamma\/}\nolimits\!\left(b-a\right)}\left(% \pm 2n\pi i\right)^{b-2a}\right)+\mathop{O\/}\nolimits\!\left(n^{-1}\mathop{% \ln\/}\nolimits n\right),$
where $n$ is a large positive integer, and the logarithm takes its principal value (§4.2(i)).
Let $P_{\alpha}$ denote the closure of the domain that is bounded by the parabola $y^{2}=4\alpha(x+\alpha)$ and contains the origin. Then $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ has no zeros in the regions $P_{\ifrac{b}{a}}$, if $0; $P_{1}$, if $1\leq a\leq b$; $P_{\alpha}$, where $\alpha=\ifrac{(2a-b+ab)}{(a(a+1))}$, if $0 and $a\leq b<\ifrac{2a}{(1-a)}$. The same results apply for the $n$th partial sums of the Maclaurin series (13.2.2) of $\mathop{M\/}\nolimits\!\left(a,b,z\right)$.
More information on the location of real zeros can be found in Zarzo et al. (1995) and Segura (2008).
For fixed $b$ and $z$ in $\Complex$ the large $a$-zeros of $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ are given by
13.9.10 $a=-\frac{\pi^{2}}{4z}\left(n^{2}+(b-\tfrac{3}{2})n\right)-\frac{1}{16z}\left((% b-\tfrac{3}{2})^{2}\pi^{2}+\tfrac{4}{3}z^{2}-8b(z-1)-4b^{2}-3\right)+\mathop{O% \/}\nolimits\!\left(n^{-1}\right),$
where $n$ is a large positive integer.
For fixed $a$ and $z$ in $\Complex$ the function $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ has only a finite number of $b$-zeros.
# §13.9(ii) Zeros of $\mathop{U\/}\nolimits\!\left(a,b,z\right)$
For fixed $a$ and $b$ in $\Complex$, $\mathop{U\/}\nolimits\!\left(a,b,z\right)$ has a finite number of $z$-zeros in the sector $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\tfrac{3}{2}\pi-\delta(<\tfrac{3}{2}\pi)$. Let $T(a,b)$ be the total number of zeros in the sector $|\mathop{\mathrm{ph}\/}\nolimits z|<\pi$, $P(a,b)$ be the corresponding number of positive zeros, and $a$, $b$, and $a-b+1$ be nonintegers. For the case $b\leq 1$
13.9.11 $T(a,b)=\left\lfloor-a\right\rfloor+1,$ $a<0$, $\mathop{\Gamma\/}\nolimits\!\left(a\right)\mathop{\Gamma\/}\nolimits\!\left(a-% b+1\right)>0$,
13.9.12 $T(a,b)=\left\lfloor-a\right\rfloor,$ $a<0$, $\mathop{\Gamma\/}\nolimits\!\left(a\right)\mathop{\Gamma\/}\nolimits\!\left(a-% b+1\right)<0$,
13.9.13 $T(a,b)=0,$ $a>0$, Symbols: $T(a,b)$: number of zeros Permalink: http://dlmf.nist.gov/13.9.E13 Encodings: TeX, pMML, png
and
13.9.14 $P(a,b)=\left\lceil b-a-1\right\rceil,$ $a+1,
13.9.15 $P(a,b)=0,$ $a+1\geq b$. Symbols: $P(a,b)$: number of positive zeros Permalink: http://dlmf.nist.gov/13.9.E15 Encodings: TeX, pMML, png
For the case $b\geq 1$ we can use $T(a,b)=T(a-b+1,2-b)$ and $P(a,b)=P(a-b+1,2-b)$.
In Wimp (1965) it is shown that if $a,b\in\Real$ and $2a-b>-1$, then $\mathop{U\/}\nolimits\!\left(a,b,z\right)$ has no zeros in the sector $|\mathop{\mathrm{ph}\/}\nolimits{z}|\leq\frac{1}{2}\pi$.
Inequalities for the zeros of $\mathop{U\/}\nolimits\!\left(a,b,x\right)$ are given in Gatteschi (1990). See also Segura (2008).
For fixed $b$ and $z$ in $\Complex$ the large $a$-zeros of $\mathop{U\/}\nolimits\!\left(a,b,z\right)$ are given by
13.9.16 $a\sim-n-\frac{2}{\pi}\sqrt{zn}-\frac{2z}{\pi^{2}}+\tfrac{1}{2}b+\tfrac{1}{4}+% \frac{z^{2}\left(\frac{1}{3}-4\pi^{-2}\right)+z-(b-1)^{2}+\frac{1}{4}}{4\pi% \sqrt{zn}}+\mathop{O\/}\nolimits\!\left(\frac{1}{n}\right),$
where $n$ is a large positive integer.
For fixed $a$ and $z$ in $\Complex$, $\mathop{U\/}\nolimits\!\left(a,b,z\right)$ has two infinite strings of $b$-zeros that are asymptotic to the imaginary axis as $|b|\to\infty$.
| 2014-12-19T12:13:32 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=M112W&home=sumtabM
|
# ${{\boldsymbol f}_{{0}}{(2200)}}$ WIDTH INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 207 \pm40}$ OUR AVERAGE
$220$ $\pm60$ ${}^{+40}_{-45}$
2005 Q
BES2 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$
$201$ $\pm51$ 1
1988
DM2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$380$ $\pm90$ 2
2005
GAMS 33 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}}{{\mathit n}}$
$\sim$$273 1994 RVUE {{\overline{\mathit p}}} {{\mathit p}} \rightarrow {{\mathit \pi}}{{\mathit \pi}} \sim$$223$
1994
RVUE ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$
1 Cannot determine spin to be 0.
2 First solution, PWA is ambiguous.
References:
ABLIKIM 2005Q
PR D72 092002 Partial Wave Analysis of ${{\mathit \chi}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$
BINON 2005
PAN 68 960 Investigation of the ${{\mathit \eta}}{{\mathit \eta}}$ System in ${{\mathit \pi}^{-}}{{\mathit p}}$ Interactions at a Momentum of 32.5 GeV/$\mathit c$ at the GAMS-4$\pi$ Spectrometer
HASAN 1994
PL B334 215 Amplitudes for ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ from 0.36 to 2.5 ${\mathrm {GeV/}}\mathit c$
AUGUSTIN 1988
PRL 60 2238 Measurement of Radiative ${{\mathit J / \psi}}$ Decays in ${{\mathit K}}{{\overline{\mathit K}}}$ States
| 2020-01-26T14:32:53 |
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|
https://docs.nersc.gov/jobs/workflow/fireworks/
|
# Fireworks¶
FireWorks is a free, open-source code for defining, managing, and executing scientific workflows. It can be used to automate calculations over arbitrary computing resources, including those that have a queueing system. Some features that distinguish FireWorks are
• Dynamic workflows
• Failure-detection routines
• Built-in tools and execution modes for running high-throughput computations at large computing centers (like NERSC!)
FireWorks uses a centralized server model, where the server manages the workflows and workers run the jobs.
FireWorks is the primary workflow engine for the Materials Project, and is also being evaluated by several other projects. For more information on Fireworks visit: https://materialsproject.github.io/fireworks/index.html
Please open a ticket with NERSC Consulting if you are interested in using FireWorks. Please say in your ticket that you would like to use FireWorks and also need a mongoDB to be set up for you.
Below is an example of how to use FireWorks at NERSC. This is based heavily on the Fireworks tutorial which you will find here.
## Terminology¶
FireWorks uses a number of terms to describe the different parts of the workflow manager.
• FireServer: MongoDB that controls the workflow. Also referred to as the LaunchPad. It contains all the tasks to be run, and whether they have run successfully etc.
• Rocket: fetches a FireWork from the LaunchPad and runs it. Could be run on a separate machine (FireWorker) or through a batch system.
We recommend that anyone wanting to use FireWorks at NERSC install it in a conda environment.
To create a new conda environment for FireWorks:
module load python
conda create -n fireworks_env python=3.7 -y
source activate fireworks_env
conda install -c conda-forge fireworks
or simply install it into your favorite existing conda environment:
source activate myfavoriteenvironment
conda install -c conda-forge fireworks
And you should be ready to go! Once you've created your FireWorks conda environment, you just need to source activate fireworks_env whenever you would like to use it. For more information about using conda environments at NERSC, check out this page.
Fireworks requires a mongoDB to define and log the progress of your tasks. Here we will assume this is running at NERSC on mongodb03.nersc.gov (the exact location will depend on where your database is allocated). You will receive this information in your ticket.
Setting up the Launchpad can be done interactively using the command lpad init, similar to the example shown below. You will need to specify the name of the database host and your own username and password - note that you need to have admin access to the database, so make sure you use the administrators username/password with which you were provided.
On a Cori login node, navigate to the directory where you will issue your fireworks commands. $SCRATCH or $HOME is a good example.
lpad init
Please supply the following configuration values
(press Enter if you want to accept the defaults)
Enter host (default: localhost) : mongodb03
Enter port (default: 27017) :
Enter name (default: fireworks) : my_db
Enter password (default: None) : my_pswd
This information will go into a file named "my_launchpad.yaml". Fireworks will look for this file in your working directory.
## Interactive example¶
To run a simple example on the interactive node, you first need to add a job to the launchpad, then run the job. Note that Fireworks automatically looks for a launchpad file named my_launchpad.yaml in the working directory. If you have named your launchpad file something else, you need to add the option -l my_launchpad_name.yaml to every command.
You must issue FireWorks commands where your my_launchpad.yaml file is
When you ran lpad init to configure your Fireworks setup, it automatically wrote a file called my_launchpad.yaml for you. When you issue Fireworks commands such as rlaunch you must be in the same directory as your my_launchpad.yaml file. Alternatively, you can copy this file into your working directory. Either way is ok-- as long as FireWorks can find your my_launchpad.yaml file.
lpad reset
lpad add_scripts 'echo "hello"' -n hello -w test_workflow
The option -n give the name of the firework (i.e. the list of tasks task), and the option -w gives the name of the workflow.
Examine the contents of the launchpad. If you have many different workflows in your launchpad, you can search for workflows by name using the option -w test_workflow.
lpad get_wflows
The json output of this command will give you some basic information about the workflow you just added - including its name and status (which should be READY).
Now you want to run (launch) the job using the command rlaunch. This will pull a job from the launchpad defined in my_launchpad.yaml. If you need to use a different launchpad file, use the option -l. The singleshot option launches one job only (we will see later how to run multiple jobs).
rlaunch singleshot
The output will look something like:
rlaunch singleshot
2016-09-23 15:45:14,929 INFO Hostname/IP lookup (this will take a few seconds)
2016-09-23 15:45:14,931 INFO Launching Rocket
2016-09-23 15:45:15,250 INFO RUNNING fw_id: 1 in directory: /global/u1/a/auser/fireworks
hello
2016-09-23 15:45:15,900 INFO Rocket finished
Now let's write a FireWork script to do this, call it "fw-test.yaml".
spec:
script: echo "howdy, your job launched successfully!" >> howdy.txt
lpad add fw-test.yaml
Now run the FireWork:
rlaunch rapidfire
In this example we have used the option rapidfire instead of singleshot. This will keep pulling jobs from the launchpad until all are completed. The output data (output files and job status) is given in launcher_* directories.
To run in batch mode, you will need to define a Fireworker. The job that is sent to the batch system will want to pull down a job from the FireServer. It does this via a FireWorker script, which can be as simple as:
name: test Cori fireworker
category: ''
query: '{}'
The commands that exist by default in the FireWorks Slurm template are as follows. If you need to add more options, you can copy this file and add to the template as described here.
#!/bin/bash
#SBATCH --nodes=$${nodes} #SBATCH --ntasks=$${ntasks}
#SBATCH --ntasks-per-node=$${ntasks_per_node} #SBATCH --cpus-per-task=$${cpus_per_task}
#SBATCH --gres=$${gres} #SBATCH --qos=$${qos}
#SBATCH --time=$${walltime} #SBATCH --partition=$${queue}
#SBATCH --account=$${account} #SBATCH --job-name=$${job_name}
#SBATCH --license=$${license} #SBATCH --output=$${job_name}-%j.out
#SBATCH --error=$${job_name}-%j.error #SBATCH --constraint=$${constraint}
$${pre_rocket} cd$${launch_dir}
$${rocket_launch}$${post_rocket}
# CommonAdapter (SLURM) completed writing Template
You will need to write a queue adapter, which defines how the jobs will be launched into the queue. Note that you need to specify here all the usual Slurm options - if you do not, Fireworks will fail to launch with an error message reading RuntimeError: queue script could not be submitted, check queue script/queue adapter/queue server status!. Here we assume that the fireworker file is called my_fireworker.yaml, and the launchpad file is my_launchpad.yaml.
_fw_name: CommonAdapter
_fw_q_type: SLURM
rocket_launch: rlaunch -w my_fireworker.yaml -l my_launchpad.yaml rapidfire
nnodes: 1
ppnode: 1
walltime: '00:20:00'
queue: debug
account: null
job_name: null
constraint: haswell
logdir: fw_logs/
pre_rocket: null
post_rocket: null
You can then submit to the batch system using the qlaunch command:
qlaunch -l my_launchpad.yaml -w my_fireworker.yaml -q qadaptor.yaml singleshot
The output will show up in the fw_logs directory.
| 2020-01-22T06:42:57 |
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|
https://control.com/textbook/chemistry/periodic-table-of-the-elements/
|
Periodic Table of the Elements
Chapter 3 - Chemistry in Industrial Instrumentation
All substances are comprised of various elements in various combinations and proportions. Elements may thus be thought of as the building-blocks of matter. A Periodic Table of the Elements is a table listing the known elements in order of their atomic numbers.
Multiple attributes appear for each element in the table. Two of these attributes – atomic number and atomic mass – are directly related to the number of particles in the nucleus of each atom. We will examine the table’s entry for the element potassium (K) to explore these concepts.
Potassium has an atomic number (number of protons in the nucleus of each potassium atom) of 19. This number defines the element. If we were somehow to add or subtract protons from the nucleus of a potassium atom, it would cease being potassium and transmutate into a different element. Note how every element in the table has its own unique atomic number, and how each of these numbers is whole (no fractions or decimals).
The atomic mass or atomic weight shown for potassium is 39.0983. This quantity is the sum of protons and neutrons found in the nucleus of each potassium atom. Like the atomic number (19), we would logically expect the atomic mass to be a whole number as well, since protons and neutrons only come in whole quantities. The primary reason we see a non-whole number for potassium’s atomic mass is that this table reflects the average atomic mass of potassium atoms as found in nature. Some potassium atoms have atomic masses greater than 39, and some have atomic masses less than 39. We know that the number of protons in every potassium atom is fixed (which is what gives potassium its elemental identity), which means the only quantity that may cause the atomic mass to vary is the number of neutrons in the nucleus. The most common form of potassium ($$^{39}$$K) atom possesses 19 protons and 20 neutrons in its nucleus, giving it an atomic mass of 39 (19 + 20). The next most common form of potassium found on Earth is ($$^{41}$$K), possessing 19 protons and 22 neutrons.
We refer to atoms of the same element with differing atomic masses as isotopes. From a chemical perspective, isotopes are identical. That is to say, they engage in the exact same chemical reactions in the exact same manner. To use potassium as an example, an atom of $$^{39}$$K will join with a chlorine atom (Cl) to form the compound potassium chloride (KCl) just as readily as an atom of $$^{41}$$K will join with a chlorine atom to form the same compound. The three isotopes of hydrogen ($$^{1}$$H, $$^{2}$$H, and $$^{3}$$H: hydrogen, deuterium, and tritium, respectively) are all chemically identical: all are highly flammable, combining with oxygen to create water (H$$_{2}$$O). However, deuterium ($$^{2}$$H) has twice the density of normal hydrogen ($$^{1}$$H), while tritium ($$^{3}$$H) has three times the density of normal hydrogen and is highly radioactive! Isotopes only differ in their mass and in their nuclear properties (such as radioactivity: the tendency for a nucleus to spontaneously decay, usually resulting in a loss or gain of protons that subsequently alters the identity of the decayed atom).
The Periodic Table is called “periodic” because its configuration reveals a repeating pattern of chemical behaviors approximately following atomic number. Horizontal rows in the table are called periods, while vertical columns are called groups. Elements in the same group (vertical column) share similar chemical reactivities – that is, they tend to engage in the same types of chemical reactions – despite having different masses and physical properties such as melting point, boiling point, etc. This periodicity is a function of how electrons are arranged around the nucleus of each atom, a subject we will explore in more detail later in this chapter. As mentioned previously, chemistry is the study of how atoms bond together to form molecules, and this bonding takes place through the interaction of the electrons surrounding the atoms’ nuclei. It makes perfect sense, then, that the configuration of those electrons determine the chemical (bonding) properties of atoms.
Some periodic tables show the first ionization energy value for each element – the amount of energy required to force the first electron of an electrically balanced atom to separate from that atom – in addition to other attributes such as atomic number and atomic mass. If we note the ionization energies of the elements, reading each element in turn from left-to-right, starting with period 1 (hydrogen and helium) and progressing to subsequent periods, we see an interesting pattern:
& & (measured in electron-volts'') \cr
Element Period First ionization energy Hydrogen (H) 1 13.5984 Helium (He) 1 24.5874 Lithium (Li) 2 5.3917 Beryllium (Be) 2 9.3227 Boron (B) 2 8.298 Carbon (C) 2 11.2603 Nitrogen (N) 2 14.5341 Oxygen (O) 2 13.6181 Fluorine (F) 2 17.4228 Neon (Ne) 2 21.5645 Sodium (Na) 3 5.1391 Magnesium (Mg) 3 7.6462 Aluminum (Al) 3 5.9858 Silicon (Si) 3 8.1517 Phosphorus (P) 3 10.4867 Sulfur (S) 3 10.36 Chlorine (Cl) 3 12.9676 Argon (Ar) 3 15.7596 Potassium (K) 4 4.3407
First ionization energy represents the relative stability of the last electron balancing the electrical charge of an atom. We see from this table that 24.5874 electron-volts of energy is needed to remove one electron from an electrically-balanced atom of helium (changing He into He$$^{1+}$$), while only 13.5984 electron-volts of energy is required to do the same to an atom of hydrogen. This tells us the electron configuration of helium is at a lower energy (and therefore more stable) than that of hydrogen.
The ionization energies increase with increasing atomic number (with an occasional down-step) until the last column of the period is reached, and then there is a comparatively enormous down-step in energy at the first column of a new period. This pattern is clearly evident when the first ionization energies are plotted against atomic number:
This periodicity suggests that as atoms grow in atomic number, the additional electrons do not simply pile on in random fashion or in a plain and simple progression from inner orbits to outer orbits. Rather, they “fill in” a structured energy pattern, with major changes in structure at the start of each new period. More details of this structured pattern will be explored later in this chapter.
The low ionization energy values for all the “Group 1” elements (far left-hand column) suggest they are relatively easy to positively ionize, and indeed we find this to be the case through experimentation. Hydrogen, lithium, sodium, potassium, and the rest all readily become positively-charged ions upon interaction with other atoms, since their low ionization energy values means they may easily lose an electron.
The high ionization energy values for all the “Group 18” elements (far right-hand column) suggest they possess a very stable electron structure, which is also verified by experiment. These are the noble elements, possessing very little reactive potential.
Looking at the “Group 17” column, just to the left of the noble elements, we notice that they are all just one electron shy of the stable electron structure enjoyed by the noble atoms when in their electrically-balanced states. This suggests it might be easy to add one more electron to atoms of these elements, which (once again!) is a principle validated by experiment. Fluorine, chlorine, bromine, iodine, and even astatine all readily ionize negatively, readily accepting an extra electron from surrounding atoms. As one might expect from this tendency, these elements readily bond through electrostatic attraction with the “Group 1” elements (hydrogen, lithium, sodium, potassium, etc.), each “Group 17” atom accepting an extra electron from each “Group 1” atom which readily provides it. Ordinary table salt (sodium chloride, or NaCl) is an example of a compound formed by this sort of bond.
Thus, Group 1 and Group 17 elements are both highly reactive in a chemical sense, but in different ways. Group 1 elements easily form bonds with Group 17 elements, but Group 1 elements do not generally bond (solely) with other Group 1 elements, and likewise Group 17 elements do not generally bond (solely) with other Group 17 elements. It is the structure of the electrons surrounding each atom’s nucleus that determines how those atoms will bond with other atoms.
• Share
Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License
| 2019-12-10T11:35:57 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=S007NE
|
# Number of Light ${{\boldsymbol \nu}}$ Types INSPIRE search
VALUE DOCUMENT ID TECN
$2.9963$ $\pm0.0074$ 1
2020
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.9918$ $\pm0.0081$ 2
2020
$2.9840$ $\pm0.0082$ 3
2006
RVUE
$3.00$ $\pm0.05$ 4
1992
RVUE
1 JANOT 2020 applies a correction to LEP-SLC 2006 using an updated Bhabha cross section calculation. This result also includes a correction to account for correlated luminosity bias as presented in VOUTSINAS 2020 .
2 VOUTSINAS 2020 applies a correction to LEP-SLC 2006 to account for correlated luminosity bias.
3 Combined fit from ALEPH, DELPHI, L3 and OPAL Experiments.
4 Simultaneous fits to all measured cross section data from all four LEP experiments.
References:
JANOT 2020
PL B803 135319 Improved Bhabha cross section at LEP and the number of light neutrino species
VOUTSINAS 2020
PL B800 135068 Beam-beam effects on the luminosity measurement at LEP and the number of light neutrino species
LEP-SLC 2006
PRPL 427 257 Precision Electroweak Measurements on the ${{\mathit Z}}$ Resonance
LEP 1992
PL B276 247 Electroweak Parameters of the ${{\mathit Z}^{0}}$ Resonance and the Standard Model
| 2021-04-11T13:47:41 |
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|
https://www.bnl.gov/event.php?q=14934
|
# Nuclear Physics Seminar
## "Examining hydrodynamical modelling of the QGP through dilepton radiation"
#### Presented by Gojko Vujanovic, Wayne State University
Tuesday, May 28, 2019, 11:00 am — Small Seminar Room, Bldg. 510
Recent viscous hydrodynamical studies at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC), show that bulk viscosity plays an important role in their phenomenological description. A temperature-dependent bulk viscosity in the hydrodynamical evolution of the medium can modify the development of the hydrodynamic momentum anisotropy differently in the high- and low-temperature regions. Thus, anisotropic flow coefficients of various particle species are affected differently depending where their surface of last scattering lies. For the case of hadronic observables, they are predominantly sensitive to low temperature regions, while electromagnetic radiation is emitted at all temperatures. Therefore, bulk viscosity should affect electromagnetic radiation differently than hadron emission. The effects of bulk viscosity on one of the electromagnetic probes, namely photons, has already been investigated. The same statement holds true for hadrons. The goal of this presentation is to study how dilepton production, the other source of electromagnetic radiation, gets modified owing to the presence of bulk viscosity at RHIC and LHC energies. With calculations at different collision energies, comparisons in the dilepton signal can be made and more robust conclusions regarding the role of bulk viscosity in high energy heavy-ion collisions can be drawn. Dilepton radiation from the dilute hadronic sector of the medium, which are radiated in addition to dileptons emitted during the hydrodynamical evolution, will also be included to ascertain whether interesting dynamics induced by bulk viscosity may have observable consequences. To complete that investigation, particular attention will be given to how the $\rho(770)$ meson, and its subsequent dilepton decay, is calculated at the end of the hydrodynamical simulation.
Hosted by: Rongrong Ma
14934 | INT/EXT | Events Calendar
| 2019-05-19T08:17:54 |
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|
https://www.aimsciences.org/article/doi/10.3934/dcdss.2019082
|
Article Contents
Article Contents
# Cores and optimal fuzzy communication structures of fuzzy games
• * Corresponding author: Jiaquan Zhan
• In real game problems not all players can cooperate directly, games with communication structures introduced by Myerson in 1977 can deal with these problems quite well. More recently, this concept has been introduced into fuzzy games. In this paper, games on (fuzzy) communication structures were studied. We proved that if a coalitional game has a nonempty core, then the game restricted on an n-person connected graph also has a nonempty core. Further, the fuzzy game restricted on the n-person connected graph also has a nonempty core. Moreover, we proved the above two cores are identical and the core of the coalitional game is included in them. In addition, optimal fuzzy communication structures of fuzzy games were studied. We showed that the optimal communication structures do exist and proposed three allocating methods. In the end, a full illustrating example was given.
Mathematics Subject Classification: 91A12, 91A43.
Citation:
• Figure 1. $\gamma$ and its partion by level
• [1] J. P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research, 6 (1981), 1-13. doi: 10.1287/moor.6.1.1. [2] Y. Chen, Mean square exponential stability of uncertain singular stochastic systems with discrete and distributed delays, Journal of Interdisciplinary Mathematics, 20, 13-26. [3] D. B. Gillies, Solutions to general non-zero-sum games, Contributions to the Theory of Games IV, 4 (1959), 47-85. [4] M. Grabisch, Games induced by the partitioning of a graph, Annals of Operations Research, 201 (2012), 229-249. doi: 10.1007/s10479-012-1200-8. [5] S. Hart and A. Mas-Colell, Potential, value, and consistency, Econometrica, 57 (1989), 589-614. doi: 10.2307/1911054. [6] A. Jiménez-Losada, J. R. Fernández and M. Ordóñez, Myerson values for games with fuzzy communication structure, Fuzzy sets and systems, 213 (2013), 74-90. doi: 10.1016/j.fss.2012.05.013. [7] A. Jiménez-Losada, J. R. Fernández, M. Ordóñez and M. Grabisch, Games on fuzzy communication structures with choquet players, European Journal of Operational Research, 207 (2010), 836-847. doi: 10.1016/j.ejor.2010.06.014. [8] Y. H. Kou, Study on the property developers dynamic capabilities from the perspective of structural innovation, Journal of Discrete Mathematical Sciences & Cryptography, 19 (2016), 591-606. [9] V. G. Luneeva Olga L.—Zakirova, Integration of mathematical and natural-science knowledge in school students' project-based activity., Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 2821-2840. [10] I. Mikhailova, A proof of zhil'tsov's theorem on decidability of equational theory of epigroups, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 179-201. [11] N. Ngoc-Thanh, M. Nunez and B. Trawinski, Collective intelligent information and database systems, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 32. [12] B. Peleg and P. Sudhölter, Introduction to the theory of cooperative games, Mathematical Programming and Operations Research, 34. Springer, Berlin, 2007. [13] L. S. Shapley, On balanced sets and cores, 14, 453-460. [14] L. S. Shapley, A value for n-person games, Annals of Mathematics Studies, 28 (1953), 307-317. [15] M. Tsurumi, T. Tanino and M. Inuiguchi, A shapley function on a class of cooperative fuzzy games, European Journal of Operational Research, 129 (2001), 596-618. doi: 10.1016/S0377-2217(99)00471-3. [16] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1947. [17] J. Zhan and Z. Qiang, Optimal fuzzy coalition structure and solution concepts of a class of fuzzy games, in International Conference on Computer Science and Service System, 2011, 3971-3975.
Open Access Under a Creative Commons license
Figures(1)
| 2023-03-27T20:28:26 |
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|
https://pos.sissa.it/382/114/
|
Volume 382 - The Eighth Annual Conference on Large Hadron Collider Physics (LHCP2020) - Session : Flavour Physics
Electroweak Penguin Decays
J. De Vries* on behalf of the LHCb collaboration
*corresponding author
Full text: pdf
Pre-published on: October 13, 2020
Published on:
Abstract
Measurements of $b \to s l l$ mediated electroweak penguin decays have recently shown tantalizing discrepancies with the Standard Model. However, improved and additional measurements are required to confirm or dismiss these observations. This talk discusses two recent results from the LHCb collaboration on such transitions.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2020-10-24T08:47:39 |
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|
https://par.nsf.gov/biblio/10352518-spectroscopic-studies-type-ia-supernovae-using-lstm-neural-networks
|
This content will become publicly available on May 1, 2023
Spectroscopic Studies of Type Ia Supernovae Using LSTM Neural Networks
Abstract We present a data-driven method based on long short-term memory (LSTM) neural networks to analyze spectral time series of Type Ia supernovae (SNe Ia). The data set includes 3091 spectra from 361 individual SNe Ia. The method allows for accurate reconstruction of the spectral sequence of an SN Ia based on a single observed spectrum around maximum light. The precision of the spectral reconstruction increases with more spectral time coverages, but the significant benefit of multiple epoch data at around optical maximum is only evident for observations separated by more than a week. The method shows great power in extracting the spectral information of SNe Ia and suggests that the most critical information of an SN Ia can be derived from a single spectrum around the optical maximum. The algorithm we have developed is important for the planning of spectroscopic follow-up observations of future SN surveys with the LSST/Rubin and WFIRST/Roman telescopes.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10352518
Journal Name:
The Astrophysical Journal
Volume:
930
Issue:
1
Page Range or eLocation-ID:
70
ISSN:
0004-637X
National Science Foundation
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2. ABSTRACT
While conventional Type Ia supernova (SN Ia) cosmology analyses rely primarily on rest-frame optical light curves to determine distances, SNe Ia are excellent standard candles in near-infrared (NIR) light, which is significantly less sensitive to dust extinction. An SN Ia spectral energy distribution (SED) model capable of fitting rest-frame NIR observations is necessary to fully leverage current and future SN Ia data sets from ground- and space-based telescopes including HST, LSST, JWST, and RST. We construct a hierarchical Bayesian model for SN Ia SEDs, continuous over time and wavelength, from the optical to NIR (B through H, or $0.35{-}1.8\, \mu$m). We model the SED as a combination of physically distinct host galaxy dust and intrinsic spectral components. The distribution of intrinsic SEDs over time and wavelength is modelled with probabilistic functional principal components and the covariance of residual functions. We train the model on a nearby sample of 79 SNe Ia with joint optical and NIR light curves by sampling the global posterior distribution over dust and intrinsic latent variables, SED components and population hyperparameters. Photometric distances of SNe Ia with NIR data near maximum obtain a total RMS error of 0.10 mag with our BayeSN model, compared tomore »
3. Abstract
Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012 to 2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SNe Ia (0.2 ≲z≲ 0.6) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-zHST data with 42 SNe Ia atz< 0.1 observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical photometry) to pursue a unique avenue to constrain the dark energy equation-of-state parameter,w. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size ∼0.06-0.1 mag with 1.5σ−2.5σsignificance depending on the method and step location used. Combining our NIR sample with cosmic microwave background constraints, we find 1 +w= −0.17 ± 0.12 (statistical + systematic errors). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measureH0=more »
4. ABSTRACT
The Type Ia supernovae (SNe Ia) 2011by, hosted in NGC 3972, and 2011fe, hosted in M101, are optical ‘twins,’ having almost identical optical light-curve shapes, colours, and near-maximum-brightness spectra. However, SN 2011fe had significantly more ultraviolet (UV; 1600 < λ < 2500 Å) flux than SN 2011by before and at peak luminosity. Several theoretical models predict that SNe Ia with higher progenitor metallicity should (1) have additional UV opacity and thus lower UV flux; (2) have an essentially unchanged optical spectral-energy distribution; (3) have a similar optical light-curve shape; and (4) because of the excess neutrons, produce more stable Fe-group elements at the expense of radioactive 56Ni and thus have a lower peak luminosity. Following these predictions, Foley and Kirshner suggested that the difference in UV flux between SNe 2011by and 2011fe was the result of their progenitors having significantly different metallicities. They also measured a large, but insignificant, difference between the peak absolute magnitudes of the SNe (ΔMV, peak = 0.60 ± 0.36 mag), with SN 2011fe being more luminous. We present a new Cepheid-based distance to NGC 3972, substantially improving the precision of the distance measurement for SN 2011by. With these new data, we determine that the SNe have significantly different peak luminosities (ΔMV, peak = 0.335 ± 0.069 mag). Consequently,more »
5. ABSTRACT
We present detailed investigation of a specific i-band light-curve feature in Type Ia supernovae (SNe Ia) using the rapid cadence and high signal-to-noise ratio light curves obtained by the Carnegie Supernova Project. The feature is present in most SNe Ia and emerges a few days after the i-band maximum. It is an abrupt change in curvature in the light curve over a few days and appears as a flattening in mild cases and a strong downward concave shape, or a ‘kink’, in the most extreme cases. We computed the second derivatives of Gaussian Process interpolations to study 54 rapid-cadence light curves. From the second derivatives we measure: (1) the timing of the feature in days relative to i-band maximum; tdm2(i) and (2) the strength and direction of the concavity in mag d−2; dm2(i). 76 per cent of the SNe Ia show a negative dm2(i), representing a downward concavity – either a mild flattening or a strong ‘kink’. The tdm2(i) parameter is shown to correlate with the colour-stretch parameter sBV, a SN Ia primary parameter. The dm2(i) parameter shows no correlation with sBV and therefore provides independent information. It is also largely independent of the spectroscopic and environmental properties. Dividing the sample based on the strength of themore »
| 2023-01-31T07:56:38 |
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|
https://www.bnl.gov/event.php?q=15990
|
# CFNS seminar
## "Studies on exotic hadrons at LHCb"
#### Presented by Dr. Liupan An, Sezione, INFN di Firenze
Thursday, November 12, 2020, 10:00 am — Videoconference / Virtual Event (see link below)
Abstract: Exotic hadrons, which are composed of more than three valence quarks, can provide new insights into the internal structure and dynamics of hadrons, thus improving our knowledge of the non-perturbative regime of QCD. Since 2003, various candidates for exotic states have been observed, to which the LHCb experiment has made major contributions. This seminar discusses the studies on exotic hadrons at LHCb. The most recent observation of structure in the $J/\psi$-pair invariant mass spectrum and study of resonant structure in $B^+ \to D^+ D^- K^+$ decays are presented.
Hosted by: Yong Zhao
15990 | INT/EXT | Events Calendar
| 2021-06-23T18:35:39 |
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|
https://lammps.sandia.gov/doc/dump_image.html
|
# dump movie command
## Syntax
dump ID group-ID style N file color diameter keyword value ...
• ID = user-assigned name for the dump
• group-ID = ID of the group of atoms to be imaged
• style = image or movie = style of dump command (other styles atom or cfg or dcd or xtc or xyz or local or custom are discussed on the dump doc page)
• N = dump every this many timesteps
• file = name of file to write image to
• color = atom attribute that determines color of each atom
• diameter = atom attribute that determines size of each atom
• zero or more keyword/value pairs may be appended
• keyword = atom or adiam or bond or line or tri or body or fix or size or view or center or up or zoom or persp or box or axes or subbox or shiny or ssao
atom = yes/no = do or do not draw atoms
adiam size = numeric value for atom diameter (distance units)
bond values = color width = color and width of bonds
color = atom or type or none
width = number or atom or type or none
number = numeric value for bond width (distance units)
line = color width
color = type
width = numeric value for line width (distance units)
tri = color tflag width
color = type
tflag = 1 for just triangle, 2 for just tri edges, 3 for both
width = numeric value for tringle edge width (distance units)
body = color bflag1 bflag2
color = type
bflag1,bflag2 = 2 numeric flags to affect how bodies are drawn
fix = fixID color fflag1 fflag2
fixID = ID of fix that generates objects to dray
color = type
fflag1,fflag2 = 2 numeric flags to affect how fix objects are drawn
size values = width height = size of images
width = width of image in # of pixels
height = height of image in # of pixels
view values = theta phi = view of simulation box
theta = view angle from +z axis (degrees)
phi = azimuthal view angle (degrees)
theta or phi can be a variable (see below)
center values = flag Cx Cy Cz = center point of image
flag = "s" for static, "d" for dynamic
Cx,Cy,Cz = center point of image as fraction of box dimension (0.5 = center of box)
Cx,Cy,Cz can be variables (see below)
up values = Ux Uy Uz = direction that is "up" in image
Ux,Uy,Uz = components of up vector
Ux,Uy,Uz can be variables (see below)
zoom value = zfactor = size that simulation box appears in image
zfactor = scale image size by factor > 1 to enlarge, factor < 1 to shrink
zfactor can be a variable (see below)
persp value = pfactor = amount of "perspective" in image
pfactor = amount of perspective (0 = none, < 1 = some, > 1 = highly skewed)
pfactor can be a variable (see below)
box values = yes/no diam = draw outline of simulation box
yes/no = do or do not draw simulation box lines
diam = diameter of box lines as fraction of shortest box length
axes values = yes/no length diam = draw xyz axes
yes/no = do or do not draw xyz axes lines next to simulation box
length = length of axes lines as fraction of respective box lengths
diam = diameter of axes lines as fraction of shortest box length
subbox values = yes/no diam = draw outline of processor sub-domains
yes/no = do or do not draw sub-domain lines
diam = diameter of sub-domain lines as fraction of shortest box length
shiny value = sfactor = shinyness of spheres and cylinders
sfactor = shinyness of spheres and cylinders from 0.0 to 1.0
ssao value = yes/no seed dfactor = SSAO depth shading
yes/no = turn depth shading on/off
seed = random # seed (positive integer)
dfactor = strength of shading from 0.0 to 1.0
## Examples
dump d0 all image 100 dump.\*.jpg type type
dump d1 mobile image 500 snap.\*.png element element ssao yes 4539 0.6
dump d2 all image 200 img-\*.ppm type type zoom 2.5 adiam 1.5 size 1280 720
dump m0 all movie 1000 movie.mpg type type size 640 480
dump m1 all movie 1000 movie.avi type type size 640 480
dump m2 all movie 100 movie.m4v type type zoom 1.8 adiam v_value size 1280 720
## Description
Dump a high-quality rendered image of the atom configuration every N timesteps and save the images either as a sequence of JPEG or PNG or PPM files, or as a single movie file. The options for this command as well as the dump_modify command control what is included in the image or movie and how it appears. A series of such images can easily be manually converted into an animated movie of your simulation or the process can be automated without writing the intermediate files using the dump movie style; see further details below. Other dump styles store snapshots of numerical data associated with atoms in various formats, as discussed on the dump doc page.
Note that a set of images or a movie can be made after a simulation has been run, using the rerun command to read snapshots from an existing dump file, and using these dump commands in the rerun script to generate the images/movie.
Here are two sample images, rendered as 1024x1024 JPEG files.
Click to see the full-size images:
Only atoms in the specified group are rendered in the image. The dump_modify region and thresh commands can also alter what atoms are included in the image. The filename suffix determines whether a JPEG, PNG, or PPM file is created with the image dump style. If the suffix is “.jpg” or “.jpeg”, then a JPEG format file is created, if the suffix is “.png”, then a PNG format is created, else a PPM (aka NETPBM) format file is created. The JPEG and PNG files are binary; PPM has a text mode header followed by binary data. JPEG images have lossy compression, PNG has lossless compression, and PPM files are uncompressed but can be compressed with gzip, if LAMMPS has been compiled with -DLAMMPS_GZIP and a “.gz” suffix is used.
Similarly, the format of the resulting movie is chosen with the movie dump style. This is handled by the underlying FFmpeg converter and thus details have to be looked up in the FFmpeg documentation. Typical examples are: .avi, .mpg, .m4v, .mp4, .mkv, .flv, .mov, .gif Additional settings of the movie compression like bitrate and framerate can be set using the dump_modify command.
To write out JPEG and PNG format files, you must build LAMMPS with support for the corresponding JPEG or PNG library. To convert images into movies, LAMMPS has to be compiled with the -DLAMMPS_FFMPEG flag. See the Build settings doc page for details.
Note
Because periodic boundary conditions are enforced only on timesteps when neighbor lists are rebuilt, the coordinates of an atom in the image may be slightly outside the simulation box.
Dumps are performed on timesteps that are a multiple of N (including timestep 0) and on the last timestep of a minimization if the minimization converges. Note that this means a dump will not be performed on the initial timestep after the dump command is invoked, if the current timestep is not a multiple of N. This behavior can be changed via the dump_modify first command, which can be useful if the dump command is invoked after a minimization ended on an arbitrary timestep. N can be changed between runs by using the dump_modify every command.
Dump image filenames must contain a wildcard character “*”, so that one image file per snapshot is written. The “*” character is replaced with the timestep value. For example, tmp.dump.*.jpg becomes tmp.dump.0.jpg, tmp.dump.10000.jpg, tmp.dump.20000.jpg, etc. Note that the dump_modify pad command can be used to insure all timestep numbers are the same length (e.g. 00010), which can make it easier to convert a series of images into a movie in the correct ordering.
Dump movie filenames on the other hand, must not have any wildcard character since only one file combining all images into a single movie will be written by the movie encoder.
The color and diameter settings determine the color and size of atoms rendered in the image. They can be any atom attribute defined for the dump custom command, including type and element. This includes per-atom quantities calculated by a compute, fix, or variable, which are prefixed by “c_”, “f_”, or “v_” respectively. Note that the diameter setting can be overridden with a numeric value applied to all atoms by the optional adiam keyword.
If type is specified for the color setting, then the color of each atom is determined by its atom type. By default the mapping of types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for types > 6. This mapping can be changed by the dump_modify acolor command.
If type is specified for the diameter setting then the diameter of each atom is determined by its atom type. By default all types have diameter 1.0. This mapping can be changed by the dump_modify adiam command.
If element is specified for the color and/or diameter setting, then the color and/or diameter of each atom is determined by which element it is, which in turn is specified by the element-to-type mapping specified by the “dump_modify element” command. By default every atom type is C (carbon). Every element has a color and diameter associated with it, which is the same as the colors and sizes used by the AtomEye visualization package.
If other atom attributes are used for the color or diameter settings, they are interpreted in the following way.
If “vx”, for example, is used as the color setting, then the color of the atom will depend on the x-component of its velocity. The association of a per-atom value with a specific color is determined by a “color map”, which can be specified via the dump_modify command. The basic idea is that the atom-attribute will be within a range of values, and every value within the range is mapped to a specific color. Depending on how the color map is defined, that mapping can take place via interpolation so that a value of -3.2 is halfway between “red” and “blue”, or discretely so that the value of -3.2 is “orange”.
If “vx”, for example, is used as the diameter setting, then the atom will be rendered using the x-component of its velocity as the diameter. If the per-atom value <= 0.0, them the atom will not be drawn. Note that finite-size spherical particles, as defined by atom_style sphere define a per-particle radius or diameter, which can be used as the diameter setting.
The various keywords listed above control how the image is rendered. As listed below, all of the keywords have defaults, most of which you will likely not need to change. The dump modify also has options specific to the dump image style, particularly for assigning colors to atoms, bonds, and other image features.
The atom keyword allow you to turn off the drawing of all atoms, if the specified value is no. Note that this will not turn off the drawing of particles that are represented as lines, triangles, or bodies, as discussed below. These particles can be drawn separately if the line, tri, or body keywords are used.
The adiam keyword allows you to override the diameter setting to set a single numeric size. All atoms will be drawn with that diameter, e.g. 1.5, which is in whatever distance units the input script defines, e.g. Angstroms.
The bond keyword allows to you to alter how bonds are drawn. A bond is only drawn if both atoms in the bond are being drawn due to being in the specified group and due to other selection criteria (e.g. region, threshold settings of the dump_modify command). By default, bonds are drawn if they are defined in the input data file as read by the read_data command. Using none for both the bond color and width value will turn off the drawing of all bonds.
If atom is specified for the bond color value, then each bond is drawn in 2 halves, with the color of each half being the color of the atom at that end of the bond.
If type is specified for the color value, then the color of each bond is determined by its bond type. By default the mapping of bond types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for bond types > 6. This mapping can be changed by the dump_modify bcolor command.
The bond width value can be a numeric value or atom or type (or none as indicated above).
If a numeric value is specified, then all bonds will be drawn as cylinders with that diameter, e.g. 1.0, which is in whatever distance units the input script defines, e.g. Angstroms.
If atom is specified for the width value, then each bond will be drawn with a width corresponding to the minimum diameter of the 2 atoms in the bond.
If type is specified for the width value then the diameter of each bond is determined by its bond type. By default all types have diameter 0.5. This mapping can be changed by the dump_modify bdiam command.
The line keyword can be used when atom_style line is used to define particles as line segments, and will draw them as lines. If this keyword is not used, such particles will be drawn as spheres, the same as if they were regular atoms. The only setting currently allowed for the color value is type, which will color the lines according to the atom type of the particle. By default the mapping of types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for types > 6. There is not yet an option to change this via the dump_modify command.
The line width can only be a numeric value, which specifies that all lines will be drawn as cylinders with that diameter, e.g. 1.0, which is in whatever distance units the input script defines, e.g. Angstroms.
The tri keyword can be used when atom_style tri is used to define particles as triangles, and will draw them as triangles or edges (3 lines) or both, depending on the setting for tflag. If edges are drawn, the width setting determines the diameters of the line segments. If this keyword is not used, triangle particles will be drawn as spheres, the same as if they were regular atoms. The only setting currently allowed for the color value is type, which will color the triangles according to the atom type of the particle. By default the mapping of types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for types > 6. There is not yet an option to change this via the dump_modify command.
The body keyword can be used when atom_style body is used to define body particles with internal state (e.g. sub-particles), and will drawn them in a manner specific to the body style. If this keyword is not used, such particles will be drawn as spheres, the same as if they were regular atoms.
The Howto body doc page describes the body styles LAMMPS currently supports, and provides more details as to the kind of body particles they represent and how they are drawn by this dump image command. For all the body styles, individual atoms can be either a body particle or a usual point (non-body) particle. Non-body particles will be drawn the same way they would be as a regular atom. The bflag1 and bflag2 settings are numerical values which are passed to the body style to affect how the drawing of a body particle is done. See the Howto body doc page for a description of what these parameters mean for each body style.
The only setting currently allowed for the color value is type, which will color the body particles according to the atom type of the particle. By default the mapping of types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for types > 6. There is not yet an option to change this via the dump_modify command.
The fix keyword can be used with a fix that produces objects to be drawn.
The fflag1 and fflag2 settings are numerical values which are passed to the fix to affect how the drawing of its objects is done. See the individual fix doc page for a description of what these parameters mean for a particular fix.
The only setting currently allowed for the color value is type, which will color the fix objects according to their type. By default the mapping of types to colors is as follows:
• type 1 = red
• type 2 = green
• type 3 = blue
• type 4 = yellow
• type 5 = aqua
• type 6 = cyan
and repeats itself for types > 6. There is not yet an option to change this via the dump_modify command.
The size keyword sets the width and height of the created images, i.e. the number of pixels in each direction.
The view, center, up, zoom, and persp values determine how 3d simulation space is mapped to the 2d plane of the image. Basically they control how the simulation box appears in the image.
All of the view, center, up, zoom, and persp values can be specified as numeric quantities, whose meaning is explained below. Any of them can also be specified as an equal-style variable, by using v_name as the value, where “name” is the variable name. In this case the variable will be evaluated on the timestep each image is created to create a new value. If the equal-style variable is time-dependent, this is a means of changing the way the simulation box appears from image to image, effectively doing a pan or fly-by view of your simulation.
The view keyword determines the viewpoint from which the simulation box is viewed, looking towards the center point. The theta value is the vertical angle from the +z axis, and must be an angle from 0 to 180 degrees. The phi value is an azimuthal angle around the z axis and can be positive or negative. A value of 0.0 is a view along the +x axis, towards the center point. If theta or phi are specified via variables, then the variable values should be in degrees.
The center keyword determines the point in simulation space that will be at the center of the image. Cx, Cy, and Cz are specified as fractions of the box dimensions, so that (0.5,0.5,0.5) is the center of the simulation box. These values do not have to be between 0.0 and 1.0, if you want the simulation box to be offset from the center of the image. Note, however, that if you choose strange values for Cx, Cy, or Cz you may get a blank image. Internally, Cx, Cy, and Cz are converted into a point in simulation space. If flag is set to “s” for static, then this conversion is done once, at the time the dump command is issued. If flag is set to “d” for dynamic then the conversion is performed every time a new image is created. If the box size or shape is changing, this will adjust the center point in simulation space.
The up keyword determines what direction in simulation space will be “up” in the image. Internally it is stored as a vector that is in the plane perpendicular to the view vector implied by the theta and pni values, and which is also in the plane defined by the view vector and user-specified up vector. Thus this internal vector is computed from the user-specified up vector as
up_internal = view cross (up cross view)
This means the only restriction on the specified up vector is that it cannot be parallel to the view vector, implied by the theta and phi values.
The zoom keyword scales the size of the simulation box as it appears in the image. The default zfactor value of 1 should display an image mostly filled by the atoms in the simulation box. A zfactor > 1 will make the simulation box larger; a zfactor < 1 will make it smaller. Zfactor must be a value > 0.0.
The persp keyword determines how much depth perspective is present in the image. Depth perspective makes lines that are parallel in simulation space appear non-parallel in the image. A pfactor value of 0.0 means that parallel lines will meet at infinity (1.0/pfactor), which is an orthographic rendering with no perspective. A pfactor value between 0.0 and 1.0 will introduce more perspective. A pfactor value > 1 will create a highly skewed image with a large amount of perspective.
Note
The persp keyword is not yet supported as an option.
The box keyword determines if and how the simulation box boundaries are rendered as thin cylinders in the image. If no is set, then the box boundaries are not drawn and the diam setting is ignored. If yes is set, the 12 edges of the box are drawn, with a diameter that is a fraction of the shortest box length in x,y,z (for 3d) or x,y (for 2d). The color of the box boundaries can be set with the dump_modify boxcolor command.
The axes keyword determines if and how the coordinate axes are rendered as thin cylinders in the image. If no is set, then the axes are not drawn and the length and diam settings are ignored. If yes is set, 3 thin cylinders are drawn to represent the x,y,z axes in colors red,green,blue. The origin of these cylinders will be offset from the lower left corner of the box by 10%. The length setting determines how long the cylinders will be as a fraction of the respective box lengths. The diam setting determines their thickness as a fraction of the shortest box length in x,y,z (for 3d) or x,y (for 2d).
The subbox keyword determines if and how processor sub-domain boundaries are rendered as thin cylinders in the image. If no is set (default), then the sub-domain boundaries are not drawn and the diam setting is ignored. If yes is set, the 12 edges of each processor sub-domain are drawn, with a diameter that is a fraction of the shortest box length in x,y,z (for 3d) or x,y (for 2d). The color of the sub-domain boundaries can be set with the dump_modify boxcolor command.
The shiny keyword determines how shiny the objects rendered in the image will appear. The sfactor value must be a value 0.0 <= sfactor <= 1.0, where sfactor = 1 is a highly reflective surface and sfactor = 0 is a rough non-shiny surface.
The ssao keyword turns on/off a screen space ambient occlusion (SSAO) model for depth shading. If yes is set, then atoms further away from the viewer are darkened via a randomized process, which is perceived as depth. The calculation of this effect can increase the cost of computing the image by roughly 2x. The strength of the effect can be scaled by the dfactor parameter. If no is set, no depth shading is performed.
A series of JPEG, PNG, or PPM images can be converted into a movie file and then played as a movie using commonly available tools. Using dump style movie automates this step and avoids the intermediate step of writing (many) image snapshot file. But LAMMPS has to be compiled with -DLAMMPS_FFMPEG and an FFmpeg executable have to be installed.
To manually convert JPEG, PNG or PPM files into an animated GIF or MPEG or other movie file you can use:
1. Use the ImageMagick convert program.
% convert *.jpg foo.gif
% convert -loop 1 *.ppm foo.mpg
Animated GIF files from ImageMagick are not optimized. You can use a program like gifsicle to optimize and thus massively shrink them. MPEG files created by ImageMagick are in MPEG-1 format with a rather inefficient compression and low quality compared to more modern compression styles like MPEG-4, H.264, VP8, VP9, H.265 and so on.
1. Use QuickTime.
Select “Open Image Sequence” under the File menu Load the images into QuickTime to animate them Select “Export” under the File menu Save the movie as a QuickTime movie (*.mov) or in another format. QuickTime can generate very high quality and efficiently compressed movie files. Some of the supported formats require to buy a license and some are not readable on all platforms until specific runtime libraries are installed.
1. Use FFmpeg
FFmpeg is a command line tool that is available on many platforms and allows extremely flexible encoding and decoding of movies.
cat snap.*.jpg | ffmpeg -y -f image2pipe -c:v mjpeg -i - -b:v 2000k movie.m4v
cat snap.*.ppm | ffmpeg -y -f image2pipe -c:v ppm -i - -b:v 2400k movie.avi
Front ends for FFmpeg exist for multiple platforms. For more information see the FFmpeg homepage
Play the movie:
1. Use your browser to view an animated GIF movie.
Select “Open File” under the File menu Load the animated GIF file
• b) Use the freely available mplayer or ffplay tool to view a movie. Both are available for multiple OSes and support a large variety of file formats and decoders.
% mplayer foo.mpg
% ffplay bar.avi
• c) Use the Pizza.py animate tool, which works directly on a series of image files.
a = animate("foo*.jpg")
• d) QuickTime and other Windows- or MacOS-based media players can obviously play movie files directly. Similarly for corresponding tools bundled with Linux desktop environments. However, due to licensing issues with some file formats, the formats may require installing additional libraries, purchasing a license, or may not be supported.
See the Modify doc page for information on how to add new compute and fix styles to LAMMPS to calculate per-atom quantities which could then be output into dump files.
## Restrictions
To write JPEG images, you must use the -DLAMMPS_JPEG switch when building LAMMPS and link with a JPEG library. To write PNG images, you must use the -DLAMMPS_PNG switch when building LAMMPS and link with a PNG library.
To write movie dumps, you must use the -DLAMMPS_FFMPEG switch when building LAMMPS and have the FFmpeg executable available on the machine where LAMMPS is being run. Typically it’s name is lowercase, i.e. ffmpeg.
See the Build settings doc page for details.
Note that since FFmpeg is run as an external program via a pipe, LAMMPS has limited control over its execution and no knowledge about errors and warnings printed by it. Those warnings and error messages will be printed to the screen only. Due to the way image data is communicated to FFmpeg, it will often print the message
pipe:: Input/output error
which can be safely ignored. Other warnings and errors have to be addressed according to the FFmpeg documentation. One known issue is that certain movie file formats (e.g. MPEG level 1 and 2 format streams) have video bandwidth limits that can be crossed when rendering too large of image sizes. Typical warnings look like this:
[mpeg @ 0x98b5e0] packet too large, ignoring buffer limits to mux it
[mpeg @ 0x98b5e0] buffer underflow st=0 bufi=281407 size=285018
[mpeg @ 0x98b5e0] buffer underflow st=0 bufi=283448 size=285018
In this case it is recommended to either reduce the size of the image or encode in a different format that is also supported by your copy of FFmpeg, and which does not have this limitation (e.g. .avi, .mkv, mp4).
## Default
The defaults for the keywords are as follows:
• adiam = not specified (use diameter setting)
• atom = yes
• bond = none none (if no bonds in system)
• bond = atom 0.5 (if bonds in system)
• size = 512 512
• view = 60 30 (for 3d)
• view = 0 0 (for 2d)
• center = s 0.5 0.5 0.5
• up = 0 0 1 (for 3d)
• up = 0 1 0 (for 2d)
• zoom = 1.0
• persp = 0.0
• box = yes 0.02
• axes = no 0.0 0.0
• subbox no 0.0
• shiny = 1.0
• ssao = no
| 2020-09-20T05:41:49 |
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|
https://par.nsf.gov/biblio/10376413-uniform-recalibration-common-spectrophotometry-standard-stars-onto-calspec-system-using-supernova-integral-field-spectrograph
|
Uniform Recalibration of Common Spectrophotometry Standard Stars onto the CALSPEC System Using the SuperNova Integral Field Spectrograph
Abstract
We calibrate spectrophotometric optical spectra of 32 stars commonly used as standard stars, referenced to 14 stars already on the Hubble Space Telescope–based CALSPEC flux system. Observations of CALSPEC and non-CALSPEC stars were obtained with the SuperNova Integral Field Spectrograph over the wavelength range 3300–9400 Å as calibration for the Nearby Supernova Factory cosmology experiment. In total, this analysis used 4289 standard-star spectra taken on photometric nights. As a modern cosmology analysis, all presubmission methodological decisions were made with the flux scale and external comparison results blinded. The large number of spectra per star allows us to treat the wavelength-by-wavelength calibration for all nights simultaneously with a Bayesian hierarchical model, thereby enabling a consistent treatment of the Type Ia supernova cosmology analysis and the calibration on which it critically relies. We determine the typical per-observation repeatability (median 14 mmag for exposures ≳5 s), the Maunakea atmospheric transmission distribution (median dispersion of 7 mmag with uncertainty 1 mmag), and the scatter internal to our CALSPEC reference stars (median of 8 mmag). We also check our standards against literature filter photometry, finding generally good agreement over the full 12 mag range. Overall, the mean of our system is calibrated to the more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10376413
Journal Name:
The Astrophysical Journal Supplement Series
Volume:
263
Issue:
1
Page Range or eLocation-ID:
Article No. 1
ISSN:
0067-0049
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. We introduce the ongoing MaStar project, which is going to construct a large, well-calibrated, high quality empirical stellar library with more than 8000 stars covering the wavelength range 3,622 - 10,354Å at a resolution of R̃2000, and with better than 3% relative flux calibration. The spectra are taken using hexagonal fibre bundles feeding the BOSS spectrographs on the 2.5m Sloan Foundation Telescope, by piggybacking on the SDSS-IV/APOGEE-2 observations. Compared to previous efforts of empirical libraries, the MaStar Library will have a more comprehensive stellar parameter coverage, especially in cool dwarfs, low metallicity stars, and stars with different [α/Fe]. This is achieved by a target selection method based on large spectroscopic catalogs from APOGEE, LAMOST, and SEGUE, combined with photometric selection. This empirical library will provide a new basis for calibrating theoretical spectral libraries and for stellar population synthesis. In addition, with identical spectral coverage and resolution to the ongoing integral field spectroscopy survey of nearby galaxies -- SDSS-IV/MaNGA (Mapping Nearby Galaxies at APO). this library is ideal for spectral modelling and stellar population analysis of MaNGA data.
2. ABSTRACT
Clouds and other features in exoplanet and brown dwarf atmospheres cause variations in brightness as they rotate in and out of view. Ground-based instruments reach the high contrasts and small inner working angles needed to monitor these faint companions, but their small fields of view lack simultaneous photometric references to correct for non-astrophysical variations. We present a novel approach for making ground-based light curves of directly imaged companions using high-cadence differential spectrophotometric monitoring, where the simultaneous reference is provided by a double-grating 360○ vector Apodizing Phase Plate (dgvAPP360) coronagraph. The dgvAPP360 enables high-contrast companion detections without blocking the host star, allowing it to be used as a simultaneous reference. To further reduce systematic noise, we emulate exoplanet transmission spectroscopy, where the light is spectrally dispersed and then recombined into white-light flux. We do this by combining the dgvAPP360 with the infrared Arizona Lenslets for Exoplanet Spectroscopy integral field spectrograph on the Large Binocular Telescope Interferometer. To demonstrate, we observed the red companion HD 1160 B (separation ∼780 mas) for one night, and detect $8.8{{\ \rm per\ cent}}$ semi-amplitude sinusoidal variability with an ∼3.24 h period in its detrended white-light curve. We achieve the greatest precision in ground-based high-contrast imaging light curves ofmore »
3. Context. The variety of physical processes at play in chemically peculiar stars makes it difficult to determine their fundamental parameters. In particular, for the magnetic ones, called Ap stars, the strong magnetic fields and the induced spotted stellar surfaces may lead to biased effective temperatures when these values are derived through spectro-photometry. Aims. We propose to benefit from the exquisite angular resolution provided by long-baseline interferometry in the visible to determine the accurate angular diameters of a number of Ap stars, and thus estimate their radii by a method that is as independent as possible of atmospheric models. Methods. We used the visible spectrograph VEGA at the CHARA interferometric array to complete the sample of Ap stars currently observable with this technique. We estimated the angular diameter and radius of six new targets. We estimated their bolometric flux based solely on observational spectroscopic and photometric data to derive nearly model-independent luminosities and effective temperatures. Results. We extend to 14 the number of Ap stars for which interferometric angular diameters have been measured. The fundamental parameters we derived for the complete Ap sample are compared with those obtained through a self-consistent spectroscopic analysis. Based on a model fitting approach of high-resolutionmore »
4. We present optical photometry and spectroscopy of the Type II supernova ASASSN-14jb, together with Very Large Telescope (VLT) Multi Unit Spectroscopic Explorer (MUSE) integral field observations of its host galaxy and a nebular-phase spectrum. This supernova, in the nearby galaxy ESO 467-G051 ( z = 0.006), was discovered and followed-up by the all-sky automated survey for supernovae (ASAS-SN). We obtained well-sampled las cumbres network (LCOGTN) B V g r i and Swift w 2 m 1 w 1 u b v optical, near-UV/optical light curves, and several optical spectra in the early photospheric phases. The transient ASASSN-14jb exploded ∼2 kpc above the star-forming disk of ESO 467-G051, an edge-on disk galaxy. The large projected distance from the disk of the supernova position and the non-detection of any H II region in a 1.4 kpc radius in projection are in conflict with the standard environment of core-collapse supernova progenitors and suggests the possible scenario that the progenitor received a kick in a binary interaction. We present analysis of the optical light curves and spectra, from which we derived a distance of 25 ± 2 Mpc using state-of-the-art empirical methods for Type II SNe, physical properties of the SN explosion ( 56 Ni mass, explosionmore »
5. We present the goals, strategy and first results of the high-cadence Galactic plane survey using the Zwicky Transient Facility (ZTF). The goal of the survey is to unveil the Galactic population of short-period variable stars, including short period binaries and stellar pulsators with periods less than a few hours. Between June 2018 and January 2019, we observed 64 ZTF fields resulting in 2990 deg2 of high stellar density in ZTF-r band along the Galactic Plane. Each field was observed continuously for 1.5 to 6 hrs with a cadence of 40 sec. Most fields have between 200 and 400 observations obtained over 2-3 continuous nights. As part of this survey we extract a total of ≈230 million individual objects with at least 80 epochs obtained during the high-cadence Galactic Plane survey reaching an average depth of ZTF-r ≈20.5 mag. For four selected fields with 2 million to 10 million individual objects per field we calculate different variability statistics and find that ≈1-2% of the objects are astrophysically variable over the observed period. We present a progress report on recent discoveries, including a new class of compact pulsators, the first members of a new class of Roche Lobe filling hot subdwarf binariesmore »
| 2023-03-21T17:35:41 |
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|
https://publons.com/publon/2803/
|
0 pre-pub reviews
2 post-pub reviews
##### Abstract
We present a reflectance model for dielectric cylinders with rough surfaces such as human hair fibers. Our model is energy conserving and can evaluate arbitrarily many orders of internal reflection. Accounting for compression and contraction of specular cones produces a new longitudinal scattering function which is non-Gaussian and includes an off-specular peak. Accounting for roughness in the azimuthal direction leads to an integral across the hair fiber which is efficiently evaluated using a Gaussian quadrature. Solving cubic equations is avoided, caustics are included in the model in a consistent fashion, and more accurate colors are predicted by considering many internal pathways.
##### Authors
d'Eon, Eugene; Francois, Guillaume; Hill, Martin; Letteri, Joe; Aubry, Jean-Marie
• 1 author
• 1 reviewer
• Review of
### An Energy-Conserving Hair Reflectance Model
Following presentation by Eugene d'Eon of the paper in Prague I can recall two questions:
1) Ravi Ramamoorthi: "It seems that there is an analogous relationship between the Marschner model and the spherical Gaussian M function in your paper much like the difference between Blinn Phong and Phong specular lobes for surfaces". Response: "Hmmm, I'm not sure."
2) Marcos Fajardo: "We found an importance sampling scheme for the Marschner model. Can you comment on importance sampling for your new model?" Response: "No, haven't thought about it." (However, a method was later published in a SIGGRAPH 2013 technical brief that importance samples it completely and analytically).
Published in
Reviewed by
• Review of
### An Energy-Conserving Hair Reflectance Model
For very narrow spherical Gaussians, numerical issues can arise in finite precision floating calculations. We found the following special cases useful in our implementation. To evaluate the $M$ function when the variance is low, $v < 0.1$, we use $$M\left(v,\theta _{\text{cone}},\theta _o\right) \approx \exp \left(\log \left(I_0\left(a\right)\right)+b-\frac{1}{v}+0.6931+\log \left(\frac{1}{2 v}\right)\right)$$ where $a = \cos \theta _{\text{cone}} \cos \theta_o / v$ and $b = \sin \theta _{\text{cone}} \sin \theta_o / v$. The log of the Bessel function can also be problematic for large arguments for we use the following special case for $\log( I_0(x))$ when $x > 12$: $$\log( I_0(x)) \approx x + 0.5 \left( -\log ( 2 \pi ) + \log \frac{1}{x} + \frac{1}{8x} \right).$$
Published in
Reviewed by
All peer review content displayed here is covered by a Creative Commons CC BY 4.0 license.
| 2021-01-19T06:11:25 |
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|
https://lammps.sandia.gov/doc/kspace_modify.html
|
# kspace_modify command
## Syntax
kspace_modify keyword value ...
• one or more keyword/value pairs may be listed
• keyword = collective or compute or cutoff/adjust or diff or disp/auto or fftbench or force/disp/kspace or force/disp/real or force or gewald/disp or gewald or kmax/ewald or mesh or minorder or mix/disp or order/disp or order or overlap or scafacos or slab or splittol
collective value = yes or no
compute value = yes or no
cutoff/adjust value = yes or no
diff value = ad or ik = 2 or 4 FFTs for PPPM in smoothed or non-smoothed mode
disp/auto value = yes or no
fftbench value = yes or no
force/disp/real value = accuracy (force units)
force/disp/kspace value = accuracy (force units)
force value = accuracy (force units)
gewald value = rinv (1/distance units)
rinv = G-ewald parameter for Coulombics
gewald/disp value = rinv (1/distance units)
rinv = G-ewald parameter for dispersion
kmax/ewald value = kx ky kz
kx,ky,kz = number of Ewald sum kspace vectors in each dimension
mesh value = x y z
x,y,z = grid size in each dimension for long-range Coulombics
mesh/disp value = x y z
x,y,z = grid size in each dimension for 1/r^6 dispersion
minorder value = M
M = min allowed extent of Gaussian when auto-adjusting to minimize grid communication
mix/disp value = pair or geom or none
order value = N
N = extent of Gaussian for PPPM or MSM mapping of charge to grid
order/disp value = N
N = extent of Gaussian for PPPM mapping of dispersion term to grid
overlap = yes or no = whether the grid stencil for PPPM is allowed to overlap into more than the nearest-neighbor processor
pressure/scalar value = yes or no
scafacos values = option value1 value2 ...
option = tolerance
value = energy or energy_rel or field or field_rel or potential or potential_rel
option = fmm_tuning
value = 0 or 1
slab value = volfactor or nozforce
volfactor = ratio of the total extended volume used in the
2d approximation compared with the volume of the simulation domain
nozforce turns off kspace forces in the z direction
splittol value = tol
tol = relative size of two eigenvalues (see discussion below)
## Examples
kspace_modify mesh 24 24 30 order 6
kspace_modify slab 3.0
kspace_modify scafacos tolerance energy
## Description
Set parameters used by the kspace solvers defined by the kspace_style command. Not all parameters are relevant to all kspace styles.
The collective keyword applies only to PPPM. It is set to no by default, except on IBM BlueGene machines. If this option is set to yes, LAMMPS will use MPI collective operations to remap data for 3d-FFT operations instead of the default point-to-point communication. This is faster on IBM BlueGene machines, and may also be faster on other machines if they have an efficient implementation of MPI collective operations and adequate hardware.
The compute keyword allows Kspace computations to be turned off, even though a kspace_style is defined. This is not useful for running a real simulation, but can be useful for debugging purposes or for computing only partial forces that do not include the Kspace contribution. You can also do this by simply not defining a kspace_style, but a Kspace-compatible pair_style requires a kspace style to be defined. This keyword gives you that option.
The cutoff/adjust keyword applies only to MSM. If this option is turned on, the Coulombic cutoff will be automatically adjusted at the beginning of the run to give the desired estimated error. Other cutoffs such as LJ will not be affected. If the grid is not set using the mesh command, this command will also attempt to use the optimal grid that minimizes cost using an estimate given by (Hardy). Note that this cost estimate is not exact, somewhat experimental, and still may not yield the optimal parameters.
The diff keyword specifies the differentiation scheme used by the PPPM method to compute forces on particles given electrostatic potentials on the PPPM mesh. The ik approach is the default for PPPM and is the original formulation used in (Hockney). It performs differentiation in Kspace, and uses 3 FFTs to transfer each component of the computed fields back to real space for total of 4 FFTs per timestep.
The analytic differentiation ad approach uses only 1 FFT to transfer information back to real space for a total of 2 FFTs per timestep. It then performs analytic differentiation on the single quantity to generate the 3 components of the electric field at each grid point. This is sometimes referred to as “smoothed” PPPM. This approach requires a somewhat larger PPPM mesh to achieve the same accuracy as the ik method. Currently, only the ik method (default) can be used for a triclinic simulation cell with PPPM. The ad method is always used for MSM.
Note
Currently, not all PPPM styles support the ad option. Support for those PPPM variants will be added later.
The disp/auto option controls whether the pppm/disp is allowed to generate PPPM parameters automatically. If set to no, parameters have to be specified using the gewald/disp, mesh/disp, force/disp/real or force/disp/kspace keywords, or the code will stop with an error message. When this option is set to yes, the error message will not appear and the simulation will start. For a typical application, using the automatic parameter generation will provide simulations that are either inaccurate or slow. Using this option is thus not recommended. For guidelines on how to obtain good parameters, see the How-To discussion.
The fftbench keyword applies only to PPPM. It is off by default. If this option is turned on, LAMMPS will perform a short FFT benchmark computation and report its timings, and will thus finish a some seconds later than it would if this option were off.
The force/disp/real and force/disp/kspace keywords set the force accuracy for the real and space computations for the dispersion part of pppm/disp. As shown in (Isele-Holder), optimal performance and accuracy in the results is obtained when these values are different.
The force keyword overrides the relative accuracy parameter set by the kspace_style command with an absolute accuracy. The accuracy determines the RMS error in per-atom forces calculated by the long-range solver and is thus specified in force units. A negative value for the accuracy setting means to use the relative accuracy parameter. The accuracy setting is used in conjunction with the pairwise cutoff to determine the number of K-space vectors for style ewald, the FFT grid size for style pppm, or the real space grid size for style msm.
The gewald keyword sets the value of the Ewald or PPPM G-ewald parameter for charge as rinv in reciprocal distance units. Without this setting, LAMMPS chooses the parameter automatically as a function of cutoff, precision, grid spacing, etc. This means it can vary from one simulation to the next which may not be desirable for matching a KSpace solver to a pre-tabulated pairwise potential. This setting can also be useful if Ewald or PPPM fails to choose a good grid spacing and G-ewald parameter automatically. If the value is set to 0.0, LAMMPS will choose the G-ewald parameter automatically. MSM does not use the gewald parameter.
The gewald/disp keyword sets the value of the Ewald or PPPM G-ewald parameter for dispersion as rinv in reciprocal distance units. It has the same meaning as the gewald setting for Coulombics.
The kmax/ewald keyword sets the number of kspace vectors in each dimension for kspace style ewald. The three values must be positive integers, or else (0,0,0), which unsets the option. When this option is not set, the Ewald sum scheme chooses its own kspace vectors, consistent with the user-specified accuracy and pairwise cutoff. In any case, if kspace style ewald is invoked, the values used are printed to the screen and the log file at the start of the run.
The mesh keyword sets the grid size for kspace style pppm or msm. In the case of PPPM, this is the FFT mesh, and each dimension must be factorizable into powers of 2, 3, and 5. In the case of MSM, this is the finest scale real-space mesh, and each dimension must be factorizable into powers of 2. When this option is not set, the PPPM or MSM solver chooses its own grid size, consistent with the user-specified accuracy and pairwise cutoff. Values for x,y,z of 0,0,0 unset the option.
The mesh/disp keyword sets the grid size for kspace style pppm/disp. This is the FFT mesh for long-range dispersion and ach dimension must be factorizable into powers of 2, 3, and 5. When this option is not set, the PPPM solver chooses its own grid size, consistent with the user-specified accuracy and pairwise cutoff. Values for x,y,z of 0,0,0 unset the option.
The minorder keyword allows LAMMPS to reduce the order setting if necessary to keep the communication of ghost grid point limited to exchanges between nearest-neighbor processors. See the discussion of the overlap keyword for details. If the overlap keyword is set to yes, which is the default, this is never needed. If it set to no and overlap occurs, then LAMMPS will reduce the order setting, one step at a time, until the ghost grid overlap only extends to nearest neighbor processors. The minorder keyword limits how small the order setting can become. The minimum allowed value for PPPM is 2, which is the default. If minorder is set to the same value as order then no reduction is allowed, and LAMMPS will generate an error if the grid communication is non-nearest-neighbor and overlap is set to no. The minorder keyword is not currently supported in MSM.
The mix/disp keyword selects the mixing rule for the dispersion coefficients. With pair, the dispersion coefficients of unlike types are computed as indicated with pair_modify. With geom, geometric mixing is enforced on the dispersion coefficients in the kspace coefficients. When using the arithmetic mixing rule, this will speed-up the simulations but introduces some error in the force computations, as shown in (Wennberg). With none, it is assumed that no mixing rule is applicable. Splitting of the dispersion coefficients will be performed as described in (Isele-Holder).
This splitting can be influenced with the splittol keywords. Only the eigenvalues that are larger than tol compared to the largest eigenvalues are included. Using this keywords the original matrix of dispersion coefficients is approximated. This leads to faster computations, but the accuracy in the reciprocal space computations of the dispersion part is decreased.
The order keyword determines how many grid spacings an atom’s charge extends when it is mapped to the grid in kspace style pppm or msm. The default for this parameter is 5 for PPPM and 8 for MSM, which means each charge spans 5 or 8 grid cells in each dimension, respectively. For the LAMMPS implementation of MSM, the order can range from 4 to 10 and must be even. For PPPM, the minimum allowed setting is 2 and the maximum allowed setting is 7. The larger the value of this parameter, the smaller that LAMMPS will set the grid size, to achieve the requested accuracy. Conversely, the smaller the order value, the larger the grid size will be. Note that there is an inherent trade-off involved: a small grid will lower the cost of FFTs or MSM direct sum, but a larger order parameter will increase the cost of interpolating charge/fields to/from the grid.
The PPPM order parameter may be reset by LAMMPS when it sets up the FFT grid if the implied grid stencil extends beyond the grid cells owned by neighboring processors. Typically this will only occur when small problems are run on large numbers of processors. A warning will be generated indicating the order parameter is being reduced to allow LAMMPS to run the problem. Automatic adjustment of the order parameter is not supported in MSM.
The order/disp keyword determines how many grid spacings an atom’s dispersion term extends when it is mapped to the grid in kspace style pppm/disp. It has the same meaning as the order setting for Coulombics.
The overlap keyword can be used in conjunction with the minorder keyword with the PPPM styles to adjust the amount of communication that occurs when values on the FFT grid are exchanged between processors. This communication is distinct from the communication inherent in the parallel FFTs themselves, and is required because processors interpolate charge and field values using grid point values owned by neighboring processors (i.e. ghost point communication). If the overlap keyword is set to yes then this communication is allowed to extend beyond nearest-neighbor processors, e.g. when using lots of processors on a small problem. If it is set to no then the communication will be limited to nearest-neighbor processors and the order setting will be reduced if necessary, as explained by the minorder keyword discussion. The overlap keyword is always set to yes in MSM.
The pressure/scalar keyword applies only to MSM. If this option is turned on, only the scalar pressure (i.e. (Pxx + Pyy + Pzz)/3.0) will be computed, which can be used, for example, to run an isotropic barostat. Computing the full pressure tensor with MSM is expensive, and this option provides a faster alternative. The scalar pressure is computed using a relationship between the Coulombic energy and pressure (Hummer) instead of using the virial equation. This option cannot be used to access individual components of the pressure tensor, to compute per-atom virial, or with suffix kspace/pair styles of MSM, like OMP or GPU.
The scafacos keyword is used for settings that are passed to the ScaFaCoS library when using kspace_style scafacos.
The tolerance option affects how the accuracy specified with the kspace_style command is interpreted by ScaFaCoS. The following values may be used:
• energy = absolute accuracy in total Coulombic energy
• energy_rel = relative accuracy in total Coulombic energy
• potential = absolute accuracy in total Coulombic potential
• potential_rel = relative accuracy in total Coulombic potential
• field = absolute accuracy in electric field
• field_rel = relative accuracy in electric field
The values with suffix _rel indicate the tolerance is a relative tolerance; the other values impose an absolute tolerance on the given quantity. Absolute tolerance in this case means, that for a given quantity q and a given absolute tolerance of t_a the result should be between q-t_a and q+t_a. For a relative tolerance t_r the relative error should not be greater than t_r, i.e. abs(1 - (result/q)) < t_r. As a consequence of this, the tolerance type should be checked, when performing computations with a high absolute field / energy. E.g. if the total energy in the system is 1000000.0 an absolute tolerance of 1e-3 would mean that the result has to be between 999999.999 and 1000000.001, which would be equivalent to a relative tolerance of 1e-9.
The energy and energy_rel values, set a tolerance based on the total Coulombic energy of the system. The potential and potential_rel set a tolerance based on the per-atom Coulombic energy. The field and field_rel tolerance types set a tolerance based on the electric field values computed by ScaFaCoS. Since per-atom forces are derived from the per-atom electric field, this effectively sets a tolerance on the forces, similar to other LAMMPS KSpace styles, as explained on the kspace_style doc page.
Note that not all ScaFaCoS solvers support all tolerance types. These are the allowed values for each method:
• fmm = energy and energy_rel
• p2nfft = field (1d-,2d-,3d-periodic systems) or potential (0d-periodic)
• p3m = field
• ewald = field
• direct = has no tolerance tuning
If the tolerance type is not changed, the default values for the tolerance type are the first values in the above list, e.g. energy is the default tolerance type for the fmm solver.
The fmm_tuning option is only relevant when using the FMM method. It activates (value=1) or deactivates (value=0) an internal tuning mechanism for the FMM solver. The tuning operation runs sequentially and can be very time-consuming. Usually it is not needed for systems with a homogeneous charge distribution. The default for this option is therefore 0. The FMM internal tuning is performed once, when the solver is set up.
The slab keyword allows an Ewald or PPPM solver to be used for a systems that are periodic in x,y but non-periodic in z - a boundary setting of “boundary p p f”. This is done by treating the system as if it were periodic in z, but inserting empty volume between atom slabs and removing dipole inter-slab interactions so that slab-slab interactions are effectively turned off. The volfactor value sets the ratio of the extended dimension in z divided by the actual dimension in z. The recommended value is 3.0. A larger value is inefficient; a smaller value introduces unwanted slab-slab interactions. The use of fixed boundaries in z means that the user must prevent particle migration beyond the initial z-bounds, typically by providing a wall-style fix. The methodology behind the slab option is explained in the paper by (Yeh). The slab option is also extended to non-neutral systems (Ballenegger).
An alternative slab option can be invoked with the nozforce keyword in lieu of the volfactor. This turns off all kspace forces in the z direction. The nozforce option is not supported by MSM. For MSM, any combination of periodic, non-periodic, or shrink-wrapped boundaries can be set using boundary (the slab approximation in not needed). The slab keyword is not currently supported by Ewald or PPPM when using a triclinic simulation cell. The slab correction has also been extended to point dipole interactions (Klapp) in kspace_style ewald/disp, ewald/dipole, and pppm/dipole.
Note
If you wish to apply an electric field in the Z-direction, in conjunction with the slab keyword, you should do it by adding explicit charged particles to the +/- Z surfaces. If you do it via the fix efield command, it will not give the correct dielectric constant due to the Yeh/Berkowitz (Yeh) correction not being compatible with how fix efield works.
The force/disp/real and force/disp/kspace keywords set the force accuracy for the real and space computations for the dispersion part of pppm/disp. As shown in (Isele-Holder), optimal performance and accuracy in the results is obtained when these values are different.
The disp/auto option controls whether the pppm/disp is allowed to generate PPPM parameters automatically. If set to no, parameters have to be specified using the gewald/disp, mesh/disp, force/disp/real or force/disp/kspace keywords, or the code will stop with an error message. When this option is set to yes, the error message will not appear and the simulation will start. For a typical application, using the automatic parameter generation will provide simulations that are either inaccurate or slow. Using this option is thus not recommended. For guidelines on how to obtain good parameters, see the Howto dispersion doc page.
none
## Default
The option defaults are mesh = mesh/disp = 0 0 0, order = order/disp = 5 (PPPM), order = 10 (MSM), minorder = 2, overlap = yes, force = -1.0, gewald = gewald/disp = 0.0, slab = 1.0, compute = yes, cutoff/adjust = yes (MSM), pressure/scalar = yes (MSM), fftbench = no (PPPM), diff = ik (PPPM), mix/disp = pair, force/disp/real = -1.0, force/disp/kspace = -1.0, split = 0, tol = 1.0e-6, and disp/auto = no. For pppm/intel, order = order/disp = 7. For scafacos settings, the scafacos tolerance option depends on the method chosen, as documented above. The scafacos fmm_tuning default = 0.
(Hockney) Hockney and Eastwood, Computer Simulation Using Particles, Adam Hilger, NY (1989).
(Yeh) Yeh and Berkowitz, J Chem Phys, 111, 3155 (1999).
(Ballenegger) Ballenegger, Arnold, Cerda, J Chem Phys, 131, 094107 (2009).
(Klapp) Klapp, Schoen, J Chem Phys, 117, 8050 (2002).
(Hardy) David Hardy thesis: Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules, University of Illinois at Urbana-Champaign, (2006).
(Hummer) Hummer, Gronbech-Jensen, Neumann, J Chem Phys, 109, 2791 (1998)
(Isele-Holder) Isele-Holder, Mitchell, Hammond, Kohlmeyer, Ismail, J Chem Theory Comput, 9, 5412 (2013).
(Wennberg) Wennberg, Murtola, Hess, Lindahl, J Chem Theory Comput, 9, 3527 (2013).
| 2019-06-20T01:06:58 |
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|
http://lammps.sandia.gov/doc/fix_deposit.html
|
# fix deposit command
## Syntax
fix ID group-ID deposit N type M seed keyword values ...
• ID, group-ID are documented in fix command
• deposit = style name of this fix command
• N = # of atoms or molecules to insert
• type = atom type to assign to inserted atoms (offset for molecule insertion)
• M = insert a single atom or molecule every M steps
• seed = random # seed (positive integer)
• one or more keyword/value pairs may be appended to args
• keyword = region or id or global or local or near or gaussian or attempt or rate or vx or vy or vz or mol or rigid or shake or units
region value = region-ID
region-ID = ID of region to use as insertion volume
id value = max or next
max = atom ID for new atom(s) is max ID of all current atoms plus one
next = atom ID for new atom(s) increments by one for every deposition
global values = lo hi
lo,hi = put new atom/molecule a distance lo-hi above all other atoms (distance units)
local values = lo hi delta
lo,hi = put new atom/molecule a distance lo-hi above any nearby atom beneath it (distance units)
delta = lateral distance within which a neighbor is considered "nearby" (distance units)
near value = R
R = only insert atom/molecule if further than R from existing particles (distance units)
gaussian values = xmid ymid zmid sigma
xmid,ymid,zmid = center of the gaussian distribution (distance units)
sigma = width of gaussian distribution (distance units)
attempt value = Q
Q = attempt a single insertion up to Q times
rate value = V
V = z velocity (y in 2d) at which insertion volume moves (velocity units)
vx values = vxlo vxhi
vxlo,vxhi = range of x velocities for inserted atom/molecule (velocity units)
vy values = vylo vyhi
vylo,vyhi = range of y velocities for inserted atom/molecule (velocity units)
vz values = vzlo vzhi
vzlo,vzhi = range of z velocities for inserted atom/molecule (velocity units)
target values = tx ty tz
tx,ty,tz = location of target point (distance units)
mol value = template-ID
template-ID = ID of molecule template specified in a separate molecule command
molfrac values = f1 f2 ... fN
f1 to fN = relative probability of creating each of N molecules in template-ID
rigid value = fix-ID
fix-ID = ID of fix rigid/small command
shake value = fix-ID
fix-ID = ID of fix shake command
units value = lattice or box
lattice = the geometry is defined in lattice units
box = the geometry is defined in simulation box units
## Examples
fix 3 all deposit 1000 2 100 29494 region myblock local 1.0 1.0 1.0 units box
fix 2 newatoms deposit 10000 1 500 12345 region disk near 2.0 vz -1.0 -0.8
fix 4 sputter deposit 1000 2 500 12235 region sphere vz -1.0 -1.0 target 5.0 5.0 0.0 units lattice
fix 5 insert deposit 200 2 100 777 region disk gaussian 5.0 5.0 9.0 1.0 units box
## Description
Insert a single atom or molecule into the simulation domain every M timesteps until N atoms or molecules have been inserted. This is useful for simulating deposition onto a surface. For the remainder of this doc page, a single inserted atom or molecule is referred to as a “particle”.
If inserted particles are individual atoms, they are assigned the specified atom type. If they are molecules, the type of each atom in the inserted molecule is specified in the file read by the molecule command, and those values are added to the specified atom type. E.g. if the file specifies atom types 1,2,3, and those are the atom types you want for inserted molecules, then specify type = 0. If you specify type = 2, the in the inserted molecule will have atom types 3,4,5.
All atoms in the inserted particle are assigned to two groups: the default group “all” and the group specified in the fix deposit command (which can also be “all”).
If you are computing temperature values which include inserted particles, you will want to use the compute_modify dynamic option, which insures the current number of atoms is used as a normalizing factor each time the temperature is computed.
Care must be taken that inserted particles are not too near existing atoms, using the options described below. When inserting particles above a surface in a non-periodic box (see the boundary command), the possibility of a particle escaping the surface and flying upward should be considered, since the particle may be lost or the box size may grow infinitely large. A fix wall/reflect command can be used to prevent this behavior. Note that if a shrink-wrap boundary is used, it is OK to insert the new particle outside the box, however the box will immediately be expanded to include the new particle. When simulating a sputtering experiment it is probably more realistic to ignore those atoms using the thermo_modify command with the lost ignore option and a fixed boundary.
The fix deposit command must use the region keyword to define an insertion volume. The specified region must have been previously defined with a region command. It must be defined with side = in.
Note
LAMMPS checks that the specified region is wholly inside the simulation box. It can do this correctly for orthonormal simulation boxes. However for triclinic boxes, it only tests against the larger orthonormal box that bounds the tilted simulation box. If the specified region includes volume outside the tilted box, then an insertion will likely fail, leading to a “lost atoms” error. Thus for triclinic boxes you should insure the specified region is wholly inside the simulation box.
The locations of inserted particles are taken from uniform distributed random numbers, unless the gaussian keyword is used. Then the individual coordinates are taken from a gaussian distribution of width sigma centered on xmid,ymid,zmid.
Individual atoms are inserted, unless the mol keyword is used. It specifies a template-ID previously defined using the molecule command, which reads files that define one or more molecules. The coordinates, atom types, charges, etc, as well as any bond/angle/etc and special neighbor information for the molecule can be specified in the molecule file. See the molecule command for details. The only settings required to be in each file are the coordinates and types of atoms in the molecule.
If the molecule template contains more than one molecule, the relative probability of depositing each molecule can be specified by the molfrac keyword. N relative probabilities, each from 0.0 to 1.0, are specified, where N is the number of molecules in the template. Each time a molecule is deposited, a random number is used to sample from the list of relative probabilities. The N values must sum to 1.0.
If you wish to insert molecules via the mol keyword, that will be treated as rigid bodies, use the rigid keyword, specifying as its value the ID of a separate fix rigid/small command which also appears in your input script.
Note
If you wish the new rigid molecules (and other rigid molecules) to be thermostatted correctly via fix rigid/small/nvt or fix rigid/small/npt, then you need to use the “fix_modify dynamic/dof yes” command for the rigid fix. This is to inform that fix that the molecule count will vary dynamically.
If you wish to insert molecules via the mol keyword, that will have their bonds or angles constrained via SHAKE, use the shake keyword, specifying as its value the ID of a separate fix shake command which also appears in your input script.
Each timestep a particle is inserted, the coordinates for its atoms are chosen as follows. For insertion of individual atoms, the “position” referred to in the following description is the coordinate of the atom. For insertion of molecule, the “position” is the geometric center of the molecule; see the molecule doc page for details. A random rotation of the molecule around its center point is performed, which determines the coordinates all the individual atoms.
A random position within the region insertion volume is generated. If neither the global or local keyword is used, the random position is the trial position. If the global keyword is used, the random x,y values are used, but the z position of the new particle is set above the highest current atom in the simulation by a distance randomly chosen between lo/hi. (For a 2d simulation, this is done for the y position.) If the local keyword is used, the z position is set a distance between lo/hi above the highest current atom in the simulation that is “nearby” the chosen x,y position. In this context, “nearby” means the lateral distance (in x,y) between the new and old particles is less than the delta setting.
Once a trial x,y,z position has been selected, the insertion is only performed if no current atom in the simulation is within a distance R of any atom in the new particle, including the effect of periodic boundary conditions if applicable. R is defined by the near keyword. Note that the default value for R is 0.0, which will allow atoms to strongly overlap if you are inserting where other atoms are present. This distance test is performed independently for each atom in an inserted molecule, based on the randomly rotated configuration of the molecule. If this test fails, a new random position within the insertion volume is chosen and another trial is made. Up to Q attempts are made. If the particle is not successfully inserted, LAMMPS prints a warning message.
Note
If you are inserting finite size particles or a molecule or rigid body consisting of finite-size particles, then you should typically set R larger than the distance at which any inserted particle may overlap with either a previously inserted particle or an existing particle. LAMMPS will issue a warning if R is smaller than this value, based on the radii of existing and inserted particles.
The rate option moves the insertion volume in the z direction (3d) or y direction (2d). This enables particles to be inserted from a successively higher height over time. Note that this parameter is ignored if the global or local keywords are used, since those options choose a z-coordinate for insertion independently.
The vx, vy, and vz components of velocity for the inserted particle are set using the values specified for the vx, vy, and vz keywords. Note that normally, new particles should be a assigned a negative vertical velocity so that they move towards the surface. For molecules, the same velocity is given to every particle (no rotation or bond vibration).
If the target option is used, the velocity vector of the inserted particle is changed so that it points from the insertion position towards the specified target point. The magnitude of the velocity is unchanged. This can be useful, for example, for simulating a sputtering process. E.g. the target point can be far away, so that all incident particles strike the surface as if they are in an incident beam of particles at a prescribed angle.
The id keyword determines how atom IDs and molecule IDs are assigned to newly deposited particles. Molecule IDs are only assigned if molecules are being inserted. For the max setting, the atom and molecule IDs of all current atoms are checked. Atoms in the new particle are assigned IDs starting with the current maximum plus one. If a molecule is inserted it is assigned an ID = current maximum plus one. This means that if particles leave the system, the new IDs may replace the lost ones. For the next setting, the maximum ID of any atom and molecule is stored at the time the fix is defined. Each time a new particle is added, this value is incremented to assign IDs to the new atom(s) or molecule. Thus atom and molecule IDs for deposited particles will be consecutive even if particles leave the system over time.
The units keyword determines the meaning of the distance units used for the other deposition parameters. A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacing. Note that the units choice affects all the keyword values that have units of distance or velocity.
Note
If you are monitoring the temperature of a system where the atom count is changing due to adding particles, you typically should use the compute_modify dynamic yes command for the temperature compute you are using.
Restart, fix_modify, output, run start/stop, minimize info:
This fix writes the state of the deposition to binary restart files. This includes information about how many particles have been depositied, the random number generator seed, the next timestep for deposition, etc. See the read_restart command for info on how to re-specify a fix in an input script that reads a restart file, so that the operation of the fix continues in an uninterrupted fashion.
None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
## Restrictions
This fix is part of the MISC package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.
The specified insertion region cannot be a “dynamic” region, as defined by the region command.
## Default
Insertions are performed for individual atoms, i.e. no mol setting is defined. If the mol keyword is used, the default for molfrac is an equal probabilities for all molecules in the template. Additional option defaults are id = max, delta = 0.0, near = 0.0, attempt = 10, rate = 0.0, vx = 0.0 0.0, vy = 0.0 0.0, vz = 0.0 0.0, and units = lattice.
| 2018-04-19T19:29:22 |
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|
https://mooseframework.inl.gov/source/postprocessors/DiscreteNucleationData.html
|
# DiscreteNucleationData
Output diagnostic data on a DiscreteNucleationInserter
The data to be extracted from the DiscreteNucleationInserter is selected using the value parameter, which has the following options:
valueOutput
COUNTNumber of currently active nucleation sites maintained by the inserter
UPDATEBoolean (0/1) value denoting if at least one new nucleus was inserted or removed (i.e. its hold time expired) for the current timestep
RATETotal nucleation rate per unit time for the entire domain
INSERTIONSNumber of new nucleation points added to the inserter's list
DELETIONSNumber of nucleation points that were removed due to their hold time having expired
The DiscreteNucleationData postprocessor is part of the Discrete Nucleation system.
## Input Parameters
• inserterDiscreteNucleationInserter user object
C++ Type:UserObjectName
Options:
Description:DiscreteNucleationInserter user object
• valueCOUNTSelect to output number of active nuclei, wether a change to the nucleus list occurred, the total rate over the entire domain, and numbers of insertions and deletions applied to the nucleus list.
Default:COUNT
C++ Type:MooseEnum
Options:COUNT UPDATE RATE INSERTIONS DELETIONS
Description:Select to output number of active nuclei, wether a change to the nucleus list occurred, the total rate over the entire domain, and numbers of insertions and deletions applied to the nucleus list.
### Required Parameters
• execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
• force_preauxFalseForces the GeneralUserObject to be executed in PREAUX
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREAUX
| 2018-12-11T19:55:28 |
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|
https://www.anl.gov/article/energy-department-to-invest-16-million-in-computer-design-of-materials
|
# Argonne National Laboratory
Press Release | Argonne National Laboratory
# Energy Department to invest $16 million in computer design of materials The U.S. Department of Energy (DOE) announced that it will invest$16 million over the next four years to accelerate the design of new materials through use of supercomputers.
Two four-year projects — one team led by DOE’s Oak Ridge National Laboratory (ORNL), the other team led by DOE’s Lawrence Berkeley National Laboratory (LBNL) — will take advantage of superfast computers at DOE national laboratories by developing software to design fundamentally new functional materials destined to revolutionize applications in alternative and renewable energy, electronics and a wide range of other fields. The research teams include experts from universities and other national labs.
The new grants — part of DOE’s Computational Materials Sciences (CMS) program begun in 2015 as part of the U.S. Materials Genome Initiative — reflect the enormous recent growth in computing power and the increasing capability of high-performance computers to model and simulate the behavior of matter at the atomic and molecular scales.
Given the importance of materials to virtually all technologies, computational materials science is a critical area in which the United States needs to be competitive in the twenty-first century and beyond through global leadership in innovation.”
The teams are expected to develop sophisticated and user-friendly open-source software that captures the essential physics of relevant systems and can be used by the broader research community and by industry to accelerate the design of new functional materials.
Given the importance of materials to virtually all technologies, computational materials science is a critical area in which the United States needs to be competitive in the twenty-first century and beyond through global leadership in innovation,” said Cherry Murray, director of DOE’s Office of Science, which is funding the research. These projects will both harness DOE existing high-performance computing capabilities and help pave the way toward ever-more sophisticated software for future generations of machines.”
ORNL researchers will partner with scientists from national labs and universities to develop software to accurately predict the properties of quantum materials with novel magnetism, optical properties and exotic quantum phases that make them well-suited to energy applications,” said Paul Kent of ORNL, director of the Center for Predictive Simulation of Functional Materials, which includes partners from Argonne, Lawrence Livermore, Oak Ridge and Sandia National Laboratories and North Carolina State University and the University of California–Berkeley. Our simulations will rely on current petascale and future exascale capabilities at DOE supercomputing centers. To validate the predictions about material behavior, we’ll conduct experiments and use the facilities of the Advanced Photon Source, Spallation Neutron Source and the Nanoscale Science Research Centers.”
Said the center’s thrust leader for prediction and validation, Olle Heinonen, At Argonne, our expertise in combining state-of-the-art, oxide molecular beam epitaxy growth of new materials with characterization at the Advanced Photon Source and the Center for Nanoscale Materials will enable us to offer new and precise insight into the complex properties important to materials design. We are excited to bring our particular capabilities in materials, as well as expertise in software, to the center so that the labs can comprehensively tackle this challenge.”
Researchers are expected to make use of the 30-petaflop/s Cori supercomputer now being installed at the National Energy Research Scientific Computing Center (NERSC) at Berkeley Lab, the 27-petaflop/s Titan computer at the Oak Ridge Leadership Computing Facility (OLCF) and the 10-petaflop/s Mira computer at Argonne Leadership Computing Facility (ALCF). OLCF, ALCF and NERSC are all DOE Office of Science User Facilities. One petaflop is 1015 or a million times a billion floating-point operations per second.
In addition, a new generation of machines is scheduled for deployment between 2016 and 2019 that will take peak performance as high as 200 petaflops. Ultimately, the software produced by these projects is expected to evolve to run on exascale machines, capable of 1,000 petaflops and projected for deployment in the mid-2020s.
Research will combine theory and software development with experimental validation, drawing on the resources of multiple DOE Office of Science User Facilities, including the Advanced Light Source at LBNL, the Advanced Photon Source at Argonne National Laboratory, the Spallation Neutron Source at ORNL, and several of the five Nanoscience Research Centers across the DOE National Laboratory complex.
The new research projects will begin in Fiscal Year 2016. They expand the ongoing CMS research effort, which began in FY 2015 with three initial projects, led respectively by Argonne, Brookhaven National Laboratory and the University of Southern California.
Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the Office of Science website.
| 2020-02-28T19:01:25 |
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|
https://scaron.info/teaching/zmp-support-area.html
|
# ZMP support area
When a legged robot walks over a regular terrain, we can simplify its dynamics to a reduced model like the linear inverted pendulum where the center of mass (CoM) is controlled via the zero-tilting moment point (ZMP) of contact forces with the ground. To be physically feasible, the ZMP must lie in a support area, which is roughly "the area between the feet" in simple cases, and a bit more complex but still computable in the presence of additional contacts such as a hand on a wall or a knee on the ground.
## Modelling
### Whole-body model
The constrained equations of motion of our whole-body model are:
\begin{equation*} \begin{array}{rcl} \bfM(\bfq) \qdd + \qd^\top \bfC(\bfq) \qd & = & \bfS^\top \bftau + \bftau_g(\bfq) + \bftau_\mathit{ext} + \bfJ(\bfq)^\top \bff \\ \bfF(\bfq) \bff & \leq & \bfzero \end{array} \end{equation*}
The configuration $$\bfq$$ consists of its $$n$$ actuated degrees of freedom and 6 unactuated floating base coordinates. Contact forces from the environment are stacked in the vector $$\bff$$ and constrained by the matrix $$\bfF(\bfq)$$ of Coulomb friction cones.
### Reduced model
The constrained equations of motion of our reduced model are point-by-point similar to the whole-body:
\begin{equation*} \begin{array}{rcl} \bfpdd_G & = & \omega^2 (\bfp_G - \bfp_Z) \\ \bfA(\bfp_G) \bfp_Z & \leq & \bfb(\bfp_G) \end{array} \end{equation*}
The configuration $$\bfp_G$$ consists of the the 2D horizontal position of the center of mass. Contact forces from the environment are aggregated in the position $$\bfp_Z$$ of the ZMP and constrained by the polygonal half-space inequality $$\bfA(\bfp_G) \bfp_z \leq \bfb(\bfp_G)$$.
## Derivation
The matrix $$\bfA(\bfp_G)$$ and vector $$\bfb(\bfp_G)$$ can be computed from the contact geometry and friction information encoded in $$\bfJ(\bfq)$$ and $$\bfF(\bfq)$$ by polyhedral projection. This method is described in Section IV of this paper.
## Simplification on flat floors
In pre-2010 robotics papers, we often see the ZMP support area defined as the "convex hull of ground contact points", where $$\bfA$$ and $$\bfb$$ do not depend on $$\bfp_G$$ any more and can be readily computed from ground contact points by a convex hull algorithm (a particular case of polyhedral projection). This simplification is only valid if we make two assumptions:
• All ground contact points are coplanar.
• The coefficient of friction for the interaction between robot feet and the ground is infinite.
If we follow the general algorithm from the previous section, which takes the CoM position $$\bfp_G$$ as an input, it is not clear how the ZMP support area becomes independent from $$\bfp_G$$ under these two conditions. Let us detail this step by step.
### Infinite friction
Let us consider for simplicity of calculations that our flat ground contact plane is horizontal (othogonal to gravity). In the absence of friction constaints, our friction cone inequalities are reduced to contact unilaterality constraints:
\begin{equation*} \forall \textrm{ contact } i, \ f_i^z > 0 \end{equation*}
This means we can exert arbitrary horizontal forces $$f_i^x$$ and $$f_i^y$$ at every contact point $$i$$.
### Newton-Euler equations
Our contact forces are bound to the CoM and ZMP by Newton and Euler equations. First, Newton equation gives us:
\begin{equation*} \sum_{\textrm{contact } i} \bff_i = \bff = \frac{m g}{h} (\bfp_G - \bfp_Z) \end{equation*}
with $$m$$ the total mass, $$g$$ the gravity constant and $$h$$ the CoM height above ground. Second, Euler equation (with no angular momentum at the center of mass since we are in a pendular model) gives us:
\begin{equation*} \sum_{\textrm{ contact } i} \bfp_i \times \bff_i = \bfp_G \times \bff \end{equation*}
Let's unwrap it to understand better what it says. On flat floor, we have $$z_i = 0$$ for all contact points $$i$$, so that the vector cross products expand to:
\begin{equation*} \begin{array}{rcl} \sum_{i} y_i f_i^z & = & y_G f^z - h f^y \\ \sum_{i} -x_i f_i^z & = & -x_G f^z + h f^x \\ \sum_{i} (x_i f_i^y - y_i f_i^x) & = & x_G f^y - y_G f^x \end{array} \end{equation*}
Since we are not limited by friction, the third equation always has a solution and we can trim it out. In the other two equations, we can replace $$\bff$$ by its expression $$mg (\bfp_G - p_Z) / h$$ from the linear inverted pendulum model, for instance:
\begin{equation*} \begin{array}{rcl} y_G f^z & = & y_G m g (h - 0) / h = y_G m g \\ h f^y & = & m g (y_G - y_Z) \\ y_G f^z - h f^y & = & m g y_Z \\ mg y_Z & = & \sum_i {f_i^z} y_i \end{array} \end{equation*}
and similarly for the other equation. Defining $$\alpha_i = \frac{f_i^z}{mg}$$, we get:
\begin{equation*} \begin{array}{rcl} \bfp_Z & = & \sum_{i} \alpha_i \bfp_i \\ \forall i, \alpha_i & \geq & 0 \end{array} \end{equation*}
which is the vertex representation of the convex hull of ground contact points $$\bfp_i$$.
## To go further
ZMP support areas can be derived in any multi-contact configurations, but in this case they depend (nonlinearly) on the position of the center of mass. Simplified ZMP support areas can be applied for walking over both horizontal and inclined. For instance, they have been used by biped robots to climb stairs and quadruped robots to trot over inclined surfaces.
Pages of this website are under the CC-BY 4.0 license.
| 2020-12-04T14:38:59 |
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|
http://pdglive.lbl.gov/DataBlock.action;jsessionid=5AF9815C5B546CAC1F92B0541681C4AA?node=B170M&init=0
|
# ${{\boldsymbol \Xi}_{{b}}{(5955)}^{-}}$ MASS INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$5955.33$ $\pm0.12$ $\pm0.05$ 1
2015 H
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
1 Not independent of the mass difference measurement below. Observed in ${{\mathit \Xi}_{{b}}^{0}}{{\mathit \pi}^{-}}$ channel with ${{\mathit \Xi}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \Xi}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ .
References:
AAIJ 2015H
PRL 114 062004 Observation of Two New ${{\mathit \Xi}_{{b}}^{-}}$ Baryon Resonances
| 2019-01-18T03:15:00 |
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|
https://pt.overleaf.com/articles/latex-assignment-4/rjdqzptjcsfv
|
# LaTeX Assignment 4
Author
Jonathan Guiang
License
Creative Commons CC BY 4.0
AbstractThis was an assignment for a college physics course. Please let me know what you think! :)
| 2021-06-21T00:42:35 |
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|
https://subs.emis.de/LIPIcs/frontdoor_da27.html
|
License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2022.33
URN: urn:nbn:de:0030-drops-170968
URL: https://drops.dagstuhl.de/opus/volltexte/2022/17096/
Go to the corresponding LIPIcs Volume Portal
### Pareto-Rational Verification
pdf-format:
### Abstract
We study the rational verification problem which consists in verifying the correctness of a system executing in an environment that is assumed to behave rationally. We consider the model of rationality in which the environment only executes behaviors that are Pareto-optimal with regard to its set of objectives, given the behavior of the system (which is committed in advance of any interaction). We examine two ways of specifying this behavior, first by means of a deterministic Moore machine, and then by lifting its determinism. In the latter case the machine may embed several different behaviors for the system, and the universal rational verification problem aims at verifying that all of them are correct when the environment is rational. For parity objectives, we prove that the Pareto-rational verification problem is co-NP-complete and that its universal version is in PSPACE and both NP-hard and co-NP-hard. For Boolean Büchi objectives, the former problem is Π₂𝖯-complete and the latter is PSPACE-complete. We also study the case where the objectives are expressed using LTL formulas and show that the first problem is PSPACE-complete, and that the second is 2EXPTIME-complete. Both problems are also shown to be fixed-parameter tractable for parity and Boolean Büchi objectives.
### BibTeX - Entry
@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2022.33,
author = {Bruy\{e}re, V\'{e}ronique and Raskin, Jean-Fran\c{c}ois and Tamines, Cl\'{e}ment},
title = {{Pareto-Rational Verification}},
booktitle = {33rd International Conference on Concurrency Theory (CONCUR 2022)},
pages = {33:1--33:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-246-4},
ISSN = {1868-8969},
year = {2022},
volume = {243},
editor = {Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17096},
URN = {urn:nbn:de:0030-drops-170968},
doi = {10.4230/LIPIcs.CONCUR.2022.33},
annote = {Keywords: Rational verification, Model-checking, Pareto-optimality, \omega-regular objectives}
}`
Keywords: Rational verification, Model-checking, Pareto-optimality, ω-regular objectives Collection: 33rd International Conference on Concurrency Theory (CONCUR 2022) Issue Date: 2022 Date of publication: 06.09.2022
DROPS-Home | Fulltext Search | Imprint | Privacy
| 2023-01-31T04:34:29 |
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http://itl.nist.gov/div898/software/dataplot/refman1/auxillar/ks2samp.htm
|
Dataplot Vol 1 Vol 2
KOLMOGOROV SMIRNOV TWO SAMPLE
Name:
... KOLMOGOROV SMIRNOV TWO SAMPLE TEST
Type:
Analysis Command
Purpose:
Perform a Kolmogorov-Smirnov two sample test that two data samples come from the same distribution. Note that we are not specifying what that common distribution is.
Description:
The one sample Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N data points Y1, Y2, ..., YN the ECDF is defined as
$$E_{N} = \frac{n_{i}}{N}$$
where ni is the number of points less than Yi. This is a step function that increases by 1/N at the value of each data point. We can graph a plot of the empirical distribution function with a cumulative distribution function for a given distribution. The one sample K-S test is based on the maximum distance between these two curves. That is,
$$D = \max_{1 \le i \le N}|F(Y_{i}) - \frac{i} {N}|$$
where F is the theoretical cumulative distribution function.
The two sample K-S test is a variation of this. However, instead of comparing an empirical distribution function to a theoretical distribution function, we compare the two empirical distribution functions. That is,
$$D = |E_1(i) - E_2(i)|$$
where E1 and E2 are the empirical distribution functions for the two samples. Note that we compute E1 and E2 at each point in both samples (that is both E1 and E2 are computed at each point in each sample).
More formally, the Kolmogorov-Smirnov two sample test statistic can be defined as follows.
H0: The two samples come from a common distribution. Ha: The two samples do not come from a common distribution. Test Statistic: The Kolmogorov-Smirnov two sample test statistic is defined as $$D = |E_1(i) - E_2(i)|$$ where E1 and E2 are the empirical distribution functions for the two samples. Significance Level: $$\alpha$$ Critical Region: The hypothesis regarding the distributional form is rejected if the test statistic, D, is greater than the critical value obtained from a table. There are several variations of these tables in the literature that use somewhat different scalings for the K-S test statistic and critical regions. These alternative formulations should be equivalent, but it is necessary to ensure that the test statistic is calculated in a way that is consistent with how the critical values were tabulated. Dataplot uses the critical values from Chakravart, Laha, and Roy (see Reference: below).
The quantile-quantile plot, bihistogram, and Tukey mean-difference plot are graphical alternatives to the two sample K-S test.
Syntax:
KOLMOGOROV SMIRNOV TWO SAMPLE TEST <y1> <y2>
<SUBSET/EXCEPT/FOR/qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
KOLMOGOROV-SMIRNOV TWO SAMPLE TEST Y1 Y2
KOLMOGOROV-SMIRNOV TWO SAMPLE TEST Y1 Y2 SUBSET Y2 > 0
Note:
The KOLMOGOROV-SMIRNOV TWO SAMPLE TEST command automatically saves the following parameters.
STATVAL - value of the K-S two sample statistic CUTUPP90 - 90% critical value (alpha = 0.10) for the K-S two sample test statistic CUTUPP95 - 95% critical value (alpha = 0.05) for the K-S two sample test statistic CUTUPP99 - 99% critical value (alpha = 0.01) for the K-S two sample test statistic
These parameters can be used in subsequent analysis.
Default:
None
Synonyms:
The word test in the command is optional. Also, TWO can be entered as 2. For example,
KOLMOGOROV SMIRNOV 2 SAMPLE Y1 Y2
Related Commands:
KOMOGOROV SMIRNOV GOODNESS OF FIT TEST = Perform Kolmogorov-Snirnov goodness of fit test. CHI-SQUARE TWO SAMPLE TEST = Perform chi-square two sample test. BIHISTOGRAM = Generates a bihistogram. QUANTILE-QUANTILE PLOT = Generates a quantile-quantile plot. TUKEY MEAN DIFFERENCE PLOT = Generates a Tukey mean difference plot.
Reference:
Chakravart, Laha, and Roy (1967), "Handbook of Methods of Applied Statistics, Volume I," John Wiley, pp. 392-394.
Press, Teukolsky, Vetterling, and Flannery (1992), "Numerical Recipes in Fortan: The Art of Scientific Computing," Second Edition, Cambridge University Press, pp. 614-622.
Applications:
Distributional Analysis
Implementation Date:
1998/12
Program:
SKIP 25
.
DELETE Y2 SUBSET Y2 < 0
SET WRITE DECIMALS 4
KOLMOGOROV-SMIRNOPV TWO SAMPLE TEST Y1 Y2
The following output is generated.
Kolmogorov-Smirnov Two Sample Test
First Response Variable: Y1
Second Response Variable: Y2
H0: The Two Samples Come From the
Same (Unspecified) Distribution
Ha: The Two Samples Come From
Different Distributions
Sample One Summary Statistics:
Number of Observations: 249
Sample Mean: 20.1446
Sample Standard Deviation: 6.4147
Sample Minimum: 9.0000
Sample Maximum: 39.0000
Sample Two Summary Statistics:
Number of Observations: 79
Sample Mean: 30.4810
Sample Standard Deviation: 6.1077
Sample Minimum: 18.0000
Sample Maximum: 47.0000
Test Statistic Value: 0.6003
Conclusions (Upper 1-Tailed Test)
------------------------------------------------------------------------
Null
Null Significance Test Critical Hypothesis
Hypothesis Level Statistic Region (>=) Conclusion
------------------------------------------------------------------------
Same 90.0% 0.6003 0.1575 REJECT
Same 95.0% 0.6003 0.1756 REJECT
Same 99.0% 0.6003 0.2105 REJECT
NIST is an agency of the U.S. Commerce Department.
Date created: 6/5/2001
Last updated: 10/30/2015
| 2016-02-14T18:44:31 |
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|
https://www.usgs.gov/center-news/volcano-watch-mauna-loa-signals-a-change-spring-arrives
|
# Volcano Watch - Mauna Loa signals a change as Spring arrives
Release Date:
Each week since October 2002, seismologists at the U.S. Geological Survey's Hawaiʻian Volcano Observatory (HVO) have provided brief synopses of the ongoing rumblings beneath Mauna Loa. Our last detailed discussion of the activity occurred last Thanksgiving, when we proclaimed the continuation of deep, long-period (3-5 cycles per second) Mauna Loa seismic events.
At that time, we had located over 1,300 earthquakes in just over five months.
What has happened since Thanksgiving? Another burst of activity, mostly of the long-period type, occurred between December 14 and Christmas, generally originating at depths between 35 and 50 km (22 and 31 miles) in the upper mantle. It pushed the cumulative number of cataloged earthquakes to over 1,700 since July. By the end of the year, it appeared that we would reach 2,000 earthquakes in short order. The extension rate across the summit caldera had risen to about 6 centimeters (2.4 inches) per year between November and January, with even higher rates of up to 19 centimeters (7.5 inches) per year on northwest-southeast trending lines just crossing the northern edge of the summit caldera.
Just as the thought of 2,000 earthquakes crossed the minds of HVO seismologists, seismic activity beneath Mauna Loa dropped dramatically at the beginning of 2005, to the lowest level seen since the onset of the long-period activity. Only 34 earthquakes were cataloged in the month of January, as compared with 365 in December. From August 2004 to December 2004, 1,650 earthquakes, representing 98 per cent of the total catalogued in the Mauna Loa area, were classified as deep (greater than 13 km {8 miles}). In January, the number of deep events plummeted to 21, comprising 62 per cent of the total.
As seismic activity beneath Mauna Loa changed, Kīlauea began stirring, with a significant increase in horizontal extension across its summit, from 8 centimeters (3.1 inches) per year to over 40 centimeters (15.7 inches) per year. An increase in shallow seismic activity beneath Kīlauea and its upper east rift accompanied this extension, startling residents in the Volcano area, who felt several of the larger events in late January and early February.
During much of January, Puu Oo, the tube system downrift, and associated surface flows showed a dramatic increase in activity, resulting in several spectacular new ocean entries. By the third week of February, extension across Kīlauea caldera ceased, and line lengths have since contracted. Seismic activity beneath Kīlauea summit dropped considerably by the end of February, although the east rift zone remains active.
Meanwhile, extension across Mauna Loa's summit became erratic around the beginning of February. In fact, during most of the month, summit inflation slowed considerably, and horizontal line lengths remained fairly constant. Earthquake activity remained low, with just 25 earthquakes cataloged during the month of February. Of these, 60 per cent fell into the deep-focus category.
Over the past two weeks, Mauna Loa has begun to extend once again, although seismic activity continues at a low level, averaging less than one catalogued event per day. More notably, none of the earthquakes since February 27 have been of the deep, long-period type that dominated the 2004 activity. To date, since last July, just over 1,800 earthquakes have been cataloged in the Mauna Loa region. It could be awhile before we catalog our 2,000th earthquake.
Scientists at the Hawaiʻian Volcano Observatory continue to vigilantly monitor Mauna Loa. A significant increase in earthquake activity northwest of Mokuaweoweo at intermediate depths between 5 and 13 km (3 and 8 miles) has yet to occur, as it did prior to both the 1975 and 1984 eruptions. Monthly totals of all catalogued Mauna Loa earthquakes shallower than 13 km (8 miles) have remained fairly constant since July, numbering anywhere from 6 (in October) to 13 (in September and January). Deformation instruments have not yet shown the large, rapid changes indicating that an eruption is imminent.
As changes occur in Mauna Loa's behavior, we will inform you through these weekly updates, our web pages, and through the Hawaii County Civil Defense, as needed. HVO's current Mauna Loa activity web page.
### Volcano Activity Update
Eruptive activity at Puu Oo continues. The Puu Oo crater camera is offline for repair.
The PKK flow continues to host substantial breakouts from atop Pulama pali to the coastal plain. Open channels have been visible intermittently on Pulama pali, particulary on the east branch of the PKK flow. Three ocean entries are currently active at Highcastle, East Laeapuki and Kailiili. Much of the lava delta at Ka 'iliili collapsed into the sea on March 19. Highcastle, East Laeapuki and Kailiili entries are about 3.7 km (2.3 miles), 4.9 km (3 miles) and 7.5 km (4.7 miles), respectively from the ranger shed on Chain of Craters Road. Expect a 1.5- to 2- hour walk each way to the Highcastle entry. Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Heed the National Park warning signs.
During the week ending March 23, only one earthquake was felt on Hawai`i Island. The magnitude-3.2 quake occurred 5 km (3 miles) southwest of Pahala at a depth of 38 km (24 miles) at 10:38 a.m. on Wednesday, March 23. The earthquake was felt at Pahala.
Mauna Loa is not erupting. During the week ending March 23, only two earthquakes were recorded beneath the summit area. Inflation continues at rates of 6 cm/yr (2.4 in/yr) at the summit and near 20 cm/yr (8 in/yr) on the flanks.
| 2020-01-24T08:52:18 |
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|
https://mooseframework.inl.gov/help/libmesh_issues.html
|
## Compiling libMesh
Compiling libMesh requires a proper environment. Lets verify a few things before attempting to build it (or possibly re-build it in your case):
• Verify you have a proper compiler present:
• Linux:
which $CC /opt/moose/mpich-3.2/gcc-7.3.1/bin/mpicc mpicc -show gcc -I/opt/moose/mpich-3.2/gcc-7.3.1/include -L/opt/moose/mpich-3.2/gcc-7.3.1/lib -Wl,-rpath -Wl,/opt/moose/mpich-3.2/gcc-7.3.1/lib -Wl,--enable-new-dtags -lmpi which gcc /opt/moose/gcc-7.3.1/bin/gcc • Macintosh: which$CC
/opt/moose/mpich-3.2/clang-6.0.1/bin/mpicc
mpicc -show
clang -Wl,-commons,use_dylibs -I/opt/moose/mpich-3.2/clang-6.0.1/include -L/opt/moose/mpich-3.2/clang-6.0.1/lib -lmpi -lpmpi
which clang
/opt/moose/llvm-6.0.1/bin/clang
What you are looking for is that which and mpicc -show are returning proper paths. If these paths are not set, or which is not returning anything, see Modules for help on setting up a proper environment. Once set up, return here and verify the above commands return the proper messages.
• Check that PETSC_DIR is set and does exist:
• Linux:
echo $PETSC_DIR /opt/moose/petsc-3.9.4/mpich-__MPICH___gcc-7.3.1-opt file$PETSC_DIR
/opt/moose/petsc-3.9.4/mpich-__MPICH___gcc-7.3.1-opt: directory
• Macintosh:
echo $PETSC_DIR /opt/moose/petsc-3.9.4/mpich-__MPICH___clang-6.0.1-opt file$PETSC_DIR
/opt/moose/petsc-3.9.4/mpich-__MPICH___clang-6.0.1-opt: directory
• If echo $PETSC_DIR returns nothing, this would indicate your environment is not complete. See Modules for help on setting up a proper environment. Once set up, return here and verify the above commands return the proper messages. • If file$PETSC_DIR returns an error (possible if you are performing a Manual Install), it would appear you have not yet ran configure. Configure builds this directory.
• With the above all taken care of, try to build libMesh:
cd moose/scripts
./update_and_rebuild_libmesh.sh
If you encounter errors during this step, we would like to hear from you! Please seek help on our mailing list. Provide the diagnostic and libmesh configure logs. Those two files can be found in the following locations:
• moose/libmesh/build/config.log
• moose/scripts/libmesh_diagnostic.log
• If libMesh built successfully, return to the beginning of the step that lead you here, and try that step again.
| 2019-03-18T14:06:06 |
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|
https://cordis.europa.eu/project/id/691246/results
|
# New Geometry of Quantum Dynamics
## Deliverables
Dissemination: NCG seminar (Trimming and growing of graphs for graph algebras)
D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.
Dissemination: NCG seminar (Noncommutative spectral geometry for quantum group homogeneous spaces)
D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.
Focus programme (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Simons Semester at the Banach Center (Noncommutative bordism of quantum fibrations)
D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).
Proceedings (Trimming and growing of graphs for graph algebras)
D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.
Special issue (Noncommutative spectral geometry for quantum group homogeneous spaces)
D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.
Focus programme (Trimming and growing of graphs for graph algebras)
D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Special issue (Trimming and growing of graphs for graph algebras)
D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.
Research papers (Noncommutative bordism of quantum fibrations)
D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.
Simons Semester at the Banach Center (Trimming and growing of graphs for graph algebras)
D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).
Special issue (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.
Proceedings (Noncommutative bordism of quantum fibrations)
D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.
Research papers (Noncommutative Borsuk–Ulam-type conjectures)
D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.
Focus programme (Noncommutative spectral geometry for quantum group homogeneous spaces)
D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Research papers (Trimming and growing of graphs for graph algebras)
D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.
Dissemination: NCG seminar (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.
Proceedings (Noncommutative spectral geometry for quantum group homogeneous spaces)
D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.
Research papers (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.
Simons Semester at the Banach Center (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).
Proceedings (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)
D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.
Research papers (Noncommutative spectral geometry for quantum group homogeneous spaces)
D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.
Special issue (Noncommutative Borsuk–Ulam-type conjectures)
D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.
Focus programme (Noncommutative bordism of quantum fibrations)
D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Focus programme (Noncommutative Borsuk–Ulam-type conjectures)
D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Proceedings (Noncommutative Borsuk–Ulam-type conjectures)
D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.
Dissemination: NCG seminar (Noncommutative Borsuk–Ulam-type conjectures)
D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.
Simons Semester at the Banach Center (Noncommutative Borsuk–Ulam-type conjectures)
D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).
Special issue (Noncommutative bordism of quantum fibrations)
D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.
Dissemination: NCG seminar (Noncommutative bordism of quantum fibrations)
D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.
Simons Semester at the Banach Center (Noncommutative spectral geometry for quantum group homogeneous spaces)
D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).
Dedicated Web page (Management)
D3 dedicated Web page shall be created at the beginning of the project and updated on a continuous basis: page will hold all information pertaining to the project: about secondments, dissemination (publications, preprints, talks, seminars) and events which involve and/or are related to the project. The internal section of the web page (which includes internal reports) shall be available to project team.
Progress report (Management)
Progress report will summarize the scientific achievements, secondments, dissemination and commmunication (outreach activities) by the participants. Deliverable shall be archived/stored at IMPAN, electronic vesions shall be available on the Web page.
Progress report 2 (Management)
Progress report will summarize the scientific achievements, secondments, dissemination and commmunication (outreach activities) by the participants. Deliverable shall be archived/stored at IMPAN, electronic vesions shall be available on the Web page.
Searching for OpenAIRE data...
## Publications
Continuity of spectral radius and type I $C^*$-algebras
Author(s): Tatiana Shulman
Published in: Proceedings of the American Mathematical Society, Issue 147/2, 2019, Page(s) 641-646, ISSN 0002-9939
DOI: 10.1090/proc/14169
Quantum actions on discrete quantum spaces and a generalization of Clifford’s theory of representations
Author(s): Kenny De Commer, Paweł Kasprzak, Adam Skalski, Piotr M. Sołtan
Published in: Israel Journal of Mathematics, Issue 226/1, 2018, Page(s) 475-503, ISSN 0021-2172
DOI: 10.1007/s11856-018-1709-x
I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type
Author(s): Kenny De Commer
Published in: Journal of Functional Analysis, Issue 274/1, 2018, Page(s) 152-221, ISSN 0022-1236
DOI: 10.1016/j.jfa.2017.09.005
Partial actions of $C^{*}$ -quantum groups
Author(s): Franziska Kraken, Paula Quast, Thomas Timmermann
Published in: Banach Journal of Mathematical Analysis, Issue 12/4, 2018, Page(s) 843-872, ISSN 1735-8787
DOI: 10.1215/17358787-2017-0056
Ribbon Braided Module Categories, Quantum Symmetric Pairs and Knizhnik–Zamolodchikov Equations
Author(s): Kenny De Commer, Sergey Neshveyev, Lars Tuset, Makoto Yamashita
Published in: Communications in Mathematical Physics, Issue 367/3, 2019, Page(s) 717-769, ISSN 0010-3616
DOI: 10.1007/s00220-019-03317-7
Free products with amalgamation over central $\mathrm {C}^*$-subalgebras
Author(s): Kristin Courtney, Tatiana Shulman
Published in: Proceedings of the American Mathematical Society, Issue 148/2, 2020, Page(s) 765-776, ISSN 0002-9939
DOI: 10.1090/proc/14746
The field of quantum $$GL(N,\pmb {\mathbb {C}})$$ G L ( N , C )
Author(s): Kenny De Commer, Matthias Floré
Published in: Selecta Mathematica, Issue 25/1, 2019, ISSN 1022-1824
DOI: 10.1007/s00029-019-0456-0
Geometric Classification of Graph C*-algebras over Finite Graphs
Author(s): Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Published in: Canadian Journal of Mathematics, Issue 70/2, 2018, Page(s) 294-353, ISSN 0008-414X
DOI: 10.4153/cjm-2017-016-7
A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras
Author(s): SARA E. ARKLINT, SØREN EILERS, EFREN RUIZ
Published in: Ergodic Theory and Dynamical Systems, Issue 38/7, 2018, Page(s) 2401-2421, ISSN 0143-3857
DOI: 10.1017/etds.2016.141
Projective Modules Over Quantum Projective Line
Author(s): Albert Jeu-Liang Sheu
Published in: International Journal of Mathematics, Issue 28/03, 2017, Page(s) 1750022, ISSN 0129-167X
DOI: 10.1142/s0129167x17500227
Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems
Author(s): Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen, Sooran Kang, Judith Packer
Published in: Journal of Mathematical Analysis and Applications, Issue 468/2, 2018, Page(s) 766-798, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2018.08.051
Projections over quantum homogeneous odd-dimensional spheres
Author(s): Albert Jeu-Liang Sheu
Published in: Journal of Functional Analysis, Issue 277/10, 2019, Page(s) 3491-3512, ISSN 0022-1236
DOI: 10.1016/j.jfa.2019.05.006
Noncommutative solenoids and the Gromov-Hausdorff propinquity
Author(s): Frédéric Latrémolière, Judith Packer
Published in: Proceedings of the American Mathematical Society, Issue 145/5, 2017, Page(s) 2043-2057, ISSN 0002-9939
DOI: 10.1090/proc/13229
Equivalence of quantum metrics with a common domain
Author(s): Frédéric Latrémolière
Published in: Journal of Mathematical Analysis and Applications, Issue 443/2, 2016, Page(s) 1179-1195, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2016.05.045
Vector bundles for “Matrix algebras converge to the sphere”
Author(s): Marc A. Rieffel
Published in: Journal of Geometry and Physics, Issue 132, 2018, Page(s) 181-204, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2018.06.003
The Podleś sphere as a spectral metric space
Published in: Journal of Geometry and Physics, Issue 133, 2018, Page(s) 260-278, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2018.07.015
Convergence of Cauchy sequences for the covariant Gromov–Hausdorff propinquity
Author(s): Frédéric Latrémolière
Published in: Journal of Mathematical Analysis and Applications, Issue 469/1, 2019, Page(s) 378-404, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2018.09.018
The Standard Model in noncommutative geometry: fundamental fermions as internal forms
Author(s): Ludwik Dąbrowski, Francesco D’Andrea, Andrzej Sitarz
Published in: Letters in Mathematical Physics, Issue 108/5, 2018, Page(s) 1323-1340, ISSN 0377-9017
DOI: 10.1007/s11005-017-1036-x
Gauss-Bonnet for matrix conformally rescaled Dirac
Author(s): Masoud Khalkhali, Andrzej Sitarz
Published in: Journal of Mathematical Physics, Issue 59/6, 2018, Page(s) 063505, ISSN 0022-2488
DOI: 10.1063/1.4997381
Spectral triples on the Jiang-Su algebra
Author(s): Jacopo Bassi, Ludwik Dąbrowski
Published in: Journal of Mathematical Physics, Issue 59/5, 2018, Page(s) 053507, ISSN 0022-2488
DOI: 10.1063/1.5026311
Families of spectral triples and foliations of space(time)
Author(s): Koen van den Dungen
Published in: Journal of Mathematical Physics, Issue 59/6, 2018, Page(s) 063507, ISSN 0022-2488
DOI: 10.1063/1.5021305
K-theory and index pairings for C*-algebras generated by $q$-normal operators
Author(s): Ismael Cohen, Elmar Wagner
Published in: Rocky Mountain Journal of Mathematics, Issue 48/5, 2018, Page(s) 1485-1510, ISSN 0035-7596
DOI: 10.1216/rmj-2018-48-5-1485
Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model
Author(s): Ludwik Dąbrowski, Andrzej Sitarz
Published in: Journal of High Energy Physics, Issue 2019/2, 2019, ISSN 1029-8479
DOI: 10.1007/jhep02(2019)068
Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
Author(s): K. De Commer, M. Matassa
Published in: Advances in Mathematics, Issue 366, 2020, Page(s) 107029, ISSN 0001-8708
DOI: 10.1016/j.aim.2020.107029
Triviality of equivariant maps in crossed products and matrix algebras
Author(s): Benjamin W Passer
Published in: The Quarterly Journal of Mathematics, Issue 70/1, 2018, Page(s) 289-303, ISSN 0033-5606
DOI: 10.1093/qmath/hay044
Representations of quantum SU(2) operators on a local chart
Author(s): Elmar Wagner
Published in: Journal of Physics: Conference Series, Issue 670, 2016, Page(s) 012053, ISSN 1742-6588
DOI: 10.1088/1742-6596/670/1/012053
Integrable lifts for transitive Lie algebroids
Author(s): Iakovos Androulidakis, Paolo Antonini
Published in: International Journal of Mathematics, Issue 29/09, 2018, Page(s) 1850062, ISSN 0129-167X
DOI: 10.1142/S0129167X18500623
Noncommutative Borsuk-Ulam-type conjectures
Author(s): Paul F. Baum, Ludwik Dąbrowski, Piotr M. Hajac
Published in: Banach Center Publications, Issue 106, 2015, Page(s) 9-18, ISSN 0137-6934
DOI: 10.4064/bc106-0-1
Variations of projectivity for C∗-algebras
Published in: Pacific Journal of Mathematics, Issue 301/2, 2019, Page(s) 421-440, ISSN 0030-8730
DOI: 10.2140/pjm.2019.301.421
The index of generalised Dirac–Schrödinger operators
Author(s): Koen van den Dungen
Published in: Journal of Spectral Theory, Issue 9/4, 2019, Page(s) 1459-1506, ISSN 1664-039X
DOI: 10.4171/JST/283
A Correspondence Between Homogeneous and Galois Coactions of Hopf Algebras
Author(s): Kenny De Commer, Johan Konings
Published in: Algebras and Representation Theory, 2020, ISSN 1386-923X
DOI: 10.1007/s10468-019-09892-6
The modular Gromov–Hausdorff propinquity
Author(s): Frédéric Latrémolière
Published in: Dissertationes Mathematicae, Issue 544, 2019, Page(s) 1-70, ISSN 0012-3862
DOI: 10.4064/dm778-5-2019
The covariant Gromov–Hausdorff propinquity
Author(s): Frédéric Latrémolière
Published in: Studia Mathematica, Issue 251/2, 2020, Page(s) 135-169, ISSN 0039-3223
DOI: 10.4064/sm180610-28-12
Monic representations of finite higher-rank graphs
Author(s): CARLA FARSI, ELIZABETH GILLASPY, PALLE JORGENSEN, SOORAN KANG, JUDITH PACKER
Published in: Ergodic Theory and Dynamical Systems, Issue 40/5, 2020, Page(s) 1238-1267, ISSN 0143-3857
DOI: 10.1017/etds.2018.79
Actions of categories by Lipschitz morphisms on limits for the Gromov–Hausdorff propinquity
Author(s): Frédéric Latrémolière
Published in: Journal of Geometry and Physics, Issue 146, 2019, Page(s) 103481, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2019.103481
Spin geometry of the rational noncommutative torus
Author(s): Alessandro Carotenuto, Ludwik Dąbrowski
Published in: Journal of Geometry and Physics, Issue 144, 2019, Page(s) 28-42, ISSN 0393-0440
DOI: 10.1016/j.geomphys.2019.05.008
Model theory and Rokhlin dimension for compact quantum group actions
Author(s): Eusebio Gardella, Mehrdad Kalantar, Martino Lupini
Published in: Journal of Noncommutative Geometry, Issue 13/2, 2019, Page(s) 711-767, ISSN 1661-6952
DOI: 10.4171/jncg/337
Compact group actions on topological and noncommutative joins
Author(s): Alexandru Chirvasitu, Benjamin Passer
Published in: Proceedings of the American Mathematical Society, Issue 146/8, 2018, Page(s) 3217-3232, ISSN 0002-9939
DOI: 10.1090/proc/13941
Dirac operator and its cohomology for the quantum group Uq()
Author(s): Pavle Pandžić, Petr Somberg
Published in: Journal of Mathematical Physics, Issue 58/4, 2017, Page(s) 041702, ISSN 0022-2488
DOI: 10.1063/1.4979623
Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals
Published in: Journal of Operator Theory, 2019, ISSN 0379-4024
DOI: 10.7900/jot.2018jun13.2222
Cuntz Semigroups of Compact-Type Hopf C*-Algebras
Author(s): Dan Kučerovský
Published in: Axioms, Issue 6/4, 2017, Page(s) 1, ISSN 2075-1680
DOI: 10.3390/axioms6010001
Cotangent bundles for “matrix algebras converge to the sphere”
Author(s): Marc A. Rieffel
Published in: Expositiones Mathematicae, 2020, ISSN 0723-0869
DOI: 10.1016/j.exmath.2020.01.006
Filtered K-theory for graph algebras
Author(s): Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Published in: MATRIX Book Series, Issue 1, 2018, Page(s) 229–249
On Noncommutative Geometry of the Standard Model: Fermion Multiplet as Internal Forms
Author(s): Ludwik Dąbrowski
Published in: Geometric Methods in Physics XXXVI, 2017
Dirac Operator on a Noncommutative Toeplitz Torus
Author(s): Fredy Díaz García, Elmar Wagner
Published in: Geometric Methods in Physics XXXVI - Workshop and Summer School, Białowieża, Poland, 2017, 2019, Page(s) 103-109
DOI: 10.1007/978-3-030-01156-7_11
Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces
Author(s): Francesca Arici, Piotr M. Hajac, Mariusz Tobolski
Published in: Quantum Dynamics, 2020
Standard homogeneous C*-algebras as compact quantum metric spaces
Published in: Quantum Dynamics, 2020
Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity
Published in: Quantum Dynamics, 2020
Translations in quantum groups
Author(s): Alexandru Chirvasitu
Published in: Quantum Dynamics, 2020
From Hopf algebras to topological quantum groups. A short history, various aspects and some problems
Author(s): Alfons Van Daele
Published in: Quantum Dynamics, 2020
A spectral triple for noncommutative compact surfaces
Author(s): Fredy Díaz García, Elmar Wagner
Published in: Quantum Dynamics, 2020
A note on the injectivity of action by compact quantum groups on a class of C∗-algebras
Author(s): D Goswami, S Joardar
Published in: Quantum Dynamics, 2020
A graded pullback structure of Leavitt path algebras of trimmable graphs
Author(s): Piotr M. Hajac, Atabey Kaygun, Mariusz Tobolski
Published in: Quantum Dynamics, 2020
Pullbacks of graph C*-algebras from admissible pushouts of graphs
Author(s): Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski
Published in: Quantum Dynamics, 2020
The asymptotic Connes-Moscovici characteristic map and the index cocycles
Author(s): Atabey Kaygun, Serkan Sütlü
Published in: Quantum Dynamics, 2020
K-theory of cluster C*-algebras
Author(s): Igor Nikolaev
Published in: Quantum Dynamics, 2020
Epsilon factors as algebraic characters on the smooth dual of GLn
Author(s): Roger Plymen
Published in: Quantum Dynamics, 2020
A Note on the Quantum Family of Maps
Author(s): Albert Jeu-Liang Sheu, Thomas Timmermann
Published in: Quantum Dynamics, 2020
Equivariant Dimensions of Graph C*-algebras
Author(s): Alexandru Chirvasitu, Benjamin Passer, Mariusz Tobolski
Published in: The Journal of Functional Analysis, 2020, ISSN 0022-1236
Invariant quantum measure on q-deformed twisted adjoint orbits
Author(s): Kenny De Commer
Published in: Representation Theory, 2020, ISSN 1088-4165
Twisted Dirac operator on quantum SU(2) in disc coordinates
Author(s): Ulrich Kraehmer, Elmar Wagner
Published in: Operator Theory: Advances and Applications, 2020, ISSN 2543-0483
Vector Bundles over Multipullback Quantum Complex Projective Spaces
Author(s): Albert Jeu-Liang Sheu
Published in: Journal of Noncommutative Geometry, 2020, ISSN 1661-6952
Global symbolic calculus of pseudo-differential operators on homogeneous vector bundles
Author(s): Mitsuru Wilson
Published in: SIGMA, 2020, ISSN 1815-0659
The classification of Rokhlin flows on C*-algebras
Author(s): Gabor Szabo
Published in: Communications in Mathematical Physics, 2020, ISSN 1432-0916
Noncommutative Borsuk-Ulam-type conjectures revisited
Author(s): Ludwik Dąbrowski, Piotr M. Hajac, Sergey Neshveyev
Published in: JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2020, ISSN 1661-6960
DOI: 10.4171/jncg/xxx
| 2021-06-22T02:07:14 |
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https://csrc.nist.gov/Projects/interoperable-randomness-beacons/apps
|
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# Interoperable Randomness Beacons
### Applications
A generic application (app, for short) of beacon randomness is enabling public-verifiability of randomized procedures. For example, when randomly sampling for audits, auditors are prevented from biasing the selections (or being accused of it), and auditees are prevented from knowing the selections in advance (or being accused of it).
An interesting randomness/determinism duality: although beacon applications relate to the use of randomness, their public auditability requires a well specified deterministic operation (which then uses as input the needed random values).
The remainder of this page gives a few examples, at a high level, of applications of beacon randomness.
#### Generic procedure:
1. Commit upfront: publish a statement $$S$$ that explains the deterministic operation that will use the Beacon randomness (the output value randOut) from future time $$t$$;
2. Derive a seed: Get $$R={\tt randOut}[t]$$ (from the pulse with timestamp $$t$$), and set the seed as $$Z=Hash(S||R)$$
3. Perform the operation: Do what the statement $$S$$ promised, using $$Z$$ as the seed for all needed pseudo-randomness.
A possible refinement: To prevent even the Beacon from predicting the result of the seed $$Z$$, the procedure statement $$S$$ can be refined to also be a commitment of a secret value. Then, after the needed pulse is available, the application uses the secret value to derive the seed, and publicly reveals it or a ZK-proof that is has been properly used. That way not even a malicious beacon targeting the application could predict the result of the seed $$Z$$.
Note: Real-life constraints can make this type of solution challenging, especially as it may require foreseeing procedures to adapt to unforeseen failure of selections (e.g., if a selected element is not available, a new one may have to be selected).
#### App example #1: Randomized clinical trials
Setting: a placebo-controlled clinical trial assigns patients to either the treatment group or the control group.
Goals: Enables select test and control groups for clinical trials; the public can check the trial was properly randomized.
Challenges: Apply commitments and zero-knowledge proofs to hide private data while proving correctness.
#### App example #2: Select random government officials for financial audits
(Example motivated by an application-project by the Random UChile Beacon)
Suppose a setting where a few subjects are to be selected from a large pool of candidates, with some weighting on private attributes. As a toy example, consider the following table of attributes, where a and b are abstract attributes (e.g., salary level and years on the job) that determine a risk score w. The probability of selection should be proportional to the risk score.
Procedure:
Commit to all attributes and publish the table of commitments ... then prove in ZK:
1. $$a_i \in A$$ (e.g., annual salary); $$b_i \in B$$ (e.g., years in position);
2. $$w_i = f(a_i,b_i)$$w_i = f(ai, bi) (correct probability weight);
3. $$\sum_i w_i =1$$ (correct sum of weights);
4. $$W_i = w_i + W_{i-1}$$ (correct accumulator);
5. $$\{N_i\} = \textrm{NAMES}$$ (non-repeated names from an appropriate set);
Following the procedure mentioned above, publish a statement $$S$$ explaining the procedure that follows.
At the specified future time $$t$$, derive a random $${\color{blue}R}:0<{\color{blue}R}\leq 1$$ (random) from the Beacon and determine $$\#\red{j}: W_{max(1,\red{j}-1)} < {\color{blue}R} \leq W_{\red{j}}$$# j: Wmax(1,j−1) < R ≤ Wj
Prove in ZK that $$\red{j}$$j is consistent with $${\color{blue}R}$$ and the table of commitments
Some references: slides 2020
#### App example #3: Freshness of proofs in legal metrology
Goal: Ensure freshness of proofs of software possession by measuring instruments.
A system employs zero-knowledge proofs of knowledge to enhance security in a system of measuring instruments. Beacon randomness is used to ensure unpredictability of the challenges and freshness of the proofs.
Some references: poster 2020, ZKASP paper (earlier version appeared at OIML)
#### Examples of other possible apps:
• Judge selection. Defenders and prosecutors verify unbiased assignment of a judge to a court case, avoiding forum shopping.
• Quality control. Sample random lots for quality-measuring procedures, preventing auditors from biasing selections (or being accused of it), and preventing auditees from learning in advance which items “will be” selected. The use of a beacon facilitates the audit trail for later verification of the sample selection.
• Lotteries. Provide entropy to digital lotteries.
• Randomized security checks. When faced with "You have been randomly chosen for additional security screening", individuals would be able to confirm that the selection was really random.
Some references: poster 2019, poster 2021
#### Contacts
Reach us at:
[email protected]
René Peralta
[email protected]
Harold Booth
Luís T. A. N. Brandão
John Kelsey
Carl Miller
#### Topics
Security and Privacy: cryptography
Created June 03, 2019, Updated February 03, 2023
| 2023-03-31T21:41:46 |
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http://www.itl.nist.gov/div898/handbook/pri/section5/pri58.htm
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5. Process Improvement
## What are small composite designs?
Small composite designs save runs, compared to Resolution V response surface designs, by adding star points to a Resolution III design Response surface designs (RSD) were described earlier. A typical RSD requires about 13 runs for 2 factors, 20 runs for 3 factors, 31 runs for 4 factors, and 32 runs for 5 factors. It is obvious that, once you have four or more factors you wish to include in a RSD, you will need more than one lot (i.e., batch) of experimental units for your basic design. This is what most statistical software today will give you. However, there is a way to cut down on the number of runs, as suggested by H.O. Hartley in his paper 'Smallest Composite Designs for Quadratic Response Surfaces', published in Biometrics, December 1959.
This method addresses the theory that using a Resolution V design as the smallest fractional design to create a RSD is unnecessary. The method adds star points to designs of Resolution III and uses the star points to clear the main effects of aliasing with the two-factor interactions. The resulting design allows estimation of the higher-order interactions. It also provides poor interaction coefficient estimates and should not be used unless the error variability is negligible compared to the systematic effects of the factors.
Useful for 4 or 5 factors This could be particularly useful when you have a design containing four or five factors and you wish to only use the experimental units from one lot (i.e., batch).
Table containing design matrix for four factors The following is a design for four factors. You would want to randomize these runs before implementing them; -1 and +1 represent the low and high settings, respectively, of each factor.
TABLE 5.11 Four factors: Factorial design section is based on a generator of I = X1*X2*X3, Resolution III; -α and +α are the star points, calculated beyond the factorial range; 0 represents the midpoint of the factor range.
Row X1 X2 X3 X4
1 +1 -1 -1 -1
2 -1 +1 -1 -1
3 -1 -1 +1 -1
4 +1 +1 +1 -1
5 +1 -1 -1 +1
6 -1 +1 -1 +1
7 -1 -1 +1 +1
8 +1 +1 +1 +1
9 -α 0 0 0
10 α 0 0 0
11 0 -α 0 0
12 0 α 0 0
13 0 0 -α 0
14 0 0 α 0
15 0 0 0 -α
16 0 0 0 α
17 0 0 0 0
18 0 0 0 0
19 0 0 0 0
20 0 0 0 0
Determining α in Small Composite Designs
α based on number of treatment combinations in the factorial portion To maintain rotatability for usual CCD's, the value of α is determined by the number of treatment combinations in the factorial portion of the central composite design:
$$\alpha = \left[ \mbox{number of factorial runs} \right] ^{1/4}$$
Small composite designs not rotatable However, small composite designs are not rotatable, regardless of the choice of α. For small composite designs, α should not be smaller than [number of factorial runs]1/4 nor larger than k1/2.
| 2017-10-18T16:54:59 |
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https://www.itl.nist.gov/div898/handbook/prc/section2/prc25.htm
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7. Product and Process Comparisons
7.2. Comparisons based on data from one process
## Does the defect density meet requirements?
Testing defect densities is based on the Poisson distribution The number of defects observed in an area of size $$A$$ units is often assumed to have a Poisson distribution with parameter $$A \times D$$, where $$D$$ is the actual process defect density ($$D$$ is defects per unit area). In other words: $$P(\mbox{Number of Defects } = n) = \frac{(AD)^n}{n!} e^{-AD} \, .$$ The questions of primary interest for quality control are:
1. Is the defect density within prescribed limits?
2. Is the defect density less than a prescribed limit?
3. Is the defect density greater than a prescribed limit?
Normal approximation to the Poisson We assume that $$AD$$ is large enough so that the normal approximation to the Poisson applies (in other words, $$AD >$$ 10 for a reasonable approximation and $$AD >$$ 20 for a good one). That translates to $$P(\mbox{Number of Defects } < n) = \Phi \left( \frac{n-AD}{\sqrt{AD}} \right) \, ,$$ where $$\Phi$$ is the standard normal distribution function.
Test statistic based on a normal approximation If, for a sample of area $$A$$ with a defect density target of $$D_0$$, a defect count of $$C$$ is observed, then the test statistic, $$Z = \frac{C - AD_0}{\sqrt{AD_0}} \, ,$$ can be used exactly as shown in the discussion of the test statistic for fraction defectives in the preceding section.
Testing the hypothesis that the process defect density is less than or equal to $$D_0$$ For example, after choosing a sample size of area $$A$$ (see below for sample size calculation) we can reject that the process defect density is less than or equal to the target $$D_0$$ if the number of defects $$C$$ in the sample is greater than $$C_A$$, where $$C_A = z_{1-\alpha} \sqrt{AD_0} + AD_0 \, ,$$ and $$z_{1-\alpha}$$ is the $$100(1-\alpha)$$ percentile of the standard normal distribution. The test significance level is $$100(1-\alpha)$$. For a 90 % significance level use $$z_{0.90}$$ = 1.282 and for a 95 % test use $$z_{0.95}$$ = 1.645. $$\alpha$$ is the maximum risk that an acceptable process with a defect density at least as low as $$D_0$$ "fails" the test.
Choice of sample size (or area) to examine for defects In order to determine a suitable area $$A$$ to examine for defects, you first need to choose an unacceptable defect density level. Call this unacceptable defect density $$D_1 = k D_0$$, where $$k >$$ 1.
We want to have a probability of less than or equal to $$\beta$$ is of "passing" the test (and not rejecting the hypothesis that the true level is $$D_0$$ or better) when, in fact, the true defect level is $$D_1$$ or worse. Typically $$\beta$$ will be 0.2, 0.1 or 0.05. Then we need to count defects in a sample size of area $$A$$, where $$A$$ is equal to $$A = \frac{k}{D_0} \left( \frac{\frac{z_{1-\alpha}} {\sqrt{k}} - z_\beta} {k-1} \right)^2 \, .$$
Example Suppose the target is $$D_0$$ = 4 defects per wafer and we want to verify a new process meets that target. We choose $$\alpha$$ = 0.1 to be the chance of failing the test if the new process is as good as $$D_0$$ ($$\alpha$$ = the Type I error probability or the "producer's risk") and we choose $$\beta$$ = 0.1 for the chance of passing the test if the new process is as bad as 6 defects per wafer ($$\beta$$ = the Type II error probability or the "consumer's risk"). That means $$z_{1-\alpha}$$ = 1.282 and $$z_{\beta}$$ = -1.282.
The sample size needed is $$A$$ wafers, where $$A = \frac{1.5}{4} \left( \frac{\frac{1.282}{\sqrt{1.5}} - (-1.282)}{k-1} \right) ^ 2 = 8.1 \, ,$$
which we round up to 9.
The test criteria is to "accept" that the new process meets target unless the number of defects in the sample of 9 wafers exceeds $$C_A = z_{1-\alpha} \sqrt{AD_0} + AD_0 = 1.282 \sqrt{36} + 36 = 43.7 \, .$$ In other words, the reject criteria for the test of the new process is 44 or more defects in the sample of 9 wafers.
Note: Technically, all we can say if we run this test and end up not rejecting is that we do not have statistically significant evidence that the new process exceeds target. However, the way we chose the sample size for this test assures us we most likely would have had statistically significant evidence for rejection if the process had been as bad as 1.5 times the target.
| 2018-08-17T20:45:39 |
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|
https://nasa.fandom.com/wiki/SeaWiFS
|
## FANDOM
SeaWIFS (Sea-Viewing Wide Field-of-View Sensor) was a satellite-borne sensor that was designed to collect global ocean biological data. Its primary mission was to quantify chlorophyll produced by marine phytoplankton (microscopic plants).
## InstrumentEdit
SeaWiFS was the only scientific instrument on GeoEye's OrbView-2 (AKA SeaStar) satellite, and was a follow-on experiment to the Coastal Zone Color Scanner on Nimbus 7. Launched August 1, 1997 on an Orbital Sciences Pegasus small air-launched rocket, SeaWiFS began scientific operations on September 18, 1997 and stopped collecting data on December 11, 2010.,[1] far exceeding its designed operating period of 5 years.[2] The sensor resolution is 1.1 km (LAC), 4.5 km (GAC). The sensor recorded information in the following optical bands:
Band Wavelength
1 402-422 nm
2 433-453 nm
3 480-500 nm
4 500-520 nm
5 545-565 nm
6 660-680 nm
7 745-785 nm
8 845-885 nm
The instrument was specifically designed to monitor ocean characteristics such as chlorophyll-a concentration and water clarity. It was able to tilt up to 20 degrees to avoid sunlight from the sea surface. This feature is important at equatorial latitudes where glint from sunlight often obscures water colour. SeaWiFS had used the Marine Optical Buoy for vicarious calibration.
The SeaWiFS Mission is an industry/government partnership, with NASA's Ocean Biology Processing Group at Goddard Space Flight Center having responsibility for the data collection, processing, calibration, validation, archive and distribution. The current SeaWiFS Project manager is Gene Carl Feldman.
## Chlorophyll EstimationEdit
Chlorophyll concentrations are derived from images of the ocean’s color. Generally speaking, the greener the water, the more phytoplankton are present in the water, and the higher the chlorophyll concentrations. Chlorophyll a absorbs more blue and red light than green, with the resulting reflected light changing from blue to green as the amount of chlorophyll in the water increases. Using this knowledge, scientists were able to use ratios of different reflected colors to estimate chlorophyll concentrations.
Many formulas estimate chlorophyll by comparing the ratio of blue to green light and relating those ratios to known chlorophyll concentrations from the same times and locations as the satellite observations. The color of light is defined by its wavelength, and visible light has wavelengths from 400 to 700 nanometers, progressing from violet (400 nm) to red (700 nm). A typical formula used for SeaWiFS data (termed OC4v4) divides the reflectance of the maximum of several wavelengths (443, 490, or 510 nm) by the reflectance at 550 nm. This roughly equates to a ratio of blue light to green light for two of the numerator wavelengths, and a ratio of two different green wavelengths for the other possible combination.
The reflectance (R) returned by this formula is then plugged into a cubic polynomial that relates the band ratio to chlorophyll.[3]
$Chl = antilog(0.366-3.067\mathsf{R}+1.93\mathsf{R}^2 +0.64\mathsf{R}^3 -1.53\mathsf{R}^4)$[4]
This formula, along with others, was derived empirically using observed chlorophyll concentrations. To facilitate these comparisons, NASA maintains a system of oceanographic and atmospheric data called SeaBASS (SeaWiFS Bio-optical Archive and Storage System). This data archive is used to develop new algorithms and validate satellite data products by matching chlorophyll concentrations measured directly with those estimated remotely from a satellite. These data can also be used to assess atmospheric correction (discussed below) that also can greatly influence chlorophyll concentration calculations.
Numerous chlorophyll algorithms were tested to see which ones best matched chlorophyll globally. Various algorithms perform differently in different environments. Many algorithms estimate chlorophyll concentrations more accurately in deep clear water than in shallow water. In shallow waters reflectance from other pigments, detritus, and the ocean bottom may cause inaccuracies. The stated goals of the SeaWiFS chlorophyll estimates are “… to produce water leaving radiances with an uncertainty of 5% in clear-water regions and chlorophyll a concentrations within ±35% over the range of 0.05–50 mg m-3.”.[2] When accuracy is assessed on a global scale, and all observations are grouped together, then this goal is clearly met.[5] Many satellite estimates range from one-third to three times of those directly recorded at sea, though the overall relationship is still quite good.[4] Differences arise when examined by region, though overall the values are still very useful. One pixel may not be particularly accurate, though when averages are taken over larger areas, the values average out and provide a useful and accurate view of the larger patterns. The benefits of chlorophyll data from satellites far outweigh any flaws in their accuracy simply by the spatial and temporal coverage possible. Ship-based measurements of chlorophyll cannot come close to the frequency and spatial coverage provided by satellite data.
## Atmospheric CorrectionEdit
Light reflected from the sub-surface ocean is called water-leaving radiance and is used to estimate chlorophyll concentrations. However, only about 5-10% of light at the top of the atmosphere is from water-leaving radiance.[6][7] The remainder of light is reflected from the atmosphere and from aerosols within the atmosphere. In order to estimate chlorophyll concentrations this non-water-leaving radiance must be accounted for. Some light reflected from the ocean, such as from whitecaps and sun glint, must also be removed from chlorophyll calculations since they are representative ocean waves or the angle of the sun instead of the subsurface ocean. The process of removing these components is called atmospheric correction.[8]
A description of the light, or radiance, observed by the satellite’s sensor can be more formally expressed by the following radiative transfer equation:
$L_T(\lambda) = L_r(\lambda)+L_a(\lambda)+L_{ra}(\lambda)+TL_g(\lambda)+t(L_f(\lambda)+L_W(\lambda))$
Where LT(λ) is total radiance at the top of the atmosphere, Lr(λ) is Rayleigh scattering by air molecules, La(λ) is scattering by aerosols in the absence of air, Lra(λ) is interactions between air molecules and aerosols, TLg(λ) is reflections from glint, t(Lf(λ) is reflections from foam, and LW(λ)) is reflections from the subsurface of the water, or the water-leaving radiance.[2] Others may divide radiance into some slightly different components,[8] though in each case the reflectance parameters must be resolved in order to estimate water-leaving radiance and thus chlorophyll concentrations.
## Data productsEdit
Though SeaWiFS was designed primarily to monitor ocean chlorophyll a concentrations from space, it also collected many other parameters that are freely available to the public for research and educational purposes. These parameters aside from chlorophyll a include reflectance, the diffuse attenuation coefficient, particulate organic carbon concentration (POC), particulate inorganic carbon concentration (PIC), colored dissolved organic matter (CDOM) index, photosynthetically active radiation (PAR), and normalized fluorescence line height (NFLH). In addition, despite being designed to measure ocean chlorophyll, SeaWiFS also estimates Normalized Difference Vegetation Index (NDVI), which is a measure of photosynthesis on land.
## Data AccessEdit
SeaWiFS data are freely accessible from a variety of websites, most of which are government run. The primary location for SeaWiFS data is NASA’s OceanColor website [2], which maintains the time series of the entire SeaWiFS mission. The website allows users to browse individual SeaWiFS images based on time and area selections. The website also allows for browsing of different temporal and spatial scales with spatial scales ranging from 4 km to 9 km for mapped data. Data are provided at numerous temporal scales including daily, multiple days (e.g., 3, 8), monthly, and seasonal images, all the way up to composites of the entire mission. Data are also available via ftp and bulk download.
Data can be browsed and retrieved in a variety of formats and levels of processing, with four general levels from unprocessed to modeled output.[9] Level 0 is unprocessed data that is not usually provided to users. Level 1 data are reconstructed but either unprocessed or minimally processed. Level 2 data contain derived geophysical variables, though are not on a uniform space/time grid. Level 3 data contain derived geophysical variables binned or mapped to a uniform grid. Lastly, Level 4 data contain modeled or derived variables such as ocean primary productivity .
Scientists who aim to create calculations of chlorophyll or other parameters that differ from those provided on the OceanColor website would likely use Level 1 or 2 data. This might be done, for example, to calculate parameters for a specific region of the globe, whereas the standard SeaWiFS data products are designed for global accuracy with necessary tradeoffs for specific regions. Scientists who are more interested in relating the standard SeaWiFS outputs to other processes will commonly use Level 3 data, particularly if they do not have the capacity, training, or interest in working with Level 1 or 2 data. Level 4 data may be used for similar research if interested in a modeled product.
## SoftwareEdit
NASA offers free software designed specifically to work with SeaWiFS data through the ocean color website. This software, entitled SeaDAS (SeaWiFS Data Analysis System), is built for visualization and processing of satellite data and can work with Level 1, 2, and 3 data. Though it was originally designed for SeaWiFS data, its capabilities have since been expanded to work with many other satellite data sources. Other software or programming languages can also be used to read in and work with SeaWiFS data, such as Matlab, IDL, or Python.
## ApplicationsEdit
Estimating the amount of global or regional chlorophyll, and therefore phytoplankton, has large implications for climate change and fisheries production. Phytoplankton play a huge role in the uptake of the world's carbon dioxide, a primary contributor to climate change. A percentage of these phytoplankton sink to ocean floor, effectively taking carbon dioxide out of the atmosphere and sequestering it in the deep ocean for at least a thousand years. Therefore, the degree of primary production from the ocean could play a large role in slowing climate change. Or, if primary production slows, climate change could be accelerated. Some have proposed fertilizing the ocean with iron in order to promote phytoplankton blooms and remove carbon dioxide from the atmosphere. Whether these experiments are undertaken or not, estimating chlorophyll concentrations in the world's oceans and their role in the ocean's biological pump could play a key role in our ability to foresee and adapt to climate change.
Phytoplankton is a key component in the base of the oceanic food chain and oceanographers have hypothesized a link between oceanic chlorophyll and fisheries production for some time.[10] The degree to which phytoplankton relates to marine fish production depends on the number of trophic links in the food chain, and how efficient each link is. Estimates of the number of trophic links and trophic efficiencies from phytoplankton to commercial fisheries have been widely debated, though they have been little substantiated.[11] More recent research suggests that positive relationships between chlorophyll a and fisheries production can be modeled[12] and can be very highly correlated when examined on the proper scale. For example, Ware and Thomson (2005) found an r2 of 0.87 between resident fish yield (metric tons km-2) and mean annual chlorophyll a concentrations (mg m-3).[13] Others have found the Pacific's Transition Zone Chlorophyll Front (chlorophyll density of 0.2 mg m-3) to be defining feature in loggerhead turtle distribution.[14]
## ReferencesEdit
• Cracknell, A. P., S. K. Newcombe, A. F. Black and N. E. Kirby (2001). The ABDMAP (Algal Bloom Detection, Monitoring and Prediction) Concerted Action. International Journal of Remote Sensing, 22: 205-247
1. NASA, Goddard Space Flight Center (February 14, 2011). "Ocean Color Browse". Retrieved February 14, 2011.
2. 2.0 2.1 2.2 Template:Cite journal
3. Template:Cite journal
4. 4.0 4.1 Template:Cite book
5. Template:Cite journal
6. Gene Carl Feldman, [1],”SeaWiFS Project – Detailed Description”, OceanColor WEB, 7/30/2003
7. Template:Cite journal
8. 8.0 8.1 Franz, Brian. "Algorithm for Retrieval of Remote Sensing Reflectance from Satellite Ocean Color Sensors". Ocean Color Web. Retrieved 29 October 2013.
9. "Product Level Descriptions". Ocean ColorWeb. Retrieved 29 October 2013.
10. Template:Cite journal
11. Template:Cite journal
12. Template:Cite journal
13. Template:Cite journal
14. Template:Cite journal
## Edit
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-10-14T19:58:23 |
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|
https://pavpanchekha.com/blog/treap.html
|
## By Pavel Panchekha
### 14 May 2011
Share under CC-BY-SA.
# Treaps: The Magical Awesome BBT
Treaps are the awesome balanced binary tree. A little randomness makes a tree that is expected to have logarithmic height but is easy to code, requiring none of the special-cases that characterize red-black trees. Here, I code up a complete treap implementation in Lisp (particularly, pylisp).
## Our Goals
Our goal is to create a treap-based implementation of a map. I'll be using Lisp, in particular pylisp; feel free to follow along in any other language.
A treap map supports the following interface:
(get key treap)
Get the value associated with key from our treap.
(in key treap)
Return #t if key is in your treap, and #f if not.
(set key val treap)
Return a new treap, which is the same as the old one except associates key with val.
(del key treap)
Return a new treap, which is the same as the old except does not associate anything with key.
Note that our treap is functional, so set and del return new treaps with the necessary modifications made. Furthermore, each of these methods run in $$O(\log n)$$ time.
## Binary Trees and Heaps
###### Note
What I'm calling a "binary tree" here is normally called a binary search tree.
Quick review: what's a binary tree? Simply put, it's a tree where each node has both a key and a value, and for each node, the left subtree has smaller keys and the right subtree has larger keys.1 [1 I'm ignoring duplicate keys, but they don't change much.] This rule makes lookups for any key fast: we binary search the keys. But this speed requires the left and right subtrees to be approximately equal in size. When that's roughly true for every node, the tree is called “balanced”.
### Balancing
There exist many, many algorithms to “balance” binary trees, ensuring that any node's subtrees are similarly sized, but most of them are horrible, confusing things with thousands of special cases. Which is a pity! Binary trees work well in functional code (unlike hash tables) because they can share structure. And they provide an ordered map, so you can iterate over the keys in order without having to sort.
For example, say you're writing an address book, so you need a map from contacts to phone numbers. With a hash table, you need to sort the contacts to display them in order. By storing the contacts as a binary tree, you transform $$O(n \log n)$$ sort into an $$O(n)$$ iteration.
So let us embark on a journey to balanced binary trees with treaps.
### Heaps
The second data structure treaps build upon is the heap. In a heap, every node has a priority, and this priority is the lowest priority of its subtree. Heaps are often used to implement priority queues, and are otherwise a pretty niche data structure.
###### Note
Technically, I've described a "min-heap", where the root is the minimum element. In a "max-heap", the root is the maximum element. Normally, one does not actually care which a heap is, since the main property is that the root is extremal.
### Tree Rotations
One binary tree can be transformed into another with rotations, which modify the tree while preserving its order properties:
In this picture, the Greek letters represent subtrees that don't change during a rotation. Rotation retains the tree's order properties: both trees are sorted $$\alpha < x < \beta < y < \gamma$$. This order-preservation is the most important property of the rotation, but it also moves nodes up and down in the tree—here, x moves up and y moves down. Another rotation could move x yet further and further, until it became the root of the tree.
## The Basic Idea
A treap is a cross between a binary tree and a heap: each node has both a key and a priority, and the tree is both a binary tree (on the key) and a heap (on the priority).
Now does there always exist a treap for a given set of keys and priorities? Is that treap unique?
A simple argument answers both in the positive. Clearly, the root node must be the node with lowest priority. This partitions the remaining nodes into two sets: those with key less than the root, and those with key greater. Recurse onto each of those sets, building treaps out of them, until there are no more nodes left, and you have a valid treap.
Now, in a map, keys are assigned by the user, but where do priorities come from? A treap assigns the priorities at random; this tends to move values with middling keys into the root of the tree.
Let's prove that this results in a tree with logarithmic height. Now consider the root node, and ask: what's the size of the larger of its subtrees, as a percentage of the total tree? Well, we know that the root of the treap is the node with the smallest priority, and since priorities are chosen randomly, it has a 50% chance of being between the first and third quartiles of keys. Imagine, now, taking some path from the root down. On average, every time we go down two nodes, at least one quarter of the tree is no longer in our subtree. So if there are $$n$$ nodes, we expect our path to end after $$2 \log_{3/4} n = O(\log n)$$ steps.
Now that the theory is clear, let's implement treaps.
## Lookup and Containment
It's time to start programming: spewing out s-expressions at machine gun speeds. Buckle up. First things first, let's define a data structure for nodes:
(class::simple Node (p key val left right))
Unfamiliar with pylisp? This defines a class with fields p, key, val, left, and right, and also a constructor for this class.
Now, let's implement some methods. First up: the get function. Since our treap is already a binary tree, we use the standard binary tree lookup algorithm, completely ignoring priorities:
(def get (key root)
(cond
((not root)
(signal '(error not-found key get) key))
((< key root.key)
(get key root.left))
((> key root.key)
(get key root.right))
((= key root.key)
root.val)))
Containment, in, is basically identical:
(def in (key root)
(cond
((not root)
#f)
((< key root.key)
(in key root.left))
((> key root.key)
(in key root.right))
((= key root.key)
#t)))
## Insertion
Now on to the more difficult modification operations.
How do we insert an element or update a value? Well, we can spider down to the place where the new node should live using the same algorithm as get above. But we can't just add the new node there if its (randomly chosen) priority is larger than its parent's. Instead, we have to move it upwards in the tree, while maintaining the ordering property of binary trees.
Well, I've already mentioned that tree rotation move nodes up and down and preserve ordering. So let's implement left and right rotations:
(def left-rotate (node)
(Node node.left.p node.left.key node.left.val
node.left.left
(Node node.p node.key node.val node.left.right node.right)))
(def right-rotate (node)
(Node node.right.p node.right.key node.right.val
(Node node.p node.key node.val node.left node.right.left)
node.right.right))
With that out of the way, let's start on insertion itself.
First, we'll need to import the random module to get priorities:
(use random)
The new node needs a random priority before we inserted, and I'm going to pass that priority up and down the call stack instead of generating it once we get to the leaves of the tree. Trust me on this one.
With that set, here's a rough skeleton for set:
(def set (key val root #:(p (random.randint 0 1000000000)))
(cond
((not root)
?) ; Just generate the new node
((< key root.key)
?) ; Recurse leftwards, then do a left-rotation if necessary
((> key root.key)
?) ; Same as the (<) case, but recurse and rotate to the right
((= key root.key)
?))) ; Update existing node. So, just create the new node
Alright, let's fill this baby in. The first case, with an empty treap, is easy:2 [2 Note that #0, the null object, is my representation of the null treap.]
((not root)
(Node p key val #0 #0))
Next, let's do the last case, where we are updating a value, not adding a new key:
((= key root.key)
(Node root.p root.key val root.left root.right))
Note that I'm not updating the priority; it would have been fine to do so, but would only have lead to extra tree rotations later.
We have only the two middle cases left, and they're basically identical. First, we recurse to insert into one of the subtrees. But that might have upset the heap property, so we may have to carry out the appropriate rotation:
((< key root.key)
(let (new (Node root.p root.key root.val
(set key val root.left #:(p p))
root.right))
(if (< new.left.p new.p)
(left-rotate new)
new)))
((> key root.key)
(let (new (Node root.p root.key root.val
root.left
(set key val root.right #:(p p))))
(if (< new.right.p new.p)
(right-rotate new)
new)))
Putting it together, we have:
(def set (key val root #:(p (random.randint 0 1000000000)))
(cond
((not root)
(Node p key val #0 #0))
((< key root.key)
(let (new (Node root.p root.key root.val
(set key val root.left #:(p p))
root.right))
(if (< new.left.p new.p)
(left-rotate new)
new)))
((> key root.key)
(let (new (Node root.p root.key root.val
root.left
(set key val root.right #:(p p))))
(if (< new.right.p new.p)
(right-rotate new)
new)))
((= key root.key)
(Node root.p root.key val root.left root.right))))
Yeah, it looks big now, but all the pieces make sense. And note that this is functional—not a single set! call. Recursion mixes oh so well with functional programming. Yes it does.
## Split & Merge
Before we tackle deletion, let's take a quick detour to splitting and merging. Splitting takes one treap and produces two, a left treap and a right treap, where the left treap contains the values less than a given key and the right treap contains the values greater than a given key. We assume that the key is not in the treap.3 [3 Otherwise, which output would it go in?] Of course, the left and right treaps that result from the splitting must themselves be valid treaps.
To do that, we're gonna cheat. First, we add in a new node with the given key, but give it a really low priority (I'm going with -1) so that it becomes the root. Then we can just pluck off left and right subtreaps and return those. Nice and simple, huh?
(def split (key root)
(let (ins (set key #0 root #:(p (- 1))))
(pair ins.left ins.right)))
Because insertion is functional, we never have to explicitly remove the dummy node.
The opposite of splitting is merging. Merging takes two treaps that might have been the result of a split, and merges them into one treap.
How can we implement that? Well, the root element of the new treap must be the root of one of the two treaps—whichever has the lowest priority. Let's say it's the root of the right treap; in that case, the new root's right child must be the right treap's right child, since that already contains all the nodes larger than the new root. Meanwhile, the left child must be the merger of the left treap and the right treap's left child.4 [4 The #t below is the pylisp syntax for the true boolean, so it's the default clause of the conditional.]
(def merge (left right)
(cond
((not left)
right)
((not right)
left)
((< left.p right.p)
(Node left.p left.key left.val left.left (merge left.right right)))
(#t
(Node right.p right.key right.val (merge right.left left) right.right))))
###### Note
The first time I wrote this, there were errors. They are now fixed. The new code is deceptively similar; but then again, even minor changes are crucial in recursive functions, since those errors propogate.
## Deletion
Deletion is the grave yard of balanced binary trees—for red-black trees, Wikipedia lists six cases. But deletion for treaps is very nice and intuitive. Intuitive!
Consider the node you want to delete. If your node is a leaf node, just delete it. If it has one child, remove the node and replace it by its child. And if the node has two children? Then, when you remove it, merge its two subtreaps into a replacement:
(def del (key root)
(cond
((not root)
(signal '(error not-found key del) key))
((< key root.key)
(Node root.p root.key root.val (del key root.left) root.right))
((> key root.key)
(Node root.p root.key root.val root.left (del key root.right)))
((= key root.key)
(merge root.left root.right))))
But we can do even simpler:
(def del (key root)
(let (halves (split key root))
(merge (car halves) (cdr halves))))
Note the pure, happy simplicity of this method! Oh, the joys of treaps!
## Usage
I like to add some test code to the bottom of my files. Not exhaustive unit tests,5 [5 We don't want import taking forever, do we?] but a quick sanity test, just to make sure everything works. Let's do that here:
(use tester)
(test "Sanity check"
(let (treap #0)
(set! treap (set 5 'a treap))
(set! treap (set 7 'b treap))
(assert (= (get 5 treap) 'a))
(assert (= (get 7 treap) 'b))
(set! treap (set 2 'c treap))
(assert (= (get 2 treap) 'c))
(set! treap (set 2 'd treap))
(assert (= (get 2 treap) 'd))
(set! treap (del 5 treap))
(assert (not (in 5 treap)))))
That checks that the treap works. But is it balanced?
(test "Fairly Balanced"
(let (treap #0)
(signal '(warning test slow-test) "Balancing test")
(for (i (range 1000))
(set! treap (set i #0 treap))
(print i))
(assert (< (depth treap) 40))))
## Wrapping up
Overall, this code weighs in under 100 lines, and if that's not impressive, go implement red-black trees. We'll see who's laughing.
What about cool optimizations? Anything in that department? Well, it's a good thing you ask. There're all these priorities floating around. Don't you just get the urge to fiddle with them?
One simple optimization would decrease the priority of a node every time it is accessed (whether by get or set). This will slowly migrate your commonly-accessed nodes up to the top of the treap, where they're faster to get at. But this can slow down accesses, because you'd need to rewrite the treap.
I'm not providing code for this variant, because it's not worth it in my experience. If you have a treap of several thousand elements but you only ever access three of them, you're doing something else wrong. If you do implement it,make sure split deals with non-unique priorities correctly. But as always, look before you leap, benchmark when in doubt, beware of dog.
### A quick problem
Suppose we want to create a sorted array; that is, we want to be able to retrieve the $n$-th largest key, in $$O(\log n)$$ time. Treaps (or, really, any balanced binary tree) provide a nice way to do this. As a hint, consider the fact that we're not using the value stored in each node for anything, thus leaving it open to be appropriated for some purpose.
### Acknowledgments
Thanks to Sam Fingeret for first introducing me to treaps, and for helping out with the details of the proof that the height is expected to be logarithmic. Thank you as well to Mark Velednitsky for editing this writeup, even though he can't stand the sight of Lisp. I also edited the page in 2019 to make it 20% shorter. I hope you find the results short but clear.
Thanks also to folks on Hacker News who provided a lively discussion, and to Patrick Stein who did an implementation in Common Lisp.
## Footnotes:
1
I'm ignoring duplicate keys, but they don't change much.
2
Note that #0, the null object, is my representation of the null treap.
3
Otherwise, which output would it go in?
4
The #t below is the pylisp syntax for the true boolean, so it's the default clause of the conditional.
5
We don't want import taking forever, do we?
| 2021-07-27T01:18:45 |
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|
http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/diffaad.htm
|
Dataplot Vol 2 Vol 1
Name:
Type:
Let Subcommand
Purpose:
Compute the difference between the average absolute deviations (AAD) for two response variables.
Description
The average absolute deviation is defined as
$$AAD = \frac{\sum_{i=1}^{n}{|x - \bar{x}|}}{n}$$
with $$\bar{x}$$ denoting the mean of the variable and n denoting the number of observations. This statistic is sometimes used as an alternative to the standard deviation.
For the difference of average absolute deviations, the average absolute deviation is computed for each of two samples then their difference is taken.
Syntax:
LET <par> = DIFFERENCE OF AAD <y1> <y2> <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the first response variable;
<par> is a parameter where the computed difference of the average absolute deviations is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = DIFFERENCE OF AAD Y1 Y2
LET A = DIFFERENCE OF AAD Y1 Y2 SUBSET X > 1
Note:
Prior to the 2014/07 version, the AVERAGE ABSOLUTE DEVIATION command computed the difference from the median rather than the mean. The 2014/07 version corrected this command to compute differences from the mean and added the command
AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN
to compute differences from the median.
Since the DIFFERENCE OF AVERAGE ABSOLUTE DEVIATIONS was based on the average absolute deviation computation, these changes apply to it as well.
Note:
Dataplot statistics can be used in a number of commands. For details, enter
Default:
None
Synonyms:
AVERAGE ABSOLUTE DEVIATION is a synonym for AAD.
Related Commands:
AVERAGE ABSOLUTE DEVIATION = Compute the absolute average deviation from the mean of a variable. AVERAGE ABSOSOLUTE DEVIATION FROM THE MEDIAN = Compute the average absolute deviation from the median of a variable. MEDIAN ABSOLUTE DEVIATION = Compute the median absolute deviation of a variable. STANDARD DEVIATION = = Compute the standard deviation of a variable. VARIANCE = Compute the variance of a variable. RANGE = Compute the range of a variable.
Applications:
Data Analysis
Implementation Date:
3/2002
Program:
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET A = DIFFERENCE OF AAD Y1 Y2
TABULATE DIFFERENCE OF AAD Y1 Y2 X
.
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
CHAR X
LINE BLANK
DIFFERENCE OF AAD PLOT Y1 Y2 X
CHAR X ALL
LINE BLANK ALL
BOOTSTRAP DIFFERENCE OF AAD PLOT Y1 Y2 X
Dataplot generated the following output.
***************************************
** LET A = DIFFERENCE OF AAD Y1 Y2 **
***************************************
THE COMPUTED VALUE OF THE CONSTANT A = 0.35400003E+00
******************************************
** TABULATE DIFFERENCE OF AAD Y1 Y2 X **
******************************************
* Y1 AND Y2
X * DIFFERENCE OF AVERAGE ABSOLUTE
**********************************************
1.00000 * -0.140000E-01
2.00000 * 0.170000
3.00000 * 0.254000
GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT
NIST is an agency of the U.S. Commerce Department.
Date created: 03/27/2003
Last updated: 11/02/2015
| 2017-10-18T16:55:09 |
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|
https://par.nsf.gov/biblio/10174389-detectability-transiting-planets-orbiting-white-dwarfs-using-lsst
|
On the detectability of transiting planets orbiting white dwarfs using LSST
ABSTRACT White dwarfs are one of the few types of stellar object for which we have yet to confirm the existence of companion planets. Recent evidence for metal contaminated atmospheres, circumstellar debris discs, and transiting planetary debris all indicates that planets may be likely. However, white dwarf transit surveys are challenging due to the intrinsic faintness of such objects, the short time-scale of the transits, and the low transit probabilities due to their compact radii. The Large Synoptic Survey Telescope (LSST) offers a remedy to these problems as a deep, half-sky survey with fast exposures encompassing approximately 10 million white dwarfs with r < 24.5 apparent magnitude (mr). We simulate LSST photometric observations of 3.5 million white dwarfs over a 10 yr period and calculate the detectability of companion planets with P < 10 d via transits. We find typical detection rates in the range of 5 × 10−6 to 4 × 10−4 for Ceres-sized bodies to Earth-sized worlds, yielding ∼50–$4000$ detections for a 100 per cent occurrence rate of each. For terrestrial planets in the continuously habitable zone, we find detection rates of ∼10−3 indicating that LSST would reveal hundreds of such worlds for occurrence rates in the range of 1–10 per cent.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10174389
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
488
Issue:
2
Page Range or eLocation-ID:
1695 to 1703
ISSN:
0035-8711
1. ABSTRACT We report on the discovery and validation of a two-planet system around a bright (V = 8.85 mag) early G dwarf (1.43 R⊙, 1.15 M⊙, TOI 2319) using data from NASA’s Transiting Exoplanet Survey Satellite (TESS). Three transit events from two planets were detected by citizen scientists in the month-long TESS light curve (sector 25), as part of the Planet Hunters TESS project. Modelling of the transits yields an orbital period of $11.6264 _{ - 0.0025 } ^ { + 0.0022 }$ d and radius of $3.41 _{ - 0.12 } ^ { + 0.14 }$ R⊕ for the inner planet, and a periodmore »
We present minute cadence photometry of 31 732 point sources observed in one 3 $\rm deg^{2}$ DECam pointing centred at RA = 09:03:02 and Dec. = −04:35:00 over eight consecutive half-nights. We use these data to search for eclipse-like events consistent with a planetary transit of a white dwarf and other sources of stellar variability within the field. We do not find any significant evidence for minute-long transits around our targets, hence we rule out planetary transits around ∼370 white dwarfs that should be present in this field. Additionally, we identify 49 variables, including 40 new systems. These include 23 detachedmore »
| 2022-08-10T22:42:01 |
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|
https://googology.wikia.org/wiki/User_talk:ArtismScrub
|
10,964 Pages
By all means visit put.com and look up the web project "Counting really,Really,REALLY High".12.144.5.2 03:58, September 20, 2017 (UTC)
[note from ArtismScrub] direct link to the page referred to
## Contents
Please add internal links instead of the direct URL when adding links to other pages on this wiki. In VisualEditor, this can be done by typing the page name instead of the URL of that page (for example, "Googolplex" instead of "http://googology.wikia.com/wiki/Googolplex"). This makes the source code of the page shorter and makes links traceable via Special:WhatLinksHere. -- ☁ I want more clouds! ⛅ 03:51, October 29, 2017 (UTC)
## Xi function ordinal
It's not correct that xi function has "growth rate" $$\varepsilon_0^{CK}$$. The claim has originated at the time when there was some confusion regarding ordinals associated with Turing machine oracles. It turns out that there is no sensible way in which, for example, Turing machines with halting oracle reach $$\omega_2^{CK}$$, and similarly the claim about SKIO has no such logical basis. Without a doubt it's true though that Rayo's function goes well beyond xi function. LittlePeng9 (talk) 07:20, January 23, 2018 (UTC)
I understand next to nothing about Turing machines, but I kind of get what you're saying.
$$\omega_1^{CK}$$ has no possible fundamental sequence, and so it cannot be a valid growth rate. ArtismScrub (talk) 17:25, January 23, 2018 (UTC)
$$\omega_1^{CK}$$ does have a fundamental sequence. It's just uncomputable. PsiCubed2 (talk) 22:13, March 3, 2018 (UTC)
How is an uncomputable fundamental sequence possible? Shouldn't a fundamental sequence follow some sort of pattern? ArtismScrub (talk) 22:22, March 3, 2018 (UTC)
There is no such requirement in the definition. A fundamental sequence only needs to be increasing and have the given ordinal as the limit.
Also, I suppose one could argue that those fundamental sequences will follow "some pattern", but that pattern will be uncomputable. LittlePeng9 (talk) 22:26, March 3, 2018 (UTC)
## You Can't Stop Gabe Newel
File:The Real Gabe Newel.ogg —Preceding unsigned comment added by Gabe Newel the Internet Troll (talkcontribs) 02:38, March 8, 2018 (UTC)
Dude,t his isn't funny. Don't create pages about inappropraite things. And don't sguggest people like those things! Now GET OUT!!!! Or Cloudy will do it for you!!! Bye! Username5243 (talk) 02:40, March 8, 2018 (UTC)
Four exclamation marks? A sure sign of an insane mind. Gabe Newel the Internet Troll (talk) 03:01, March 8, 2018 (UTC)
you know i had to do it to em ArtismScrub (talk) 04:08, March 8, 2018 (UTC)
## U NO STOP BIG BIN!=
Now i'm angry, big bin good elegant number,why you say delete~!!!! FAGGOOT!!! Shang Shang Yang (talk) 03:36, March 13, 2018 (UTC)
## completely unrelated remark
i'm getting a 500 error every time i try to go to the videos page of your channel lol
Nishada 02:49, March 22, 2018 (UTC)
Community content is available under CC-BY-SA unless otherwise noted.
| 2021-07-25T09:20:51 |
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|
https://lammps.sandia.gov/doc/bond_morse.html
|
# bond_style morse/omp command
## Syntax
bond_style morse
## Examples
bond_style morse
bond_coeff 5 1.0 2.0 1.2
## Description
The morse bond style uses the potential
where r0 is the equilibrium bond distance, alpha is a stiffness parameter, and D determines the depth of the potential well.
The following coefficients must be defined for each bond type via the bond_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:
• D (energy)
• alpha (inverse distance)
• r0 (distance)
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc page for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See the Speed packages doc page for more instructions on how to use the accelerated styles effectively.
## Restrictions
This bond style can only be used if LAMMPS was built with the MOLECULE package. See the Build package doc page for more info.
| 2018-08-15T22:13:54 |
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|
http://www.scstatehouse.gov/sess118_2009-2010/sj09/20090512.htm
|
South Carolina General Assembly
118th Session, 2009-2010
Journal of the Senate
Tuesday, May 12, 2009
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
Paul wrote to those he loved in Rome, saying:
"Do not think of yourself more highly that you ought, but rather think of yourself with sober judgment, in accordance with the measure of faith God has given you." (Romans 12:3)
Please bow with me as we pray:
How easy it becomes, O Lord, to fall into the traps of pride and of self-love. It happens to all of us, we know; it is a part of our human nature. Moreover, it is a special challenge to those who, one way or another, often find themselves in the limelight. Yet, we ask You to strengthen us, dear God. Keep us from being victims of false praise. And especially lead each of these dedicated Senators and their staff members to focus always on what truly matters: which is being of service to the people of this State, and doing so in ways that honor You. In Your loving name we pray, dear Lord.
Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Mark C. Sanford:
Statewide Appointments
Initial Appointment, Charleston Naval Facilities Redevelopment Authority, with the term to commence April 24, 2009, and to expire April 24, 2013
At-Large:
Louis C. Mintz, P. O. Box 1474, Mount Pleasant, SC 29465 VICE James C. Bryan
Referred to the Committee on Labor, Commerce and Industry.
Initial Appointment, John de la Howe School Board of Trustees, with the term to commence April 1, 2009, and to expire April 1, 2014
At-Large:
Mary O. Morales, 301 Westbrook Way, Lexington, SC 29072 VICE Harriet S. Johnson
Referred to the Committee on Education.
REGULATION WITHDRAWN AND RESUBMITTED
Document No. 3198
Agency: Department of Health and Environmental Control
SUBJECT: Solid Waste Management - Demonstration of Need
Received by Lieutenant Governor January 13, 2009
Referred to Medical Affairs Committee
Legislative Review Expiration May 13, 2009
Withdrawn and resubmitted: May 7, 2009
Revised expiration date: May 27, 2009
Doctor of the Day
Senator FAIR introduced Dr. Ted Watson of Anderson, S.C., Doctor of the Day.
S. 560 (Word version) Sen. Davis
S. 628 (Word version) Sen. Davis
S. 535 (Word version) Sen. Davis
Leave of Absence
At 1:50 P.M., Senator JACKSON requested a leave of absence beginning at 5:00 P.M. and lasting until 11:00 A.M. tomorrow.
Leave of Absence
At 1:50 P.M., Senator FORD requested a leave of absence from 2:00 - 6:00 P.M. this evening.
RECALLED
S. 793 (Word version) -- Senators Pinckney and Davis: A BILL RELATING TO THE BEAUFORT-JASPER WATER AND SEWER AUTHORITY, TO REMOVE CERTAIN RESTRICTIONS ON THE AREAS IN WHICH IT PROVIDES SERVICES TO FURTHER PRESCRIBE ITS FUNCTIONS AND POWERS REG,ARDING WATER AND WASTE WATER SERVICES, TO PRESCRIBE THE CONDITIONS AND TERMS UPON WHICH MUNICIPAL CORPORATIONS AND OTHER PUBLIC BODIES OR AGENCIES OPERATING WATER DISTRIBUTION AND WASTE WATER SYSTEMS IN BEAUFORT, JASPER, HAMPTON, AND COLLETON COUNTIES MAY ACQUIRE SERVICES FROM THE AUTHORITY, AND TO CHANGE THE NAME OF THE AUTHORITY TO THE BEAUFORT-JASPER WATER AND SEWER AUTHORITY.
Senator DAVIS asked unanimous consent to make a motion to recall the Bill from the Committee on Judiciary.
The Bill was recalled from the Committee on Judiciary and ordered placed on the Calendar for consideration tomorrow.
S. 755 (Word version) -- Senator Massey: A CONCURRENT RESOLUTION TO URGE THE CITIZENS OF SOUTH CAROLINA TO PRACTICE SAFE BOATING HABITS, ESPECIALLY THE WEARING OF LIFE JACKETS, AND TO DECLARE MAY 16-22, 2009, AS SAFE BOATING WEEK IN SOUTH CAROLINA.
Senator MASSEY asked unanimous consent to make a motion to recall the Concurrent Resolution from the Committee on Fish, Game and Forestry.
There was no objection and the Concurrent Resolution was recalled from the Committee on Fish, Game and Forestry.
On motion of Senator MASSEY, with unanimous consent, the Concurrent Resolution was taken up for immediate consideration.
On motion of Senator MASSEY, with unanimous consent, the Concurrent Resolution was adopted, ordered sent to the House.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 804 (Word version) -- Senators Campbell and Grooms: A SENATE RESOLUTION TO RECOGNIZE AND CONGRATULATE MR. JOHNNY EUGENE WARD OF MONCKS CORNER, SOUTH CAROLINA, UPON RECEIVING AN HONORARY DOCTORATE OF PUBLIC SERVICE FROM CHARLESTON SOUTHERN UNIVERSITY FOR HIS MANY YEARS OF DEDICATED SERVICE TO THE UNIVERSITY AND HIS COMMUNITY.
l:\s-res\lkg\010ward.mrh.lkg.docx
S. 805 (Word version) -- Senator Grooms: A BILL TO AMEND CHAPTER 3, TITLE 56 OF THE 1976 CODE, RELATING TO MOTOR VEHICLE REGISTRATION AND LICENSING, BY ADDING ARTICLE 79 TO PROVIDE FOR SPECIAL MOTOR VEHICLE AND MOTORCYCLE LICENSED PLATES TO BE ISSUED BY THE DEPARTMENT OF MOTOR VEHICLES THAT HAVE "REDUCE, REUSE, RECYCLE" AND THE RECYCLING LOGO IMPRINTED ON THE PLATE, AND TO PROVIDE FOR THE PROCEEDS FROM THE PLATE.
l:\s-res\lkg\009recy.kmm.lkg.docx
Read the first time and referred to the Committee on Transportation.
S. 806 (Word version) -- Medical Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO SOLID WASTE MANAGEMENT: DEMONSTRATION-OF-NEED, DESIGNATED AS REGULATION DOCUMENT NUMBER 3198, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
l:\council\bills\nbd\11496ac09.docx
Read the first time and ordered placed on the Calendar without reference.
S. 807 (Word version) -- Senator Lourie: A SENATE RESOLUTION TO RECOGNIZE AND HONOR THE A.C. FLORA HIGH SCHOOL MATH TEAM AND TO CONGRATULATE THE MATHEMATICIANS, COACHES, AND SCHOOL OFFICIALS FOR AN OUTSTANDING SEASON IN MATH COMPETITIONS.
l:\council\bills\gm\24356bb09.docx
S. 808 (Word version) -- Senators Bright, Grooms, Bryant and Davis: A BILL TO AMEND THE 1976 CODE BY ADDING SECTION 56-5-2960 TO PROVIDE THAT AN ARRESTING OFFICER MUST DIRECT AND A DRIVER OF A MOTOR VEHICLE INVOLVED IN AN ACCIDENT THAT CAUSES THE DEATH OF ANOTHER PERSON TO SUBMIT TO CHEMICAL TESTS OF THE DRIVER'S BREATH, BLOOD, OR URINE TO DETERMINE THE PRESENCE OF ALCOHOL OR DRUGS, OR THE COMBINATION OF BOTH, FOR AN OFFENSE ARISING OUT OF ACTS ALLEGED TO HAVE BEEN COMMITTED WHILE THE PERSON WAS DRIVING THE MOTOR VEHICLE UNDER THE INFLUENCE OF ALCOHOL, DRUGS, OR BOTH.
l:\s-res\lb\030offi.mrh.lb.docx
Read the first time and referred to the Committee on Judiciary.
S. 809 (Word version) -- Senator Cleary: A SENATE RESOLUTION TO COMMEND THE REPUBLIC OF CHINA (TAIWAN) FOR ITS RELATIONS WITH THE UNITED STATES AND FOR OTHER PURPOSES.
l:\council\bills\gm\24358htc09.docx
The Senate Resolution was introduced and referred to the General Committee.
S. 810 (Word version) -- Senator Courson: A SENATE RESOLUTION TO RECOGNIZE AND HONOR RONALD C. OSBORNE OF COLUMBIA, DIRECTOR OF THE SOUTH CAROLINA EMERGENCY MANAGEMENT DIVISION, OFFICE OF THE ADJUTANT GENERAL, UPON THE OCCASION OF HIS RETIREMENT, TO THANK HIM FOR HIS MANY YEARS OF OUTSTANDING PUBLIC SERVICE, AND TO WISH HIM MUCH FULFILLMENT AND SUCCESS IN ALL HIS FUTURE ENDEAVORS.
l:\council\bills\rm\1258ac09.docx
H. 3467 (Word version) -- Reps. M. A. Pitts, Brantley, Allison, Horne, Rice and Spires: A BILL TO AMEND SECTION 8-11-83, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PAYROLL DEDUCTION FOR DUES OF THE STATE EMPLOYEES' ASSOCIATION AND THE SOUTH CAROLINA TROOPERS' ASSOCIATION, SO AS TO ALSO AUTHORIZE A PAYROLL DEDUCTION FOR DUES OF THE SOUTH CAROLINA FRATERNAL ORDER OF POLICE.
Read the first time and referred to the Committee on Finance.
H. 3678 (Word version) -- Reps. D. C. Moss, Whipper, Anthony, Herbkersman, Merrill, Nanney, G. M. Smith, Thompson and Weeks: A BILL TO AMEND SECTION 56-5-4140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE MAXIMUM ALLOWABLE GROSS WEIGHTS OF VEHICLES THAT MAY BE OPERATED ALONG THE STATE'S HIGHWAYS, SO AS TO MAKE A TECHNICAL CHANGE.
Read the first time and ordered placed on the Calendar without reference.
H. 3794 (Word version) -- Rep. Umphlett: A BILL TO AMEND SECTION 50-11-2200, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ESTABLISHMENT OF WILDLIFE MANAGEMENT AREAS, SO AS TO SPECIFY ADDITIONAL PROHIBITED ACTIVITIES; TO AMEND SECTION 50-11-2210, RELATING TO ABUSE OF WILDLIFE MANAGEMENT AREA LANDS, SO AS TO INCLUDE HERITAGE TRUST AND DEPARTMENT OWNED LANDS; TO AMEND SECTION 50-11-2220, AS AMENDED, RELATING TO ADDITIONAL PENALTIES FOR ABUSING WILDLIFE MANAGEMENT AREA LANDS, SO AS TO INCLUDE HERITAGE TRUST AND DEPARTMENT OWNED LANDS; AND BY ADDING SECTION 50-11-2225 SO AS TO CREATE A MISDEMEANOR CRIMINAL OFFENSE FOR ENTERING OR REMAINING ON A CLOSED AREA CONTRARY TO THE INSTRUCTIONS OF A LAW ENFORCEMENT OFFICER, MANAGER, OR DEPARTMENT CUSTODIAL PERSONNEL.
Read the first time and referred to the Committee on Fish, Game and Forestry.
REPORTS OF STANDING COMMITTEES
Senator LEATHERMAN from the Committee on Finance submitted a favorable report on:
S. 417 (Word version) -- Senators Knotts, Land, Campbell, Coleman, Cromer, Setzler, Courson, Thomas and O'Dell: A BILL TO AMEND SECTION 1-11-720, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ENTITIES WHOSE EMPLOYEES, RETIREES, AND THEIR DEPENDENTS ARE ELIGIBLE TO PARTICIPATE IN THE STATE HEALTH AND DENTAL INSURANCE PLANS, SO AS TO EXTEND THIS ELIGIBILITY TO THE SOUTH CAROLINA ATHLETIC COACHES ASSOCIATION.
Ordered for consideration tomorrow.
Senator LEATHERMAN from the Committee on Finance submitted a favorable report on:
S. 697 (Word version) -- Senator Leatherman: A BILL TO AMEND CHAPTER 35, TITLE 11 OF THE 1976 CODE, RELATING TO CONSOLIDATED PROCUREMENT CODE, TO PROVIDE THAT WHERE A PROCUREMENT INVOLVES THE EXPENDITURE OF A FEDERAL GRANT, THE GOVERNMENTAL BODY SHALL ALSO COMPLY WITH FEDERAL LAW AND AUTHORIZED REGULATIONS, TO PROVIDE THAT WHERE FEDERAL ASSISTANCE, GRANT, OR CONTRACT FUNDS ARE USED IN A PROCUREMENT BY A GOVERNMENTAL BODY, THE PROCUREMENT CODE INCLUDING ANY REQUIREMENTS THAT ARE MORE RESTRICTIVE THAN FEDERAL REQUIREMENTS MUST BE FOLLOWED, EXCEPT TO THE EXTENT THAT THE ACTION WOULD RENDER THE GOVERNMENTAL BODY INELIGIBLE TO RECEIVE FEDERAL FUNDS WHOSE RECEIPT IS CONDITIONED ON COMPLIANCE WITH MANDATORILY APPLICABLE FEDERAL LAW, TO PROVIDE FOR BID PROCEDURES FOR CONSTRUCTION CONTRACTS, TO PROVIDE FOR CONFIDENTIALITY IN THE PROCUREMENT REVIEW PANEL PROCESS, AND TO REPEAL SECTIONS 11-35-3025 AND 11-35-3310.
Ordered for consideration tomorrow.
Senator KNOTTS from the Committee on Invitations polled out S. 801 favorable:
S. 801 (Word version) -- Senator Courson: A SENATE RESOLUTION TO RECOGNIZE THE HEROIC SERVICE AND SACRIFICE OF THE U.S. NAVY CREW OF THE USS COLUMBIA CL-56 DURING THE PACIFIC CAMPAIGN OF WORLD WAR II, TO COMMEMORATE THE COLUMBIA'S HISTORIC ROLE IN WORLD WAR II, AND TO DECLARE OCTOBER 15, 2009, AS "USS COLUMBIA DAY".
Poll of the Invitations Committee
Polled 10; Ayes 10; Nays 0; Not Voting 1
AYES
Alexander Campsen Cromer
Elliott Ford Knotts
McGill O'Dell Reese
Verdin
Total--10
NAYS
Total--0
NOT VOTING
Malloy
Total--1
Ordered for consideration tomorrow.
Senator LEATHERMAN from the Committee on Finance submitted a favorable with amendment report on:
H. 3018 (Word version) -- Reps. E.H. Pitts, Huggins, Gunn, Bales, Limehouse, Barfield, Hardwick, Hearn, Edge, Gambrell, Thompson, Bowen, Harrison, Umphlett, Sandifer, Herbkersman, G.M. Smith, Lowe, Vick, H.B. Brown, R.L. Brown, Viers, Clemmons, Ballentine, Mitchell and M.A. Pitts: A BILL TO AMEND SECTION 12-37-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROPERTY TAX EXEMPTIONS, SO AS TO EXEMPT FROM PROPERTY TAX THE VALUE OF IMPROVEMENTS TO REAL PROPERTY CONSISTING OF A NEWLY CONSTRUCTED DETACHED SINGLE FAMILY HOME THROUGH THE EARLIER OF THE PROPERTY TAX IN WHICH THE HOME IS OCCUPIED, OR THE SECOND PROPERTY TAX YEAR ENDING DECEMBER THIRTY-FIRST AFTER THE HOME IS COMPLETED AND A CERTIFICATE FOR OCCUPANCY ISSUED THEREON IF REQUIRED.
Ordered for consideration tomorrow.
Senator CROMER from the Committee on Fish, Game and Forestry submitted a favorable report on:
H. 3131 (Word version) -- Reps. Toole, M.A. Pitts and Umphlett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 1-1-711 SO AS TO DESIGNATE THE "SUMMER DUCK" AS THE OFFICIAL STATE DUCK.
Ordered for consideration tomorrow.
Senator RYBERG from the Committee on Labor, Commerce and Industry submitted a majority favorable and Senator LEVENTIS a minority unfavorable report on:
H. 3222 (Word version) -- Reps. Bedingfield, Gullick, Erickson, Crawford, Duncan, Allison, Ballentine, Cato, Forrester, Hamilton, Harrell, Harrison, Horne, Kelly, Littlejohn, Millwood, Nanney, E.H. Pitts, M.A. Pitts, Rice, D.C. Smith, G.R. Smith, J.R. Smith, Stringer, A.D. Young, T.R. Young, Daning, Owens, Umphlett, Wylie, Parker and Clemmons: A CONCURRENT RESOLUTION MEMORIALIZING THE SOUTH CAROLINA CONGRESSIONAL DELEGATION TO OPPOSE LEGISLATION THAT DISENFRANCHISES SOUTH CAROLINA WORKERS BY REMOVING THEIR RIGHT TO A PRIVATE BALLOT UNION ELECTION.
Ordered for consideration tomorrow.
Senator LEATHERMAN from the Committee on Finance submitted a favorable with amendment report on:
H. 3482 (Word version) -- Reps. Harrell, Cooper, Mack and Bannister: A BILL TO AMEND SECTION 12-37-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROPERTY TAX EXEMPTIONS, SO AS TO EXEMPT FROM PROPERTY TAX ALL PERSONAL PROPERTY, INCLUDING AIRCRAFT, OF A COMPANY ENGAGED IN AIR TRANSPORT OF SPECIALIZED CARGO.
Ordered for consideration tomorrow.
HOUSE CONCURRENCE
S. 797 (Word version) -- Senator Verdin: A CONCURRENT RESOLUTION TO CONGRATULATE NANCY THOMPSON OF LAURENS, SOUTH CAROLINA, UPON THE OCCASION OF HER RETIREMENT AND TO WISH HER MUCH HAPPINESS IN THE FUTURE.
Returned with concurrence.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
ORDERED ENROLLED FOR RATIFICATION
The following Joint Resolution was read the third time and, having received three readings in both Houses, it was ordered that the title be changed to that of an Act and enrolled for Ratification:
H. 3730 (Word version) -- Rep. Cooper: A JOINT RESOLUTION TO PROVIDE THAT ALL FUNDS RECEIVED UNDER THE AMERICAN RECOVERY AND REINVESTMENT ACT OF 2009 (RECOVERY ACT) FOR THE CLEAN WATER STATE REVOLVING FUND AND DRINKING WATER STATE REVOLVING FUND MAY BE RECEIVED AND EXPENDED PURSUANT TO PROVISIONS OF THE RECOVERY ACT FOR SO LONG AS MONIES ARE AVAILABLE UNDER THE RECOVERY ACT.
H. 3730--Recorded Vote
Senators BRIGHT, BRYANT and RYBERG desired to be recorded as voting against the third reading of the Bill.
The following Bills were read the third time and ordered sent to the House of Representatives:
S. 144 (Word version) -- Senators Campsen and Ford: A BILL TO RATIFY AN AMENDMENT TO SECTION 33, ARTICLE III OF THE CONSTITUTION OF SOUTH CAROLINA, 1895, RELATING TO THE PROVISION PROVIDING THAT NO UNMARRIED WOMAN UNDER THE AGE OF FOURTEEN YEARS OLD MAY LEGALLY CONSENT TO SEXUAL INTERCOURSE, SO AS TO DELETE THAT PROVISION.
S. 282 (Word version) -- Senators McConnell and Ford: A BILL TO AMEND SECTION 22-5-110, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATED TO MAGISTRATES' POWERS AND DUTIES REGARDING THE ISSUANCE OF ARREST WARRANTS AND COURTESY SUMMONS, SO AS TO PROVIDE THAT NO ARREST WARRANT SHALL BE ISSUED FOR THE ARREST OF A PERSON UNLESS SOUGHT BY A MEMBER OF A LAW ENFORCEMENT AGENCY ACTING IN THEIR OFFICIAL CAPACITY; AND TO PROVIDE THAT IF AN ARREST WARRANT IS SOUGHT BY SOMEONE OTHER THAN A LAW ENFORCEMENT OFFICER, THE COURT MUST ISSUE A COURTESY SUMMONS, EXCEPT WHEN A BUSINESS IS SEEKING AN ARREST WARRANT FOR ANY OFFENSE AGAINST THE BUSINESS OR A PERSON IS SEEKING AN ARREST WARRANT FOR A FRAUDULENT CHECK, IF THE FRAUDULENT CHECK IS PRESENTED TO THE MAGISTRATE AT THE TIME THE WARRANT IS SOUGHT.
S. 372 (Word version) -- Senators Hayes and Ford: A BILL TO AMEND SECTION 62-2-207, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DETERMINATION OF AN ELECTIVE SHARE OF A SPOUSE, SO AS TO CLARIFY THAT AN INTEREST AS A BENEFICIARY IN A TESTAMENTARY TRUST OR IN PROPERTY PASSING TO AN INTER VIVOS TRUST THROUGH THE DECEDENT'S WILL IS A BENEFICIAL INTEREST CHARGEABLE TO THE ELECTIVE SHARE; AND TO AMEND SECTION 62-7-401, AS AMENDED, RELATING TO CREATION OF A TRUST, SO AS TO PROVIDE FOR THE INCLUSION OF A SURVIVING SPOUSE'S BENEFICIAL INTERESTS IN TRUST PROPERTY IN CALCULATING THE ELECTIVE SHARE.
Senator HAYES asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
S. 382 (Word version) -- Senator Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 62-2-805 SO AS TO PROVIDE FOR A PRESUMPTION THAT A DECEDENT AND THE DECEDENT'S SPOUSE HELD TANGIBLE PERSONAL PROPERTY IN A JOINT TENANCY WITH RIGHT OF SURVIVORSHIP, FOR EXCEPTIONS TO THE PRESUMPTION, AND FOR THE STANDARD OF PROOF TO OVERCOME THE PRESUMPTION.
Senator HAYES asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
S. 446 (Word version) -- Senator Land: A BILL TO PROVIDE THAT FROM JUNE 1, 2009, TO SEPTEMBER 30, 2009, A NONRESIDENT MAY OBTAIN A LIFETIME COMBINATION LICENSE FROM THE DEPARTMENT OF NATURAL RESOURCES UNDER CERTAIN CIRCUMSTANCES.
S. 446--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
S. 495 (Word version) -- Senators Massey, Hutto and S. Martin: A BILL TO AMEND SECTION 50-11-2100 OF THE 1976 CODE, RELATING TO FIELD TRIALS, TO PROVIDE THAT A PARTICIPANT IN FIELD TRIALS PERMITTED BY THE DEPARTMENT OF NATURAL RESOURCES IS NOT REQUIRED TO OBTAIN A HUNTING LICENSE IF THE PARTICIPANT IS NOT CARRYING A FIREARM AND NO GAME IS TAKEN, AND TO PROVIDE THAT NO FIELD TRIALS MAY BE HELD OUTSIDE OF THE REGULAR SEASON EXCEPT AS PERMITTED BY THE DEPARTMENT.
S. 495--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
S. 554 (Word version) -- Senators Hutto and Ford: A BILL TO AMEND SECTION 63-11-1950, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PURPOSE AND DUTIES OF THE STATE CHILD FATALITY COMMITTEE, SO AS TO PROVIDE THAT THE COMMITTEE MAY REQUEST THE DEPARTMENT OF SOCIAL SERVICES TO OPEN A CASE ON THE FAMILY WHERE THE FATALITY OCCURRED IF THE COMMITTEE SUSPECTS CRIMINAL DOMESTIC VIOLENCE, DRUG ABUSE, ABUSE, OR NEGLECT IN THE HOME AND CHILDREN CONTINUE TO LIVE IN THE HOME.
S. 554--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
S. 668 (Word version) -- Senators Courson, Knotts, Cromer, Setzler, Jackson, Scott, Lourie and Rose: A BILL TO AMEND SECTIONS 53-5-10 AND 53-5-15, RELATING TO LEGAL HOLIDAYS FOR STATE EMPLOYEES, TO ESTABLISH CHRISTMAS EVE AS A LEGAL HOLIDAY.
S. 668--Recorded Vote
Senator BRYANT desired to be recorded as voting against third reading of the Bill.
S. 668--Recorded Vote
Senator RYBERG desired to be recorded as voting in favor of third reading of the Bill.
SENT TO THE HOUSE
S. 671 (Word version) -- Senator Knotts: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 50-13-400 SO AS TO ESTABLISH CREEL AND SIZE LIMITS FOR CRAPPIE TAKEN IN LAKE MURRAY.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator CLEARY asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Having received the requisite number of votes under the provisions of Rule 26B, the following amendment was taken up for immediate consideration.
Senator CLEARY proposed the following amendment (671R002.REC), which was adopted:
Amend the bill, as and if amended, by adding an appropriately numbered new SECTION to read:
/ SECTION ___. Chapter 13, Title 50 of the 1976 Code is amended by adding:
"Section 50-13-2017. (A) There is established the Flounder Population Study Program to be administered by the Department of Natural Resources. The program shall study the effects of flounder catch limits and the prohibition of artificial illumination powered by generators on flounder of the species Paralichthys dentatus, commonly known as the summer flounder, located in the waters of Murrells Inlet Estuary, Pawleys Island Estuary, and the creeks of Litchfield flowing into Pawleys Island Estuary. For purposes of this resolution, 'gigging' means using a rod with one or multiple prongs to spear a fish.
(B) During the term of the program in the area defined in subsection (A):
(1) the lawful flounder gigging and fishing catch limit is ten per day for any individual, not to exceed twenty flounder in any one day on any boat;
(2) it is unlawful to use any type of artificial illumination powered by generator while gigging or fishing for flounder from a boat or while wading in the water.
(C) A person violating a provision of subsection (B) is guilty of a misdemeanor and, upon conviction, must be fined not less than ten dollars or more than one hundred dollars per fish, or imprisoned not less than ten days or more than thirty days, or both.
(D) The program shall run for five years, beginning January 1, 2010, and ending December 31, 2015.
(E) The Department of Natural Resources must compile its findings and submit the report to the General Assembly by March 16, 2016."/
Renumber sections to conform.
Amend title to conform.
Senator CLEARY explained the amendment.
There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments.
S. 671--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
RETURNED TO THE HOUSE WITH AMENDMENTS
H. 3572 (Word version) -- Rep. Umphlett: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY REPEALING SECTION 50-5-1707 RELATING TO SHARK CATCH LIMITS.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator KNOTTS asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Having received the requisite number of votes under the provisions of Rule 26B, the following amendments were taken up for immediate consideration.
Senator KNOTTS proposed the following amendment (3572R002.JMK), which was adopted:
Amend the bill, as and if amended, page 1, by adding an appropriately numbered new SECTION to read:
/ SECTION ___. Article 1, Chapter 13, Title 50 of the 1976 Code is amended by adding:
"Section 50-13-400. (A) In Lake Murray it is unlawful to take or possess more than twenty crappie (Pomoxis spp.) per day.
(B) In Lake Murray it is unlawful to take or possess crappie (Pomoxis spp.) less than eight inches in total length." /
Renumber sections to conform.
Amend title to conform.
Senator KNOTTS explained the amendment.
Senator CLEARY proposed the following amendment (3572R003.REC), which was adopted:
Amend the bill, as and if amended, by adding an appropriately numbered new SECTION to read:
/ SECTION ___. Chapter 13, Title 50 of the 1976 Code is amended by adding:
"Section 50-13-2017. (A) There is established the Flounder Population Study Program to be administered by the Department of Natural Resources. The program shall study the effects of flounder catch limits and the prohibition of artificial illumination powered by generators on flounder of the species Paralichthys dentatus, commonly known as the summer flounder, located in the waters of Murrells Inlet Estuary, Pawleys Island Estuary, and the creeks of Litchfield flowing into Pawleys Island Estuary. For purposes of this resolution, 'gigging' means using a rod with one or multiple prongs to spear a fish.
(B) During the term of the program in the area defined in subsection (A):
(1) the lawful flounder gigging and fishing catch limit is ten per day for any individual, not to exceed twenty flounder in any one day on any boat;
(2) it is unlawful to use any type of artificial illumination powered by generator while gigging or fishing for flounder from a boat or while wading in the water.
(C) A person violating a provision of subsection (B) is guilty of a misdemeanor and, upon conviction, must be fined not less than ten dollars or more than one hundred dollars per fish, or imprisoned not less than ten days or more than thirty days, or both.
(D) The program shall run for five years, beginning January 1, 2010, and ending December 31, 2015.
(E) The Department of Natural Resources must compile its findings and submit the report to the General Assembly by March 16, 2016."/
Renumber sections to conform.
Amend title to conform.
Senator CLEARY explained the amendment.
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
H. 3572--Recorded Vote
Senators BRYANT and RYBERG desired to be recorded as voting in favor of the third reading of the Bill.
The following Bills and Joint Resolution, having been read the second time, were ordered placed on the Third Reading Calendar:
H. 3042 (Word version) -- Reps. Merrill, Parker, Huggins, H.B. Brown, Anderson, J.E. Smith, Miller, M.A. Pitts, Toole, Hayes, Bales, Jennings, Herbkersman, Vick, Rutherford, Hart, Sellers, McLeod, Moss, Hiott, Alexander, Gambrell, Bingham, Brady, Sandifer, Bedingfield, Ott, Hutto, G.R. Smith, Millwood, Whipper and Bannister: A BILL TO AMEND SECTIONS 40-81-20, 40-81-50, 40-81-70, 40-81-230, 40-81-280, 40-81-430, AND 40-81-480, CODE OF LAWS OF SOUTH CAROLINA, 1976, ALL RELATING TO REGULATIONS OF VARIOUS ATHLETIC AND SPORTING ACTIVITIES BY THE STATE ATHLETIC COMMISSION; BY ADDING SECTION 40-81-445 SO AS TO MAKE THE COMBATIVE SPORT OF MIXED MARTIAL ARTS LEGAL IN SOUTH CAROLINA, AND TO PROVIDE FOR THE MANNER IN WHICH THE STATE ATHLETIC COMMISSION SHALL SUPERVISE AND REGULATE MIXED MARTIAL ARTS COMPETITIONS; AND TO REPEAL SECTION 40-81-530 RELATING TO ULTIMATE FIGHTING EVENTS AS BEING UNLAWFUL.
H. 3550 (Word version) -- Reps. Cato, Herbkersman, Agnew, Merrill, Stavrinakis, Funderburk, Brady, Anderson, R.L. Brown, Kelly, Limehouse, J.E. Smith, Whipper, Hutto, Allison, Parker, Sottile, Erickson and Bales: A BILL TO AMEND CHAPTER 10, TITLE 6, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BUILDING ENERGY EFFICIENCY STANDARD ACT, SO AS TO REVISE THE TITLE OF THE ACT TO THE "ENERGY STANDARD ACT", TO REVISE DEFINITIONS, TO ADOPT THE INTERNATIONAL ENERGY CONSERVATION CODE AS THE ENERGY STANDARD AND TO PROVIDE THAT ALL NEW AND RENOVATED BUILDINGS MUST COMPLY WITH THIS STANDARD, TO PROVIDE THAT LOCAL BUILDING OFFICIALS SHALL ENFORCE THE ENERGY STANDARD AND TO PROVIDE ALTERNATIVE ENFORCERS IN AREAS WITHOUT A BUILDING OFFICIAL, TO PROVIDE THAT BUILDING OFFICIALS SHALL ISSUE AND REVOKE BUILDING PERMITS AND INSPECT CONSTRUCTION OF BUILDINGS PURSUANT TO THE PERMITS ISSUED, TO REQUIRE LOCAL JURISDICTIONS TO PROVIDE AN APPEALS BOARD AND PROCESS FOR GRANTING OF CERTAIN VARIANCES, TO PROVIDE AN EXCEPTION AND TO ALLOW CERTAIN APPEALS TO BE HEARD BY THE SOUTH CAROLINA BUILDING CODES COUNCIL, AND TO PROVIDE THAT A PERSON OR PARTY MAY OBTAIN INJUNCTIVE RELIEF; AND TO AMEND SECTION 6-9-50, AS AMENDED, RELATING TO THE MANDATORY ADOPTION OF CERTAIN NATIONAL BUILDING CODES, BUILDING ENVELOPE REQUIREMENTS OF THE ENERGY CODE, FREE ACCESS TO CODE DOCUMENTS, AND THREE STORY HOMES, SO AS TO DELETE PROVISIONS RELATING TO WHAT CONSTITUTES COMPLIANCE WITH THE BUILDING ENVELOPE REQUIREMENTS OF THE ENERGY CODE, FREE ACCESS TO DOCUMENTS CONTAINING CODES ADOPTED BY THE BUILDING CODES COUNCIL, AND BUILDING PERMITS FOR THREE STORY HOMES.
Senator RYBERG explained the Bill.
H. 3653 (Word version) -- Rep. McLeod: A JOINT RESOLUTION TO DELAY IMPLEMENTATION OF THE PROVISIONS OF ACT 270 OF 2008, RELATING TO THE REQUIREMENT THAT MUNICIPAL COURT JURY LISTS INCLUDE OTHERWISE QUALIFIED RESIDENTS OF THE MUNICIPALITY WHO HOLD A VALID SOUTH CAROLINA DRIVER'S LICENSE OR IDENTIFICATION CARD, SO AS TO POSTPONE THIS EXPANSION OF THE MUNICIPAL COURT JURY LIST UNTIL DECEMBER 31, 2009.
Senator L. MARTIN explained the Joint Resolution.
S. 249 (Word version) -- Senator Rose: A BILL TO AMEND CHAPTER 29, TITLE 6 OF THE 1976 CODE, BY ADDING SECTION 6-29-1153 TO PROVIDE THAT A GOVERNING BODY AND A LOCAL PLANNING COMMISSION SERVICING AN AREA IN A HIGH GROWTH COUNTY MUST PROVIDE THE LOCAL SCHOOL DISTRICT LAND DEVELOPMENT APPLICATIONS THAT INCLUDE RESIDENTIAL HOUSING WHICH MEET CERTAIN CRITERIA; AND TO REQUIRE THE SUPERINTENDENT AND BOARD OF TRUSTEES OF THE SCHOOL DISTRICT TO DETERMINE WHETHER A PARTICULAR PROJECT WILL RESULT IN A SUBSTANTIAL IMPACT ON THE DISTRICT'S ABILITY TO PROVIDE SERVICES TO THE ADDITIONAL STUDENT POPULATION AND TO PREPARE A REPORT TO THE GOVERNING BODY AND THE LOCAL PLANNING COMMISSION DETAILING THE IMPACT AND NEED FOR ADDITIONAL RESOURCES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
Senators MULVANEY and ROSE proposed the following amendment (JUD0249.008), which was adopted:
Amend the Committee Report, as and if amended, page [249-2], lines 1-7, by striking these lines in their entirety and inserting the following:
/ (2) 'Superintendent of the school district' means a superintendent whose school district has been required by a law that was enacted prior to March 1, 2009, to prepare and submit and obtain proof of delivery to the governing body and to the land planning commission of the county and each municipality within land encompassed by the district a report describing the current and projected status and needs of the district, and which report must include, but not be limited to, the following: /
Renumber sections to conform.
Amend title to conform.
Senator MULVANEY explained the perfecting amendment.
The Committee on Judiciary proposed the following amendment (JUD0249.005), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Chapter 29, Title 6 of the 1976 Code is amended by adding:
"Section 6-29-1153. (A) A local planning commission shall provide all applications and accompanying materials for land development projects that include residential housing to the superintendent of the school district in which the project is to be located, if the project:
(1) is greater than twenty-five acres in size; or
(2) includes one hundred or more dwelling units.
The planning commission shall determine whether any land development project meets these criteria and shall provide the information at no charge to the superintendent within fifteen business days of receiving the application. The local planning commission and superintendent may agree that the information is to be provided electronically or by some other suitable means.
(B) For purposes of this section:
(1) 'Dwelling units' means all residential units, including, but not limited to, single-family attached, single-family detached, duplex, condominium, townhouse, multi-family, apartment, and mobile home, but excluding hotels and motels.
(2) 'Superintendent of the school district' means a superintendent whose school district has been required by law to prepare and submit and obtain proof of delivery to the governing body and to the land planning commission of the county and each municipality within land encompassed by the district a report describing the current and projected status and needs of the district, and which report must include, but not be limited to, the following:
(a) a list of all schools in the district with the number of classrooms, current enrollment, and the enrollment capacity of each school and of the entire district;
(b) the district's student enrollment over the previous ten years and projected enrollment over the next ten years;
(c) the district's capital improvement program, including all schools existing, under construction, or planned and plans for funding those schools;
(d) current and projected construction costs for new schools and the cost of mobile classrooms, the causes of any cost increases over previous estimates, and the sources for the information;
(e) the most recent five year history of the audited operating and capital expenditures of the district;
(f) the most recent five year history of the county assessed tax base used for financing purposes in the district;
(g) identification of federal, state, and local laws or regulations which the district recommends be repealed or relaxed to save costs and increase efficiency for the district and an explanation of how the savings and increased efficiency could occur;
(h) a list of additional facilities, teachers, and other resources projected to be necessary to service the additional student population of the district over the next ten years; and
(i) all other information and recommendations by the district regarding how county or municipal governments could help the district better meet its needs and the needs of its students.
(C) The superintendent shall review all land development projects described in subsection (A) received by the district and report the results of that review to the board of trustees of the district. The superintendent and the board of trustees both will determine whether the additional anticipated increase in student population resulting from the land development project will have a substantial impact on the district's ability to provide services to the additional student population. If either determination is positive, the superintendent and the board shall prepare a report that describes the impact and details the need for additional facilities, teachers, and other resources necessary to service the additional student population. In determining whether a particular project results in a substantial impact, the superintendent and the board shall consider not only the impact of the particular project, but also the aggregate impact of the project with other projects pending at the time the superintendent conducts his review. The report must be provided within thirty days of the district's receipt of the application to the governing body and to the local planning commission of the applicable county or municipality. However, upon request by the school district to the local planning commission, a fifteen day extension of time to submit the report shall be granted. Failure of the school district to provide the requested report to the local planning commission within any time period prescribed by these provisions shall not delay or otherwise affect any time limits that the local planning commission is required by other existing law to follow. The report must be maintained as part of the land development application and made available to the public promptly and, if possible, before any public hearing on the application."
SECTION 2. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 405 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 12-37-220 OF THE 1976 CODE, RELATING TO PROPERTY TAX EXEMPTIONS, TO CLARIFY THAT A WATERCRAFT AND ITS MOTOR MAY NOT RECEIVE A FORTY-TWO AND 75/100 PERCENT EXEMPTION IF THE BOAT OR WATERCRAFT IS CLASSIFIED AS A PRIMARY OR SECONDARY RESIDENCE FOR PROPERTY TAX PURPOSES; TO AMEND SECTION 12-37-224, RELATING TO BOATS AS A PRIMARY OR SECONDARY RESIDENCE, TO PROVIDE THAT A BOAT OR WATERCRAFT THAT CONTAINS A COOKING AREA WITH AN ONBOARD POWER SOURCE, A TOILET WITH EXTERIOR EVACUATION, AND A SLEEPING QUARTER, SHALL BE CONSIDERED A PRIMARY OR SECONDARY RESIDENCE FOR PURPOSES OF AD VALOREM PROPERTY TAXATION IN THIS STATE; AND TO AMEND SECTION 12-37-714, RELATING TO BOATS WITH A SITUS IN THIS STATE, TO PROVIDE THAT UPON AN ORDINANCE PASSED BY THE LOCAL GOVERNING BODY, A COUNTY MAY SUBJECT A BOAT, INCLUDING ITS MOTOR IF THE MOTOR IS SEPARATELY TAXED, TO PROPERTY TAX IF IT IS WITHIN THIS STATE FOR NINETY DAYS IN THE AGGREGATE, REGARDLESS OF THE NUMBER OF CONSECUTIVE DAYS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Finance.
The Committee on Finance proposed the following amendment (405FIN002), which was adopted:
Amend the bill, as and if amended, by deleting SECTION 2.
Renumber sections to conform.
Amend title to conform.
Senator HAYES explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 775 (Word version) -- Senators Grooms and Knotts: A BILL TO AMEND SECTION 56-1-130, AS AMENDED, RELATING TO CLASSIFIED DRIVER'S LICENSES, SO AS TO PROVIDE THAT AN OPERATOR OF A MOTORCYCLE THREE-WHEEL VEHICLE IS ONLY REQUIRED TO HAVE A BASIC DRIVER'S LICENSE OR A MOTORCYCLE LICENSE, RATHER THAN A MOTORCYCLE LICENSE WITH A SPECIAL ENDORSEMENT.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Transportation.
The Committee on Transportation proposed the following amendment (775R001.LKG), which was adopted:
Amend the bill, as and if amended, in SECTION 1, starting on page 2, line 9 by striking subsections (C) and (D) from Section 56-1-130 and inserting:
/ (C) A basic driver's license authorizes the licensee to operate motor vehicles, automotive three-wheel vehicles, motorcycle three-wheel vehicles, excluding a motorcycle with a detachable side car, or combinations of vehicles which do not exceed twenty-six thousand pounds gross vehicle weight rating; provided, that the driver has successfully demonstrated the ability to exercise ordinary and reasonable control in the operation of a motor vehicle in this category. A basic driver's license also authorizes the licensee to operate farm trucks provided for in Sections 56-3-670, 56-3-680, and 56-3-690, which are used exclusively by the owner for agricultural, horticultural, and dairying operations or livestock and poultry raising. Notwithstanding any other provision of law, the holder of a conditional license, or special restricted license operating a farm truck for the purposes provided in this subsection, may operate the farm truck without an accompanying adult after six o'clock a.m. and no later than nine o'clock p.m., but may not operate a farm truck on a freeway. A person operating a farm truck while holding a conditional driver's license or a special restricted license may not use the farm truck for ordinary domestic purposes or general transportation.
A classified driver's license shall authorize the licensee to operate a motorcycle, motorcycle three-wheel vehicle, including a motorcycle with a detachable side car, or those vehicles in excess of twenty-six thousand pounds gross vehicle weight rating which are indicated by endorsement on the license. The endorsement may include classifications such as: motorcycle, motorcycle three-wheel vehicle, two-axle truck, three- or more axle truck, combination of vehicles, motor busses, or oversize or overweight vehicles. The department shall determine from the driving demonstration the endorsements to be indicated on the license.
(D) The department shall include a noncommercial endorsement to the motorcycle classification license to indicate the type of motorcycle to be operated. The "M" classification is for motorcycle operation only. The 'D' endorsement to the "M" classification is for motorcycle three-wheel vehicle and motorcycle with detachable side car. The "C" endorsement to the "M" classification is for motorcycle, motorcycle three-wheel vehicle, and motorcycle with detachable side car." /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3022 (Word version) -- Reps. Kirsh, Wylie, G.M. Smith, Weeks and Mitchell: A BILL TO AMEND SECTION 17-1-40, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESTRUCTION OF CRIMINAL RECORDS WHEN A CHARGE IS DISMISSED OR THE PERSON IS FOUND INNOCENT OF THE CHARGE, SO AS TO SPECIFICALLY INCLUDE THAT A CIRCUIT SOLICITOR'S OFFICE OR CLERK OF COURT MAY NOT CHARGE A FEE FOR THE DESTRUCTION OR EXPUNGEMENT OF RECORDS OR FOR THE APPLICATION PROCESS REGARDING THE DESTRUCTION OR EXPUNGEMENT OF RECORDS UNDER CERTAIN CIRCUMSTANCES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD3022.001), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. This act may be cited as the "Uniform Expungement of Criminal Records Act".
SECTION 2. Chapter 22, Title 17 of the 1976 Code is amended by adding:
"Article 9
Uniform Expungement of Criminal Records
Section 17-22-910. Applications for expungement of all criminal records must be administered by the solicitor's office in each circuit in the State as authorized pursuant to:
(1) Section 34-11-90(e), first offense misdemeanor fraudulent check;
(2) Section 44-53-450(b), conditional discharge for simple possession of marijuana or hashish;
(3) Section 22-5-910, first offense conviction in magistrates court;
(4) Section 22-5-920, youthful offender act;
(5) Section 56-5-750(f), first offense failure to stop when signaled by a law enforcement vehicle;
(6) Section 17-22-150(a), pretrial intervention;
(7) Section 17-1-40, criminal records destruction, except as provided in Section 17-22-950;
(8) Section 20-7-8525, juvenile expungements;
(9) Section 17-22-530(a), alcohol education program; and
(10) any other statutory authorization.
Section 17-22-920. The clerk of court shall direct all inquiries concerning the expungement process to the corresponding solicitor's office to make application for expungement.
Section 17-22-930. A person applying to expunge a criminal record shall obtain the appropriate blank expungement order form from the solicitor's office in the judicial circuit where the charge originated. The use of this form is mandatory and to the exclusion of all other expungement forms.
Section 17-22-940. (A) In exchange for an expungement service that is provided by the solicitor's office, the applicant is responsible for payment to the solicitor's office of an administrative fee in the amount of two hundred fifty dollars per individual order, which must be retained by that office and used to defray the costs associated with the expungement process, except as provided in subsection (B). The two hundred fifty dollar fee is nonrefundable, regardless of whether the offense is later determined to be statutorily ineligible for expungement or the solicitor or his designee does not consent to the expungement.
(B) Any person who applies to the solicitor's office for an expungement of General Sessions charges pursuant to Section 17-1-40 is exempt from paying the administrative fee, unless the charge that is the subject of the expungement request was dismissed, discharged, or nolle prossed as part of a plea arrangement under which the defendant pled guilty and was sentenced on other charges.
(C) The solicitor's office shall implement policies and procedures consistent with this section to ensure that the expungement process is properly conducted. This includes, but is not limited to:
(1) assisting the applicant in completing the expungement order form;
(2) collecting from the applicant and distributing to the appropriate agencies separate certified checks or money orders for charges prescribed by this article;
(3) coordinating with the South Carolina Law Enforcement Division (SLED) and, in the case of juvenile expungements, the Department of Juvenile Justice, to confirm that the criminal charge is statutorily appropriate for expungement;
(4) obtaining and verifying the presence of all necessary signatures;
(5) filing the completed expungement order with the clerk of court; and
(6) providing copies of the completed expungement order to all governmental agencies which must receive the order including, but not limited to, the:
(a) arresting law enforcement agency;
(b) detention facility or jail;
(c) solicitor's office;
(d) magistrates or municipal court where the arrest warrant originated;
(e) magistrates or municipal court that was involved in any way in the criminal process of the charge sought to be expunged;
(f) Department of Juvenile Justice; and
(g) SLED.
(D) The solicitor or his designee also must provide a copy of the completed expungement order to the applicant or his retained counsel.
(E) In cases when charges are sought to be expunged pursuant to Section 17-22-150(a), 17-22-530(a), 22-5-910, or 44-53-450(b), the circuit pretrial intervention director, alcohol education program director, or summary court judge shall attest by signature on the application to the eligibility of the charge for expungement before either the solicitor or his designee and then the circuit court judge, or the family court judge in the case of a juvenile, signs the application for expungement.
(F) SLED shall verify and document that the criminal charges in all cases, except in cases when charges are sought to be expunged pursuant to Section 17-1-40, are appropriate for expungement before the solicitor or his designee, and then a circuit court judge, or a family court judge in the case of a juvenile, signs the application for expungement. If the expungement is sought pursuant to Section 34-11-90(e), Section 22-5-910, Section 22-5-920, or Section 56-5-750(f), the conviction for any traffic related offense which is punishable only by a fine or loss of points will not be considered as a bar to expungement.
(1) SLED shall receive a twenty-five dollar certified check or money order from the solicitor or his designee on behalf of the applicant made payable to SLED for each verification request, except that no verification fee may be charged when an expungement is sought pursuant to Section 17-1-40, 17-22-150(a), or 44-53-450(b). SLED then shall forward the necessary documentation back to the solicitor's office involved in the process.
(2) In the case of juvenile expungements, verification and documentation that the charge is statutorily appropriate for expungement must first be accomplished by the Department of Juvenile Justice and then SLED.
(3) Neither SLED, the Department of Juvenile Justice, nor any other official shall allow the applicant to take possession of the application for expungement during the expungement process.
(G) The applicant also is responsible to the clerk of court for the filing fee per individual order as required by Section 8-21-310(21), which must be forwarded to the clerk of court by the solicitor or his designee and deposited in the county general fund. If the charge is determined to be statutorily ineligible for expungement, this prepaid clerk of court filing fee must be refunded to the applicant by the solicitor or his designee.
(H) Each expungement order may contain only one charge sought to be expunged, except in those circumstances when expungement is sought for multiple charges occurring out of a single incident and subject to expungement pursuant to Section 17-1-40 or 17-22-150(a). Only in those circumstances may more than one charge be included on a single application for expungement and, when applicable, only one two hundred fifty dollar fee, one twenty-five dollar SLED verification fee, and one thirty-five dollar clerk of court filing fee may be charged.
(I) A filing fee may not be charged by the clerk's office to an applicant seeking the expungement of a criminal record pursuant to Section 17-1-40, when the charge was discharged, dismissed, nolle prossed, or the applicant was acquitted.
(J) Nothing in this article precludes an applicant from retaining counsel to apply to the solicitor's office on his behalf or precludes retained counsel from initiating an action in circuit court seeking a judicial determination of eligibility when the solicitor, in his discretion, does not consent to the expungement. In either event, retained counsel is responsible to the solicitor or his designee, when applicable, for the two hundred fifty dollar fee, the twenty-five dollar SLED verification fee, and the thirty-five dollar clerk of court filing fee which must be paid by retained counsel's client.
(K) The solicitor or his designee has the discretion to waive the two hundred fifty dollar fee only in those cases when it is determined that a person has been falsely accused of a crime as a result of identity theft.
(L) Each solicitor's office shall maintain a record of all fees collected related to the expungement of criminal records, which must be made available to the chairmen of the House and Senate Judiciary Committees. Those records shall remain confidential otherwise.
Section 17-22-950. (A) When criminal charges are brought in a summary court and the accused person is found not guilty or if the charges are dismissed or nolle prossed, pursuant to Section 17-1-40, the presiding judge of the summary court, at no cost to the accused person, immediately shall issue an order to expunge the criminal records of the accused person unless the dismissal of the charges occurs at a preliminary hearing or unless the accused person has charges pending in summary court and a court of general sessions and such charges arise out of the same course of events. This expungement must occur no sooner than the appeal expiration date and no later than thirty days after the appeal expiration date. Upon issuance of the order, the judge of the summary court or a member of the summary court staff must coordinate with SLED to confirm that the criminal charge is statutorily appropriate for expungement; obtain and verify the presence of all necessary signatures; file the completed expungement order with the clerk of court; provide copies of the completed expungement order to all governmental agencies which must receive the order including, but not limited to, the arresting law enforcement agency, the detention facility or jail, the solicitor's office, the magistrates or municipal court where the arrest warrant originated, the magistrates or municipal court that was involved in any way in the criminal process of the charge sought to be expunged, and SLED. The judge of the summary court or a member of the summary court staff also must provide a copy of the completed expungement order to the applicant or his retained counsel. The prosecuting agency or appropriate law enforcement agency may file an objection to a summary court expungement. If an objection is filed by the prosecuting agency or law enforcement agency, that expungement then must be heard by the judge of a general sessions court. The prosecuting agency's or the appropriate law enforcement agency's reason for objecting must be that the:
(1) accused person has other charges pending;
(2) prosecuting agency or the appropriate law enforcement agency believes that the evidence in the case needs to be preserved; or
(3) accused person's charges were dismissed as a part of a plea agreement.
(B) If the prosecuting agency or the appropriate law enforcement agency objects to an expungement order being issued pursuant to subsection (A)(2), the prosecuting agency or appropriate law enforcement agency must notify the accused person of the objection. This notice must be given in writing at the address listed on the accused person's bond form, or through his attorney, no later than thirty days after the person is found not guilty or his charges are dismissed or nolle prossed."
SECTION 3. Section 17-1-40(A) of the 1976 Code, as last amended by Act 82 of 2007, is further amended to read:
"(A) A person who after being charged with a criminal offense and the charge is discharged, proceedings against the person are dismissed, or the person is found to be innocent not guilty of the charge, the arrest and booking record, files, mug shots, and fingerprints of the person must be destroyed and no evidence of the record pertaining to the charge may be retained by any municipal, county, or state law enforcement agency. Provided, however, that local and state detention and correctional facilities may retain booking records, identifying documentation and materials, and other institutional reports and files under seal, on all persons who have been processed, detained, or incarcerated, for a period not to exceed three years from the date of the expungement order to manage their statistical and professional information needs and, where necessary, to defend such facilities during litigation proceedings. Information retained by a local or state detention or correctional facility as permitted under this section after an expungement order has been issued is not a public document and is exempt from disclosure. Such information may only be disclosed by judicial order or as needed during litigation proceedings. A person who otherwise intentionally retains the arrest and booking record, files, mugshots, fingerprints, or any evidence of the record pertaining to a charge discharged or dismissed pursuant to this section is guilty of contempt of court."
SECTION 4. Section 17-1-45 is added to the 1976 Code of Laws to read:
"Section 17-1-45. South Carolina Court Administration shall include on all bond paperwork and courtesy summons the following notice: 'If the charges that have been brought against you are discharged, dismissed, or nolle prossed or if you are found not guilty, you may have your record expunged'."
SECTION 5. Section 22-5-910(A) and (B) of the 1976 Code is amended to read:
"(A) Following a first offense conviction in a magistrates court or a municipal court, for a crime carrying a penalty of not more than thirty days imprisonment or a fine of five hundred dollars, or both, the defendant after three years from the date of the conviction may apply, or cause someone acting on his behalf to apply, to the circuit court for an order expunging the records of the arrest and conviction. However, this section does not apply to:
(1) an offense involving the operation of a motor vehicle;
(2) a violation of Title 50 or the regulations promulgated pursuant to Title 50 for which points are assessed, suspension provided for, or enhanced penalties for subsequent offenses are authorized; or
(3) an offense contained in Chapter 25 of Title 16, except first offense criminal domestic violence as contained in Section 16-25-20, which may be expunged five years from the date of the conviction.
(B) If the defendant has had no other conviction during the three-year period, or during the five-year period as provided in subsection (A)(3), following the first offense conviction in a magistrates court or a municipal court, for a crime carrying a penalty of not more than thirty days imprisonment or a fine of not more than five hundred dollars, or both, the circuit court may issue an order expunging the records. No person may have his records expunged under this section more than once. A person may have his record expunged even though the conviction occurred prior to June 1, 1992."
SECTION 6. Section 22-5-920(B) of the 1976 Code is amended to read:
"(B) Following a first offense conviction as a youthful offender, the defendant after fifteen five years from the date of the conviction completion of his sentence, including probation and parole, may apply, or cause someone acting on his behalf to apply, to the circuit court for an order expunging the records of the arrest and conviction. However, this section does not apply to an offense involving the operation of a motor vehicle, to a violation of Title 50 or the regulations promulgated under it for which points are assessed, suspension provided for, or enhanced penalties for subsequent offenses authorized, to an offense classified as a violent crime in Section 16-1-60, or to an offense contained in Chapter 25 of Title 16, except as otherwise provided in Section 16-25-30. If the defendant has had no other conviction during the fifteen five-year period following the completion of his sentence, including probation and parole, for a first offense conviction as a youthful offender, the circuit court may issue an order expunging the records. No person may have his records expunged under this section more than once. A person may have his record expunged even though the conviction occurred before the effective date of this section."
SECTION 7. Section 44-53-450(b) of the 1976 Code is amended to read:
"(B) Upon the dismissal of such the person and discharge of the proceedings against him under pursuant to subsection (a)of this section, such person if he was not over twenty-five years of age at the time of the offense, and if the offense did not involve a controlled substance classified in Schedule I which is a narcotic drug and Schedule II which is a narcotic drug, may apply to the court for an order to expunge from all official records (other than the nonpublic records to be retained as provided in subsection (a)of this section) all recordation relating to his arrest, indictment or information, trial, finding of guilty, and dismissal and discharge pursuant to this section. If the court determines, after hearing, that such the person was dismissed and the proceedings against him discharged and that he was not over twenty-five years of age at the time of the offense, it shall enter such the order. The effect of such the order shall be is to restore such the person, in the contemplation of the law, to the status he occupied before such the arrest or indictment or information. No person as to whom such the order has been entered shall may be held thereafter under any pursuant to another provision of any law to be guilty of perjury or otherwise giving a false statement by reason of his failures failure to recite or acknowledge such the arrest, or indictment or information, or trial in response to any an inquiry made of him for any purpose."
SECTION 8. The deadline requiring all circuit solicitors to have a traffic education program in effect, as provided in SECTION 5 of Act 176 of 2008, is extended from July 1, 2009, to July 1, 2010. No person has the right to apply to the program until the program is established. SECTION 9. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
Senator KNOTTS spoke on the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3347 (Word version) -- Reps. Clemmons, McLeod and Harrell: A BILL TO AMEND SECTION 56-1-143, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF MOTOR VEHICLES GIVING APPLICANTS FOR CERTAIN SERVICES THE OPTION TO MAKE A VOLUNTARY CONTRIBUTION TO DONATE LIFE OF SOUTH CAROLINA, SO AS TO INCREASE THE AMOUNT THAT MAY BE DONATED.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator GROOMS proposed the following amendment (3347R003.LKG), which was adopted:
Amend the bill, as and if amended, page 1, by adding an appropriately numbered new SECTION to read:
/ SECTION ___. Section 56-1-130 of the 1976 Code, as last amended by Act 347 of 2008, is further amended to read:
"Section 56-1-130. (A) The Department of Motor Vehicles shall examine every applicant for a driver's license, except as otherwise provided in this article. The examination shall include a test of the applicant's eyesight, his ability to read and understand highway signs regulating, warning, and directing traffic, and his knowledge of the traffic laws of this State and shall include an actual demonstration of ability to exercise ordinary and reasonable control in the operation of the type motor vehicle, including motorcycles, for which a license is sought. The department may require a further physical and mental examination as it considers necessary to determine the applicant's fitness to operate a motor vehicle upon the highways, the further examination to be at the applicant's expense. The department shall make provisions for giving an examination in the county where the applicant resides, except for motorcycle three-wheel vehicles. The motorcycle three-wheel vehicle examination must be provided at the sites where the knowledge and skill examination for the commercial driver's license is offered. The department shall charge an appropriate fee for each complete examination or reexamination required in this article.
(B) No persons, except those exempted under Section 56-1-30 and Section 56-1-60 or those holding beginner's permits under Section 56-1-50, shall operate any classification of motor vehicle without first being examined and duly licensed by the driver examiner as a qualified driver of that classification of motor vehicle.
(C) A basic driver's license authorizes the licensee to operate motor vehicles, automotive three-wheel vehicles, motorcycle three-wheel vehicles, excluding a motorcycle with a detachable side car, or combinations of vehicles which do not exceed twenty-six thousand pounds gross vehicle weight rating; provided, that the driver has successfully demonstrated the ability to exercise ordinary and reasonable control in the operation of a motor vehicle in this category. A basic driver's license also authorizes the licensee to operate farm trucks provided for in Sections 56-3-670, 56-3-680, and 56-3-690, which are used exclusively by the owner for agricultural, horticultural, and dairying operations or livestock and poultry raising. Notwithstanding any other provision of law, the holder of a conditional license, or special restricted license operating a farm truck for the purposes provided in this subsection, may operate the farm truck without an accompanying adult after six o'clock a.m. and no later than nine o'clock p.m., but may not operate a farm truck on a freeway. A person operating a farm truck while holding a conditional driver's license or a special restricted license may not use the farm truck for ordinary domestic purposes or general transportation.
A classified driver's license shall authorize the licensee to operate a motorcycle, motorcycle three-wheel vehicle, including a motorcycle with a detachable side car, or those vehicles in excess of twenty-six thousand pounds gross vehicle weight rating which are indicated by endorsement on the license. The endorsement may include classifications such as: motorcycle, motorcycle three-wheel vehicle, two-axle truck, three- or more axle truck, combination of vehicles, motor busses, or oversize or overweight vehicles. The department shall determine from the driving demonstration the endorsements to be indicated on the license.
(D) The department shall include a noncommercial endorsement to the motorcycle classification license to indicate the type of motorcycle to be operated. The 'M' classification is for motorcycle operation only. The 'D' endorsement to the 'M' classification is for motorcycle three-wheel vehicle and motorcycle with detachable side car. The 'C' endorsement to the 'M' classification is for motorcycle, motorcycle three-wheel vehicle, and motorcycle with detachable side car." /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3762 (Word version) -- Reps. Duncan, Umphlett, Dillard, Ott, Forrester, Moss, Parker, Stringer, Vick, Hodges and Knight: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 77 TO CHAPTER 3, TITLE 56 SO AS TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ISSUE "OUR FARMS-OUR FUTURE" SPECIAL LICENSE PLATES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Transportation.
The Committee on Transportation proposed the following amendment (SWB\5909CM09), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Chapter 3, Title 56 of the 1976 Code is amended by adding:
"Article 77
Our Farms-Our Future Special License Plates
Section 56-3-7890. (A) The Department of Motor Vehicles may issue special motor vehicle license plates to owners of private passenger carrying motor vehicles as defined in Section 56-3-630, or motorcycles registered in their names which shall have imprinted on the plate 'Our Farms-Our Future' and which may have a design representative of agriculture. The South Carolina Farm Bureau Federation shall submit to the department for its approval a design it desires to be used for this special license plate. The South Carolina Farm Bureau Federation may request a change in the design not more than once every five years. The fee for this special license plate is seventy dollars every two years in addition to the regular motor vehicle registration fee set forth in Article 5, Chapter 3, Title 56. This special license plate must be of the same size and general design of regular motor vehicle license plates. This special license plate must be issued or revalidated for a biennial period which expires twenty-four months from the month it is issued.
(B) The fees collected pursuant to this section above the cost of the regular motor vehicle registration fee must be distributed to the 501(c)(3) nonprofit South Carolina Farm Bureau Federation 'Ag in the Classroom' Fund.
(C) The guidelines for the production of a special license plate under this section must meet the requirements of Section 56-3-8100."
SECTION 2. This act takes effect upon approval by the Governor. /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the committee amendment.
Senator GROOMS proposed the following amendment (3762R002.LKG), which was adopted:
Amend the bill, as and if amended, page 2, by adding appropriately numbered new SECTIONS to read:
/ SECTION __. A. Article 45, Chapter 3, Title 56 of the 1976 Code, is amended to read:
"Article 45
SPECIAL COMMEMORATIVE SOUTH CAROLINA WILDLIFE LICENSE PLATES
(B) Of the fees collected pursuant to this section, the Comptroller General shall place sufficient funds into a special restricted account to be used by the Department of Motor Vehicles to defray the expenses of the department in producing and administering this special license plate collection. The remaining funds collected from each special motor vehicle license plate fee must be deposited in the Game Protection Fund provided for in Title 50.
(C) The department simultaneously may make available more than one special license plate. However, before the department produces and distributes a special license plate with the South Carolina Wildlife collection pursuant to this section, it must comply with the provisions contained in Section 56-3-8100."
B. The name of the "Game Protection Fund" as contained in Title 50 is hereby changed to the "Fish and Wildlife Protection Fund". Wherever the term "Game Protection Fund" appears in the 1976 Code, it shall mean the "Fish and Wildlife Protection Fund" and the Code Commissioner is directed to change this reference at a time and in a manner that is timely and cost effective.
SECTION ___. Section 56-3-9910 of the 1976 Code is amended to read:
"Section 56-3-9910. (A) The Department of Motor Vehicles may issue 'Gold Star Family' special license plates to owners of private passenger motor vehicles as defined in Section 56-3-630 registered in their names who are immediate family members of members of the armed forces killed in action. The There is no fee for this special license plate must be the regular motor vehicle license fee contained in Article 5, Chapter 3 of this title and the special fee required by Section 56-3-2020. The license plates issued pursuant to this section must conform to a design agreed to by the department and the Chief Executive Officer of the South Carolina Chapter of American Gold Star Mothers, Inc. or other similar organization operating in this State. Notwithstanding any other provision of law, of the fees collected for the special license plate, the Comptroller General shall place sufficient funds into a special restricted account to be used by the Department of Motor Vehicles to defray the expenses of the Department of Motor Vehicles in producing and administering the special plate.
(B) Notwithstanding another provision of law, the provisions contained in Section 56-3-8000(B) and (C) do not apply to the production and distribution of 'Gold Star Family' special license plates.
(C) For the purposes of this section, 'immediate family member' means a person who is a spouse, a child, claimed as a dependent for income tax purposes, or a sibling." /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
CARRIED OVER
H. 3942 (Word version) -- Agriculture, Natural Resources and Environmental Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE RIVERBANKS PARKS COMMISSION, RELATING TO RIVERBANKS PARKS COMMISSION, DESIGNATED AS REGULATION DOCUMENT NUMBER 4022, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
On motion of Senator L. MARTIN, the Joint Resolution was carried over.
H. 3274 (Word version) -- Reps. Gilliard, Alexander, Brantley, Clyburn, Cobb-Hunter, Forrester, Govan, Gunn, Hosey, Howard, Hutto, Jefferson, Kirsh, Mack, Miller, Sottile, Stavrinakis, Whipper and R.L. Brown: A CONCURRENT RESOLUTION TO MEMORIALIZE THE UNITED STATES CONGRESS TO APPROPRIATE THE FUNDS NECESSARY TO ALLOW THE STATE OF SOUTH CAROLINA AND THE CITY OF CHARLESTON TO COMPLETE THE SPRING STREET/FISHBURNE STREET/UNITED STATES HIGHWAY 17 DRAINAGE BASIN IMPROVEMENTS PROJECT LOCATED IN THE CITY OF CHARLESTON, SOUTH CAROLINA.
On motion of Senator LEATHERMAN, the Concurrent Resolution was carried over.
OBJECTION
H. 3413 (Word version) -- Rep. Harrison: A BILL TO AMEND SECTION 61-4-1910, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS REGARDING BEER KEG REGISTRATION REQUIREMENTS, SO AS TO REVISE THE DEFINITION OF "KEG".
Senator HUTTO objected to further consideration of the Bill.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
On motion of Senator L. MARTIN, the Senate agreed to dispense with the Motion Period.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CARRIED OVER
On motion of Senator HUTTO, the Bill was carried over.
CARRIED OVER
S. 491 (Word version) -- Senator Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 18 TO CHAPTER 23, TITLE 57 SO AS TO DESIGNATE CERTAIN HIGHWAYS IN WESTERN YORK COUNTY AS THE WESTERN YORK COUNTY SCENIC BYWAY, AND TO MAKE IT SUBJECT TO THE REGULATIONS OF THE SOUTH CAROLINA DEPARTMENT OF TRANSPORTATION AND THE SOUTH CAROLINA SCENIC HIGHWAYS COMMITTEE.
On motion of Senator HAYES, the Bill was carried over.
THE SENATE PROCEEDED TO A CONSIDERATION OF VETOES.
VETO CARRIED OVER
(R26, S540 (Word version)) -- Senator Alexander: A JOINT RESOLUTION TO PROVIDE THAT THE SCHOOL DAY MISSED BY THE STUDENTS OF THE SCHOOL DISTRICT OF OCONEE COUNTY ON MARCH 2, 2009, DUE TO SNOW, IS EXEMPT FROM THE MAKE-UP REQUIREMENT THAT FULL SCHOOL DAYS MISSED DUE TO SNOW, EXTREME WEATHER, OR OTHER DISRUPTIONS BE MADE UP.
The veto of the Governor was taken up for immediate consideration.
On motion of Senator ALEXANDER, the veto of the Governor was carried over.
On motion of Senator McCONNELL, with unanimous consent, the Senate agreed that, when the Senate adjourns today, it stand adjourned to meet tomorrow at 11:00 A.M.
THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE.
DEBATE INTERRUPTED
H. 3301 (Word version) -- Reps. Harrell, Cato, Sandifer, Sellers, Neilson, Erickson, Bannister, Bedingfield, Merrill, Mitchell, Anthony, Bingham, Huggins, Vick, Cooper, Chalk, J.R. Smith, Willis, Gilliard, Allison, Anderson, Bales, Battle, Bowers, Brady, G.A. Brown, H.B. Brown, Cole, Daning, Duncan, Edge, Forrester, Gambrell, Gullick, Hamilton, Hayes, Herbkersman, Hiott, Jefferson, Horne, Kirsh, Limehouse, Littlejohn, Long, Lowe, Lucas, Miller, Millwood, Nanney, Ott, Owens, Parker, Pinson, E.H. Pitts, M.A. Pitts, Scott, Simrill, Skelton, D.C. Smith, G.R. Smith, Sottile, Spires, Stewart, Stringer, Thompson, Toole, Umphlett, White, Whitmire and Wylie: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 34-39-175 SO AS TO REQUIRE THE CONSUMER FINANCE DIVISION OF THE BOARD OF FINANCIAL INSTITUTIONS TO IMPLEMENT A REAL-TIME INTERNET ACCESSIBLE DATABASE FOR DEFERRED PRESENTMENT PROVIDERS TO VERIFY IF DEFERRED PRESENTMENT TRANSACTIONS ARE OUTSTANDING FOR A PARTICULAR PERSON; BY ADDING SECTION 34-39-270 SO AS TO PROHIBIT A DEFERRED PRESENTMENT PROVIDER FROM ENTERING INTO A DEFERRED PRESENTMENT TRANSACTION WITH A PERSON WHO HAS AN OUTSTANDING DEFERRED PRESENTMENT TRANSACTION OR WHO HAS ENTERED INTO AN EXTENDED PAYMENT PLAN AGREEMENT AND TO REQUIRE A DEFERRED PRESENTMENT PROVIDER TO VERIFY WHETHER AN INDIVIDUAL IS ELIGIBLE TO ENTER INTO A DEFERRED PRESENTMENT TRANSACTION; BY ADDING SECTION 34-39-280 SO AS TO REQUIRE THOSE APPLYING FOR LICENSES TO ENGAGE IN THE BUSINESS OF DEFERRED PRESENTMENT TO PROVIDE CERTAIN INFORMATION REGARDING EXTENDED PAYMENT PLANS; TO AMEND SECTION 34-39-130, RELATING TO LICENSURE REQUIREMENTS FOR DEFERRED PRESENTMENT PROVIDERS, SO AS TO PROHIBIT A PERSON FROM ENGAGING IN THE BUSINESS OF DEFERRED PRESENTMENT SERVICES WITH A RESIDENT OF SOUTH CAROLINA EXCEPT IN ACCORDANCE WITH THE PROVISIONS OF CHAPTER 39, TITLE 34; TO AMEND SECTION 34-39-180, RELATING TO DEFERRED PRESENTMENT RESTRICTIONS AND REQUIREMENTS, SO AS TO PROVIDE THAT THE TOTAL AMOUNT ADVANCED TO A CUSTOMER FOR DEFERRED PRESENTMENT OR DEPOSIT, EXCLUSIVE OF PERMISSIBLE FEES, MAY NOT EXCEED SIX HUNDRED DOLLARS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Banking and Insurance.
Senator L. MARTIN spoke on the Bill.
On motion of Senator O'DELL, with unanimous consent, Senators O'DELL, PEELER, FAIR, ELLIOTT and REESE were granted leave to attend a subcommittee meeting and were granted leave to vote from the balcony.
Senator L. MARTIN spoke on the Bill.
On motion of Senator McCONNELL, with unanimous consent, debate was interrupted by recess.
RECESS
At 1:43 P.M., on motion of Senator McCONNELL, the Senate receded from business until 5:00 P.M.
NIGHT SESSION
The Senate reassembled at 5:12 P.M. and was called to order by the PRESIDENT Pro Tempore.
Point of Quorum
At 5:12 P.M., Senator L. MARTIN made the point that a quorum was not present. It was ascertained that a quorum was not present.
Call of the Senate
Senator L. MARTIN moved that a Call of the Senate be made. The following Senators answered the Call:
Alexander Anderson Bright
Bryant Campbell Campsen
Cleary Courson Cromer
Davis Fair Grooms
Hayes Hutto Jackson
Knotts Land Leatherman
Leventis Lourie Malloy
Martin, L. Martin, S. Massey
Matthews McConnell McGill
Mulvaney Nicholson O'Dell
Peeler Rankin Rose
Scott Setzler Sheheen
Shoopman Thomas Verdin
Williams
A quorum being present, the Senate resumed.
RECESS
At 5:17 P.M., on motion of Senator L. MARTIN, the Senate receded from business subject to the Call of the Chair.
At 5:25 P.M., the Senate resumed.
Message from the House
Columbia, S.C., May 12, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to:
H. 4000 (Word version) -- Rep. Harrell: A CONCURRENT RESOLUTION TO PROVIDE THAT PURSUANT TO ARTICLE III, SECTION 9 OF THE CONSTITUTION OF THIS STATE AND SECTION 2-1-180 OF THE 1976 CODE, WHEN THE RESPECTIVE HOUSES OF THE GENERAL ASSEMBLY ADJOURN ON THURSDAY, MAY 21, 2009, NOT LATER THAN 5:00 P.M., EACH HOUSE SHALL STAND ADJOURNED TO MEET AT A TIME MUTUALLY AGREED UPON BY THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES NOT EARLIER THAN NOON ON TUESDAY, JUNE 16, 2009, FOR A PERIOD NOT TO EXCEED THREE STATEWIDE LEGISLATIVE DAYS FOR THE CONSIDERATION OF CERTAIN MATTERS, TO PROVIDE THAT WHEN EACH HOUSE ADJOURNS AFTER THIS THREE-DAY PERIOD NOT LATER THAN 5:00 P.M. ON THE THIRD LEGISLATIVE DAY, EACH HOUSE SHALL STAND ADJOURNED TO MEET AT A TIME MUTUALLY AGREED UPON BY THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES UPON CERTAIN OCCURRENCES AND FOR THE CONSIDERATION OF SPECIFIED MATTERS, AND TO PROVIDE THAT UNLESS ADJOURNED EARLIER, THE GENERAL ASSEMBLY SHALL STAND ADJOURNED SINE DIE NO LATER THAN 5:00 P.M. ON MONDAY, JANUARY 11, 2010.
Very respectfully,
Speaker of the House
Message from the House
Columbia, S.C., May 12, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to:
H. 3616 (Word version) -- Rep. Simrill: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 25 TO CHAPTER 53, TITLE 59 SO AS TO PROVIDE FOR THE YORK TECHNICAL COLLEGE ENTERPRISE CAMPUS, AND TO PROVIDE FOR ITS POWERS AND DUTIES.
and has ordered the Bill enrolled for Ratification.
Very respectfully,
Speaker of the House
Message from the House
Columbia, S.C., May 12, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 12 (Word version) -- Senators Leatherman, Alexander, Ford, Rankin, O'Dell, Cleary, Leventis, Elliott, Lourie, Malloy and Setzler: A BILL TO ESTABLISH THE SOUTH CAROLINA TAXATION REALIGNMENT COMMISSION, TO PROVIDE FOR THE COMMISSION'S MEMBERSHIP, POWERS, DUTIES, AND RESPONSIBILITIES, TO PROVIDE THAT THE COMMISSION MUST CONDUCT A COMPREHENSIVE STUDY OF THE STATE'S TAX SYSTEM AND SUBMIT A REPORT OF ITS RECOMMENDED CHANGES TO FURTHER THE GOAL OF MAINTAINING AND ENHANCING THE STATE AS AN OPTIMUM COMPETITOR IN THE EFFORT TO ATTRACT BUSINESSES AND INDIVIDUALS TO LOCATE, LIVE, WORK, AND INVEST IN THE STATE, AND TO PROVIDE FOR PROCEDURES GOVERNING THE CONSIDERATION OF LEGISLATION RESULTING FROM THE COMMISSION'S RECOMMENDATIONS.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., May 12, 2009
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
H. 3560 -- Ways and Means Committee: A BILL TO MAKE APPROPRIATIONS AND TO PROVIDE REVENUES TO MEET THE ORDINARY EXPENSES OF STATE GOVERNMENT FOR THE FISCAL YEAR BEGINNING JULY 1, 2009, TO REGULATE THE EXPENDITURE OF SUCH FUNDS, AND TO FURTHER PROVIDE FOR THIS OPERATION OF STATE GOVERNMENT DURING THIS FISCAL YEAR AND FOR OTHER PURPOSES.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
S. 791 (Word version) -- Senator L. Martin: A BILL TO REQUIRE THE SOUTH CAROLINA BUILDING CODES COUNCIL TO ADOPT CERTAIN SEISMIC AND WIND MAPS FOR THE STATE UNTIL THE YEAR 2012 WHEN THE INTERNATIONAL RESIDENTIAL CODE (IRC) IS ADOPTED IN THIS STATE; AND TO AMEND SECTION 6-9-40, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BUILDING CODE ADOPTION PROCEDURE, SO AS TO PROVIDE THAT THE COMMUNITY MAY OPT OUT OF THESE BUILDING CODE MODIFICATIONS IN CERTAIN CIRCUMSTANCES.
Senator L. MARTIN asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Labor, Commerce and Industry.
The Committee on Labor, Commerce, and Industry proposed the following amendment (791R003.MM), which was adopted:
Amend the bill, as and if amended, by deleting SECTION 2 in its entirety and inserting:
/ SECTION 2. Chapter 6, Title 9 of the 1976 Code is amended by adding:
"Section 6-9-135. Notwithstanding any other provision of law, a county or municipality may adopt by reference or otherwise the provisions in the latest edition of the International Residential Code (IRC), including the wind and seismic provisions, necessary to prevent the community's rating for purposes of premium credits from being retrograded to a lower class through one of the following:
(1) the Community Rating System community classification developed by the National Flood Insurance Program; or
(2) the Building Code Effectiveness Grading Schedule classification developed by the Insurance Services Office.
This exclusion also includes class improvements or new enrollments for the Community Rating System. /
Renumber sections to conform.
Amend title to conform.
Senator L. MARTIN explained the committee amendment.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 553 (Word version) -- Senator Hutto: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 13 TO CHAPTER 13, TITLE 63 SO AS TO PROVIDE FOR THE LICENSURE AND REGULATION OF SUMMER CAMPS BY THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL; TO DEFINE SUMMER CAMPS AS RESIDENT CAMPS AND DAY CAMPS; TO PROHIBIT PERSONS WHO ARE LISTED AS A PERPETRATOR IN THE CENTRAL REGISTRY OF CHILD ABUSE AND NEGLECT, WHO ARE REQUIRED TO REGISTER UNDER THE SEX OFFENDER REGISTRY, OR WHO HAVE BEEN CONVICTED OF CERTAIN CRIMES TO BE LICENSED TO OPERATE A SUMMER CAMP OR TO BE EMPLOYED BY A SUMMER CAMP AND TO PROVIDE THAT IS A CRIMINAL OFFENSE FOR A PERSON WHO HAS BEEN CONVICTED OF SUCH A CRIME TO APPLY FOR SUCH A LICENSE OR EMPLOYMENT; TO REQUIRE STATE AND FEDERAL FINGERPRINT REVIEWS AS A PREREQUISITE TO LICENSURE AND EMPLOYMENT; TO PROVIDE FOR THE ISSUANCE OF PROVISIONAL LICENSES WHEN THE APPLICANT MEETS CERTAIN PRELIMINARY REQUIREMENTS; TO REQUIRE THE DEPARTMENT TO CONDUCT AN INVESTIGATION OF A SUMMER CAMP APPLICANT FOR LICENSURE; TO REQUIRE A SUMMER CAMP TO HAVE A PERSON ON SITE WHO IS CERTIFIED IN FIRST AID AND IN CHILD-INFANT CARDIOPULMONARY RESUSCITATION; TO REQUIRE A SUMMER CAMP TO NOTIFY THE DEPARTMENT WHEN A CHILD DIES AT THE SUMMER CAMP; TO REQUIRE THE DEPARTMENT TO ESTABLISH PROCEDURES FOR RECEIVING COMPLAINTS; TO AUTHORIZE THE DEPARTMENT TO CONDUCT INVESTIGATIONS AND INSPECTIONS OF SUMMER DAY CAMPS; TO PROVIDE PROCEDURES FOR ISSUING CORRECTION NOTICES FOR DEFICIENCIES, FOR OBTAINING INJUNCTIONS, AND FOR APPEALS OF DEPARTMENT DECISIONS; TO PROHIBIT A PERSON SEEKING EMPLOYMENT IN THE DEPARTMENT'S SUMMER CAMP LICENSING PROGRAM FROM HAVING BEEN CONVICTED OF CERTAIN CRIMES AND TO PROVIDE THAT IT IS A CRIMINAL OFFENSE FOR A PERSON WHO HAS BEEN CONVICTED OF SUCH AN OFFENSE TO SEEK EMPLOYMENT; AND TO AMEND SECTION 63-13-20, RELATING TO DEFINITIONS IN THE LICENSURE AND REGULATION OF CHILDCARE FACILITIES, SO AS TO REVISE THE EXEMPTIONS FROM CHILDCARE LICENSURE FOR SCHOOL CAMPS AND SUMMER RESIDENT CAMPS.
Senator HUTTO asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
Senator BRYANT proposed the following amendment (JUD0553.004), which was adopted:
Amend the Committee Report, as and if amended, page [553-1] by striking lines 5 through 8 and inserting therein the following:
/ the recommendation of the SCRPA;
(7) one member representing the South Carolina Afterschool Care Alliance (SCACA), chosen by the chairperson upon the recommendation of the SCACA; and
(8) three members appointed by the Governor, of which at least two members must be from religious-affiliated groups that operate summer camp programs in South Carolina. /
Renumber sections to conform.
Amend title to conform.
Senator HUTTO explained the perfecting amendment.
The Committee on Judiciary proposed the following amendment (JUD0553.003), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting language and inserting therein the following:
/ SECTION 1. (A) A South Carolina Summer Camp Study Committee is created to study the summer camps in the State and to recommend legislation, if appropriate, related to the licensing and regulation of summer camps.
(B) The study committee must be composed of the following members:
(1) the Director of the Department of Social Services, or her designee, who shall serve as the chairperson for the study committee;
(2) the Commissioner of the Department of Health and Environmental Control, or his designee, who shall serve as the co-chairperson of the study committee;
(3) the Director of the South Carolina Law Enforcement Division, or his designee;
(4) one member of the Joint Citizens and Legislative Committee on Children, chosen by the Chairperson of the JCLCC;
(5) one member representing the YMCA, chosen by the chairperson upon the recommendation of the YMCA;
(6) one member representing the South Carolina Recreation and Parks Association (SCRPA), chosen by the chairperson upon the recommendation of the SCRPA; and
(7) one member representing the South Carolina Afterschool Care Alliance (SCACA), chosen by the chairperson upon the recommendation of the SCACA.
(C) The study committee must review all information it considers relevant related to summer camps, any current statutes or regulations governing summer camps, and any deficiencies related to the operation or regulation of summer camps. The study committee must develop and recommend statewide minimum requirements it deems necessary for the care and protection of children attending summer camps and recommend a mechanism for the enforcement of the requirements. The study committee must complete and render a written public report detailing its findings and recommendations, to include any recommended legislation, to the Governor, the President Pro Tempore of the Senate, and the Speaker of the House of Representatives by no later than January 31, 2010, at which time the study committee must be dissolved.
(D) The staffing for the committee must be provided by the South Carolina Department of Social Services.
(E) Members of the study committee shall serve without compensation.
(F) Except as otherwise provided, the study committee may organize and collect information in the manner it deems to be best suited to accomplish its objectives.
SECTION 2. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
HOUSE AMENDMENTS AMENDED
RETURNED TO THE HOUSE WITH AMENDMENTS
The House returned the Bill with amendments.
Senator SHEHEEN asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being concurrence with the House amendments.
Senators SHEHEEN and GROOMS proposed the following amendment (126R006.VAS), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 56-3-1910 of the 1976 Code is amended to read:
"Section 56-3-1910. (A) As used in this article, 'handicapped' means a person who has one or more of the following conditions:
(1) an inability to ordinarily walk one hundred feet nonstop without aggravating an existing medical condition, including the increase of pain;
(2) an inability to ordinarily walk without the use of, or assistance from a brace, cane, crutch, another person, prosthetic device, wheelchair, or other assistive device;
(3) a restriction by lung disease to the extent that the person's forced expiratory volume for one second when measured by spirometry is less than one liter, or the arterial oxygen tension is less than sixty mm/hg on room air at rest;
(4) requires use of portable oxygen;
(5) a cardiac condition to the extent that the person's functional limitations are classified in severity as Class III or Class IV according to standards established by the American Heart Association. If the person's status improves to a higher level, for example as a result of bypass surgery or transplantation, he no longer meets this criteria;
(6) a substantial limitation in the ability to walk due to an arthritic, neurological, or orthopedic condition, for example, coordination problems and muscle spasticity due to conditions that include Parkinson's disease, cerebral palsy, or multiple sclerosis; or
(7) blindness.
(B) Upon payment of the regular motor vehicle license fee, the department may issue a license tag plate with a special number or identification indicating that the tag license plate was issued to a person (a) disabled by an impairment in the use of one or more limbs and required to use a wheelchair or (b) disabled by an impairment in mobility, but otherwise qualified for a driver's license as determined by the department. Each application for the license must be accompanied by the certificate of a licensed physician as defined in Section 40-47-5 as to the permanency of limb impairment or as to the severity or the permanency of mobility impairment. certified as permanently handicapped, but otherwise qualified to obtain a driver's license. A license plate issued pursuant to this section must be accompanied by a certification form completed by a licensed physician.
(C)(1) The department must develop a standardized certification form designed to capture criteria related information relating to persons considered handicapped. The form shall indicate whether the applicant meets one or more of the criteria, whether the condition is permanent or temporary, and if temporary, the expected duration.
(2) All persons that have been issued a handicapped license plate as of the effective date of this section will be issued a certificate upon renewal of the license plate. To renew the plate and receive the certificate, the person must be certified as permanently handicapped as provided in this section. Failure to carry a certificate as required by this section by a person that has been issued a handicapped license plate as of the effective date of this section is not a violation of the provisions of this section until after the person renews his license plate.
(D) Forms must be completed by physicians licensed to practice in South Carolina as defined in Section 40-47-5.
(E) The special license plate authorized by this section also may be issued for a vehicle of special design and equipment designed to transport a disabled person who meets the requirements of this section if the vehicle is owned and titled in the name of the disabled person or in the name of a member of his immediate family.
(F) The special license tag plate authorized by this section may also be issued for a vehicle of special design and equipment designed to transport a disabled person who meets is certified as meeting the requirements of this section if the vehicle is owned and titled in the name of the disabled person or in the name of a member of his immediate family or for a vehicle used by an agency, organization, or facility that is designed to transport a handicapped or disabled person if the vehicle is titled in the name of the agency, organization, or facility. Proof that the agency, organization, or facility transports a handicapped or disabled person must be in a manner prescribed by the department. A certificate from a licensed physician is not required to apply for the special license tag plate issued to the agency, organization, or facility. (G) When processing applications for special license plates pursuant to this section, the department shall also issue a license plate registration certificate that must be carried at all times in the vehicle driven by or transporting the disabled individual. The certificate must display the name of the individual or organization to which the plate was issued.
(H) Vehicles displaying a special handicapped license plate may only park in designated handicapped parking spaces if that vehicle is driven by or transporting the disabled individual whose name appears on the license plate registration certificate, or if the certificate lists the name of the agency, organization, or facility authorized under subsection (G). The driver of the vehicle displaying the plate must present the registration when requested by law enforcement entities or their duly authorized agents.
(I) A person who qualifies for a license plate under this section and also qualifies as a disabled veteran under Section 56-3-1110 must be issued the license plate provided for in this section free of charge.
(J)(1) Except as provided in item (2), a person violating the provisions of this section is guilty of a misdemeanor and, upon conviction, must be fined not less than five hundred dollars nor more than one thousand dollars or imprisoned for not more than thirty days for each offense.
(2) A person who illegally duplicates, forges, or sells a handicapped license plate or a person who falsifies information on an application form for a handicapped license plate is guilty of a misdemeanor and, upon conviction, must be imprisoned for thirty days and fined not less than five hundred dollars and not more than one thousand dollars."
SECTION 2. Section 56-3-1950 of the 1976 Code is amended to read:
(1) 'Handicapped' 'handicapped' means a person who:
(a) has an obvious physical disability that impairs the ability to walk or requires the use of a wheelchair, braces, walkers, or crutches;
(b) has lost the use of one or both legs;
(c) suffers from lung disease to such an extent that he is unable to walk without the aid of a respirator;
(d) is disabled by an impairment in mobility; or
(e) is determined by the Social Security Administration or the Veterans Administration to be totally and permanently disabled.
(2) A licensed physician shall certify that the total and permanent disability substantially impairs the ability to walk, unless the applicant is an agency or organization complying with Section 56-3-1910. as defined in Section 56-3-1910;
(2) 'access aisle' means a designated space for maneuvering a wheelchair or other mobility device when entering or exiting a vehicle, and that is immediately adjacent to a properly designated parking space for handicapped persons, on public or private property. Access aisles must be marked so as to discourage parking in them."
SECTION 3. Section 56-3-1960 of the 1976 Code is amended to read:
The permanent placards may be issued and renewed only for a maximum period of four years renewable on the owner's birth date; however, placards issued to an agency, organization, or facility must be renewed every four years. The placards must be of a color as determined by the department which is easily recognizable by law enforcement personnel. The placard shall indicate on its face when it expires.
(3) A vehicle displaying an out-of-state handicapped license plate or placard or other evidence of handicap issued by the appropriate authority as determined by the department is entitled to the parking privileges provided for in this section.
(B) The placards authorized by this section also may be issued for a vehicle of special design and equipment designed to transport a disabled person who is certified as meeting the requirements of this section for a vehicle used by an agency, organization, or facility that is designed to transport a handicapped or disabled person if the vehicle is titled in the name of the agency, organization, or facility. Proof that the agency, organization, or facility transports a handicapped or disabled person must be in a manner prescribed by the department. A certificate from a licensed physician is not required to apply for placards issued to an agency, organization, or facility. At the time of qualification, applicants qualifying for a placard under this section also must be issued a placard registration certificate that must be carried at all times in the vehicle transporting handicapped or disabled individuals. The certificate will display the name of the agency, organization, or facility to which the placard was issued.
(C) The placards shall conform to specifications set forth in the standards established for compliance with the Americans with Disabilities Act. The design must incorporate a means for hanging the placard from a vehicle windshield rearview mirror, and:
(1) contain the international symbol of access;
(2) be color-coded to reflect user status in the following manner:
(a) dark blue - permanently disabled; and
(b) red - temporarily disabled.
(D) Blue and red placards shall contain the qualified user's photograph. The photograph must be taken from the qualified user's driver's license or identification card on file with the department. However, a photograph is not required for a placard issued to an agency, organization, or facility.
(E) Each placard shall contain the placard's expiration date.
(F) When qualified users park in designated spaces, the placard must be displayed in the windshield of the vehicle by hanging it from the rearview mirror. In vehicles in which hanging may not be feasible, the placard must be placed on the side of the dashboard so that it is clearly visible through the windshield. When more than one placard holder is transported in the same vehicle, only one placard needs to be displayed.
(G) Placards used for parking in designated handicapped spaces must be displayed on vehicles driven by or transporting the handicapped individual whose name appears on the placard registration certificate. When parked in designated spaces, the driver of the vehicle displaying the placard must present the placard registration certificate when requested by law enforcement entities or their duly authorized agents.
(H) Placards and placard registration certificates for permanently disabled persons may be issued and renewed for a maximum period of four years and are renewable on the owner's birth date. Placards issued to an agency, organization, or facility must be renewed every four years.
(I) A vehicle displaying a valid out-of-state handicapped license plate or placard or other evidence of handicap issued by the appropriate authority as determined by the department is entitled to the parking privileges provided in this section. Handicapped individuals from other states seeking permanent residence in South Carolina have forty-five days after becoming a resident to obtain South Carolina certification.
(J) Placards issued prior to the effective date of this section must be renewed by the expiration date on the placard or by January 1, 2013, whichever is sooner. To renew the placard and receive the certificate, the person must be certified as permanently handicapped as provided in Section 56-3-1910. Upon renewal, the department will issue a certificate as required by this section. Failure to carry a certificate as required by this section by a person using a placard issued prior to the effective date of this section is not a violation of the provisions of this section until after the placard is renewed or January 1, 2013, whichever is sooner.
(K)(1) Except as provided in item (2), a person that violates the provisions of this section is guilty of a misdemeanor and, upon conviction, must be fined not less than five hundred dollars nor more than one thousand dollars or imprisoned for not more than thirty days, or both, for each offense.
(2) A person who illegally duplicates, forges, or sells a handicapped placard or a person who falsifies information on an application form for a handicapped placard is guilty of a misdemeanor and, upon conviction, must be imprisoned for thirty days and fined not less than five hundred dollars and not more than one thousand dollars."
SECTION 4. Section 56-3-1965 of the 1976 Code is amended to read:
"Section 56-3-1965. Those municipalities having marked parking spaces shall provide appropriately designated space or spaces reserved for the parking of handicapped persons. A person who is handicapped as defined in this article must be allowed to park in metered or timed parking places without being subject to parking fees or fines. This section does not apply to areas or during times in which the stopping, parking, or standing of all vehicles is prohibited or to areas which are reserved for special types of vehicles. A vehicle must display a distinguishing license plate which must be issued by the department, pursuant to Section 56-3-1910, or Section 56-3-1110, or a distinguishing placard which must be issued by the department, pursuant to Section 56-3-1960 when parked in metered or timed parking places."
SECTION 5. Section 56-3-2010 of the 1976 Code is amended by adding at the end:
"(C) If a person who qualifies for the special license plate issued under this section also qualifies for the handicapped license plate issued pursuant to Section 56-3-1910, then the license plate issued pursuant to this section also shall include a decal with the International Symbol of Access used on license plates issued pursuant to Section 56-3-1910. The decal can only be used if space is available to place the decal on the license plate without covering any identifying numbers or letters on the license plate."
SECTION 6. Section 56-3-1970 of the 1976 Code is amended to read:
"Section 56-3-1970. (A) It is unlawful to park any vehicle in a parking place clearly designated for handicapped persons unless the vehicle bears the distinguishing license plate provided in Section 56-3-1910 or placard provided in Section 56-3-1960.
(B) It is unlawful for any person who is not handicapped or who is not transporting a handicapped person to exercise the parking privileges granted handicapped persons pursuant to Section 56-3-1910, Section 56-3-1960, and Section 56-3-1965.
(C) A person violating the provisions of this section is guilty of a misdemeanor and, upon conviction, must be fined not less than one five hundred dollars nor more than two hundred one thousand dollars or imprisoned for not more than thirty days for each offense."
SECTION 7. Section 56-3-1975 of the 1976 Code is amended to read:
"Section 56-3-1975. Each handicapped parking place must be clearly identified as a handicapped parking place. The handicapped parking place includes all access aisles. If the handicapped parking place is on public property, the marker must be maintained by the political subdivision having jurisdiction over the public property or the street or highway where the handicapped parking place is located. If the handicapped parking place is on private property, the marker must be maintained by the owner of the property."
SECTION 8. This act takes effect six months after approval by the Governor. /
Amend title to conform.
Senator SHEHEEN explained the amendment.
There being no further amendments, the Bill was ordered returned to the House with amendments.
RECALLED
H. 3926 (Word version) -- Reps. Knight, Horne and A.D. Young: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION ERECT APPROPRIATE MARKERS OR SIGNS AT THE BRIDGE THAT CROSSES FOUR HOLE SWAMP WHERE IT FLOWS INTO THE EDISTO RIVER ALONG WIRE ROAD IN DORCHESTER COUNTY THAT CONTAIN THE WORDS "MUCKENFUSS (1792 - 1813) MINUS (1813 - 1848) HARLEY (1848 - 1862) BRIDGE".
Senator GROOMS asked unanimous consent to make a motion to recall the Bill from the Committee on Transportation.
On motion of Senator GROOMS, the Bill was recalled from the Committee on Transportation and ordered placed on the Calendar for consideration tomorrow.
| 2014-10-22T08:17:25 |
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## Bär, Christian
Compute Distance To:
Author ID: bar.christian Published as: Bär, Christian; Bär, C.; Bär, Ch. External Links: MGP · Wikidata · GND
Documents Indexed: 73 Publications since 1990, including 9 Books 4 Contributions as Editor Reviewing Activity: 178 Reviews Co-Authors: 29 Co-Authors with 37 Joint Publications 789 Co-Co-Authors
all top 5
### Co-Authors
39 single-authored 4 Ammann, Bernd Eberhard 4 Pfäffle, Frank Jochen 3 Becker, Christian 3 Dahl, Mattias 3 Ginoux, Nicolas 3 Strohmaier, Alexander 2 Ballmann, Hans Werner 2 Bleecker, David D. 2 Fredenhagen, Klaus 1 Atiyah, Michael Francis 1 Bandara, Lashi 1 Bourguignon, Jean-Pierre 1 Brunetti, Romeo 1 Dappiaggi, Claudio 1 Gauduchon, Paul 1 Greuel, Gert-Martin 1 Hannes, Sebastian 1 Lohkamp, Joachim 1 Manin, Yuri Ivanovich 1 Mazzeo, Rafe R. 1 Moroianu, Andrei 1 Moroianu, Sergiu 1 Bessa, Gregório Pacelli 1 Sanz-Solé, Marta 1 Schmutz Schaller, Paul 1 Schopka, Sven 1 Schwarz, Matthias 1 Sitarz, Andrzej 1 Wafo, Roger Tagne
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### Serials
6 Communications in Mathematical Physics 5 Annals of Global Analysis and Geometry 2 Journal of Geometry and Physics 2 Archiv der Mathematik 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Proceedings of the American Mathematical Society 2 Differential Geometry and its Applications 2 Geometric and Functional Analysis. GAFA 2 Acta Physica Polonica B 2 Oberwolfach Reports 2 Bonner Mathematische Schriften 2 De Gruyter Studium 1 Journal of Mathematical Physics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 American Journal of Mathematics 1 Geometriae Dedicata 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 International Journal of Mathematics 1 Linear Algebra and its Applications 1 Communications in Analysis and Geometry 1 Matemática Contemporânea 1 European Mathematical Society Newsletter 1 Mathematical Physics, Analysis and Geometry 1 Lecture Notes in Mathematics 1 Lecture Notes in Physics 1 Journal of Noncommutative Geometry 1 International Journal of Differential Equations 1 Springer Proceedings in Mathematics 1 ESI Lectures in Mathematics and Physics
all top 5
### Fields
55 Global analysis, analysis on manifolds (58-XX) 43 Differential geometry (53-XX) 14 Partial differential equations (35-XX) 14 Quantum theory (81-XX) 6 Manifolds and cell complexes (57-XX) 5 Operator theory (47-XX) 4 General and overarching topics; collections (00-XX) 3 Algebraic topology (55-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functional analysis (46-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Numerical analysis (65-XX) 1 Optics, electromagnetic theory (78-XX)
### Citations contained in zbMATH Open
55 Publications have been cited 862 times in 620 Documents Cited by Year
Real Killing spinors and holonomy. Zbl 0778.53037
Bär, Christian
1993
Wave equations on Lorentzian manifolds and quantization. Zbl 1118.58016
Bär, Christian; Ginoux, Nicolas; Pfäffle, Frank
2007
Extrinsic bounds for eigenvalues of the Dirac operator. Zbl 0921.58065
Bär, Christian
1998
Generalized cylinders in semi-Riemannian and spin geometry. Zbl 1068.53030
Bär, Christian; Gauduchon, Paul; Moroianu, Andrei
2005
Metrics with harmonic spinors. Zbl 0867.53037
Bär, C.
1996
Zero sets of solutions to semilinear elliptic systems of first order. Zbl 0942.35064
Bär, Christian
1999
The Dirac operator on space forms of positive curvature. Zbl 0848.58046
Bär, Christian
1996
Lower eigenvalue estimates for Dirac operators. Zbl 0741.58046
Bär, Christian
1992
Green-hyperbolic operators on globally hyperbolic spacetimes. Zbl 1316.58027
Bär, Christian
2015
On Nodal Sets for Dirac and Laplace Operators. Zbl 0888.47028
Bär, Christian
1997
The Dirac operator on nilmanifolds and collapsing circle bundles. Zbl 0911.58037
Ammann, Bernd; Bär, Christian
1998
Classical and quantum fields on Lorentzian manifolds. Zbl 1254.81044
Bär, Christian; Ginoux, Nicolas
2012
Boundary value problems for elliptic differential operators of first order. Zbl 1331.58022
Bär, Christian; Ballmann, Werner
2012
Quantum field theory on curved spacetimes. Concepts and mathematical foundations. Extended lecture notes of the compact course quantum field theory on curved spacetimes, Potsdam, Germany, October 2007. Zbl 1178.81003
2009
The Dirac operator on hyperbolic manifolds of finite volume. Zbl 1030.58021
Bär, Christian
2000
Harmonic spinors on Riemann surfaces. Zbl 0763.30017
Bär, Christian; Schmutz, Paul
1992
The Dirac operator on homogeneous spaces and its spectrum on 3- dimensional lens spaces. Zbl 0786.53030
Bär, Christian
1992
Surgery and the spectrum of the Dirac operator. Zbl 1017.58019
Bär, Christian; Dahl, Mattias
2002
A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Zbl 1350.81029
Bär, Christian; Strohmaier, Alexander
2016
Guide to elliptic boundary value problems for Dirac-type operators. Zbl 1377.58022
Bär, Christian; Ballmann, Werner
2016
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. Zbl 1429.83004
Bär, Christian; Strohmaier, Alexander
2019
Dirac eigenvalue estimates on surfaces. Zbl 1007.58014
Ammann, Bernd; Bär, Christian
2002
Initial value problems for wave equations on manifolds. Zbl 1338.58018
Bär, Christian; Wafo, Roger Tagne
2015
Stochastic completeness and volume growth. Zbl 1201.58024
Bär, Christian; Bessa, G. Pacelli
2010
CCR- versus CAR-quantization on curved spacetimes. Zbl 1250.81073
Bär, Christian; Ginoux, Nicolas
2012
Differential characters. Zbl 1296.58002
Bär, Christian; Becker, Christian
2014
Spectral bounds for Dirac operators on open manifolds. Zbl 1193.53119
Bär, Christian
2009
Harmonic spinors for twisted Dirac operators. Zbl 0889.53025
Bär, Christian
1997
The spectrum of Dirac operators. (Das Spektrum von Dirac-Operatoren.) Zbl 0748.53022
Bär, Christian
1990
Geometrically formal 4-manifolds with nonnegative sectional curvature. Zbl 1319.53027
Bär, Christian
2015
Asymptotic heat kernel expansion in the semi-classical limit. Zbl 1211.58018
Bär, Christian; Pfäffle, Frank
2010
The first Dirac eigenvalues on manifolds with positive scalar curvature. Zbl 1053.58012
Bär, Christian; Dahl, Mattias
2004
The Einstein-Hilbert action as a spectral action. Zbl 1255.81218
Ammann, Bernd; Bär, Christian
2002
Elementary differential geometry. 2nd revised and enlarged ed. (Elementare Differentialgeometrie.) Zbl 1191.53001
Bär, Christian
2010
Small eigenvalues of the conformal Laplacian. Zbl 1030.58003
Bär, Christian; Dahl, Matthias
2003
Path integrals on manifolds by finite dimensional approximation. Zbl 1165.58015
Bär, Christian; Pfäffle, Frank
2008
On harmonic spinors. Zbl 1010.58016
Bär, C.
1998
Differential characters and geometric chains. Zbl 1304.53019
Bär, Christian; Becker, Christian
2014
Semi-bounded restrictions of Dirac type operators and the unique continuation property. Zbl 1031.58008
Bär, Christian; Strohmaier, Alexander
2001
Heat kernel asymptotics for roots of generalized Laplacians. Zbl 1079.58020
Bär, Christian; Moroianu, Sergiu
2003
Wiener measures on Riemannian manifolds and the Feynman-Kac formula. Zbl 1302.58017
Bär, Christian; Pfäffle, Frank
2011
$$C^*$$-algebras. Zbl 1185.46037
Bär, Christian; Becker, Christian
2009
Conformal structures in noncommutative geometry. Zbl 1153.58010
Bär, Christian
2007
Dirac eigenvalues and total scalar curvature. Zbl 0960.58014
Ammann, Bernd; Bär, Christian
2000
Localization and semibounded energy – a weak unique continuation theorem. Zbl 0969.58007
Bär, Christian
2000
The Dirac determinant of spherical space forms. Zbl 1049.58030
Bär, Christian; Schopka, Sven
2003
Elliptic symbols. Zbl 0946.58020
Bär, Christian
1999
Upper eigenvalue estimates for Dirac operators. Zbl 0770.53026
Bär, Christian
1992
Dependence of the Dirac spectrum on the spin structure. Zbl 0995.58020
Bär, Christian
2000
The spectrum of the Dirac operator. Zbl 1103.58015
Bär, Christian
2005
A remark on positively curved 4-manifolds. Zbl 0796.53039
Bär, Christian
1994
Heat operator and $$\zeta$$-function estimates for surfaces. Zbl 0917.58047
Bär, Christian
1998
Renormalized integrals and a path integral formula for the heat kernel on a manifold. Zbl 1317.58039
Bär, Christian
2012
The Dirac fundamental tone of the hyperbolic space. Zbl 0757.53020
Bär, Christian
1992
Manifolds with many Rarita-Schwinger fields. Zbl 1479.53061
Bär, Christian; Mazzeo, Rafe
2021
Manifolds with many Rarita-Schwinger fields. Zbl 1479.53061
Bär, Christian; Mazzeo, Rafe
2021
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. Zbl 1429.83004
Bär, Christian; Strohmaier, Alexander
2019
A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Zbl 1350.81029
Bär, Christian; Strohmaier, Alexander
2016
Guide to elliptic boundary value problems for Dirac-type operators. Zbl 1377.58022
Bär, Christian; Ballmann, Werner
2016
Green-hyperbolic operators on globally hyperbolic spacetimes. Zbl 1316.58027
Bär, Christian
2015
Initial value problems for wave equations on manifolds. Zbl 1338.58018
Bär, Christian; Wafo, Roger Tagne
2015
Geometrically formal 4-manifolds with nonnegative sectional curvature. Zbl 1319.53027
Bär, Christian
2015
Differential characters. Zbl 1296.58002
Bär, Christian; Becker, Christian
2014
Differential characters and geometric chains. Zbl 1304.53019
Bär, Christian; Becker, Christian
2014
Classical and quantum fields on Lorentzian manifolds. Zbl 1254.81044
Bär, Christian; Ginoux, Nicolas
2012
Boundary value problems for elliptic differential operators of first order. Zbl 1331.58022
Bär, Christian; Ballmann, Werner
2012
CCR- versus CAR-quantization on curved spacetimes. Zbl 1250.81073
Bär, Christian; Ginoux, Nicolas
2012
Renormalized integrals and a path integral formula for the heat kernel on a manifold. Zbl 1317.58039
Bär, Christian
2012
Wiener measures on Riemannian manifolds and the Feynman-Kac formula. Zbl 1302.58017
Bär, Christian; Pfäffle, Frank
2011
Stochastic completeness and volume growth. Zbl 1201.58024
Bär, Christian; Bessa, G. Pacelli
2010
Asymptotic heat kernel expansion in the semi-classical limit. Zbl 1211.58018
Bär, Christian; Pfäffle, Frank
2010
Elementary differential geometry. 2nd revised and enlarged ed. (Elementare Differentialgeometrie.) Zbl 1191.53001
Bär, Christian
2010
Quantum field theory on curved spacetimes. Concepts and mathematical foundations. Extended lecture notes of the compact course quantum field theory on curved spacetimes, Potsdam, Germany, October 2007. Zbl 1178.81003
2009
Spectral bounds for Dirac operators on open manifolds. Zbl 1193.53119
Bär, Christian
2009
$$C^*$$-algebras. Zbl 1185.46037
Bär, Christian; Becker, Christian
2009
Path integrals on manifolds by finite dimensional approximation. Zbl 1165.58015
Bär, Christian; Pfäffle, Frank
2008
Wave equations on Lorentzian manifolds and quantization. Zbl 1118.58016
Bär, Christian; Ginoux, Nicolas; Pfäffle, Frank
2007
Conformal structures in noncommutative geometry. Zbl 1153.58010
Bär, Christian
2007
Generalized cylinders in semi-Riemannian and spin geometry. Zbl 1068.53030
Bär, Christian; Gauduchon, Paul; Moroianu, Andrei
2005
The spectrum of the Dirac operator. Zbl 1103.58015
Bär, Christian
2005
The first Dirac eigenvalues on manifolds with positive scalar curvature. Zbl 1053.58012
Bär, Christian; Dahl, Mattias
2004
Small eigenvalues of the conformal Laplacian. Zbl 1030.58003
Bär, Christian; Dahl, Matthias
2003
Heat kernel asymptotics for roots of generalized Laplacians. Zbl 1079.58020
Bär, Christian; Moroianu, Sergiu
2003
The Dirac determinant of spherical space forms. Zbl 1049.58030
Bär, Christian; Schopka, Sven
2003
Surgery and the spectrum of the Dirac operator. Zbl 1017.58019
Bär, Christian; Dahl, Mattias
2002
Dirac eigenvalue estimates on surfaces. Zbl 1007.58014
Ammann, Bernd; Bär, Christian
2002
The Einstein-Hilbert action as a spectral action. Zbl 1255.81218
Ammann, Bernd; Bär, Christian
2002
Semi-bounded restrictions of Dirac type operators and the unique continuation property. Zbl 1031.58008
Bär, Christian; Strohmaier, Alexander
2001
The Dirac operator on hyperbolic manifolds of finite volume. Zbl 1030.58021
Bär, Christian
2000
Dirac eigenvalues and total scalar curvature. Zbl 0960.58014
Ammann, Bernd; Bär, Christian
2000
Localization and semibounded energy – a weak unique continuation theorem. Zbl 0969.58007
Bär, Christian
2000
Dependence of the Dirac spectrum on the spin structure. Zbl 0995.58020
Bär, Christian
2000
Zero sets of solutions to semilinear elliptic systems of first order. Zbl 0942.35064
Bär, Christian
1999
Elliptic symbols. Zbl 0946.58020
Bär, Christian
1999
Extrinsic bounds for eigenvalues of the Dirac operator. Zbl 0921.58065
Bär, Christian
1998
The Dirac operator on nilmanifolds and collapsing circle bundles. Zbl 0911.58037
Ammann, Bernd; Bär, Christian
1998
On harmonic spinors. Zbl 1010.58016
Bär, C.
1998
Heat operator and $$\zeta$$-function estimates for surfaces. Zbl 0917.58047
Bär, Christian
1998
On Nodal Sets for Dirac and Laplace Operators. Zbl 0888.47028
Bär, Christian
1997
Harmonic spinors for twisted Dirac operators. Zbl 0889.53025
Bär, Christian
1997
Metrics with harmonic spinors. Zbl 0867.53037
Bär, C.
1996
The Dirac operator on space forms of positive curvature. Zbl 0848.58046
Bär, Christian
1996
A remark on positively curved 4-manifolds. Zbl 0796.53039
Bär, Christian
1994
Real Killing spinors and holonomy. Zbl 0778.53037
Bär, Christian
1993
Lower eigenvalue estimates for Dirac operators. Zbl 0741.58046
Bär, Christian
1992
Harmonic spinors on Riemann surfaces. Zbl 0763.30017
Bär, Christian; Schmutz, Paul
1992
The Dirac operator on homogeneous spaces and its spectrum on 3- dimensional lens spaces. Zbl 0786.53030
Bär, Christian
1992
Upper eigenvalue estimates for Dirac operators. Zbl 0770.53026
Bär, Christian
1992
The Dirac fundamental tone of the hyperbolic space. Zbl 0757.53020
Bär, Christian
1992
The spectrum of Dirac operators. (Das Spektrum von Dirac-Operatoren.) Zbl 0748.53022
Bär, Christian
1990
all top 5
### Cited by 587 Authors
20 Dappiaggi, Claudio 18 Ammann, Bernd Eberhard 17 Bär, Christian 16 Ginoux, Nicolas 16 Moroianu, Andrei 12 Benini, Marco 12 Habib, Georges 12 Nakad, Roger 11 Roth, Julien 11 Schenkel, Alexander 10 Moroianu, Sergiu 10 Semmelmann, Uwe 9 Branding, Volker 9 Große, Nadine 9 Pinamonti, Nicola 8 Drago, Nicolò 7 Chen, Yongfa 7 Fewster, Christopher John 7 Friedrich, Thomas 7 Hijazi, Oussama 7 Humbert, Emmanuel 7 Lee, Yoonweon 7 Ludewig, Matthias 7 Murro, Simone 7 Raulot, Simon 7 Verch, Rainer 6 Bayard, Pierre 6 Conti, Diego 6 Fredenhagen, Klaus 6 Hack, Thomas-Paul 6 Jost, Jürgen 6 Sati, Hisham 6 Strohmaier, Alexander 6 Zhu, Miaomiao 5 Chen, Qun 5 Finster, Felix 5 Fröb, Markus B. 5 Kim, Eui Chul 5 Lawn, Marie-Amélie 5 Montiel, Sebastián 5 Rejzner, Kasia 5 Salamon, Simon Montague 5 Sanders, Ko 5 Shahbazi, Carlos S. 5 Sitarz, Andrzej 5 Zahn, Jochen 4 Baum, Helga 4 Chen, Daguang 4 Dabrowski, Ludwik 4 Dahl, Mattias 4 Kath, Ines 4 Kraus, Margarita 4 Lauret, Emilio A. 4 Lazaroiu, Calin Iuliu 4 Leistner, Thomas 4 Wrochna, Michał 4 Wu, Ruijun 4 Zabzine, Maxim 3 Agricola, Ilka 3 Alexandrov, Bogdan 3 Arrizabalaga, Naiara 3 Ballmann, Hans Werner 3 Braverman, Maxim 3 Cekić, Mihajlo 3 Chrysikos, Ioannis 3 Coriasco, Sandro 3 Cortés, Vicente 3 El Chami, Fida 3 Enciso, Alberto 3 Goette, Sebastian 3 Grady, Daniel 3 Hollands, Stefan 3 Homma, Yasushi 3 Huang, Rung-Tzung 3 Kamran, Niky 3 Le Treust, Loïc 3 Loya, Paul A. 3 Marcolli, Matilde 3 Morel, Bertrand 3 Müller, Olaf 3 Nistor, Victor 3 Nowaczyk, Nikolai 3 Ourmiéres-Bonafos, Thomas 3 Petersen, Oliver Lindblad 3 Pfäffle, Frank Jochen 3 Pigola, Stefano 3 Qiu, Jian 3 Raymond, Nicolas 3 Setti, Alberto G. 3 Shi, Pengshuai 3 Vassiliev, Dmitri G. 3 Wang, Guofang 3 Waterstraat, Nils 3 Witt, Frederik 3 Zelditch, Steve 2 Agranovsky, Mark L. 2 Alekseevskiĭ, Dmitriĭ Vladimirovich 2 Amann, Manuel 2 Avramidi, Ivan G. 2 Bakas, Ioannis ...and 487 more Authors
all top 5
### Cited in 130 Serials
77 Journal of Geometry and Physics 64 Communications in Mathematical Physics 36 Annals of Global Analysis and Geometry 23 Journal of Mathematical Physics 21 Differential Geometry and its Applications 21 Annales Henri Poincaré 20 Mathematische Zeitschrift 20 Journal of High Energy Physics 18 Letters in Mathematical Physics 16 The Journal of Geometric Analysis 14 Reviews in Mathematical Physics 12 Transactions of the American Mathematical Society 11 Calculus of Variations and Partial Differential Equations 10 Classical and Quantum Gravity 10 Journal of Functional Analysis 9 Advances in Mathematics 9 Mathematical Physics, Analysis and Geometry 9 International Journal of Geometric Methods in Modern Physics 8 Nuclear Physics. B 8 Manuscripta Mathematica 8 International Journal of Mathematics 6 Journal of Noncommutative Geometry 5 Journal of Mathematical Analysis and Applications 5 Annales de l’Institut Fourier 5 Duke Mathematical Journal 5 Results in Mathematics 5 Advances in Applied Clifford Algebras 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Mathematische Annalen 4 Potential Analysis 4 Geometry & Topology 3 International Journal of Modern Physics A 3 General Relativity and Gravitation 3 Fortschritte der Physik 3 Compositio Mathematica 3 Geometriae Dedicata 3 Journal für die Reine und Angewandte Mathematik 3 Proceedings of the American Mathematical Society 3 Geometric and Functional Analysis. GAFA 3 Communications in Partial Differential Equations 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Archiv der Mathematik 2 Chinese Annals of Mathematics. Series B 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Vietnam Journal of Mathematics 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Central European Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Foundations of Physics 2 Frontiers of Mathematics in China 2 Journal of Homotopy and Related Structures 2 Journal of Topology and Analysis 2 São Paulo Journal of Mathematical Sciences 2 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 2 Science China. Mathematics 2 Journal of Spectral Theory 1 Modern Physics Letters A 1 Archive for Rational Mechanics and Analysis 1 Inverse Problems 1 Mathematical Notes 1 Nonlinearity 1 Physics Letters. A 1 Physics Letters. B 1 Physics Reports 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Annales Polonici Mathematici 1 Canadian Journal of Mathematics 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Journal of Geometry 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Topology and its Applications 1 Revista Matemática Iberoamericana 1 Annals of Physics 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Experimental Mathematics 1 International Journal of Modern Physics D 1 Russian Journal of Mathematical Physics 1 Journal of Lie Theory 1 Selecta Mathematica. New Series 1 Advances in Differential Equations 1 Discrete and Continuous Dynamical Systems ...and 30 more Serials
all top 5
### Cited in 50 Fields
360 Differential geometry (53-XX) 268 Global analysis, analysis on manifolds (58-XX) 179 Quantum theory (81-XX) 130 Partial differential equations (35-XX) 98 Relativity and gravitational theory (83-XX) 52 Manifolds and cell complexes (57-XX) 50 Functional analysis (46-XX) 22 Several complex variables and analytic spaces (32-XX) 17 Operator theory (47-XX) 15 Algebraic geometry (14-XX) 13 Mechanics of particles and systems (70-XX) 11 Topological groups, Lie groups (22-XX) 10 Ordinary differential equations (34-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Algebraic topology (55-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 $$K$$-theory (19-XX) 8 Functions of a complex variable (30-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Nonassociative rings and algebras (17-XX) 6 Number theory (11-XX) 6 Probability theory and stochastic processes (60-XX) 4 Associative rings and algebras (16-XX) 4 Real functions (26-XX) 4 Approximations and expansions (41-XX) 4 Geometry (51-XX) 4 Astronomy and astrophysics (85-XX) 3 General and overarching topics; collections (00-XX) 3 Combinatorics (05-XX) 3 Category theory; homological algebra (18-XX) 3 Measure and integration (28-XX) 3 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Fluid mechanics (76-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 2 Numerical analysis (65-XX) 2 Optics, electromagnetic theory (78-XX) 2 Information and communication theory, circuits (94-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-05-22T17:11:07 |
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|
https://www.usgs.gov/center-news/volcano-watch-jaggars-prediction-comes-true-1935-eruption-mauna-loa
|
# Volcano Watch - Jaggar's prediction comes true—the 1935 eruption of Mauna Loa
Release Date:
Despite severely reduced funding and staffing, Jaggar made an important and successful prediction based on Mauna Loa's past pattern of eruptions.
This photo, taken by Thomas Jaggar on December 21 during the1935 Mauna Loa eruption, shows the Humuula pāhoehoe flow ponding and slowly expanding eastward. The image looks east-southeast toward Pu‘uhuluhulu from the southernmost Omaokoili cinder cone in the vicinity of today's Saddle Road and Mauna Kea Access Road juncture. USGS photo.
(Public domain.)
After working for 20 years building the Hawaiian Volcano Observatory (HVO), Thomas Jaggar had achieved almost everything he set out to do. He had directed continuous observations of Kīlauea Volcano, installed seismic monitoring instruments at four locations around the Island of Hawai‘i, and published these findings regularly. His budget for the fiscal year 1931–1932 from the U.S. Geological Survey (USGS) was his largest ever—$35,000. But these were the years of the Great Depression. Over the next two years, HVO's budget was slashed to$6,000, forcing a reduction in publishing and requiring supplemental funding from HVO's private funding source, the Hawaiian Volcano Research Association (HVRA), to pay salaries.
While government funding was being cut, volcanic and seismic activity on Hawai‘i did not diminish. In late 1933, a six-week-long swarm of earthquakes culminated in a 17-day-long eruption within Moku‘āweoweo, the summit caldera of Mauna Loa. Almost a year later, Halema‘uma‘u Crater at the summit of Kīlauea erupted for a month.
On March 26, 1934, Jaggar gave a bold speech titled "The Coming Lava Flow," in which he predicted—based on analyses of 60 years of Mauna Loa eruptions—that "A lava flow from Mauna Loa, or else another summit eruption, is expected within two years." He further predicted that, if it was a Mauna Loa lava flow, it would break out along the Northeast Rift Zone and flow in the "likely direction" of Hilo.
Jaggar also pointed out that, despite the coming lava flow, HVO had been reduced to two staff, including himself. He further campaigned for increased membership in HVRA to hopefully make up for the federal funding cuts.
The HVRA funding did not come, and, as of July 1, 1935, HVO was transferred from the USGS to the National Park Service under what was then known as Hawaii National Park (HNP). While this looked like defeat for Jaggar, it may have been a blessing.
Edward G. Wingate, a USGS topographical engineer, had worked at HVO for two years before being selected as HNP Superintendent in November 1933. After HVO was transferred to the Park, he was able to provide Jaggar with additional staff and funds when needed. So, when Mauna Loa erupted on November 21, 1935, as Jaggar had predicted, Wingate directed Park staff to the eruption site to make observations and relay information to HVO.
The 1935 Mauna Loa eruption started from a 6.4-km- (4-mi-) long fissure that extended from the summit caldera down the Northeast Rift Zone. Several lava flows moved northward down the flank of the volcano toward the Saddle area between Mauna Loa and Mauna Kea.
Contrary to Jaggar's prediction, these flows would probably flow toward Kona if they continued, not toward Hilo. Still, Jaggar's predicted time frame and location of the eruption source were spot-on.
But then, on November 27, smoke was observed from a patch of ground east of the 1935 lava flows, well away from the Northeast Rift Zone, at the 2,590 m (8,500 ft) elevation. ‘A‘ā lava (later called the Humuula flow) soon issued from that location and flowed north into the Saddle area. It stalled, but was followed by a pāhoehoe flow that ponded in a flat area between Mauna Loa's 1843 ‘a‘ā flow and Pu‘uhuluhulu, an ancient cinder cone.
After ponding for two weeks, the Humuula flow began moving and advanced eastward past Pu‘uhuluhulu. The increasingly steep slope resulted in a narrow flow advancing at an alarming rate of 1.6 km (1 mi) per day.
Fearing that the flow would reach the headwaters of the Wailuku River, which supplied water for the town of Hilo, Jaggar called on the Army Air Service on December 22 to bomb the lava flow source. His hope was that the lava tubes or channels could be destroyed, robbing the advancing flow to feed another flow that would re-cover the same area. The flow was bombed on December 27 and the flow stopped during the night or early morning of December 30-31.
Despite severely reduced funding and staffing, Jaggar made an important and successful prediction based on Mauna Loa's past pattern of eruptions. Whether or not the bombing caused the 1935 lava flow to stop is still a controversial topic.
### Volcano Activity Update
Kīlauea continues to erupt at its summit and East Rift Zone. During the past week, in concert with summit inflation and deflation, the summit lava lake level varied between about 16 m and 36.5 m (52–120 ft) below the vent rim within Halema‘uma‘u Crater. On the East Rift Zone, the "61g" lava flow continued to enter the ocean. The lava flow does not pose an immediate threat to nearby communities.
Mauna Loa is not erupting. Seismicity remains elevated relative to the long-term background rate, with earthquakes occurring mostly in Mauna Loa's south caldera and upper Southwest Rift Zone at depths less than 5 km (3 mi). Global Positioning System (GPS) measurements show deformation related to inflation of a magma reservoir beneath the summit and upper Southwest Rift Zone, with inflation occurring mainly in the southwestern part of the magma storage complex.
Four earthquakes were reported felt on the Island of Hawai‘i this past week. On September 7, 2016, at 2:03 p.m., HST, a magnitude-2.7 earthquake occurred 1.6 km (1.0 mi) southwest of Kīlauea's summit at a depth of 1.1 km (0.7 mi). On September 6 at 4:25 a.m., a magnitude-4.0 earthquake occurred 3.6 km (2.2 mi) south-southeast of Mauna Loa's summit at a depth of 1.2 km (0.7 mi). On September 3 at 8:05 p.m., a magnitude-3.3 earthquake occurred 5.1 km (3.2 mi) southeast of Waimea at a depth of 14.9 km (9.3 mi). On September 1 at 12:11 a.m., a magnitude-3.7 earthquake occurred 25 km (15.5 mi) southeast of Waimea at a depth of 24.6 km (15.3 mi).
| 2019-12-10T16:19:12 |
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|
https://indico.fnal.gov/event/53004/contributions/244481/
|
# NuFact 2022: The 23rd International Workshop on Neutrinos from Accelerators
July 30, 2022 to August 6, 2022
Cliff Lodge
US/Mountain timezone
## Ability of DUNE to establish Deviation from Maximal $\theta_{23}$
Aug 5, 2022, 4:32 PM
22m
Ballroom 2
### Ballroom 2
Talk WG1: Neutrino Oscillation Physics
### Speaker
Masoom Singh (Utkal University and Institute of Physics, Bhubaneswar)
### Description
The present global analyses of the available oscillation data still allow $\sin^{2}\theta_{23}=0.5$ at 3$\sigma$ confidence level while, the current best-fit of $\theta_{23}$ strongly suggests $\sin^{2}\theta_{23} \neq 0.5$.Thus, it is imperative to question at what significance maximal 2-3 mixing can be ruled out. We study in great detail the performance of DUNE to establish the deviation from maximality in the 2-3 sector. We also discuss the impact of $\sin^{2}\theta_{23} - \Delta m^{2}_{31}$ degeneracy in establishing non-maximal $\theta_{23}$ and show how this degeneracy can be broken by exploiting the spectral shape information in $\nu$ and $\bar{\nu}$ disappearance events. We find that a 3$\sigma$ (5$\sigma$) determination of non-maximal $\theta_{23}$ is possible in DUNE with an exposure of 336 kt$\cdot$MW$\cdot$years if the true value of $\sin^2\theta_{23} \leq 0.465~(0.450)$ or $\sin^2\theta_{23} \geq 0.554~(0.572)$ for any value of true $\delta_{\mathrm{CP}}$ and true NMO. We also study the individual contributions from appearance and disappearance channels, the impact of systematic uncertainties and marginalization over oscillation parameters, the importance of spectral analysis, and the data from both $\nu$ and $\bar\nu$ runs, while analyzing DUNE's sensitivity to discover non-maximal $\theta_{23}$.
Attendance type Virtual presentation
### Primary authors
Masoom Singh (Utkal University and Institute of Physics, Bhubaneswar) Ritam Kundu (IOP, Bhubaneswar) Sanjib Kumar Agarwalla (Institute of Physics, Bhubaneswar) Dr Suprabh Prakash (The Institute of Mathematical Sciences, Chennai, India)
| 2023-02-05T17:34:54 |
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|
https://par.nsf.gov/biblio/10373403
|
Using 3D and 2D analysis for analyzing large-scale asymmetry in galaxy spin directions
Abstract
The nature of galaxy spin is still not fully known. Iye, Yagi, and Fukumoto (2021, AJ, 907, 123) applied a 3D analysis to a dataset of bright SDSS galaxies that was used in the past for photometric analysis. They showed that the distribution of spin directions of spiral galaxies is random, providing a dipole axis with low statistical significance of 0.29σ. However, to show random distribution, two decisions were made, each of which can lead to random distribution regardless of the real distribution of the spin direction of galaxies. The first decision was to limit the dataset arbitrarily to z < 0.1, which is a redshift range in which previous literature already showed that random distribution is expected. More importantly, while the 3D analysis requires the redshift of each galaxy, the analysis was done with the photometric redshift. If the asymmetry existed, its signal is expected to be an order of magnitude weaker than the error of the photometric redshift, and therefore a low statistical signal under these conditions is expected. When using the exact same data without limiting to zphot < 0.1 and without using the photometric redshift, the distribution of the spin directions in that dataset shows more »
Authors:
Publication Date:
NSF-PAR ID:
10373403
Journal Name:
Publications of the Astronomical Society of Japan
Volume:
74
Issue:
5
Page Range or eLocation-ID:
p. 1114-1130
ISSN:
0004-6264
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. Abstract Several recent observations using large data sets of galaxies showed non-random distribution of the spin directions of spiral galaxies, even when the galaxies are too far from each other to have gravitational interaction. Here, a data set of $\sim8.7\cdot10^3$ spiral galaxies imaged by Hubble Space Telescope ( HST ) is used to test and profile a possible asymmetry between galaxy spin directions. The asymmetry between galaxies with opposite spin directions is compared to the asymmetry of galaxies from the Sloan Digital Sky Survey. The two data sets contain different galaxies at different redshift ranges, and each data set was annotated using a different annotation method. The results show that both data sets show a similar asymmetry in the COSMOS field, which is covered by both telescopes. Fitting the asymmetry of the galaxies to cosine dependence shows a dipole axis with probabilities of $\sim2.8\sigma$ and $\sim7.38\sigma$ in HST and SDSS, respectively. The most likely dipole axis identified in the HST galaxies is at $(\alpha=78^{\rm o},\delta=47^{\rm o})$ and is well within the $1\sigma$ error range compared to the location of the most likely dipole axis in the SDSS galaxies with $z>0.15$ , identified at $(\alpha=71^{\rm o},\delta=61^{\rm o})$ .
2. Observations of non-random distribution of galaxies with opposite spin directions have recently attracted considerable attention. Here, a method for identifying cosine-dependence in a dataset of galaxies annotated by their spin directions is described in the light of different aspects that can impact the statistical analysis of the data. These aspects include the presence of duplicate objects in a dataset, errors in the galaxy annotation process, and non-random distribution of the asymmetry that does not necessarily form a dipole or quadrupole axes. The results show that duplicate objects in the dataset can artificially increase the likelihood of cosine dependence detected in the data, but a very high number of duplicate objects is required to lead to a false detection of an axis. Inaccuracy in galaxy annotations has relatively minor impact on the identification of cosine dependence when the error is randomly distributed between clockwise and counterclockwise galaxies. However, when the error is not random, even a small bias of 1% leads to a statistically significant cosine dependence that peaks at the celestial pole. Experiments with artificial datasets in which the distribution was not random showed strong cosine dependence even when the data did not form a full dipole axis alignment. Themore »
3. ABSTRACT
The DESI Legacy Survey is a digital sky survey with a large footprint compared to other Earth-based surveys, covering both the Northern and Southern hemispheres. This paper shows the distribution of the spin directions of spiral galaxies imaged by DESI Legacy Survey. A
simple analysis of dividing nearly 1.3 × 106 spiral galaxies into two hemispheres shows a higher number of galaxies spinning counterclockwise in the Northern hemisphere, and a higher number of galaxies spinning clockwise in the Southern hemisphere. That distribution is consistent with previous observations, but uses a far larger number of galaxies and a larger footprint. The larger footprint allows a comprehensive analysis without the need to fit the distribution into an a priori model, making this study different from all previous analyses of this kind. Fitting the spin directions of the galaxies to cosine dependence shows a dipole axis alignment with probability of P < 10−5. The analysis is done with a trivial selection of the galaxies, as well as simple explainable annotation algorithm that does not make use of any form of machine learning, deep learning, or pattern recognition. While further work will be required, these results are aligned with previous studies suggesting themore »
4. ABSTRACT
Knowing the redshift of galaxies is one of the first requirements of many cosmological experiments, and as it is impossible to perform spectroscopy for every galaxy being observed, photometric redshift (photo-z) estimations are still of particular interest. Here, we investigate different deep learning methods for obtaining photo-z estimates directly from images, comparing these with ‘traditional’ machine learning algorithms which make use of magnitudes retrieved through photometry. As well as testing a convolutional neural network (CNN) and inception-module CNN, we introduce a novel mixed-input model that allows for both images and magnitude data to be used in the same model as a way of further improving the estimated redshifts. We also perform benchmarking as a way of demonstrating the performance and scalability of the different algorithms. The data used in the study comes entirely from the Sloan Digital Sky Survey (SDSS) from which 1 million galaxies were used, each having 5-filtre (ugriz) images with complete photometry and a spectroscopic redshift which was taken as the ground truth. The mixed-input inception CNN achieved a mean squared error (MSE) =0.009, which was a significant improvement ($30{{\ \rm per\ cent}}$) over the traditional random forest (RF), and the model performed even better atmore »
5. ABSTRACT
Luminous red galaxies, or LRGs, are representative of the most massive galaxies and were originally selected in the Sloan Digital Sky Survey as good tracers of large-scale structure. They are dominated by by uniformly old stellar populations, have low star formation rates, early type morphologies, and little cold gas. Despite having old stellar populations and little in situ star formation, studies have shown that they have grown their stellar mass since z = 1, implying that they grow predominantly via the accretion of satellites. Tests of this picture have been limited because of the lack of deep imaging data sets that both covers a large enough area of the sky to contain substantial numbers of LRGs and that also is deep enough to detect faint satellites. We use the 25 deg2 Early Data Release (EDR) of the DESI Legacy Imaging Surveys to characterize the satellite galaxy population of LRGs out to z = 0.65. The DESI Legacy Imaging Surveys are comprised of grz imaging to 2–2.5 mag deeper than SDSS and with better image quality. We use a new statistical background technique to identify excess populations of putative satellite galaxies around 1823 LRGs at 0.2 < z < 0.65. In three redshift and luminositymore »
| 2023-03-28T12:59:06 |
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|
http://dlmf.nist.gov/1.4
|
# §1.4 Calculus of One Variable
## §1.4(i) Monotonicity
If for every pair , in an interval such that , then is nondecreasing on . If the sign is replaced by , then is increasing (also called strictly increasing) on . Similarly for nonincreasing and decreasing (strictly decreasing) functions. Each of the preceding four cases is classified as monotonic; sometimes strictly monotonic is used for the strictly increasing or strictly decreasing cases.
## §1.4(ii) Continuity
A function is continuous on the right (or from above) at if
1.4.1
that is, for every arbitrarily small positive constant there exists () such that
1.4.2
for all such that . Similarly, it is continuous on the left (or from below) at if
1.4.3
And is continuous at when both (1.4.1) and (1.4.3) apply.
If is continuous at each point , then is continuous on the interval and we write . If also is continuous on the right at , and continuous on the left at , then is continuous on the interval , and we write .
A removable singularity of at occurs when but is undefined. For example, with .
A simple discontinuity of at occurs when and exist, but . If is continuous on an interval save for a finite number of simple discontinuities, then is piecewise (or sectionally) continuous on . For an example, see Figure 1.4.1
Figure 1.4.1: Piecewise continuous function on .
## §1.4(iii) Derivatives
The derivative of is defined by
1.4.4
When this limit exists is differentiable at .
1.4.5
1.4.6
1.4.7
### ¶ Higher Derivatives
If exists and is continuous on an interval , then we write . When , is continuously differentiable on . When is unbounded, is infinitely differentiable on and we write .
For ,
1.4.10
### ¶ Maxima and Minima
A necessary condition that a differentiable function has a local maximum (minimum) at , that is, , () in a neighborhood () of , is .
### ¶ Mean Value Theorem
If is continuous on and differentiable on , then there exists a point such that
1.4.11
If () () for all , then is nondecreasing (nonincreasing) (constant) on .
1.4.12
### ¶ Faà Di Bruno’s Formula
where the sum is over all nonnegative integers that satisfy , and .
### ¶ L’Hôpital’s Rule
If
1.4.14
then
1.4.15
when the last limit exists.
## §1.4(iv) Indefinite Integrals
If , then , where is a constant.
### ¶ Integration by Parts
See §§4.10, 4.26(ii), 4.26(iv), 4.40(ii), and 4.40(iv) for indefinite integrals involving the elementary functions.
For extensive tables of integrals, see Apelblat (1983), Bierens de Haan (1867), Gradshteyn and Ryzhik (2000), Gröbner and Hofreiter (1949, 1950), and Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).
## §1.4(v) Definite Integrals
Suppose is defined on . Let , and denote any point in , . Then
as . Continuity, or piecewise continuity, of on is sufficient for the limit to exist.
1.4.19
and constants.
1.4.20
1.4.21
### ¶ Infinite Integrals
1.4.22
Similarly for . Next, if , then
1.4.23
Similarly when .
When the limits in (1.4.22) and (1.4.23) exist, the integrals are said to be convergent. If the limits exist with replaced by , then the integrals are absolutely convergent. Absolute convergence also implies convergence.
### ¶ Cauchy Principal Values
Let and assume that and exist when , but not necessarily when . Then we define
1.4.24
when this limit exists.
Similarly, assume that exists for all finite values of (), but not necessarily when . Then we define
when this limit exists.
### ¶ Fundamental Theorem of Calculus
For with continuous,
1.4.26
### ¶ Change of Variables
If is continuous or piecewise continuous, then
1.4.28
### ¶ First Mean Value Theorem
For continuous and and integrable on , there exists , such that
1.4.29
### ¶ Second Mean Value Theorem
For monotonic and integrable on , there exists , such that
1.4.30
### ¶ Repeated Integrals
If is continuous or piecewise continuous on , then
### ¶ Square-Integrable Functions
A function is square-integrable if
1.4.32
### ¶ Functions of Bounded Variation
With , the total variation of on a finite or infinite interval is
1.4.33
where the supremum is over all sets of points in the closure of , that is, with added when they are finite. If , then is of bounded variation on . In this case, and are nondecreasing bounded functions and .
If is continuous on the closure of and is continuous on , then
1.4.34
whenever this integral exists.
Lastly, whether or not the real numbers and satisfy , and whether or not they are finite, we define by (1.4.34) whenever this integral exists. This definition also applies when is a complex function of the real variable . For further information on total variation see Olver (1997b, pp. 27–29).
If , then
1.4.35
1.4.36,
and
## §1.4(vii) Maxima and Minima
If is twice-differentiable, and if also and (), then is a local maximum (minimum) (§1.4(iii)) of . The overall maximum (minimum) of on will either be at a local maximum (minimum) or at one of the end points or .
## §1.4(viii) Convex Functions
A function is convex on if
1.4.38
for any , and . See Figure 1.4.2. A similar definition applies to closed intervals .
If is twice differentiable, then is convex iff on . A continuously differentiable function is convex iff the curve does not lie below its tangent at any point.
Figure 1.4.2: Convex function . , , , .
| 2013-12-10T15:47:58 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S017NOS&home=sumtabB
|
# LIMIT ON ${{\boldsymbol n}}{{\boldsymbol n}^{\,'}}$ OSCILLATIONS INSPIRE search
Lee and Yang (LEE 1956 ) proposed the existence of mirror world in an attempt to restore global parity symmetry. A possible candidate for dark matter. Limits depend on assumptions about fields ${{\mathit B}}$ and ${{\mathit B}^{\,'}}$. See the papers for details. See BEREZHIANI 2018 for a recent discussion.
VALUE (s) CL% DOCUMENT ID TECN COMMENT
$\bf{> 448}$ 90
2009 A
CNTR Assumes ${{\mathit B}^{\,'}}$ $<$ 100 nT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$>17$ 95 1
2018
CNTR UCN, scan of ${{\mathit B}}$ field
$> 12$ 95 2
2009 A
CNTR UCN, scan 0${}\leq{}{{\mathit B}}{}\leq{}$12.5 $\mu$T
$> 414$ 90
2008
CNTR UCN, ${{\mathit B}}$ field on $\&$ off
$> 103$ 95
2007
CNTR UCN, ${{\mathit B}}$ field on $\&$ off
1 The ${{\mathit B}}$ field was set to (0.09, 0.12, 0.21) G. Limits on oscillation time are valid for any mirror field ${{\mathit B}^{\,'}}$ in ($0.08 - 0.17$) G, and for aligned fields ${{\mathit B}}$ and ${{\mathit B}^{\,'}}$. For larger values of ${{\mathit B}^{\,'}}$, the limits are significantly reduced.
2 Losses of neutrons due to oscillations to mirror neutrons would be maximal when the magnetic fields ${{\mathit B}}$ and ${{\mathit B}^{\,'}}$ in the two worlds were equal. Hence the scan over ${{\mathit B}}$ by ALTAREV 2009A: the limit applies for any ${{\mathit B}^{\,'}}$ over the given range. At ${{\mathit B}^{\,'}}$ = 0, the limit is 141 s (95$\%$ CL).
References:
BEREZHIANI 2018
EPJ C78 717 New experimental limits on neutron - mirror neutron oscillations in the presence of mirror magnetic field
ALTAREV 2009A
PR D80 032003 Neutron to Mirror-Neutron Oscillations in the Presence of Mirror Magnetic Fields
SEREBROV 2009A
NIM A611 137 Search for neutronmirror neutron oscillations in a laboratory experiment with ultracold neutrons
SEREBROV 2008
PL B663 181 Experimental Search for Neutron$−$Mirror Neutron Oscillations using Storage of Ultracold Neutrons
BAN 2007
PRL 99 161603 Direct Experimental Limit on Neutron$−$Mirror-Neutron Oscillations
| 2019-06-19T20:56:12 |
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|
https://par.nsf.gov/biblio/10362907-role-plasma-instabilities-relativistic-radiation-mediated-shocks-stability-analysis-particle-cell-simulations
|
The role of plasma instabilities in relativistic radiation-mediated shocks: stability analysis and particle-in-cell simulations
ABSTRACT
Relativistic radiation-mediated shocks are likely formed in prodigious cosmic explosions. The structure and emission of such shocks are regulated by copious production of electron–positron pairs inside the shock-transition layer. It has been pointed out recently that substantial abundance of positrons inside the shock leads to a velocity separation of the different plasma constituents, which is expected to induce a rapid growth of plasma instabilities. In this paper, we study the hierarchy of plasma microinstabilities growing in an electron-ion plasma loaded with pairs and subject to a radiation force. Linear stability analysis indicates that such a system is unstable to the growth of various plasma modes which ultimately become dominated by a current filamentation instability driven by the relative drift between the ions and the pairs. These results are validated by particle-in-cell simulations that further probe the non-linear regime of the instabilities, and the pair-ion coupling in the microturbulent electromagnetic field. Based on this analysis, we derive a reduced-transport equation for the particles via pitch-angle scattering in the microturbulence and demonstrate that it can couple the different species and lead to non-adiabatic compression via a Joule-like heating. The heating of the pairs and, conceivably, the formation of non-thermal distributions, arising from more »
Authors:
; ; ; ; ;
Publication Date:
NSF-PAR ID:
10362907
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
511
Issue:
2
Page Range or eLocation-ID:
p. 3034-3045
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. ABSTRACT
The radiation drag in photon-rich environments of cosmic explosions can seed kinetic instabilities by inducing velocity spreads between relativistically streaming plasma components. Such microturbulence is likely imprinted on the breakout signals of radiation-mediated shocks. However, large-scale, transverse magnetic fields in the deceleration region of the shock transition can suppress the dominant kinetic instabilities by preventing the development of velocity separations between electron–positron pairs and a heavy ion species. We use a 1D five-fluid radiative transfer code to generate self-consistent profiles of the radiation drag force and plasma composition in the deceleration region. For increasing magnetization, our models predict rapidly growing pair multiplicities and a substantial radiative drag developing self-similarly throughout the deceleration region. We extract the critical magnetization parameter σc, determining the limiting magnetic field strength at which a three-species plasma can develop kinetic instabilities before reaching the isotropized downstream. For a relativistic, single ion plasma drifting with γu = 10 in the upstream of a relativistic radiation-mediated shock, we find the threshold σc ≈ 10−7 for the onset of microturbulence. Suppression of plasma instabilities in the case of multi-ion composition would likely require much higher values of σc. Identifying high-energy signatures of microturbulence in shock breakout signals and combiningmore »
2. Abstract
Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves, upper/lower hybrid waves, and Langmuir waves) have been observed in the upstream, downstream, and ramp regions of the collisionless interplanetary (IP) shocks. These waves may appear as short-duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies of ∼1–10 kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and require a new modeling effort. Thus, this paper is dedicated to bridging this gap in understanding. In this paper, we model the linear IAWs inside the shock ramp by devising a novel linearization method for the two-fluid magnetohydrodynamic equations with spatially dependent shock parameters. It is found that, for parallel propagating waves, the linear dispersion relation leads to a finite growth rate, which is dependent on the shock density compression ratio, as Wind data suggest. Further analysis reveals that the wave frequency grows towards the downstream region within the shock ramp, and the wave growth rate is independent of the electron-to-ion temperature ratio, as Magnetospheric Multiscale (MMS) in-situ measurements suggest, and is uniform within themore »
3. Abstract
The formation, development, and impact of slow shocks in the upstream regions of reconnecting current layers are explored. Slow shocks have been documented in the upstream regions of magnetohydrodynamic (MHD) simulations of magnetic reconnection as well as in similar simulations with thekglobalkinetic macroscale simulation model. They are therefore a candidate mechanism for preheating the plasma that is injected into the current layers that facilitate magnetic energy release in solar flares. Of particular interest is their potential role in producing the hot thermal component of electrons in flares. During multi-island reconnection, the formation and merging of flux ropes in the reconnecting current layer drives plasma flows and pressure disturbances in the upstream region. These pressure disturbances steepen into slow shocks that propagate along the reconnecting component of the magnetic field and satisfy the expected Rankine–Hugoniot jump conditions. Plasma heating arises from both compression across the shock and the parallel electric field that develops to maintain charge neutrality in a kinetic system. Shocks are weaker at lower plasmaβ, where shock steepening is slow. While these upstream slow shocks are intrinsic to the dynamics of multi-island reconnection, their contribution to electron heating remains relatively minor compared with that from Fermi reflection andmore »
4. ABSTRACT
We present general relativistic radiation magnetohydrodynamics (GRRMHD) simulations of super-Eddington accretion flows around supermassive black holes (SMBHs), which may apply to tidal disruption events (TDEs). We perform long duration ($t\ge 81,200\, GM/c^3$) simulations that achieve mass accretion rates ≳11 times the Eddington rate and produce thermal synchrotron spectra and images of their jets. Gas flowing beyond the funnel wall expands conically and drives a strong shock at the jet head while variable mass ejection and recollimation, along the jet axis, results in internal shocks and dissipation. Assuming the ion temperature (Ti) and electron temperature (Te) in the plasma are identical, the radio/submillimetre spectra peak at >100 GHz and the luminosity increases with BH spin, exceeding $\sim 10^{41} \, \rm {erg\, s^{-1}}$ in the brightest models. The emission is extremely sensitive to Ti/Te as some models show an order-of-magnitude decrease in the peak frequency and up to four orders-of-magnitude decline in their radio/submillimetre luminosity as Ti/Te approaches 20. Assuming a maximum VLBI baseline distance of 10 Gλ, 230 GHz images of Ti/Te = 1 models shows that the jet head may be bright enough for its motion to be captured with the EHT (ngEHT) at D ≲ 110 (180) Mpc at the 5σ significance level.more »
5. Abstract
Revealing the formation, dynamics, and contribution to plasma heating of magnetic field fluctuations in the solar wind is an important task for heliospheric physics and for a general plasma turbulence theory. Spacecraft observations in the solar wind are limited to spatially localized measurements, so that the evolution of fluctuation properties with solar wind propagation is mostly studied via statistical analyses of data sets collected by different spacecraft at various radial distances from the Sun. In this study we investigate the evolution of turbulence in the Earth’s magnetosheath, a plasma system sharing many properties with the solar wind. The near-Earth space environment is being explored by multiple spacecraft missions, which may allow us to trace the evolution of magnetosheath fluctuations with simultaneous measurements at different distances from their origin, the Earth’s bow shock. We compare ARTEMIS and Magnetospheric Multiscale (MMS) Mission measurements in the Earth magnetosheath and Parker Solar Probe measurements of the solar wind at different radial distances. The comparison is supported by three numerical simulations of the magnetosheath magnetic and plasma fluctuations: global hybrid simulation resolving ion kinetic and including effects of Earth’s dipole field and realistic bow shock, hybrid and Hall-MHD simulations in expanding boxes that mimicmore »
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## Bhattacharya, Rabi N.
Compute Distance To:
Author ID: bhattacharya.rabi-n Published as: Bhattacharya, Rabi; Bhattacharya, R. N.; Bhattacharya, Rabi N. Homepage: http://math.arizona.edu/~rabi/ External Links: MGP · Wikidata · ResearchGate · GND · IdRef
Documents Indexed: 112 Publications since 1957, including 16 Books Biographic References: 1 Publication Co-Authors: 35 Co-Authors with 78 Joint Publications 800 Co-Co-Authors
all top 5
### Co-Authors
30 single-authored 14 Majumdar, Mukul K. 13 Waymire, Edward C. 8 Lin, Lizhen 7 Patrangenaru, Victor 5 Ghosh, Jayanta Kumar 4 Kumar Gupta, Vijay 4 Ranga Rao, R. 3 Bhattacharya, Abhishek 3 Denker, Manfred 3 Lee, Chanho 3 Lee, Oesook 3 Thomann, Enrique A. 2 Bhattacharjee, Manish C. 2 Chen, Larry 2 Götze, Friedrich 2 Guenther, Ronald B. 2 Oliver, Rachel 2 Orum, Chris 2 Ossiander, Mina E. 1 Almudevar, Anthony 1 Athreya, Krishna Balasundaram 1 Bandulasiri, Ananda 1 Basak, Gopal Krishna 1 Bhattacharyya, Dilip K. 1 Chan, Ngai Hang 1 Dobson, Scott 1 Goswami, Alok 1 Hashimzade, Nigar 1 Kong, Maiying 1 Piegorsch, Walter W. 1 Puri, Madan Lal 1 Qumsiyeh, Maher B. 1 Sastri, Chelluri C. A. 1 Walker, Homer F. 1 Wasielak, Aramian
all top 5
### Serials
8 The Annals of Probability 7 Journal of Statistical Planning and Inference 6 Journal of Multivariate Analysis 5 The Annals of Statistics 4 Sankhyā. Series A. Methods and Techniques 4 Statistics & Probability Letters 3 SIAM Journal on Applied Mathematics 3 Wiley Series in Probability and Mathematical Statistics 2 AIAA Journal 2 Proceedings of the American Mathematical Society 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Journal of Theoretical Probability 2 The Annals of Applied Probability 2 Computational Statistics and Data Analysis 2 Economic Theory 2 Bernoulli 2 Review of Economic Design 2 Proceedings of the National Institute of Sciences of India, Part A 2 Classics in Applied Mathematics 2 Sankhyā. Series A 2 Sankhyā. Series B 2 Institute of Mathematical Statistics Monographs 2 Universitext 1 Journal of Mathematical and Physical Sciences 1 Scandinavian Journal of Statistics 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Theory of Probability and its Applications 1 Journal of Applied Probability 1 Journal of Economic Theory 1 The Mathematics Student 1 Transactions of the American Mathematical Society 1 SIAM Review 1 Stochastic Processes and their Applications 1 Probability in the Engineering and Informational Sciences 1 Stochastics and Dynamics 1 Bulletin of the American Mathematical Society 1 DMV Seminar 1 Graduate Texts in Mathematics 1 International Journal of Economic Theory 1 Annals of Mathematical Statistics 1 Springer Texts in Statistics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Contemporary Mathematicians
all top 5
### Fields
74 Probability theory and stochastic processes (60-XX) 34 Statistics (62-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Approximations and expansions (41-XX) 5 Fluid mechanics (76-XX) 3 Partial differential equations (35-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Numerical analysis (65-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX)
### Citations contained in zbMATH Open
89 Publications have been cited 1,696 times in 1,313 Documents Cited by Year
Normal approximation and asymptotic expansions. Zbl 0331.41023
Bhattacharya, R. N.; Ranga Rao, R.
1976
On the validity of the formal Edgeworth expansion. Zbl 0396.62010
Bhattacharya, R. N.; Ghosh, J. K.
1978
Large sample theory of intrinsic and extrinsic sample means on manifolds. I. Zbl 1020.62026
Bhattacharya, Rabi; Patrangenaru, Vic
2003
On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Zbl 0468.60034
Bhattacharya, R. N.
1982
Large sample theory of intrinsic and extrinsic sample means on manifolds. II. Zbl 1072.62033
Bhattacharya, Rabi; Patrangenaru, Vic
2005
Stochastic processes with applications. Zbl 0744.60032
Bhattacharya, Rabi N.; Waymire, Edward C.
1990
Normal approximation and asymptotic expansions. (Reprint of the 1976 orig. publ. by Wiley, New York. Repr. ed. with corrections & supplemental material). Zbl 0657.41001
Bhattacharya, R. N.; Ranga Rao, R.
1986
Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Zbl 0386.60056
Bhattacharya, R. N.
1978
The Hurst effect under trends. Zbl 0526.60027
Bhattacharya, R. N.; Gupta, Vijay K.; Waymire, Ed
1983
Stability in distribution for a class of singular diffusions. Zbl 0749.60073
Basak, Gopal K.; Bhattacharya, Rabi N.
1992
Normal approximation and asymptotic expansions. Updated republication of the 1986 reprint published by Robert E. Krieger Publ. Co. Zbl 1222.41002
Bhattacharya, R. N.; Ranga Rao, R.
2010
Random dynamical systems. Theory and applications. Zbl 1114.37027
Bhattacharya, Rabi; Majumdar, Mukul
2007
On geometric ergodicity of nonlinear autoregressive models. Zbl 0830.60059
Bhattacharya, Rabi; Lee, Chanho
1995
Nonparametric inference on manifolds. With applications to shape spaces. Zbl 1273.62014
Bhattacharya, Abhishek; Bhattacharya, Rabi
2012
Asymptotics of a class of Markov processes which are not in general irreducible. Zbl 0652.60028
Bhattacharya, Rabi N.; Lee, Oesook
1988
A central limit theorem for diffusions with periodic coefficients. Zbl 0575.60075
Bhattacharya, Rabi
1985
A basic course in probability theory. Zbl 1138.60001
Bhattacharya, Rabi N.; Waymire, Edward C.
2007
Nonparametic estimation of location and dispersion on Riemannian manifolds. Zbl 1031.62024
Bhattacharya, Rabi; Patrangenaru, Vic
2002
Stochastic processes with applications. Reprint of the 1990 original ed. Zbl 1171.60333
Bhattacharya, Rabi N.; Waymire, Edward C.
2009
Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces. Zbl 1353.60019
Bhattacharya, Rabi; Lin, Lizhen
2017
Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations. Zbl 1031.35115
Bhattacharya, Rabi N.; Chen, Larry; Dobson, Scott; Guenther, Ronald B.; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward C.
2003
Speed of convergence of the n-fold convolution of a probability measure on a compact group. Zbl 0247.60008
Bhattacharya, R. N.
1972
Refinements of the multidimensional central limit theorem and applications. Zbl 0361.60001
Bhattacharya, R. N.
1977
Asymptotic statistics. Zbl 0706.62049
Bhattacharya, Rabi; Denker, Manfred
1990
Second order and $$L^ p$$-comparisons between the boostrap and empirical Edgeworth expansion methodologies. Zbl 0669.62002
Bhattacharya, Rabi; Qumsiyeh, Maher
1989
Ergodicity of nonlinear first order autoregressive models. Zbl 0815.60059
Bhattacharya, Rabi N.; Lee, Chanho
1995
Controlled semi-Markov models - the discounted case. Zbl 0673.93089
Bhattacharya, Rabi N.; Majumdar, Mukul
1989
Controlled semi-Markov models under long-run average rewards. Zbl 0683.49003
Bhattacharya, Rabi N.; Majumdar, Mukul
1989
Asymptotics of solute dispersion in periodic porous media. Zbl 0664.60079
Bhattacharya, R. N.; Gupta, V. K.; Walker, H. F.
1989
Stochastic processes with applications. Zbl 0715.60046
Bhattacharya, Rabi N.; Waymire, Edward C.
1990
Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging. Zbl 1171.62028
Bandulasiri, Ananda; Bhattacharya, Rabi N.; Patrangenaru, Vic
2009
Statistics on Riemannian manifolds: asymptotic distribution and curvature. Zbl 1274.62337
Bhattacharya, Abhishek; Bhattacharya, Rabi
2008
Statistics on manifolds and landmarks based image analysis: a nonparametric theory with applications. Zbl 1278.62068
Bhattacharya, Rabi; Patrangenaru, Vic
2014
Random iterations of two quadratic maps. Zbl 0786.60095
Bhattacharya, Rabi N.; Rao, B. V.
1993
A class of $$U$$-statistics and asymptotic normality of the number of $$k$$- clusters. Zbl 0764.60025
Bhattacharya, Rabi N.; Ghosh, Jayanta K.
1992
On a class of stable random dynamical systems: Theory and applications. Zbl 0987.60083
Bhattacharya, Rabi; Majumdar, Mukul
2001
Rates of weak convergence for the multidimensional central limit theorem. Zbl 0216.46302
Bhattacharya, R. N.
1970
Recurrence and ergodicity of diffusions. Zbl 0499.60084
Bhattacharya, R. N.; Ramasubramanian, S.
1982
Some recent results on Cramér-Edgeworth expansions with applications. Zbl 0588.62029
Bhattacharya, R. N.
1985
Consistency and asymptotic normality of the estimated effective doses in bioassay. Zbl 1104.62117
Bhattacharya, Rabi; Kong, Maiying
2007
Stochastic equivalence of convex ordered distributions and applications. Zbl 0955.60019
Bhattacharjee, M. C.; Bhattacharya, R. N.
2000
A course in mathematical statistics and large sample theory. Zbl 1358.62002
Bhattacharya, Rabi; Lin, Lizhen; Patrangenaru, Victor
2016
On moment conditions for valid formal Edgeworth expansions. Zbl 0672.62030
Bhattacharya, Rabi N.; Ghosh, J. K.
1988
On a theorem of Dubins and Freedman. Zbl 0961.60064
Bhattacharya, Rabi; Majumdar, Mukul
1999
Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media. Zbl 0956.60080
Bhattacharya, Rabi
1999
Erratum to: On geometric ergodicity of nonlinear autoregressive models. Zbl 0932.60076
Bhattacharya, Rabi; Lee, Chanho
1999
Correction to: Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Zbl 0445.60063
Bhattacharya, R. N.
1980
Normal approximation and asymptotic expansions. (Approksimatsiya normal’nym raspredeleniem i asimptoticheskie razlozheniya). Transl. from the English. Zbl 0514.41002
Bhattacharya, R. N.; Ranga Rao, R.
1982
Random dynamical systems: a review. Zbl 1175.91103
Bhattacharya, Rabi; Majumdar, Mukul
2004
Semi-Markov cascade representations of local solutions to 3-D incompressible Navier-Stokes. Zbl 1104.35027
Bhattacharya, Rabi; Chen, Larry; Guenther, Ronald B.; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward C.
2005
Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales. Zbl 0962.60045
Bhattacharya, Rabi; Denker, Manfred; Goswami, Alok
1999
On the Taylor-Aris theory of solute transport in a capillary. Zbl 0537.76078
Bhattacharya, R. N.; Gupta, Vijay K.
1984
A basic course in probability theory. 2nd edition. Zbl 1357.60001
Bhattacharya, Rabi; Waymire, Edward C.
2016
A note on the distribution of integrals of geometric Brownian motion. Zbl 0990.60083
Bhattacharya, Rabi; Thomann, Enrique; Waymire, Edward
2001
Limit theorems for monotone Markov processes. Zbl 1209.60016
Bhattacharya, Rabi; Majumdar, Mukul; Hashimzade, Nigar
2010
Ergodicity and central limit theorems for a class of Markov processes. Zbl 0658.60094
Bhattacharya, Rabi N.; Lee, Oesook
1988
Berry-Esseen bounds for the multi-dimensional central limit theorem. Zbl 0179.48102
Bhattacharya, R. N.
1968
Recent results on refinements of the central limit theorem. Zbl 0266.60010
Bhattacharya, R. N.
1972
On errors of normal approximation. Zbl 0319.60013
Bhattacharya, R. N.
1975
Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis. Zbl 1271.62062
Bhattacharya, Rabi; Lin, Lizhen
2011
Stability in distribution of randomly perturbed quadratic maps as Markov processes. Zbl 1065.60090
Bhattacharya, Rabi; Majumdar, Mukul
2004
An approach to the existence of unique invariant probabilities for Markov processes. Zbl 1033.60078
Bhattacharya, R. N.; Waymire, E. C.
2002
Comparisons of chisquare, Edgeworth expansions and bootstrap approximations to the distribution of the frequency chisquare. Zbl 0885.62015
Bhattacharya, R. N.; Chan, N. H.
1996
On the order of magnitude of cumulants of von Mises functionals and related statistics. Zbl 0527.62025
Bhattacharya, R. N.; Puri, M. L.
1983
An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies. Zbl 1202.62145
Bhattacharya, Rabi; Lin, Lizhen
2010
On a statistical theory of solute transport in porous media. Zbl 0417.60080
Bhattacharya, R. N.; Gupta, V. K.
1979
Rates of weak convergence and asymptotic expansions for classical central limit theorems. Zbl 0224.60014
Bhattacharya, R. N.
1971
A nonparametric theory of statistics on manifolds. Zbl 1280.62057
Bhattacharya, Rabi
2013
Time-scales for Gaussian approximation and its breakdown under a hierarchy of periodic spatial heterogeneities. Zbl 0841.60065
Bhattacharya, Rabi N.; Götze, Friedrich
1995
Asymptotic behavior of several dimensional diffusions. Zbl 0464.60035
Bhattacharya, R. N.
1981
Correction to: On the validity of the formal Edgeworth expansion. Zbl 0465.62025
Bhattacharya, R. N.; Ghosh, J. K.
1980
Some aspects of Edgeworth expansions in statistics and probability. Zbl 0627.62019
Bhattacharya, R. N.
1987
Recent progress in the nonparametric estimation of monotone curves – with applications to bioassay and environmental risk assessment. Zbl 1468.62027
Bhattacharya, Rabi; Lin, Lizhen
2013
Problems of ruin and survival in economics: applications of limit theorems in probability. Zbl 1309.91074
Bhattacharya, Rabi; Majumdar, Mukul; Lin, Lizhen
2013
Random iterates of monotone maps. Zbl 1218.37069
Bhattacharya, Rabi; Majumdar, Mukul
2010
Estimating the probability mass of unobserved support in random sampling. Zbl 0963.62040
Almudevar, A.; Bhattacharya, R. N.; Sastri, C. C. A.
2000
Convergence to equilibrium of random dynamical systems generated by i.i.d. monotone maps, with applications to economics. Zbl 1069.37514
Bhattacharya, Rabi; Majumdar, Mukul
1999
On classical limit theorems for diffusions. Zbl 0586.60074
Bhattacharya, R. N.
1982
Nonparametric inference on manifolds. With applications to shape spaces. Reprint of the 2012 hardback ed. Zbl 1371.62001
Bhattacharya, Abhishek; Bhattacharya, Rabi
2015
On moment conditions for valid formal Edgeworth expansions. Zbl 0702.62013
Bhattacharya, Rabi N.; Ghosh, J. K.
1989
Random iteration of i. i. d. quadratic maps. Zbl 0969.60072
Athreya, K. B.; Bhattacharya, R. N.
2000
Iterated random maps and some classes of Markov processes. Zbl 0982.60070
Bhattacharya, Rabi; Waymire, Edward C.
2001
On characterizing the probability of survival in a large competitive economy. Zbl 1004.91053
Bhattacharya, Rabi N.; Majumdar, Mukul
2001
Markov processes and their applications. Zbl 1006.60068
Bhattacharya, Rabi
2001
Rates of weak convergence for the multidimensional central limit theorem. Zbl 0196.21103
Bhattacharya, R. N.
1970
Dynamical systems subject to random shocks: An introduction. Zbl 1175.91102
Bhattacharya, Rabi; Majumdar, Mukul
2004
On the central limit theorem for diffusions with almost periodic coefficients. Zbl 0648.60081
Bhattacharya, Rabi N.; Ramasubramanian, S.
1988
Ruin probabilities in models of resource management and insurance: a synthesis. Zbl 1398.91311
Bhattacharya, Rabi; Majumdar, Mukul
2015
Nonparametric analysis of non-Euclidean data on shapes and images. Zbl 1418.60014
Bhattacharya, Rabi; Oliver, Rachel
2019
Nonparametric analysis of non-Euclidean data on shapes and images. Zbl 1418.60014
Bhattacharya, Rabi; Oliver, Rachel
2019
Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces. Zbl 1353.60019
Bhattacharya, Rabi; Lin, Lizhen
2017
A course in mathematical statistics and large sample theory. Zbl 1358.62002
Bhattacharya, Rabi; Lin, Lizhen; Patrangenaru, Victor
2016
A basic course in probability theory. 2nd edition. Zbl 1357.60001
Bhattacharya, Rabi; Waymire, Edward C.
2016
Nonparametric inference on manifolds. With applications to shape spaces. Reprint of the 2012 hardback ed. Zbl 1371.62001
Bhattacharya, Abhishek; Bhattacharya, Rabi
2015
Ruin probabilities in models of resource management and insurance: a synthesis. Zbl 1398.91311
Bhattacharya, Rabi; Majumdar, Mukul
2015
Statistics on manifolds and landmarks based image analysis: a nonparametric theory with applications. Zbl 1278.62068
Bhattacharya, Rabi; Patrangenaru, Vic
2014
A nonparametric theory of statistics on manifolds. Zbl 1280.62057
Bhattacharya, Rabi
2013
Recent progress in the nonparametric estimation of monotone curves – with applications to bioassay and environmental risk assessment. Zbl 1468.62027
Bhattacharya, Rabi; Lin, Lizhen
2013
Problems of ruin and survival in economics: applications of limit theorems in probability. Zbl 1309.91074
Bhattacharya, Rabi; Majumdar, Mukul; Lin, Lizhen
2013
Nonparametric inference on manifolds. With applications to shape spaces. Zbl 1273.62014
Bhattacharya, Abhishek; Bhattacharya, Rabi
2012
Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis. Zbl 1271.62062
Bhattacharya, Rabi; Lin, Lizhen
2011
Normal approximation and asymptotic expansions. Updated republication of the 1986 reprint published by Robert E. Krieger Publ. Co. Zbl 1222.41002
Bhattacharya, R. N.; Ranga Rao, R.
2010
Limit theorems for monotone Markov processes. Zbl 1209.60016
Bhattacharya, Rabi; Majumdar, Mukul; Hashimzade, Nigar
2010
An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies. Zbl 1202.62145
Bhattacharya, Rabi; Lin, Lizhen
2010
Random iterates of monotone maps. Zbl 1218.37069
Bhattacharya, Rabi; Majumdar, Mukul
2010
Stochastic processes with applications. Reprint of the 1990 original ed. Zbl 1171.60333
Bhattacharya, Rabi N.; Waymire, Edward C.
2009
Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging. Zbl 1171.62028
Bandulasiri, Ananda; Bhattacharya, Rabi N.; Patrangenaru, Vic
2009
Statistics on Riemannian manifolds: asymptotic distribution and curvature. Zbl 1274.62337
Bhattacharya, Abhishek; Bhattacharya, Rabi
2008
Random dynamical systems. Theory and applications. Zbl 1114.37027
Bhattacharya, Rabi; Majumdar, Mukul
2007
A basic course in probability theory. Zbl 1138.60001
Bhattacharya, Rabi N.; Waymire, Edward C.
2007
Consistency and asymptotic normality of the estimated effective doses in bioassay. Zbl 1104.62117
Bhattacharya, Rabi; Kong, Maiying
2007
Large sample theory of intrinsic and extrinsic sample means on manifolds. II. Zbl 1072.62033
Bhattacharya, Rabi; Patrangenaru, Vic
2005
Semi-Markov cascade representations of local solutions to 3-D incompressible Navier-Stokes. Zbl 1104.35027
Bhattacharya, Rabi; Chen, Larry; Guenther, Ronald B.; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward C.
2005
Random dynamical systems: a review. Zbl 1175.91103
Bhattacharya, Rabi; Majumdar, Mukul
2004
Stability in distribution of randomly perturbed quadratic maps as Markov processes. Zbl 1065.60090
Bhattacharya, Rabi; Majumdar, Mukul
2004
Dynamical systems subject to random shocks: An introduction. Zbl 1175.91102
Bhattacharya, Rabi; Majumdar, Mukul
2004
Large sample theory of intrinsic and extrinsic sample means on manifolds. I. Zbl 1020.62026
Bhattacharya, Rabi; Patrangenaru, Vic
2003
Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations. Zbl 1031.35115
Bhattacharya, Rabi N.; Chen, Larry; Dobson, Scott; Guenther, Ronald B.; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward C.
2003
Nonparametic estimation of location and dispersion on Riemannian manifolds. Zbl 1031.62024
Bhattacharya, Rabi; Patrangenaru, Vic
2002
An approach to the existence of unique invariant probabilities for Markov processes. Zbl 1033.60078
Bhattacharya, R. N.; Waymire, E. C.
2002
On a class of stable random dynamical systems: Theory and applications. Zbl 0987.60083
Bhattacharya, Rabi; Majumdar, Mukul
2001
A note on the distribution of integrals of geometric Brownian motion. Zbl 0990.60083
Bhattacharya, Rabi; Thomann, Enrique; Waymire, Edward
2001
Iterated random maps and some classes of Markov processes. Zbl 0982.60070
Bhattacharya, Rabi; Waymire, Edward C.
2001
On characterizing the probability of survival in a large competitive economy. Zbl 1004.91053
Bhattacharya, Rabi N.; Majumdar, Mukul
2001
Markov processes and their applications. Zbl 1006.60068
Bhattacharya, Rabi
2001
Stochastic equivalence of convex ordered distributions and applications. Zbl 0955.60019
Bhattacharjee, M. C.; Bhattacharya, R. N.
2000
Estimating the probability mass of unobserved support in random sampling. Zbl 0963.62040
Almudevar, A.; Bhattacharya, R. N.; Sastri, C. C. A.
2000
Random iteration of i. i. d. quadratic maps. Zbl 0969.60072
Athreya, K. B.; Bhattacharya, R. N.
2000
On a theorem of Dubins and Freedman. Zbl 0961.60064
Bhattacharya, Rabi; Majumdar, Mukul
1999
Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media. Zbl 0956.60080
Bhattacharya, Rabi
1999
Erratum to: On geometric ergodicity of nonlinear autoregressive models. Zbl 0932.60076
Bhattacharya, Rabi; Lee, Chanho
1999
Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales. Zbl 0962.60045
Bhattacharya, Rabi; Denker, Manfred; Goswami, Alok
1999
Convergence to equilibrium of random dynamical systems generated by i.i.d. monotone maps, with applications to economics. Zbl 1069.37514
Bhattacharya, Rabi; Majumdar, Mukul
1999
Comparisons of chisquare, Edgeworth expansions and bootstrap approximations to the distribution of the frequency chisquare. Zbl 0885.62015
Bhattacharya, R. N.; Chan, N. H.
1996
On geometric ergodicity of nonlinear autoregressive models. Zbl 0830.60059
Bhattacharya, Rabi; Lee, Chanho
1995
Ergodicity of nonlinear first order autoregressive models. Zbl 0815.60059
Bhattacharya, Rabi N.; Lee, Chanho
1995
Time-scales for Gaussian approximation and its breakdown under a hierarchy of periodic spatial heterogeneities. Zbl 0841.60065
Bhattacharya, Rabi N.; Götze, Friedrich
1995
Random iterations of two quadratic maps. Zbl 0786.60095
Bhattacharya, Rabi N.; Rao, B. V.
1993
Stability in distribution for a class of singular diffusions. Zbl 0749.60073
Basak, Gopal K.; Bhattacharya, Rabi N.
1992
A class of $$U$$-statistics and asymptotic normality of the number of $$k$$- clusters. Zbl 0764.60025
Bhattacharya, Rabi N.; Ghosh, Jayanta K.
1992
Stochastic processes with applications. Zbl 0744.60032
Bhattacharya, Rabi N.; Waymire, Edward C.
1990
Asymptotic statistics. Zbl 0706.62049
Bhattacharya, Rabi; Denker, Manfred
1990
Stochastic processes with applications. Zbl 0715.60046
Bhattacharya, Rabi N.; Waymire, Edward C.
1990
Second order and $$L^ p$$-comparisons between the boostrap and empirical Edgeworth expansion methodologies. Zbl 0669.62002
Bhattacharya, Rabi; Qumsiyeh, Maher
1989
Controlled semi-Markov models - the discounted case. Zbl 0673.93089
Bhattacharya, Rabi N.; Majumdar, Mukul
1989
Controlled semi-Markov models under long-run average rewards. Zbl 0683.49003
Bhattacharya, Rabi N.; Majumdar, Mukul
1989
Asymptotics of solute dispersion in periodic porous media. Zbl 0664.60079
Bhattacharya, R. N.; Gupta, V. K.; Walker, H. F.
1989
On moment conditions for valid formal Edgeworth expansions. Zbl 0702.62013
Bhattacharya, Rabi N.; Ghosh, J. K.
1989
Asymptotics of a class of Markov processes which are not in general irreducible. Zbl 0652.60028
Bhattacharya, Rabi N.; Lee, Oesook
1988
On moment conditions for valid formal Edgeworth expansions. Zbl 0672.62030
Bhattacharya, Rabi N.; Ghosh, J. K.
1988
Ergodicity and central limit theorems for a class of Markov processes. Zbl 0658.60094
Bhattacharya, Rabi N.; Lee, Oesook
1988
On the central limit theorem for diffusions with almost periodic coefficients. Zbl 0648.60081
Bhattacharya, Rabi N.; Ramasubramanian, S.
1988
Some aspects of Edgeworth expansions in statistics and probability. Zbl 0627.62019
Bhattacharya, R. N.
1987
Normal approximation and asymptotic expansions. (Reprint of the 1976 orig. publ. by Wiley, New York. Repr. ed. with corrections & supplemental material). Zbl 0657.41001
Bhattacharya, R. N.; Ranga Rao, R.
1986
A central limit theorem for diffusions with periodic coefficients. Zbl 0575.60075
Bhattacharya, Rabi
1985
Some recent results on Cramér-Edgeworth expansions with applications. Zbl 0588.62029
Bhattacharya, R. N.
1985
On the Taylor-Aris theory of solute transport in a capillary. Zbl 0537.76078
Bhattacharya, R. N.; Gupta, Vijay K.
1984
The Hurst effect under trends. Zbl 0526.60027
Bhattacharya, R. N.; Gupta, Vijay K.; Waymire, Ed
1983
On the order of magnitude of cumulants of von Mises functionals and related statistics. Zbl 0527.62025
Bhattacharya, R. N.; Puri, M. L.
1983
On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Zbl 0468.60034
Bhattacharya, R. N.
1982
Recurrence and ergodicity of diffusions. Zbl 0499.60084
Bhattacharya, R. N.; Ramasubramanian, S.
1982
Normal approximation and asymptotic expansions. (Approksimatsiya normal’nym raspredeleniem i asimptoticheskie razlozheniya). Transl. from the English. Zbl 0514.41002
Bhattacharya, R. N.; Ranga Rao, R.
1982
On classical limit theorems for diffusions. Zbl 0586.60074
Bhattacharya, R. N.
1982
Asymptotic behavior of several dimensional diffusions. Zbl 0464.60035
Bhattacharya, R. N.
1981
Correction to: Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Zbl 0445.60063
Bhattacharya, R. N.
1980
Correction to: On the validity of the formal Edgeworth expansion. Zbl 0465.62025
Bhattacharya, R. N.; Ghosh, J. K.
1980
On a statistical theory of solute transport in porous media. Zbl 0417.60080
Bhattacharya, R. N.; Gupta, V. K.
1979
On the validity of the formal Edgeworth expansion. Zbl 0396.62010
Bhattacharya, R. N.; Ghosh, J. K.
1978
Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Zbl 0386.60056
Bhattacharya, R. N.
1978
Refinements of the multidimensional central limit theorem and applications. Zbl 0361.60001
Bhattacharya, R. N.
1977
Normal approximation and asymptotic expansions. Zbl 0331.41023
Bhattacharya, R. N.; Ranga Rao, R.
1976
On errors of normal approximation. Zbl 0319.60013
Bhattacharya, R. N.
1975
Speed of convergence of the n-fold convolution of a probability measure on a compact group. Zbl 0247.60008
Bhattacharya, R. N.
1972
Recent results on refinements of the central limit theorem. Zbl 0266.60010
Bhattacharya, R. N.
1972
Rates of weak convergence and asymptotic expansions for classical central limit theorems. Zbl 0224.60014
Bhattacharya, R. N.
1971
Rates of weak convergence for the multidimensional central limit theorem. Zbl 0216.46302
Bhattacharya, R. N.
1970
Rates of weak convergence for the multidimensional central limit theorem. Zbl 0196.21103
Bhattacharya, R. N.
1970
Berry-Esseen bounds for the multi-dimensional central limit theorem. Zbl 0179.48102
Bhattacharya, R. N.
1968
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### Cited by 1,676 Authors
35 Bhattacharya, Rabi N. 19 Lahiri, Soumendra Nath 19 Patrangenaru, Victor 16 Götze, Friedrich 16 Huckemann, Stephan F. 16 Kakizawa, Yoshihide 16 Withers, Christopher Stroude 14 Nadarajah, Saralees 13 Basak, Gopal Krishna 13 Hall, Peter Gavin 13 Waymire, Edward C. 10 Babu, Gutti Jogesh 10 Lin, Lizhen 10 Sunklodas, Jonas Kazys 10 Thomann, Enrique A. 9 Bobkov, Sergey Germanovich 8 Bose, Arup 8 Majumdar, Mukul K. 8 Stoltz, Gabriel 7 Bentkus, Vidmants-Kastytis 7 Eltzner, Benjamin 7 Ghosh, Mrinal Kanti 7 Hernández-Lerma, Onésimo 7 Ivanov, Aleksandr Vladimirovich 7 Lee, Oesook 7 Mitra, Tapan 7 Pagès, Gilles 7 Xu, Jin 6 Busemeyer, Jerome R. 6 Dryden, Ian L. 6 Fujikoshi, Yasunori 6 Korolev, Viktor Yur’evich 6 Marron, James Stephen 6 Mukerjee, Rahul 6 Panloup, Fabien 6 Sandrić, Nikola 6 Sekiya, Yuri 6 Stachurski, John 6 Taneichi, Nobuhiro 5 Bigot, Jéremie 5 Borkar, Vivek Shripad 5 Chistyakov, Gennadiy P. 5 Gupta, Arjun Kumar 5 Harrar, Solomon W. 5 Heinrich, Lothar 5 Horváth, Lajos 5 Hwang, Chii-Ruey 5 Iwashita, Toshiya 5 Jaśkiewicz, Anna 5 Kamihigashi, Takashi 5 Konakov, Valentin 5 Le, Huiling 5 Li, Qi 5 Mammen, Enno 5 Mirakhmedov, Sherzod Mira’zam 5 Nowak, Andrzej S. 5 Pap, Gyula 5 Wefelmeyer, Wolfgang 5 Weinmann, Andreas 5 Wood, Andrew T. A. 5 Zeitouni, Ofer 4 Barczy, Mátyás 4 Bhattacharya, Abhishek 4 Bloznelis, Mindaugas 4 Dunson, David Brian 4 Ellingson, Leif 4 Glynn, Peter W. 4 Hipp, Christian 4 Hotz, Thomas 4 Jensen, Jens Ledet 4 Jing, Bingyi 4 Kokoszka, Piotr S. 4 Lee, Chanho 4 Menozzi, Stéphane 4 Müller, Hans-Georg 4 Paditz, Ludwig 4 Pavliotis, Grigorios A. 4 Qumsiyeh, Maher B. 4 Rásonyi, Miklós 4 Rilstone, Paul 4 Simó, Amelia 4 Storath, Martin 4 Taniguchi, Masanobu 4 Tong, Jinying 4 Zhang, Zhenzhong 3 Acebrón, Juan A. 3 Akahira, Masafumi 3 Andrews, Donald Wilfrid Kao 3 Chandra, Tapas Kumar 3 Chen, Jiahua 3 Chen, Songxi 3 Cordeiro, Gauss Moutinho 3 Cox, J. Theodore 3 Das, Debraj 3 Dascaliuc, Radu 3 Demos, Antonis 3 Denker, Manfred 3 Diaconis, Persi Warren 3 Diederich, Adele 3 Dubinskaitė, Jone ...and 1,576 more Authors
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### Cited in 273 Serials
78 Journal of Multivariate Analysis 72 Statistics & Probability Letters 57 Journal of Statistical Planning and Inference 56 The Annals of Statistics 48 Stochastic Processes and their Applications 38 Journal of Econometrics 37 Communications in Statistics. Theory and Methods 36 Probability Theory and Related Fields 28 Annals of the Institute of Statistical Mathematics 28 The Annals of Applied Probability 26 The Annals of Probability 21 Lithuanian Mathematical Journal 21 Journal of Theoretical Probability 20 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 19 Statistics 16 Journal of Mathematical Analysis and Applications 15 Bernoulli 14 Journal of Time Series Analysis 12 Journal of Economic Theory 12 Transactions of the American Mathematical Society 12 Stochastic Analysis and Applications 11 Journal of Statistical Physics 10 Metrika 10 Journal of Mathematical Economics 9 Proceedings of the American Mathematical Society 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Computational Statistics and Data Analysis 9 Electronic Journal of Statistics 8 Communications in Mathematical Physics 8 Scandinavian Journal of Statistics 8 Ukrainian Mathematical Journal 8 Journal of the American Statistical Association 8 Journal of Applied Probability 8 Journal of Mathematical Psychology 8 Journal of Soviet Mathematics 8 Mathematische Nachrichten 8 Stochastics and Dynamics 7 Advances in Applied Probability 7 The Canadian Journal of Statistics 7 Communications in Statistics. Simulation and Computation 7 Journal of Statistical Computation and Simulation 7 Journal of Mathematical Sciences (New York) 7 Econometric Theory 7 Stochastic Models 7 Sankhyā. Series A 6 Nonlinearity 6 Electronic Journal of Probability 6 Journal of Nonparametric Statistics 6 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 5 Journal of Computational Physics 5 Theory of Probability and its Applications 5 Kybernetika 5 Systems & Control Letters 5 Journal of Mathematical Imaging and Vision 5 Statistical Papers 5 Journal of Applied Statistics 5 Methodology and Computing in Applied Probability 5 Stochastics 5 Statistical Methodology 4 Applied Mathematics and Optimization 4 Journal of Approximation Theory 4 Journal of Differential Equations 4 Journal of Optimization Theory and Applications 4 Scandinavian Actuarial Journal 4 Insurance Mathematics & Economics 4 Acta Applicandae Mathematicae 4 Journal of Economic Dynamics & Control 4 Annals of Operations Research 4 Test 4 International Journal of Computer Vision 4 Statistical Inference for Stochastic Processes 3 Journal of Mathematical Biology 3 Journal of Mathematical Physics 3 Mathematical Notes 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Biometrical Journal 3 Mathematics of Operations Research 3 Mathematical Social Sciences 3 American Journal of Mathematical and Management Sciences 3 Acta Mathematicae Applicatae Sinica. English Series 3 Sequential Analysis 3 Statistical Science 3 Queueing Systems 3 Pattern Recognition 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 3 Mathematical Methods of Statistics 3 Journal of Difference Equations and Applications 3 Doklady Mathematics 3 Brazilian Journal of Probability and Statistics 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Multiscale Modeling & Simulation 3 Mathematical Biosciences and Engineering 3 The Annals of Applied Statistics 3 SIAM Journal on Imaging Sciences 3 Sankhyā. Series B 3 Statistics and Computing 3 Bayesian Analysis 3 SIAM/ASA Journal on Uncertainty Quantification 3 SIAM Journal on Mathematics of Data Science ...and 173 more Serials
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### Cited in 52 Fields
661 Probability theory and stochastic processes (60-XX) 647 Statistics (62-XX) 109 Numerical analysis (65-XX) 101 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 60 Partial differential equations (35-XX) 54 Dynamical systems and ergodic theory (37-XX) 53 Operations research, mathematical programming (90-XX) 44 Systems theory; control (93-XX) 40 Biology and other natural sciences (92-XX) 35 Statistical mechanics, structure of matter (82-XX) 33 Fluid mechanics (76-XX) 31 Computer science (68-XX) 29 Differential geometry (53-XX) 26 Operator theory (47-XX) 22 Information and communication theory, circuits (94-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 18 Ordinary differential equations (34-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 12 Measure and integration (28-XX) 11 Combinatorics (05-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Quantum theory (81-XX) 9 Number theory (11-XX) 8 Approximations and expansions (41-XX) 8 Geophysics (86-XX) 7 Difference and functional equations (39-XX) 6 Potential theory (31-XX) 6 Abstract harmonic analysis (43-XX) 5 Real functions (26-XX) 4 Group theory and generalizations (20-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 4 Functional analysis (46-XX) 4 General topology (54-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Topological groups, Lie groups (22-XX) 3 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-05-22T17:33:24 |
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|
https://www.itl.nist.gov/div898/handbook/pmd/section4/pmd453.htm
|
4. Process Modeling
4.4. Data Analysis for Process Modeling
4.4.5. If my current model does not fit the data well, how can I improve it?
Accounting for Errors with a Non-Normal Distribution
Basic Approach: Transformation Unlike when correcting for non-constant variation in the random errors, there is really only one basic approach to handling data with non-normal random errors for most regression methods. This is because most methods rely on the assumption of normality and the use of linear estimation methods (like least squares) to make probabilistic inferences to answer scientific or engineering questions. For methods that rely on normality of the data, direct manipulation of the data to make the random errors approximately normal is usually the best way to try to bring the data in line with this assumption. The main alternative to transformation is to use a fitting criterion that directly takes the distribution of the random errors into account when estimating the unknown parameters. Using these types of fitting criteria, such as maximum likelihood, can provide very good results. However, they are often much harder to use than the general fitting criteria used in most process modeling methods.
Using Transformations The basic steps for using transformations to handle data with non-normally distributed random errors are essentially the same as those used to handle non-constant variation of the random errors.
1. Transform the response variable to make the distribution of the random errors approximately normal.
2. Transform the predictor variables, if necessary, to attain or restore a simple functional form for the regression function.
3. Fit and validate the model in the transformed variables.
4. Transform the predicted values back into the original units using the inverse of the transformation applied to the response variable.
The main difference between using transformations to account for non-constant variation and non-normality of the random errors is that it is harder to directly see the effect of a transformation on the distribution of the random errors. It is very often the case, however, that non-normality and non-constant standard deviation of the random errors go together, and that the same transformation will correct both problems at once. In practice, therefore, if you choose a transformation to fix any non-constant variation in the data, you will often also improve the normality of the random errors. If the data appear to have non-normally distributed random errors, but do have a constant standard deviation, you can always fit models to several sets of transformed data and then check to see which transformation appears to produce the most normally distributed residuals.
Typical Transformations for Meeting Distributional Assumptions Not surprisingly, three transformations that are often effective for making the distribution of the random errors approximately normal are:
1. $$\sqrt{y}$$,
2. $$\ln{(y)}$$ (note: the base of the logarithm does not really matter), and
3. $$\frac{1}{y}$$.
These are the same transformations often used for stabilizing the variation in the data. Other appropriate transformations to improve the distributional properties of the random errors may be suggested by scientific knowledge or selected using the data. However, these three transformations are good ones to start with since they work well in so many situations.
Example To illustrate how to use transformations to change the distribution of the random errors, we will look at a modified version of the Pressure/Temperature example in which the errors are uniformly distributed. Comparing the results obtained from fitting the data in their original units and under different transformations will directly illustrate the effects of the transformations on the distribution of the random errors.
Modified Pressure/Temperature Data with Uniform Random Errors
Fit of Model to the Untransformed Data A four-plot of the residuals obtained after fitting a straight-line model to the Pressure/Temperature data with uniformly distributed random errors is shown below. The histogram and normal probability plot on the bottom row of the four-plot are the most useful plots for assessing the distribution of the residuals. In this case the histogram suggests that the distribution is more rectangular than bell-shaped, indicating the random errors a not likely to be normally distributed. The curvature in the normal probability plot also suggests that the random errors are not normally distributed. If the random errors were normally distributed the normal probability plots should be a fairly straight line. Of course it wouldn't be perfectly straight, but smooth curvature or several points lying far from the line are fairly strong indicators of non-normality.
Residuals from Straight-Line Model of Untransformed Data with Uniform Random Errors
Selection of Appropriate Transformations Going through a set of steps similar to those used to find transformations to stabilize the random variation, different pairs of transformations of the response and predictor which have a simple functional form and will potentially have more normally distributed residuals are chosen. In the multiplots below, all of the possible combinations of basic transformations are applied to the temperature and pressure to find the pairs which have simple functional forms. In this case, which is typical, the the data with square root-square root, ln-ln, and inverse-inverse tranformations all appear to follow a straight-line model. The next step will be to fit lines to each of these sets of data and then to compare the residual plots to see whether any have random errors which appear to be normally distributed.
sqrt(Pressure) vs Different Tranformations of Temperature
log(Pressure) vs Different Tranformations of Temperature
1/Pressure vs Different Tranformations of Temperature
Fit of Model to Transformed Variables The normal probability plots and histograms below show the results of fitting straight-line models to the three sets of transformed data. The results from the fit of the model to the data in its original units are also shown for comparison. From the four normal probability plots it looks like the model fit using the ln-ln transformations produces the most normally distributed random errors. Because the normal probability plot for the ln-ln data is so straight, it seems safe to conclude that taking the ln of the pressure makes the distribution of the random errors approximately normal. The histograms seem to confirm this since the histogram of the ln-ln data looks reasonably bell-shaped while the other histograms are not particularly bell-shaped. Therefore, assuming the other residual plots also indicated that a straight line model fit this transformed data, the use of ln-ln tranformations appears to be appropriate for analysis of this data.
Residuals from the Fit to the Transformed Variables
Residuals from the Fit to the Transformed Variables
| 2018-05-24T04:20:33 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Catalogue_consolidation/chap_cu9val_cu9val/sec_cu9val_942/ssec_cu9val_942_dupl.html
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# 10.2.2 Duplicated sources
The detection system on-board Gaia may sometimes generate more than one detection for a given source. The on-ground cross match process will then have to decide if two simultaneous detections represent two sources or merely repeated detections of the same single source. With dozens of thousands of millions detections, chances are that some small fraction of the single sources end up with part of their observations labelled with one source identifier, and the rest with a different source identifier. When this happens, the various pipelines produce two sets of independent results each with their own source identifier. We will of course expect, that the two sets are essentially identical. In the final catalogue only one solution is kept and the other removed, and the published source carries a flag saying it was a ‘duplicated source’. In deciding which solution to keep, priority is given to the one with better astrometric results. Before removing the poorer solution, this set of duplicated sources from the ‘pre-DR2’ Catalogue provided an attractive opportunity for the catalogue validation. Some results are presented in Arenou et al. (2018) and others in Section 10.2.5, typically pointing to a certain underestimation of the errors.
First, however, we must decide when to consider that a close source-pair is a duplicate. From simple considerations on the image size, data acquisition, and the present state of the on-ground processing, sources can hardly be expected to be reliably resolved if they are separated by less than 0.3 ${}^{\prime\prime}$, and even that is an optimistic limit as long as no dedicated data processing for binaries is activated.
Figure 10.6 shows the relation between separation and magnitude difference for sources in a dense test field in a processing step immediately before duplicates were removed. The sign of the magnitude difference depends, for processing reasons, on which source had the highest declination and can be considered random. We notice several characteristics: a concentration at small separations (below 0.05 ${}^{\prime\prime}$) and magnitude differences; a continuation up to 0.4 ${}^{\prime\prime}$ separation with small magnitude differences; a widening up to 0.7 ${}^{\prime\prime}$; and a more gradual widening at higher separations. A tentative interpretation is that the concentration at very small separations then represents the well-behaved, single sources. The, relatively sparse, continuation to 0.4 ${}^{\prime\prime}$ is a mixture of genuine duplicate sources and actual binaries; the widening up to 0.7 ${}^{\prime\prime}$ show the gradual decrease of acquisition conflicts; and the final widening demonstrates the continued decrease of conflicts and the increasing ability to deal with magnitude contrasts. Typical acquisition windows are 0.7 ${}^{\prime\prime}$ by 2.1 ${}^{\prime\prime}$, so two sources closer than 0.7 ${}^{\prime\prime}$ will always be in conflict.
Minor conflicts, affecting a small part of the acquisition windows, are accepted in Gaia DR2, and for pairs with similar magnitudes either of them may be detected as the brighter in a given transit and get a complete window. Even so, the closeness of a neighbour of similar magnitude will be disturbing. All in all it was decided to define duplicate sources for Gaia DR2 as pairs closer than 0.4 ${}^{\prime\prime}$ at the reference epoch. The vast majority of these pairs are genuine duplicates and only a minor fraction are binaries.
Figure 10.7 shows the separations for source pairs identified as duplicates. Because of the way duplicates involving more than two sources are handled, separations may occasionally exceed 0.4 ${}^{\prime\prime}$. The left panel shows a strong peak in the centre with a short tail that gradually becomes more rectangular and end in a hint of a diagonal cross. As shown in the right panel, the more exotic behaviour only occurs for cases where the full astrometric solution had to be abandoned.
| 2018-10-19T20:06:22 |
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|
http://trove.nla.gov.au/work/105084?q&versionId=111900
|
# English, Article, Journal or magazine article edition: New Ideas Need New Space Diego Rodríguez
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Bookmark: http://trove.nla.gov.au/version/111900
Physical Description
• preprint
Language
• English
### Edition details
Title
• New Ideas Need New Space
Author
• Diego Rodríguez
Physical Description
• preprint
Notes
• We develop a setting with weak intellectual property rights, where firms' boundaries, location and knowledge spillovers are endogenous. We have two main results. The first one is that, if communication costs increase with distance, entrepreneurs concerned about information leakage have a benefit from locating away from the industry center: distance is an obstacle to collusive trades between members and non-members. The second result is that we identify a trade-off for the entrepreneur between owning a facility (controlling all its characteristics) and sharing a facility with a {\it non-member} (an agent not involved in production), therefore losing control over some of its characteristics. We focus on location" as the relevant characteristic of the facility, but location can be used as a spatial metaphor for other relevant characteristics of the facility. For the entrepreneur, sharing the facility with non-members implies that the latter, as co-owners, know the location (even if they do not have access to it). Knowledge of the location for the co-owners facilitates collusion with employees, what increases leakage. The model yields a benefit for new plants from spatial dispersion (locating at the periphery of the industry), particularly so for new plants of new firms. We relate this result with recent empirical findings on the dynamics of industry location.
• Intellectual property rights, employee hold-up, secrecy, location, endogenous spillovers
• RePEc:upf:upfgen:390
Language
• English
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| 2016-10-21T09:44:38 |
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|
https://zbmath.org/authors/?q=ai%3Abertoin.jean
|
# zbMATH — the first resource for mathematics
## Bertoin, Jean
Compute Distance To:
Author ID: bertoin.jean Published as: Bertoin, J.; Bertoin, Jean External Links: MGP · Wikidata · GND
Documents Indexed: 172 Publications since 1986, including 8 Books Reviewing Activity: 97 Reviews
all top 5
#### Co-Authors
99 single-authored 12 Yor, Marc 8 Doney, Ronald Arthur 6 Le Gall, Jean-François 4 Baur, Erich 4 Miermont, Grégory 4 Pitman, Jim William 3 Caballero, María Emilia 3 Kortchemski, Igor 3 Mallein, Bastien 3 Watson, Alexander R. 3 Werner, Wendelin 2 Berestycki, Julien 2 Chaumont, Loïc 2 Curien, Nicolas 2 Haas, Bénédicte 2 Jacod, Jean 2 Le Jan, Yves 2 Maller, Ross Arthur 2 Martinez Aguilera, Servet 2 Shi, Zhan 2 Sidoravicius, Vladas 1 Barczy, Mátyás 1 Barndorff-Nielsen, Ole Eiler 1 Barral, Julien 1 Biane, Philippe 1 Bretagnolle, Jean L. 1 Budd, Timothy G. 1 Cortines, Aser 1 Dufresne, Daniel 1 Fan, Ai Hua 1 Fontbona, Joaquin 1 Fujita, Takahiko 1 Giraud, Christophe 1 Gnedin, Alexander V. 1 Goldschmidt, Christina 1 Ibragimov, Il’dar Abdullovich 1 Isozaki, Yasuki 1 Jaffard, Stéphane 1 Jeanblanc, Monique 1 Klüppelberg, Claudia 1 Lindner, Alexander M. 1 Marsalle, Laurence 1 Martinelli, Fabio 1 Norris, James R. 1 Peres, Yuval 1 Peyrière, Jacques 1 Rouault, Alain 1 Roynette, Bernard 1 Ruiz de Chavez, Juan 1 Savov, Mladen Svetoslavov 1 Stephenson, Robin 1 Steutel, Fred Willem 1 Uribe Bravo, Gerónimo 1 van Harn, Klaas 1 Vares, Maria Eulalia 1 Wagner, Wolfgang
all top 5
#### Serials
14 The Annals of Probability 14 Probability Theory and Related Fields 10 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 8 Stochastic Processes and their Applications 8 Electronic Communications in Probability 7 Journal of Applied Probability 6 The Annals of Applied Probability 6 Electronic Journal of Probability 5 Advances in Applied Probability 5 Communications in Mathematical Physics 4 Random Structures & Algorithms 3 Journal of Statistical Physics 3 Bulletin of the London Mathematical Society 3 Statistics & Probability Letters 3 Journal of Theoretical Probability 3 Bulletin des Sciences Mathématiques 2 Stochastics 2 Journal of Functional Analysis 2 Japan Journal of Applied Mathematics 2 Forum Mathematicum 2 Stochastics and Stochastics Reports 2 Potential Analysis 2 Bernoulli 2 Journal of the European Mathematical Society (JEMS) 2 Cambridge Tracts in Mathematics 2 Lecture Notes in Mathematics 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Canadian Journal of Mathematics 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematics of Kyoto University 1 Probability and Mathematical Statistics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Combinatorics, Probability and Computing 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Markov Processes and Related Fields 1 Oberwolfach Reports 1 Cambridge Studies in Advanced Mathematics 1 Panoramas et Synthèses 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Probability Surveys 1 Annales Henri Lebesgue
all top 5
#### Fields
168 Probability theory and stochastic processes (60-XX) 11 Combinatorics (05-XX) 9 Partial differential equations (35-XX) 8 Biology and other natural sciences (92-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 4 Measure and integration (28-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Operator theory (47-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 2 Statistics (62-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX)
#### Citations contained in zbMATH
144 Publications have been cited 2,684 times in 1,733 Documents Cited by Year
Lévy processes. Zbl 0861.60003
Bertoin, Jean
1996
Random fragmentation and coagulation processes. Zbl 1107.60002
Bertoin, Jean
2006
Subordinators: Examples and applications. Zbl 0955.60046
Bertoin, Jean
1999
Exponential functionals of Lévy processes. Zbl 1189.60096
Bertoin, Jean; Yor, Marc
2005
Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Zbl 0880.60077
Bertoin, Jean
1997
On conditioning a random walk to stay nonnegative. Zbl 0834.60079
Bertoin, J.; Doney, R. A.
1994
Stochastic flows associated to coalescent processes. Zbl 1023.92018
Bertoin, Jean; Le Gall, Jean-François
2003
Self-similar fragmentations. Zbl 1002.60072
Bertoin, Jean
2002
Lévy processes. Zbl 0938.60005
Bertoin, Jean
1998
Cramér’s estimate for Lévy processes. Zbl 0809.60085
Bertoin, J.; Doney, R. A.
1994
Stochastic flows associated to coalescent processes. III: Limit theorems. Zbl 1110.60026
Bertoin, Jean; Le Gall, Jean-Francois
2006
Some asymptotic results for transient random walks. Zbl 0854.60069
Bertoin, J.; Doney, R. A.
1996
Homogeneous fragmentation processes. Zbl 0992.60076
Bertoin, Jean
2001
On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Zbl 1024.60030
Bertoin, Jean; Yor, Marc
2001
The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1004.60046
Bertoin, Jean; Yor, Marc
2002
The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Zbl 0963.60086
Bertoin, Jean; Le Gall, Jean-François
2000
The asymptotic behavior of fragmentation processes. Zbl 1042.60042
Bertoin, Jean
2003
On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1031.60038
Bertoin, Jean; Yor, Marc
2002
Splitting at the infimum and excursions in half-lines for random walks and Lévy processes. Zbl 0786.60101
Bertoin, Jean
1993
The inviscid Burgers equation with Brownian initial velocity. Zbl 0917.60063
Bertoin, Jean
1998
On the first exit time of a completely asymmetric stable process from a finite interval. Zbl 0863.60068
Bertoin, Jean
1996
Path transformations connecting Brownian bridge, excursion and meander. Zbl 0805.60076
Bertoin, Jean; Pitman, Jim
1994
Discretization methods for homogeneous fragmentations. Zbl 1077.60053
Bertoin, Jean; Rouault, Alain
2005
Asymptotic laws for nonconservative self-similar fragmentations. Zbl 1064.60075
Bertoin, Jean; Gnedin, Alexander V.
2004
Les processus de Dirichlet en tant qu’espace de Banach. (Dirichlet processes as Banach spaces). Zbl 0602.60069
Bertoin, Jean
1986
On continuity properties of the law of integrals of Lévy processes. Zbl 1180.60042
Bertoin, Jean; Lindner, Alexander; Maller, Ross
2008
Entrance from $$0+$$ for increasing semi-stable Markov processes. Zbl 1002.60032
Bertoin, Jean; Caballero, Maria-Emilia
2002
Renewal theory and level passage by subordinators. Zbl 0965.60053
Bertoin, J.; van Harn, K.; Steutel, F. W.
1999
On prolific individuals in a supercritical continuous-state branching process. Zbl 1154.60066
Bertoin, Jean; Fontbona, Joaquin; Martínez, Servet
2008
Passage of Lévy processes across power law boundaries at small times. Zbl 1140.60025
Bertoin, J.; Doney, R. A.; Maller, R. A.
2008
Stochastic flows associated to coalescent processes. II: Stochastic differential equations. Zbl 1119.60024
Bertoin, Jean; Le Gall, Jean-François
2005
Regularity of the half-line for Lévy processes. Zbl 0883.60069
Bertoin, Jean
1997
Spitzer’s condition for random walks and Lévy processes. Zbl 0880.60078
Bertoin, J.; Doney, R. A.
1997
An extension of Pitman’s theorem for spectrally positive Lévy processes. Zbl 0760.60068
Bertoin, Jean
1992
Some applications of duality for Lévy processes in a half-line. Zbl 1213.60090
2011
A fragmentation process connected to Brownian motion. Zbl 0965.60072
Bertoin, Jean
2000
Martingales in self-similar growth-fragmentations and their connections with random planar maps. Zbl 1451.60047
Bertoin, Jean; Budd, Timothy; Curien, Nicolas; Kortchemski, Igor
2018
Fires on trees. Zbl 1263.60083
Bertoin, Jean
2012
Poissonian exponential functionals, $$q$$-series, $$q$$-integrals, and the moment problem for log-normal distributions. Zbl 1056.60046
Bertoin, Jean; Biane, Philippe; Yor, Marc
2004
Eternal solutions to Smoluchowski’s coagulation equation with additive kernel and their probabilistic interpretations. Zbl 1030.60036
Bertoin, Jean
2002
Iterated Brownian motion and stable $$(1/4)$$ subordinator. Zbl 0854.60082
Bertoin, Jean
1996
Random planar maps and growth-fragmentations. Zbl 1447.60058
Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor
2018
Markovian growth-fragmentation processes. Zbl 1375.60129
Bertoin, Jean
2017
The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. Zbl 1180.92063
Bertoin, Jean
2009
Representation of measures by balayage from a regular recurrent point. Zbl 0749.60038
Bertoin, J.; Le Jan, Yves
1992
The cut-tree of large Galton-Watson trees and the Brownian CRT. Zbl 1279.60035
Bertoin, Jean; Miermont, Grégory
2013
Path transformations of first passage bridges. Zbl 1061.60083
Bertoin, Jean; Chaumont, Loïc; Pitman, Jim
2003
Sur la décomposition de la trajectoire d’un processus de Lévy spectralement positif en son infimum. (On the path decomposition at the infimum for a spectrally positive Lévy process). Zbl 0758.60073
Bertoin, Jean
1991
Sur une intégrale pour les processus à $$\alpha$$-variation bornée. (On an integral for processes with bounded $$\alpha$$-variation). Zbl 0687.60054
Bertoin, Jean
1989
On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times. Zbl 1123.60063
Bertoin, J.; Fujita, T.; Roynette, B.; Yor, M.
2006
Spatial branching processes and subordination. Zbl 0921.60078
Bertoin, Jean; Le Gall, Jean-François; Le Jan, Yves
1997
Stable windings. Zbl 0867.60045
Bertoin, Jean; Werner, Wendelin
1996
A probabilistic approach to spectral analysis of growth-fragmentation equations. Zbl 1384.35132
Bertoin, Jean; Watson, Alexander R.
2018
Self-similar scaling limits of Markov chains on the positive integers. Zbl 1352.60103
Bertoin, Jean; Kortchemski, Igor
2016
Compensated fragmentation processes and limits of dilated fragmentations. Zbl 1344.60033
Bertoin, Jean
2016
The structure of typical clusters in large sparse random configurations. Zbl 1168.82028
2009
Reflecting a Langevin process at an absorbing boundary. Zbl 1132.60057
Bertoin, Jean
2007
Fragmentation energy. Zbl 1080.60080
Bertoin, Jean; Martínez, Servet
2005
Eternal additive coalescents and certain bridges with exchangeable increments. Zbl 1019.60072
Bertoin, Jean
2001
Clustering statistics for sticky particles with Brownian initial velocity. Zbl 0959.60074
Bertoin, Jean
2000
The convex minorant of the Cauchy process. Zbl 0954.60042
Bertoin, Jean
2000
Two coalescents derived from the ranges of stable subordinators. Zbl 0949.60034
Bertoin, Jean; Pitman, Jim
2000
On the maximal offspring in a critical branching process with infinite variance. Zbl 1223.60020
Bertoin, Jean
2011
Complements on the Hilbert transform and the fractional derivative of Brownian local times. Zbl 0725.60084
Bertoin, Jean
1990
Local explosion in self-similar growth-fragmentation processes. Zbl 1346.60038
Bertoin, Jean; Stephenson, Robin
2016
Sizes of the largest clusters for supercritical percolation on random recursive trees. Zbl 1280.05117
Bertoin, Jean
2014
A limit theorem for trees of alleles in branching processes with rare neutral mutations. Zbl 1193.60099
Bertoin, Jean
2010
On small masses in self-similar fragmentations. Zbl 1075.60092
Bertoin, Jean
2004
Dual random fragmentation and coagulation and an application to the genealogy of Yule processes. Zbl 1064.60177
Bertoin, Jean; Goldschmidt, Christina
2004
The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes. Zbl 1333.60186
Baur, Erich; Bertoin, Jean
2015
Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Zbl 1165.60032
Bertoin, Jean
2008
Large-deviations estimates in Burgers turbulence with stable noise initial data. Zbl 0927.60039
Bertoin, Jean
1998
Regenerative embedding of Markov sets. Zbl 0895.60011
Bertoin, Jean
1997
Asymptotic windings of planar Brownian motion revisited via the Ornstein- Uhlenbeck process. Zbl 0814.60080
Bertoin, Jean; Werner, Wendelin
1994
Temps locaux et intégration stochastique pour les processus de Dirichlet. (Local time and stochastic integration for Dirichlet processes). Zbl 0616.60073
Bertoin, Jean
1987
Biggins’ martingale convergence for branching Lévy processes. Zbl 1402.60051
Bertoin, Jean; Mallein, Bastien
2018
Probabilistic aspects of critical growth-fragmentation equations. Zbl 1426.35213
Bertoin, Jean; Watson, Alexander R.
2016
The cut-tree of large recursive trees. Zbl 1351.60010
Bertoin, Jean
2015
Supercritical percolation on large scale-free random trees. Zbl 1309.60094
Bertoin, Jean; Bravo, Gerónimo Uribe
2015
On largest offspring in a critical branching process with finite variance. Zbl 1277.60045
Bertoin, Jean
2013
Some aspects of additive coalescents. Zbl 1007.60101
Bertoin, Jean
2002
Lévy processes that can creep downwards never increase. Zbl 0816.60073
Bertoin, Jean
1995
On the local behaviour of ladder height distributions. Zbl 0815.60065
Bertoin, J.; Doney, R. A.
1994
Increase of a Lévy process with no positive jumps. Zbl 0739.60065
Bertoin, Jean
1991
Sur la mesure d’occupation d’une classe de fonctions self-affines. (On the occupation measure of a class of self-affine functions). Zbl 0685.26007
Bertoin, Jean
1988
On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. Zbl 1433.35414
Bertoin, Jean
2019
Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Zbl 1303.60073
Bertoin, Jean; Dufresne, Daniel; Yor, Marc
2013
Almost giant clusters for percolation on large trees with logarithmic heights. Zbl 1283.60119
Bertoin, Jean
2013
Homogeneous multitype fragmentations. Zbl 1153.60046
Bertoin, Jean
2008
A second order SDE for the Langevin process reflected at a completely inelastic boundary. Zbl 1169.60009
Bertoin, Jean
2008
Structure of shocks in Burgers turbulence with stable noise initial data. Zbl 0943.60055
Bertoin, Jean
1999
Constructions of a Brownian path with a given minimum. Zbl 1021.60060
Bertoin, Jean; Pitman, Jim; Ruiz de Chavez, Juan
1999
Intersection of independent regenerative sets. Zbl 0937.60043
Bertoin, Jean
1999
Darling-Erdős theorems for normalized sums of i. i. d. variables close to a stable law. Zbl 0943.60041
Bertoin, Jean
1998
Some independence results related to the arc-sine law. Zbl 0876.60060
Bertoin, Jean; Yor, Marc
1996
On the local rate of growth of Lévy processes with no positive jumps. Zbl 0816.60072
Bertoin, Jean
1995
Asymptotic behavior of the number of windings of the planar Brownian path. Zbl 0810.60077
Bertoin, Jean; Werner, Wendelin
1994
Excursions of a $$BES_ o(d)$$ and its drift term $$(0<d<1)$$. Zbl 0665.60073
Bertoin, J.
1990
Applications de la théorie spectral des cordes vibrantes aux fonctionnelles additives principales d’un brownien réfléchi. (Applications of the spectral theory of vibrating strings to principal additive functionals of a reflected Brownian motion). Zbl 0694.60070
Bertoin, Jean
1989
Infinitely ramified point measures and branching Lévy processes. Zbl 07067278
Bertoin, Jean; Mallein, Bastien
2019
On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. Zbl 1433.35414
Bertoin, Jean
2019
Infinitely ramified point measures and branching Lévy processes. Zbl 07067278
Bertoin, Jean; Mallein, Bastien
2019
A version of Herbert A. Simon’s model with slowly fading memory and its connections to branching processes. Zbl 07107669
Bertoin, Jean
2019
Martingales in self-similar growth-fragmentations and their connections with random planar maps. Zbl 1451.60047
Bertoin, Jean; Budd, Timothy; Curien, Nicolas; Kortchemski, Igor
2018
Random planar maps and growth-fragmentations. Zbl 1447.60058
Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor
2018
A probabilistic approach to spectral analysis of growth-fragmentation equations. Zbl 1384.35132
Bertoin, Jean; Watson, Alexander R.
2018
Biggins’ martingale convergence for branching Lévy processes. Zbl 1402.60051
Bertoin, Jean; Mallein, Bastien
2018
Markovian growth-fragmentation processes. Zbl 1375.60129
Bertoin, Jean
2017
Weak limits for the largest subpopulations in Yule processes with high mutation probabilities. Zbl 1425.60066
Baur, Erich; Bertoin, Jean
2017
Self-similar scaling limits of Markov chains on the positive integers. Zbl 1352.60103
Bertoin, Jean; Kortchemski, Igor
2016
Compensated fragmentation processes and limits of dilated fragmentations. Zbl 1344.60033
Bertoin, Jean
2016
Local explosion in self-similar growth-fragmentation processes. Zbl 1346.60038
Bertoin, Jean; Stephenson, Robin
2016
Probabilistic aspects of critical growth-fragmentation equations. Zbl 1426.35213
Bertoin, Jean; Watson, Alexander R.
2016
On the destruction of large random recursive trees. Zbl 1358.05253
Baur, E.; Bertoin, J.
2016
The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes. Zbl 1333.60186
Baur, Erich; Bertoin, Jean
2015
The cut-tree of large recursive trees. Zbl 1351.60010
Bertoin, Jean
2015
Supercritical percolation on large scale-free random trees. Zbl 1309.60094
Bertoin, Jean; Bravo, Gerónimo Uribe
2015
Sizes of the largest clusters for supercritical percolation on random recursive trees. Zbl 1280.05117
Bertoin, Jean
2014
On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. Zbl 1292.60095
Bertoin, Jean
2014
Cutting edges at random in large recursive trees. Zbl 1390.60043
Baur, Erich; Bertoin, Jean
2014
Local times for functions with finite variation: two versions of Stieltjes change-of-variables formula. Zbl 1295.26011
Bertoin, Jean; Yor, Marc
2014
The cut-tree of large Galton-Watson trees and the Brownian CRT. Zbl 1279.60035
Bertoin, Jean; Miermont, Grégory
2013
On largest offspring in a critical branching process with finite variance. Zbl 1277.60045
Bertoin, Jean
2013
Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Zbl 1303.60073
Bertoin, Jean; Dufresne, Daniel; Yor, Marc
2013
Almost giant clusters for percolation on large trees with logarithmic heights. Zbl 1283.60119
Bertoin, Jean
2013
Retrieving information from subordination. Zbl 1284.60084
Bertoin, Jean; Yor, Marc
2013
Pure jump increasing processes and the change of variables formula. Zbl 1306.60120
Bertoin, Jean; Yor, Marc
2013
Fires on trees. Zbl 1263.60083
Bertoin, Jean
2012
The area of a self-similar fragmentation. Zbl 1277.60070
Bertoin, Jean
2012
Lévy processes at Saint-Flour. Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 307 (1973), 1117 (1985), 1717 (1999) and 1897 (2007). Zbl 1254.60004
Bertoin, Jean; Bretagnolle, Jean L.; Doney, Ronald A.; Ibragimov, Ildar A.; Jacod, Jean
2012
Some applications of duality for Lévy processes in a half-line. Zbl 1213.60090
2011
On the maximal offspring in a critical branching process with infinite variance. Zbl 1223.60020
Bertoin, Jean
2011
Functional limit theorems for Lévy processes satisfying Cramér’s condition. Zbl 1244.60049
Barczy, Matyas; Bertoin, Jean
2011
A limit theorem for trees of alleles in branching processes with rare neutral mutations. Zbl 1193.60099
Bertoin, Jean
2010
A system of grabbing particles related to Galton-Watson trees. Zbl 1209.60048
Bertoin, Jean; Sidoravicius, Vladas; Vares, Maria Eulalia
2010
Asymptotic regimes for the partition into colonies of a branching process with emigration. Zbl 1215.60049
Bertoin, Jean
2010
Some interactions between analysis, probability theory and fractals. To Benoît Mandelbrot, in memoriam. Zbl 1308.28002
Barral, Julien; Berestycki, Julien; Bertoin, Jean; Fan, Aihua; Haas, Bénédicte; Jaffard, Stéphane; Miermont, Grégory; Peyrière, Jacques
2010
A two-time-scale phenomenon in a fragmentation-coagulation process. Zbl 1226.60028
Bertoin, Jean
2010
The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. Zbl 1180.92063
Bertoin, Jean
2009
The structure of typical clusters in large sparse random configurations. Zbl 1168.82028
2009
Two solvable systems of coagulation equations with limited aggregations. Zbl 1179.82180
Bertoin, Jean
2009
On continuity properties of the law of integrals of Lévy processes. Zbl 1180.60042
Bertoin, Jean; Lindner, Alexander; Maller, Ross
2008
On prolific individuals in a supercritical continuous-state branching process. Zbl 1154.60066
Bertoin, Jean; Fontbona, Joaquin; Martínez, Servet
2008
Passage of Lévy processes across power law boundaries at small times. Zbl 1140.60025
Bertoin, J.; Doney, R. A.; Maller, R. A.
2008
Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Zbl 1165.60032
Bertoin, Jean
2008
Homogeneous multitype fragmentations. Zbl 1153.60046
Bertoin, Jean
2008
A second order SDE for the Langevin process reflected at a completely inelastic boundary. Zbl 1169.60009
Bertoin, Jean
2008
Asymptotic regimes for the occupancy scheme of multiplicative cascades. Zbl 1148.60013
Bertoin, Jean
2008
Reflecting a Langevin process at an absorbing boundary. Zbl 1132.60057
Bertoin, Jean
2007
Random fragmentation and coagulation processes. Zbl 1107.60002
Bertoin, Jean
2006
Stochastic flows associated to coalescent processes. III: Limit theorems. Zbl 1110.60026
Bertoin, Jean; Le Gall, Jean-Francois
2006
On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times. Zbl 1123.60063
Bertoin, J.; Fujita, T.; Roynette, B.; Yor, M.
2006
Asymptotics in Knuth’s parking problem for caravans. Zbl 1102.60006
Bertoin, Jean; Miermont, Grégory
2006
Different aspects of a model for random fragmentation processes. Zbl 1137.60045
Bertoin, J.
2006
Exponential functionals of Lévy processes. Zbl 1189.60096
Bertoin, Jean; Yor, Marc
2005
Discretization methods for homogeneous fragmentations. Zbl 1077.60053
Bertoin, Jean; Rouault, Alain
2005
Stochastic flows associated to coalescent processes. II: Stochastic differential equations. Zbl 1119.60024
Bertoin, Jean; Le Gall, Jean-François
2005
Fragmentation energy. Zbl 1080.60080
Bertoin, Jean; Martínez, Servet
2005
Asymptotic laws for nonconservative self-similar fragmentations. Zbl 1064.60075
Bertoin, Jean; Gnedin, Alexander V.
2004
Poissonian exponential functionals, $$q$$-series, $$q$$-integrals, and the moment problem for log-normal distributions. Zbl 1056.60046
Bertoin, Jean; Biane, Philippe; Yor, Marc
2004
On small masses in self-similar fragmentations. Zbl 1075.60092
Bertoin, Jean
2004
Dual random fragmentation and coagulation and an application to the genealogy of Yule processes. Zbl 1064.60177
Bertoin, Jean; Goldschmidt, Christina
2004
Random covering of an interval and a variation of Kingman’s coalescent. Zbl 1063.60009
Bertoin, Jean
2004
Stochastic flows associated to coalescent processes. Zbl 1023.92018
Bertoin, Jean; Le Gall, Jean-François
2003
The asymptotic behavior of fragmentation processes. Zbl 1042.60042
Bertoin, Jean
2003
Path transformations of first passage bridges. Zbl 1061.60083
Bertoin, Jean; Chaumont, Loïc; Pitman, Jim
2003
Self-similar fragmentations. Zbl 1002.60072
Bertoin, Jean
2002
The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1004.60046
Bertoin, Jean; Yor, Marc
2002
On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1031.60038
Bertoin, Jean; Yor, Marc
2002
Entrance from $$0+$$ for increasing semi-stable Markov processes. Zbl 1002.60032
Bertoin, Jean; Caballero, Maria-Emilia
2002
Eternal solutions to Smoluchowski’s coagulation equation with additive kernel and their probabilistic interpretations. Zbl 1030.60036
Bertoin, Jean
2002
Some aspects of additive coalescents. Zbl 1007.60101
Bertoin, Jean
2002
Self-attracting Poisson clouds in an expanding universe. Zbl 1016.83043
Bertoin, Jean
2002
Homogeneous fragmentation processes. Zbl 0992.60076
Bertoin, Jean
2001
On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Zbl 1024.60030
Bertoin, Jean; Yor, Marc
2001
Eternal additive coalescents and certain bridges with exchangeable increments. Zbl 1019.60072
Bertoin, Jean
2001
Some properties of Burgers turbulence with white or stable noise initial data. Zbl 0984.60078
Bertoin, Jean
2001
Statistics of a flux in Burgers turbulence with one-sided Brownian initial data. Zbl 0993.60067
Bertoin, J.; Giraud, C.; Isozaki, Y.
2001
The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Zbl 0963.60086
Bertoin, Jean; Le Gall, Jean-François
2000
A fragmentation process connected to Brownian motion. Zbl 0965.60072
Bertoin, Jean
2000
Clustering statistics for sticky particles with Brownian initial velocity. Zbl 0959.60074
Bertoin, Jean
2000
The convex minorant of the Cauchy process. Zbl 0954.60042
Bertoin, Jean
2000
Two coalescents derived from the ranges of stable subordinators. Zbl 0949.60034
Bertoin, Jean; Pitman, Jim
2000
Subordinators: Examples and applications. Zbl 0955.60046
Bertoin, Jean
1999
Renewal theory and level passage by subordinators. Zbl 0965.60053
Bertoin, J.; van Harn, K.; Steutel, F. W.
1999
Structure of shocks in Burgers turbulence with stable noise initial data. Zbl 0943.60055
Bertoin, Jean
1999
Constructions of a Brownian path with a given minimum. Zbl 1021.60060
Bertoin, Jean; Pitman, Jim; Ruiz de Chavez, Juan
1999
Intersection of independent regenerative sets. Zbl 0937.60043
Bertoin, Jean
1999
Renewal theory for embedded regenerative sets. Zbl 0961.60082
Bertoin, Jean
1999
Regularity of the Cauchy principal value of the local times of some Lévy processes. Zbl 0922.60073
Bertoin, Jean; Caballero, Maria-Emilia
1999
Lectures on probability theory and statistics. Ecole d’eté de Probabilités de Saint-Flour XXVII–1997, Saint-Flour, France, July 7–23, 1997. Zbl 0930.00052
Bertoin, J. (ed.); Martinelli, F. (ed.); Peres, Y. (ed.)
1999
On overshoots and hitting times for random walks. Zbl 0942.60032
Bertoin, Jean
1999
Lévy processes. Zbl 0938.60005
Bertoin, Jean
1998
The inviscid Burgers equation with Brownian initial velocity. Zbl 0917.60063
Bertoin, Jean
1998
Large-deviations estimates in Burgers turbulence with stable noise initial data. Zbl 0927.60039
Bertoin, Jean
1998
Darling-Erdős theorems for normalized sums of i. i. d. variables close to a stable law. Zbl 0943.60041
Bertoin, Jean
1998
The growth rates of subordinators. Zbl 0924.60062
Bertoin, Jean
1998
Extreme values visited by a Brownian motion with drift. Zbl 0914.60062
Bertoin, Jean; Marsalle, Laurence
1998
Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Zbl 0880.60077
Bertoin, Jean
1997
Regularity of the half-line for Lévy processes. Zbl 0883.60069
Bertoin, Jean
1997
...and 44 more Documents
all top 5
#### Cited by 1,655 Authors
56 Bertoin, Jean 54 Kyprianou, Andreas E. 29 Maller, Ross Arthur 26 Palmowski, Zbigniew 23 Pardo, Juan Carlos 23 Pitman, Jim William 23 Yor, Marc 21 Lambert, Amaury 18 Khoshnevisan, Davar 18 Zhou, Xiaowen 17 Chaumont, Loïc 17 Patie, Pierre 17 Pistorius, Martijn R. 17 Song, Renming 17 Winkel, Matthias 16 Mandjes, Michel Robertus Hendrikus 15 Curien, Nicolas 15 Meerschaert, Mark M. 15 Rivero, Víctor Manuel 15 Simon, Thomas 14 Haas, Bénédicte 14 Iksanov, Aleksander M. 14 Vondraček, Zoran 14 Xiao, Yimin 13 Berestycki, Julien 13 Delmas, Jean-François 13 Möhle, Martin 13 Shi, Zhan 12 Chen, Zhen-Qing 12 Doney, Ronald Arthur 12 Gnedin, Alexander V. 12 Kuznetsov, Alexey 12 Li, Zenghu 12 Russo, Francesco 12 Savov, Mladen Svetoslavov 12 Zwart, Bert P. 11 Avram, Florin 11 Ivanovs, Jevgeņijs 11 Nane, Erkan 11 Uribe Bravo, Gerónimo 10 Döring, Leif 10 Griffin, Philip S. 10 Kim, Panki 10 Vallois, Pierre 10 Wang, Yuebao 10 Yamazaki, Kazutoshi 9 Berestycki, Nathanaël 9 Crane, Harry 9 Huillet, Thierry E. 9 Le Gall, Jean-François 9 Pérez Garmendia, Jose Luis 8 Abraham, Romain 8 Aurzada, Frank 8 Buchmann, Boris 8 Kella, Offer 8 Miermont, Grégory 8 Mijatović, Aleksandar 8 Yin, Chuancun 7 Baurdoux, Erik Jan 7 Boxma, Onno Johan 7 Czarna, Irmina 7 Escobedo Martínez, Miguel 7 Klüppelberg, Claudia 7 Leonenko, Nikolai N. 7 Limic, Vlada 7 Lindner, Alexander M. 7 Loeffen, Ronnie L. 7 Magdziarz, Marcin 7 Schilling, René Leander 7 Schweinsberg, Jason Ross 7 Straka, Peter 7 Vazquez, Juan Luis 7 Watson, Alexander R. 6 Bansaye, Vincent 6 Bogdan, Krzysztof 6 Caballero, María Emilia 6 Dereich, Steffen 6 Doumic, Marie 6 Egami, Masahiko 6 Grzywny, Tomasz 6 He, Hui 6 James, Lancelot F. 6 Janson, Svante 6 Kersting, Götz-Dietrich 6 Le Jan, Yves 6 Mai, Jan-Frederik 6 Marynych, Alexander V. 6 Mimica, Ante 6 Mischler, Stéphane 6 Pego, Robert L. 6 Profeta, Christophe 6 Renaud, Jean-François 6 Salminen, Paavo H. 6 Samorodnitsky, Gennady Pinkhosovich 6 Sire, Yannick 6 Toaldo, Bruno 6 Van Schaik, Kees 6 Vatutin, Vladimir Alekseevich 6 Wang, Kaiyong 6 Zabczyk, Jerzy ...and 1,555 more Authors
all top 5
#### Cited in 238 Serials
235 Stochastic Processes and their Applications 137 The Annals of Probability 90 The Annals of Applied Probability 81 Journal of Applied Probability 75 Statistics & Probability Letters 71 Probability Theory and Related Fields 70 Journal of Theoretical Probability 65 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 54 Advances in Applied Probability 49 Bernoulli 39 Journal of Statistical Physics 32 Insurance Mathematics & Economics 32 Electronic Journal of Probability 30 Transactions of the American Mathematical Society 28 Potential Analysis 26 Journal of Mathematical Analysis and Applications 18 Journal of Differential Equations 18 Journal of Functional Analysis 15 Finance and Stochastics 13 Queueing Systems 12 Communications in Mathematical Physics 12 Journal of Computational and Applied Mathematics 12 Stochastics 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Electronic Communications in Probability 10 Bulletin des Sciences Mathématiques 10 ALEA. Latin American Journal of Probability and Mathematical Statistics 9 Acta Applicandae Mathematicae 9 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 9 Scandinavian Actuarial Journal 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Applied Mathematics and Computation 8 Random Structures & Algorithms 8 Methodology and Computing in Applied Probability 7 Chaos, Solitons and Fractals 7 Probability Surveys 6 Physica A 6 Journal of Statistical Planning and Inference 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Abstract and Applied Analysis 6 Science China. Mathematics 5 Advances in Mathematics 5 Journal of Econometrics 5 Osaka Journal of Mathematics 5 Proceedings of the American Mathematical Society 5 Combinatorics, Probability and Computing 5 SIAM Journal on Financial Mathematics 4 Journal of Mathematical Physics 4 Theory of Probability and its Applications 4 Journal of Multivariate Analysis 4 Stochastic Analysis and Applications 4 Physica D 4 European Journal of Operational Research 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Theory of Probability and Mathematical Statistics 4 Fractional Calculus & Applied Analysis 4 Discrete and Continuous Dynamical Systems. Series B 4 Stochastics and Dynamics 4 Frontiers of Mathematics in China 3 Archive for Rational Mechanics and Analysis 3 Israel Journal of Mathematics 3 Rocky Mountain Journal of Mathematics 3 Annals of the Institute of Statistical Mathematics 3 Journal of Mathematical Psychology 3 Mathematische Zeitschrift 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Theoretical Population Biology 3 Japan Journal of Applied Mathematics 3 Revista Matemática Iberoamericana 3 Mathematical and Computer Modelling 3 SIAM Journal on Mathematical Analysis 3 Mathematical Methods of Operations Research 3 International Journal of Theoretical and Applied Finance 3 Extremes 3 Journal of the European Mathematical Society (JEMS) 3 Acta Mathematica Sinica. English Series 3 Stochastic Models 3 Kinetic and Related Models 3 Journal of Theoretical Biology 3 Journal de l’École Polytechnique – Mathématiques 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics 2 Discrete Mathematics 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Biology 2 Lithuanian Mathematical Journal 2 Metrika 2 The Annals of Statistics 2 Applied Mathematics and Optimization 2 Illinois Journal of Mathematics 2 Journal of Combinatorial Theory. Series A 2 Journal of Mathematical Economics 2 Journal of Optimization Theory and Applications 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Quarterly of Applied Mathematics 2 Tokyo Journal of Mathematics 2 Operations Research Letters ...and 138 more Serials
all top 5
#### Cited in 51 Fields
1,526 Probability theory and stochastic processes (60-XX) 214 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 161 Partial differential equations (35-XX) 112 Statistics (62-XX) 109 Statistical mechanics, structure of matter (82-XX) 100 Biology and other natural sciences (92-XX) 88 Combinatorics (05-XX) 62 Operator theory (47-XX) 60 Numerical analysis (65-XX) 44 Real functions (26-XX) 40 Operations research, mathematical programming (90-XX) 38 Measure and integration (28-XX) 37 Integral equations (45-XX) 34 Systems theory; control (93-XX) 28 Potential theory (31-XX) 24 Ordinary differential equations (34-XX) 20 Dynamical systems and ergodic theory (37-XX) 16 Special functions (33-XX) 15 Fluid mechanics (76-XX) 14 Integral transforms, operational calculus (44-XX) 14 Functional analysis (46-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Computer science (68-XX) 13 Number theory (11-XX) 10 Functions of a complex variable (30-XX) 10 Mechanics of particles and systems (70-XX) 9 Global analysis, analysis on manifolds (58-XX) 9 Quantum theory (81-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 4 Convex and discrete geometry (52-XX) 4 General topology (54-XX) 4 Information and communication theory, circuits (94-XX) 3 Mathematical logic and foundations (03-XX) 3 Sequences, series, summability (40-XX) 3 Differential geometry (53-XX) 3 Manifolds and cell complexes (57-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-04-16T04:19:24 |
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|
http://mathonline.wikidot.com/absolutely-summable-series
|
Absolutely Summable Series
Table of Contents
# Absolutely Summable Series
Definition: Let $(X, \| \cdot \|)$ be a normed linear space. A series $\displaystyle{\sum_{i=1}^{\infty} x_i}$ is said to Converge in $X$ if the sequence of partial sums$(s_n) = \left ( \sum_{i=1}^{n} x_i \right )$ converges in $X$.
We now define absolutely summable series in a normed linear space.
Definition: Let $(X, \| \cdot \|)$ be a normed linear space. A series $\displaystyle{\sum_{i=1}^{\infty} x_i}$ in $X$ is said to be Absolutely Summable if the numerical series $\displaystyle{\sum_{i=1}^{\infty} \| x_i \|}$ converges.
It is important to note that if we consider the $\mathbb{R}$ with the Euclidean norm, then absolute summability and absolute convergence is equivalent. In $\mathbb{R}$, every absolutely convergent series converges in $\mathbb{R}$. However, in a general normed space $(X, \| \cdot \|)$, absolute summability does NOT imply convergence of a series in $X$.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2018-04-21T13:37:10 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=M072W&home=sumtabM
|
${{\boldsymbol \psi}{(4040)}}$ WIDTH INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 80 \pm10}$ OUR ESTIMATE
$84.5$ $\pm12.3$ 1
2008 D
BES2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
• • • We do not use the following data for averages, fits, limits, etc. • • •
$87$ $\pm11$ 2
2010
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$85$ $\pm10$ 3
2005 A
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$89$ $\pm6$ 4
2005 A
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons
$52$ $\pm10$
1978 C
DASP ${{\mathit e}^{+}}{{\mathit e}^{-}}$
1 Reanalysis of data presented in BAI 2002C. From a global fit over the center-of-mass energy region $3.7 - 5.0$ GeV covering the ${{\mathit \psi}{(3770)}}$, ${{\mathit \psi}{(4040)}}$, ${{\mathit \psi}{(4160)}}$, and ${{\mathit \psi}{(4415)}}$ resonances. Phase angle fixed in the fit to $\delta$ = ($130$ $\pm46)^\circ{}$.
2 Reanalysis of data presented in BAI 2000 and BAI 2002C. From a global fit over the center-of-mass energy 3.8-4.8 GeV covering the ${{\mathit \psi}{(4040)}}$, ${{\mathit \psi}{(4160)}}$ and ${{\mathit \psi}{(4415)}}$ resonances and including interference effects.
3 From a fit to Crystal Ball (OSTERHELD 1986 ) data.
4 From a fit to BES (BAI 2002C) data.
References:
MO 2010
PR D82 077501 Leptonic Partial Widths of the Excited ${{\mathit \psi}}$ States
ABLIKIM 2008D
PL B660 315 Determination of the ${{\mathit \psi}{(3770)}}$, ${{\mathit \psi}{(4040)}}$, ${{\mathit \psi}{(4160)}}$ and ${{\mathit \psi}{(4415)}}$ Resonance Parameters
SETH 2005A
PR D72 017501 Alternative Analysis of the $\mathit R$ Measurements: Resonance Parameters of the Higher Vector States of Charmonium
BRANDELIK 1978C
PL 76B 361 Total Cross Section for Hadron Production by ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Annihilation at $\mathit E_{{\mathrm {cm}}}$ between 3.6 and 5.2 GeV
| 2019-12-05T19:41:44 |
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https://www.detailedpedia.com/wiki-Narain_Karthikeyan
|
# Narain Karthikeyan
Narain Karthikeyan
Karthikeyan at the 2011 Malaysian Grand Prix.
Nationality Indian
BornKumar Ram Narain Karthikeyan
14 January 1977 (age 43)
Coimbatore, Tamil Nadu, India
Years active1992 – present
Awards
2010 NASCAR Camping World Truck Series Most Popular Driver
Formula One World Championship career
Active years2005, 20112012
TeamsJordan, HRT
Entries48 (46 starts)
Championships0
Wins0
Podiums0
Career points5
Pole positions0
Fastest laps0
First entry2005 Australian Grand Prix
Last entry2012 Brazilian Grand Prix
NASCAR Camping World Truck Series career
9 races run over 1 year
2010 position30th
First race2010 Kroger 250 (Martinsville)
Last race2010 Mountain Dew 250 (Talladega)
Wins Top tens Poles
0 0 0
24 Hours of Le Mans career
Years2009
TeamsKolles
Best finish7th in LMP1 (2009)
Class wins0
Kumar Ram Narain Karthikeyan (born 14 January 1977)[1] is a racing driver who was the first Formula One driver from India.[2]
He has previously competed in A1GP, and the Le Mans Series. He has won multiple races in A1GP, British F3, World series by Nissan, AutoGP, Formula Asia, British Formula Ford & Opel series in his single-seater career. He won the British Formula Ford Winter Series in 1994 & Formula Asia Championship in 1996. He also finished fourth overall in British F3 in 2000 & the World Nissan series in 2003. He made his Formula One debut in 2005 with the Jordan team, and was a Williams F1 test driver in 2006 and 2007. Like several other former F1 drivers, Karthikeyan moved to stock car racing and drove the No. 60 Safe Auto Insurance Company Toyota Tundra for Wyler Racing in the 2010 NASCAR Camping World Truck Series.
In 2011, he returned to F1 with the HRT team, continued with the team in 2012 and was expected to drive for them in the 2013 season as well.
However, HRT was not included in the FIA's 2013 entry list, and thus Karthikeyan was left without a drive. From 2014–2018, Karthikeyan raced in Japanese Super Formula series.[3] In 2019, he ended his single-seater career by joining SuperGT series in Japan.
The Government of India awarded him the fourth highest civilian honour of Padma Shri in 2010.[4]
## Family background and early career
Karthikeyan was born in Coimbatore, Tamil Nadu.[5] He did his schooling at Stanes Anglo Indian Higher Secondary School in Coimbatore. His interest in motorsport began at an early age, as his father was a former Indian national rally champion winning South India Rally seven times. With the ambition of becoming India's first Formula One driver, Karthikeyan finished on the podium in his first ever race, at Sriperumpudur in a Formula Maruti (a.k.a. FISSME). He then went on to the Elf Winfield Racing School in France, showing his talent by becoming a semi-finalist in the Pilote Elf Competition for Formula Renault cars in 1992. He returned to India to race in Formula Maruti for the 1993 season, and in the same year, he also competed in the Formula Vauxhall Junior championship in Great Britain. This gave him valuable experience in European racing, and he was keen to return for the following year.
In 1994, he returned to the UK, racing in the Formula Ford Zetec series as the number two works Vector driver for the Foundation Racing team. The highlight of the season was a podium finish in a support race for the Portuguese Grand Prix held at Estoril. He also took part in the British Formula Ford Winter Series, and became the first Indian driver to win any championship in Europe.
In 1995, Karthikeyan graduated to the Formula Asia Championship for just four races. However, he showed pace immediately and was able to finish second in the race at Shah Alam, Malaysia. In 1996, he had a full season in the series and became the first Indian and the first Asian to win the Formula Asia International series. He moved back to Britain in 1997 to compete in the British Formula Opel Championship with the Nemesis Motorsport team, taking a pole position and win at Donington Park and finishing sixth in the overall points standings.
In 1998, Karthikeyan made his debut in the British Formula 3 Championship with the Carlin Motorsport team. Competing in only 10 rounds, he managed two third-place finishes in the final two races of the season, at Spa-Francorchamps and Silverstone, to finish 12th overall. He continued in the championship for 1999, finishing on the podium five times, including two wins at Brands Hatch. His season also included two pole positions, three fastest laps and two lap records, helping him to sixth in the championship. He also competed in the Macau Grand Prix, qualifying in sixth position and finishing sixth in the second race. He was the first racing driver to record a win for Carlin in British F3 ever since then Carlin have been invincible in terms of race wins in the British F3 Championship. Continuing his drive in the British F3 Championship in 2000, he finished fourth overall in the standings, and also took pole position and fastest laps in the Macau Grand Prix. He also won both the International F3 race at Spa-Francorchamps and the Korea Super Prix.
Karthikeyan started 2001 in the Formula Nippon F3000 Championship, finishing the year amongst the top ten. In the same year, he became the first Indian to ever drive a Formula One car, testing for the Jaguar Racing team at Silverstone on 14 June. Impressed with his performance, he was then offered a test drive in the Jordan-Honda EJ11 at Silverstone in September. Karthikeyan again tested for Jordan, at Mugello in Italy on 5 October, finishing just half a second off the pace off Jordan's lead driver Jean Alesi.
In 2002, he moved into the Telefónica World Series with Team Tata RC Motorsport, taking a pole position and setting the fastest non-Formula One lap time at the Interlagos Circuit in Brazil. Continuing in the renamed Superfund World Series in 2003, Karthikeyan won two races and took three other podium positions on his way to fourth overall in the championship. These results earned him another Formula One test drive, this time with the Minardi team. He was offered a race drive for the 2004 season, but was unable to raise the necessary sponsorship funds to seal the deal.
He continued in the Nissan World Series in 2004, taking wins in Valencia, Spain and Magny-Cours, France.
## Formula One career
### Jordan (2005)
Karthikeyan locking his brakes during qualifying at the 2005 United States Grand Prix
On 1 February 2005, Karthikeyan announced that he had signed a preliminary deal with the Jordan Formula One team and said that he would be their main driver for the 2005 Formula One season, making him India's first Formula One racing driver. His partner was Portuguese driver Tiago Monteiro. Karthikeyan completed the necessary testing distance of 300 km in an F1 car in order to gain his superlicence at the Silverstone Circuit on 10 February.
In his first race, the Australian Grand Prix, Karthikeyan qualified in 12th position. After a poor start which saw him drop to 18th place by the end of the first lap, he finished in 15th, two laps behind winner Giancarlo Fisichella. He achieved his first points in the 2005 United States Grand Prix where all but three teams pulled out due to an argument over tyre safety. He finished fourth, finishing ahead of the two Minardi drivers but behind teammate Monteiro. Apart from the USGP, his highest finish was 11th place. In the 2005 Japanese Grand Prix free practice, he was fastest for a long period and eventually qualified 11th. At the 2005 Chinese Grand Prix he qualified in 15th place. In an unlucky end to his 2005 season, Karthikeyan crashed his Jordan into a wall at the Chinese race, but was unhurt and able to provide an interview afterwards.
### A1 GP
In 2007 season Karthikeyan also drove for A1 Team India. He made his A1 GP debut in New Zealand and he finished 10th in the sprint race and 7th in the Feature Race.[25]
Karthikeyan won the A1GP of Zhuhai (China) for Team India on 16 December 2007. This was India's first A1GP win.[26] Karthikeyan is also the first to take pole position for India in the A1GP. He got pole in the feature race in Brands Hatch in 2008. Karthikeyan won two feature races in the 2007–2008 season, including the season finale at Brands Hatch starting from pole position. This helped India finish in the top ten, ahead of such as Australia, Brazil, China and Italy.
The 4th season for Team India was disastrous as the team lost its title sponsor, which resulted in severe financial constraints. On 3 May 2009 A1 Team India finished the season with a podium finish in the Sprint Race at Brands Hatch. Karthikeyan qualified the A1 Team India car in 7th place on the starting grid for the race. The Feature Race ended abruptly for Karthikeyan, as he was taken out by the spinning car of A1 Team China in front of him on the first corner of the first lap.[27]
The team finished 12th overall in the 2008–09 season.[28]
### 24 Hours of Le Mans
In the second week of March 2009, Karthikeyan tested for the Kolles Le Mans Team. It was later confirmed that for the 2009 season, he will be partnered by Christijan Albers. Team Kolles – headed by ex-Force India Team Principal Colin Kolles – will be taking part in the championship with two Audi R10 turbo diesel machines. The car boasts a successful racing history with three Le Mans 24h victories and 22 individual race wins to its name. Team Kolles joins the championship for the first time in 2009.[29][30][31]
On 11 May 2009, Karthikeyan finished sixth in his first ever Le Mans series race while driving for the Kolles Audi team in the second round of the 2009 championship held at the Spa-Francorchamps circuit in Belgium.[32] On 14 June 2009 Karthikeyan dislocated his shoulder in a fall just before the start of the race. He had come up with strong performances in the practice and the qualifying, and was scheduled to do the opening double stint. At 1:00 am the ACO organisation declared him unsuitable to drive, even though the Audi doctor approved it.[33]
### NASCAR
Karthikeyan made his NASCAR debut at Martinsville Speedway on 27 March 2010 driving in the Kroger 250 Camping World Truck Series for Wyler Racing in the #60 Safe Auto Insurance Company Chevrolet Silverado. Qualifying was rained out and the field set by 2009 owner points, putting the first Indian-born driver to compete in NASCAR in the 11th starting spot. After a slow start and coming to grips with driving a race truck and racing on an American oval short track for the first time, Karthikeyan did manage to put in a very respectable effort and finished on the lead lap in 13th place. Karthikeyan went on to win the NASCAR Camping World Truck Series Most Popular Driver Award for the 2010 season which was voted by the fans, becoming the first foreign-born driver to win the award.
### Superleague Formula
Karthikeyan drove for the PSV Eindhoven team in SLF in 2010. He won the 2nd race at Brands Hatch, Great Britain and finished 16th in the Championship on 288 points, taking part in six of the twelve race weekends.
Karthikeyan during the 2014 Super Formula season.
### Auto GP
Karthikeyan drove for Zele Racing and Super Nova Racing in the Auto GP series in 2013. After switching from Zele Racing to Super Nova Racing, in the latter part of the series, he won 5 races and secure 4 pole positions and in the process finished 4th in the championship & became the highest points scorer in the second half of the season.[34]
### Super Formula
In 2014, Karthikeyan returned to the Japanese Top Formula series Super Formula for the first time since 2001 with the same Team IMPUL. In the 2015 season, Karthikeyan moved to Honda-powered Docomo Team Dandelion. Karthikeyan moved to Sunoco Team LeMans for the 2016 season after DoCoMo Dandelion Racing chose McLaren Honda F1 Reserve Stoffel Vandoorne.
### Super GT
In 2019, Karthikeyan raced with Nakajima Racing for one race, winning the Fuji Super GT x DTM Dream Race in Fuji, gaining the fastest lap during the race. He then raced with Modulo Epson NSX-GT Team for 8 races, gaining one podium.
## Racing record
### Career summary
Season Series Team Races Wins Poles F/Laps Podiums Points Position
1992 Pilote Elf Competition for Formula Renault ? ? 1 ? ? ? ? ?
1993 Indian Formula Maruti ? ? ? ? ? ? ? ?
British Formula Vauxhall Junior ? ? ? ? ? ? ? ?
1994 British Formula Ford Winter Series ? ? ? ? ? ? ? 1st
1995 Formula Asia ? 4 ? ? ? ? ? ?
1996 Formula Asia Marlboro Castrol Meritus Racing Team ? ? ? ? ? ? 1st
1997 British Formula Vauxhall ? ? ? ? ? ? ? 8th
1998 British Formula 3 Championship Carlin Motorsport 10 0 0 0 2 44 12th
1999 British Formula 3 Championship Carlin Motorsport 16 2 2 3 4 104 6th
2000 British Formula 3 Championship Stewart Racing 14 0 0 0 4 100 4th
2001 Formula Nippon Team Impul 10 0 0 0 0 2 14th
2002 World Series by Nissan Tata RC Motorsport 18 0 1 0 1 51 9th
2003 World Series by Nissan Carlin Motorsport 18 0 0 0 4 121 4th
2004 World Series by Nissan Tata RC Motorsport 18 2 1 0 4 100 6th
2005 Formula One Jordan Grand Prix 19 0 0 0 0 5 18th
2006 Formula One Williams F1 Team Test driver
2006–07 A1 Grand Prix A1 Team India 10 0 0 0 0 13 16th
2007 Formula One Williams F1 Team Test driver
2007–08 A1 Grand Prix A1 Team India 18 2 1 0 2 61 10th
2008–09 A1 Grand Prix A1 Team India 12 0 0 0 1 19 12th
2009 24 Hours of Le Mans Kolles 1 0 0 0 0 N/A 7th
2010 Superleague Formula PSV Eindhoven 12 1 1 0 1 288 16th
NASCAR Camping World Truck Series Wyler Racing 9 0 0 0 0 963 30th
2011 Formula One HRT Formula 1 Team 9 0 0 0 0 0 26th
2012 Formula One HRT Formula 1 Team 20 0 0 0 0 0 24th
2013 Auto GP Zele Racing 6 0 0 1 0 195 4th
Super Nova International 10 5 4 2 7
2014 Super Formula Lenovo Team Impul 9 0 0 0 0 5 13th
2015 Super Formula Docomo Team Dandelion Racing 8 0 0 1 1 6 11th
2016 Super Formula Sunoco Team LeMans 9 0 0 1 1 5 14th
2016–17 MRF Challenge Formula 2000 MRF Racing 4 0 0 0 0 0 NC†
2017 Super Formula TCS Nakajima Racing 7 0 0 0 0 0 19th
2018 Super Formula TCS Nakajima Racing 6 0 0 0 0 4 15th
2019 Super GT Modulo Nakajima Racing 8 0 0 0 1 23.5 12th
Super GT × DTM Dream Race – Race 2 1 1 0 1 1 N/A 1st
As Karthikeyan was a guest driver, he was ineligible for points.
### Complete Formula Nippon/Super Formula results
(key)
Year Entrant 1 2 3 4 5 6 7 8 9 10 DC Points
2001 excite Impul SUZ
6
MOT
7
MIN
9
FUJ
Ret
SUZ
Ret
SUG
13
FUJ
9
MIN
Ret
MOT
14
SUZ
6
14th 2
2014 Lenovo Team Impul SUZ
Ret
FUJ
7
FUJ
6
FUJ
7
MOT
Ret
AUT
17
SUG
11
SUZ
10
SUZ
8
13th 5
2015 Docomo Team Dandelion Racing SUZ
3
OKA
10
FUJ
Ret
MOT
9
AUT
14
SUG
13
SUZ
12
SUZ
14
11th 6
2016 Sunoco Team LeMans SUZ
Ret
OKA
16
FUJ
7
MOT
Ret
OKA
3
OKA
Ret
SUG
12
SUZ
15
SUZ
14
14th 5
2017 TCS Nakajima Racing SUZ
13
OKA
17
OKA
13
FUJ
14
MOT
Ret
AUT
Ret
SUG
13
SUZ
C
SUZ
C
19th 0
2018 TCS Nakajima Racing SUZ
17
AUT
C
SUG
5
FUJ
16
MOT
11
OKA
13
SUZ
17
15th 4
### Complete Formula One results
(key)
Year Entrant Chassis Engine 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 WDC Points
2005 Jordan Grand Prix Jordan EJ15 Toyota RVX-05 3.0 V10 AUS
15
MAL
11
BHR
Ret
SMR
12
ESP
13
MON
Ret
EUR
16
CAN
Ret
USA
4
FRA
15
GBR
Ret
GER
16
HUN
12
TUR
14
ITA
20
18th 5
Jordan EJ15B BEL
11
BRA
15
JPN
15
CHN
Ret
2011 Hispania Racing F1 Team Hispania F111 Cosworth CA2011 2.4 V8 AUS
DNQ
MAL
Ret
CHN
23
TUR
21
ESP
21
MON
17
CAN
17
EUR
24
GBR 26th 0
HRT Formula 1 Team GER
TD
HUN BEL ITA SIN
TD
JPN
TD
KOR
TD
IND
17
ABU BRA
2012 HRT Formula 1 Team HRT F112 Cosworth CA2012 2.4 V8 AUS
DNQ
MAL
22
CHN
22
BHR
21
ESP
Ret
MON
15
CAN
Ret
EUR
18
GBR
21
GER
23
HUN
Ret
BEL
Ret
ITA
19
SIN
Ret
JPN
Ret
KOR
20
IND
21
ABU
Ret
USA
22
BRA
18
24th 0
### Complete A1 Grand Prix results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Year Entrant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 DC Points
2006–07 India NED
SPR
NED
FEA
CZE
SPR
CZE
FEA
CHN
SPR
CHN
FEA
MYS
SPR
MYS
FEA
IDN
SPR
IDN
FEA
NZL
SPR
10
NZL
FEA
7
AUS
SPR
AUS
FEA
RSA
SPR
15
RSA
FEA
9
MEX
SPR
11
MEX
FEA
18
CHN
SPR
7
CHN
FEA
17
GBR
SPR
7
GBR
SPR
4
16th 13
2007–08 NED
SPR
10
NED
FEA
Ret
CZE
SPR
21
CZE
FEA
9
MYS
SPR
11
MYS
FEA
6
CHN
SPR
7
CHN
FEA
1
NZL
SPR
10
NZL
FEA
Ret
AUS
SPR
11
AUS
FEA
11
RSA
SPR
RSA
FEA
MEX
SPR
13
MEX
FEA
9
CHN
SPR
5
CHN
FEA
7
GBR
SPR
5
GBR
FEA
1
10th 61
2008–09 NED
SPR
NED
FEA
CHN
SPR
10
CHN
FEA
10
MYS
SPR
Ret
MYS
FEA
Ret
NZL
SPR
9
NZL
FEA
7
RSA
SPR
6
RSA
FEA
12
POR
SPR
6
POR
FEA
11
GBR
SPR
2
GBR
FEA
Ret
12th 19
### Superleague Formula
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Year Team Operator 1 2 3 4 5 6 7 8 9 10 11 12 Position Points
2010 PSV Eindhoven Racing for Holland SIL
ASS
MAG
JAR
NÜR
ZOL
BRH
POR
ORD
BEI
NAV
16th 288
12 15 X 13 9 X 11 15 X 13 16 X 10 14 X 18 1 X
### 24 Hours of Le Mans results
Year Team Co-Drivers Car Class Laps Pos. Class
Pos.
2009 Kolles Charles Zwolsman, Jr.
André Lotterer
Audi R10 TDI LMP1 369 7th 7th
### Complete Auto GP results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Year Entrant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pos Points
2013 Zele Racing MNZ
1
5
MNZ
2
Ret
MAR
1
6
MAR
2
Ret
HUN
1
8
HUN
2
4
4th 195
Super Nova International SIL
1
1
SIL
2
12
MUG
1
3
MUG
2
1
NÜR
1
1
NÜR
2
5
DON
1
2
DON
2
1
BRN
1
1
BRN
2
DSQ
### NASCAR
(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
#### Camping World Truck Series
NASCAR Camping World Truck Series results
Year Team No. Make 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 NCWTC Pts
2010 Wyler Racing 60 Chevy DAY ATL MAR
13
NSH KAN
36
DOV CLT
17
TEX
11
MCH IOW GTY IRP
20
POC NSH
17
DAR BRI CHI
14
KEN NHA LVS
27
MAR TAL
13
TEX PHO HOM 30th 963
### Complete Super GT results
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
Year Team Car Class 1 2 3 4 5 6 7 8 DC Points
2019 Modulo Nakajima Racing Honda NSX-GT GT500 OKA
10
FUJ
10
SUZ
11
CHA
10
FUJ
10
AUT
7
SUG
2
MOT
12
12th 23.5
## References
1. ^ "Narain Karthikeyan biography, Hispania Racing". HispaniaF1Team.com. 10 April 2011. Archived from the original on 6 September 2012.
2. ^ Pande, Vinayak (16 March 2011). "Didn't want to spend my life thinking what if: Narain Karthikeyan". Hindustan Times. New Delhi: HT Media Limited. Archived from the original on 20 March 2011. Retrieved 15 March 2011.
3. ^ "Narain Karthikeyan to race in 2014 Super Formula season". Daily News and Analysis. 5 February 2014.
4. ^ "Padma Awards" (PDF). Ministry of Home Affairs, Government of India. 2015. Archived from the original (PDF) on 15 October 2015. Retrieved 21 July 2015.
5. ^ TV9 Telugu (26 April 2015). "Manaku Teliyani Mana Charitra – Coimbatore – Tv9". Retrieved 1 December 2016 – via YouTube.
6. ^ "Williams Confirms Narain Karthikeyan". NewsOnF1.com. 27 January 2006. Retrieved 4 May 2006.
7. ^ "Williams retain Karthikeyan for 2007". 28 September 2006. Archived from the original on 21 August 2019. Retrieved 28 September 2006.
8. ^ "Karthikeyan 'Blown away' by F1 contrast". F1racing.net. 12 December 2006. Retrieved 24 October 2006.
9. ^ "Karthikeyan versus Piquet for Spyker". grandprix.com. 10 July 2007. Retrieved 12 July 2007.
10. ^ Noble, Jonathan (4 March 2010). "Chandhok announced as HRT driver". Autosport. Retrieved 4 March 2010.
11. ^ Noble, Jonathan (6 January 2011). "Karthikeyan signs race deal with HRT". Autosport. Retrieved 6 January 2011.
12. ^ Weeks, Jimmy (6 January 2011). "KARTHIKEYAN LANDS HISPANIA DRIVE FOR 2011". F1Badger.com. Archived from the original on 11 January 2011. Retrieved 6 January 2011.
13. ^ "European Grand Prix from the pit lane". BBC. 26 June 2011. Retrieved 26 June 2011.
14. ^
15. ^ "Karthikeyan to race in India for HRT". Formula One. 17 September 2011.
16. ^ "Karthikeyan to replace Liuzzi for Indian GP". ManipeF1.com. 23 October 2011. Archived from the original on 28 October 2011.
17. ^ "2011 Airtel Formula 1 Grand Prix of India Qualifying Results". Formula One. 29 October 2011.
18. ^ Elizalde, Pablo (29 October 2011). "Karthikeyan penalised for impeding Schumacher during qualifying". Autosport. Retrieved 9 November 2011.
19. ^ "Karthikeyan proved his worth at the Indian Grand Prix 2011". aaformula1.com. 30 October 2011. Archived from the original on 2 November 2011.
20. ^ "2011 Airtel Formula 1 Grand Prix of India Race (Timing Archive)". Formula One. 30 October 2011.
21. ^ "Liuzzi braces for 'tricky' Yas circuit". Gulf News. 8 November 2011.
22. ^ "Narain Karthikeyan joins HRT F1 team for 2012 season". BBC Sport. BBC. 3 February 2012. Retrieved 13 October 2017.
23. ^ "Sebastian Vettel criticises 'idiot' backmarker in Malaysian GP". BBC. 26 March 2012. Retrieved 30 March 2012.
24. ^ a b "Karthikeyan keen to move on from Vettel 'cry baby' comment". BBC. 30 March 2012. Retrieved 30 March 2012.
25. ^ "With change of heart, Narain says yes to A-1". Hindustan Times. 16 January 2007. Archived from the original on 30 September 2007. Retrieved 17 January 2007.
26. ^ "Earth Times: show/159637.html". earthtimes.org. Retrieved 1 December 2016.
27. ^ "Archived copy". Archived from the original on 9 October 2009. Retrieved 14 May 2009.CS1 maint: archived copy as title (link)
28. ^ "Archived copy". Archived from the original on 9 October 2008. Retrieved 14 May 2009.CS1 maint: archived copy as title (link)
29. ^ "Karthikeyan invited to Kolles Le Mans test". GPUpdate.net. 4 March 2009. Retrieved 31 January 2011.
30. ^ "Albers signs with Kolles Le Mans team". GPUpdate.net. 1 April 2009. Retrieved 31 January 2011.
31. ^ Release, News (31 March 2009). "Team Kolles confirms drivers and Audi R10 livery". planetlemans.com. Retrieved 1 December 2016.
32. ^ "Karthikeyan does well to finish 6th". The Telegraph. Calcutta, India. 12 May 2009.
33. ^ "Karthikeyan rejected to drive at Le Mans". f1technical.net. Retrieved 1 December 2016.
34. ^ "Narain Karthikeyan ends Auto GP season with five wins". DNA India. 6 October 2013.
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| 2022-01-19T02:01:55 |
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|
https://par.nsf.gov/biblio/10129949-optimal-decision-tree-noisy-outcomes
|
Optimal Decision Tree with Noisy Outcomes
A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis). Our new approximation algorithms provide guarantees that are nearly best-possible and work for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades smoothly with this number. Our results adapt and generalize more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10129949
Journal Name:
Advances in neural information processing systems
Page Range or eLocation-ID:
3298-3308
ISSN:
1049-5258
National Science Foundation
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2. Abstract—Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing elimination in polylogarithmic time per elimination and query. We then study the problem of using this data structure in the minimum degree algorithm, which is a widely- used heuristic for producing elimination orderings for sparse matrices by repeatedly eliminating the vertex with (approx- imate) minimum fill degree. This leads to a nearly-linear time algorithm for generating approximate greedy minimum degree orderings. Despite extensive studies of algorithms for elimination orderings in combinatorial scientific computing, our result is the first rigorous incorporation of randomized tools in this setting, as well as the first nearly-linear time algorithm for producing elimination orderings with provable approximation guarantees. While our sketching data structure readily works in the oblivious adversary model, by repeatedly querying and greed- ily updating itself, it enters the adaptive adversarial model where the underlying sketches become prone to failure due to dependency issues with their internal randomness. We show how to use an additional sampling procedure to circumvent this problem and to create an independent access sequence. Ourmore »
3. Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing elimination in O(polylog(n)) time per elimination and query. We then study the problem of using this data structure in the minimum degree algorithm, which is a widely-used heuristic for producing elimination orderings for sparse matrices by repeatedly eliminating the vertex with (approximate) minimum fill degree. This leads to a nearly-linear time algorithm for generating approximate greedy minimum degree orderings. Despite extensive studies of algorithms for elimination orderings in combinatorial scientific computing, our result is the first rigorous incorporation of randomized tools in this setting, as well as the first nearly-linear time algorithm for producing elimination orderings with provable approximation guarantees. While our sketching data structure readily works in the oblivious adversary model, by repeatedly querying and greedily updating itself, it enters the adaptive adversarial model where the underlying sketches become prone to failure due to dependency issues with their internal randomness. We show how to use an additional sampling procedure to circumvent this problem and to create an independent access sequence. Our technique for decorrelatingmore »
4. ; (Ed.)
We consider the following surveillance problem: Given a set P of n sites in a metric space and a set R of k robots with the same maximum speed, compute a patrol schedule of minimum latency for the robots. Here a patrol schedule specifies for each robot an infinite sequence of sites to visit (in the given order) and the latency L of a schedule is the maximum latency of any site, where the latency of a site s is the supremum of the lengths of the time intervals between consecutive visits to s. When k = 1 the problem is equivalent to the travelling salesman problem (TSP) and thus it is NP-hard. For k ≥ 2 (which is the version we are interested in) the problem becomes even more challenging; for example, it is not even clear if the decision version of the problem is decidable, in particular in the Euclidean case. We have two main results. We consider cyclic solutions in which the set of sites must be partitioned into 𝓁 groups, for some 𝓁 ≤ k, and each group is assigned a subset of the robots that move along the travelling salesman tour of the group atmore »
5. Abstract
In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical testing, DNA sequencing, communication protocols and many more. In this paper, we study (i) a sparsity-constrained version of the problem, in which the testing procedure is subjected to one of the following two constraints: items are finitely divisible and thus may participate in at most $\gamma$ tests; or tests are size-constrained to pool no more than $\rho$ items per test; and (ii) a noisy version of the problem, where each test outcome is independently flipped with some constant probability. Under each of these settings, considering the for-each recovery guarantee with asymptotically vanishing error probability, we introduce a fast splitting algorithm and establish its near-optimality not only in terms of the number of tests, but also in terms of the decoding time. While the most basic formulations of our algorithms require $\varOmega (n)$ storage for each algorithm, we also provide low-storage variants based on hashing, with similar recovery guarantees.
| 2023-03-23T10:28:56 |
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|
http://dlmf.nist.gov/24.16
|
# §24.16 Generalizations
## §24.16(i) Higher-Order Analogs
### ¶ Polynomials and Numbers of Integer Order
For , Bernoulli and Euler polynomials of order are defined respectively by
When they reduce to the Bernoulli and Euler numbers of order :
Also for ,
For this and other properties see Milne-Thomson (1933, pp. 126–153) or Nörlund (1924, pp. 144–162).
For extensions of to complex values of , , and , and also for uniform asymptotic expansions for large and large , see Temme (1995b).
### ¶ Degenerate Bernoulli Numbers
For sufficiently small ,
24.16.7
Here again denotes the Stirling number of the first kind.
### ¶ Nörlund Polynomials
is a polynomial in of degree . (This notation is consistent with (24.16.3) when .)
## §24.16(ii) Character Analogs
Let be a primitive Dirichlet character (see §27.8). Then is called the conductor of . Generalized Bernoulli numbers and polynomials belonging to are defined by
Let be the trivial character and the unique (nontrivial) character with ; that is, , , . Then
For further properties see Berndt (1975a).
## §24.16(iii) Other Generalizations
In no particular order, other generalizations include: Bernoulli numbers and polynomials with arbitrary complex index (Butzer et al. (1992)); Euler numbers and polynomials with arbitrary complex index (Butzer et al. (1994)); q-analogs (Carlitz (1954b), Andrews and Foata (1980)); conjugate Bernoulli and Euler polynomials (Hauss (1997, 1998)); Bernoulli–Hurwitz numbers (Katz (1975)); poly-Bernoulli numbers (Kaneko (1997)); Universal Bernoulli numbers (Clarke (1989)); -adic integer order Bernoulli numbers (Adelberg (1996)); -adic -Bernoulli numbers (Kim and Kim (1999)); periodic Bernoulli numbers (Berndt (1975b)); cotangent numbers (Girstmair (1990b)); Bernoulli–Carlitz numbers (Goss (1978)); Bernoulli-Padé numbers (Dilcher (2002)); Bernoulli numbers belonging to periodic functions (Urbanowicz (1988)); cyclotomic Bernoulli numbers (Girstmair (1990a)); modified Bernoulli numbers (Zagier (1998)); higher-order Bernoulli and Euler polynomials with multiple parameters (Erdélyi et al. (1953a, §§1.13.1, 1.14.1)).
| 2014-03-09T03:22:35 |
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|
https://www.usgs.gov/center-news/volcano-watch-ten-year-lava-flow-k-laueas-episode-51-continues
|
# Volcano Watch — Ten-year lava flow from Kīlauea's episode 51 continues
Release Date:
The 10-year long eruption of Kīlauea Volcano continues from the episode 51 vents located on the west flank of the Puu Oo cone. The flows advanced slowly from October 3 until October 28, when they began to flow over the pali above Kamoamoa.
The 10-year long eruption of Kīlauea Volcano continues from the episode 51 vents located on the west flank of the Puu Oo cone. The flows advanced slowly from October 3 until October 28, when they began to flow over the pali above Kamoamoa.
By Wednesday afternoon, this aa flow had advanced rapidly to roughly the 1,000-foot level. By Friday morning, the flow had advanced only a little more, to the 900-foot level, but was getting wider as the lavaspread out. These new flows are located west of the westernmost aa flow erupted in 1986 from the Puu Oo cone. The last flows to advance this far moved down the pali to the east of the 1986 aa flow to the 1,000-foot level in late July. These active flows are clearly visible from the Chain of Craters Road near Kamoamoa inside Hawaii Volcanoes National Park.
The earthquake that preceded the start of the episode 52 eruption on October 2 has apparently changed the plumbing beneath Puu Oo. Before the earthquake occurred, the lava pond inside Puu Oo had been at high levels, perhaps 125 feet below the rim of the cone, during eruptive intervals and around 250 feet below the rim, during pauses in the eruption. Soon after the start of episode 52, and the slightly later start-up of the episode 51 vents, the pond has remained deep, around 250 feet below the rim, yet the eruption at the episode 51 vents continues.
In addition, the level of activity inside the Puu Oo pond has been higher than previously seen. These high levels of activity apparently cause the extremely strong harmonic tremor (ground variation) that we have recorded periodically on our seismic stations during the last week and a half. The lava has been streaming across the pond surface from the north side toward the east side, where it cascades 40 to 50 feet back into a deeper level in the cone.
The episode 51 vents have been the site of intense degassing in the last month, but no glow or spatter has been observed there since late September. The lava from the episode 51 vents is being fed downslope through tubes above the 2,100-foot elevation. Below that point, there are small pahoehoe flows above the pali, but most of the lava is flowing down the steep pali as a channelized aa flow. At times these flows stagnate and solidify, and at other times, the incandescent aa surges downslope.
Most of the eruptive intervals since last February have lasted one to two weeks. These active periods were separated by inactive periods. After each inactive period, the lava reoccupies only a small part of the lava tubesystem, so the flows pond near the vent. With longer eruptive periods, the tube system develops, and lava can flow far from the vents, eventually reaching the pali, or beyond. The longest occurred from June 21 to July 23 for a total of 32 days. The current eruptive interval started on October 2, so has already been active for 27 days. If we use past behavior to predict the future, then it seems likely that this eruptive interval will stop within a few days before the flows advance across the coastal plain to the Chain of Craters Road and the ocean beyond. However, the October 2 earthquake changed the volcanic system, and the maximum duration of past active periods may no longer be applicable. If this eruption continues longer than any previous active periods, the flows will slowly advance towards the ocean near Laeapuki, just west of Kamoamoa.
| 2020-09-24T19:24:34 |
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|
https://lammps.sandia.gov/doc/fix_python_move.html
|
# fix python/move command
## Syntax
fix python/move pymodule.CLASS
pymodule.CLASS = use class CLASS in module/file pymodule to compute how to move atoms
## Examples
fix 1 all python/move py_nve.NVE
fix 1 all python/move py_nve.NVE_OPT
## Description
The python/move fix style provides a way to define ways how particles are moved during an MD run from python script code, that is loaded from a file into LAMMPS and executed at the various steps where other fixes can be executed. This python script must contain specific python class definitions.
This allows to implement complex position updates and also modified time integration methods. Due to python being an interpreted language, however, the performance of this fix can be moderately to significantly slower than the corresponding C++ code. For specific cases, this performance penalty can be limited through effective use of NumPy.
from __future__ import print_function
import lammps
import ctypes
import traceback
import numpy as np
#
class LAMMPSFix(object):
def __init__(self, ptr, group_name="all"):
self.lmp = lammps.lammps(ptr=ptr)
self.group_name = group_name
#
class LAMMPSFixMove(LAMMPSFix):
def __init__(self, ptr, group_name="all"):
super(LAMMPSFixMove, self).__init__(ptr, group_name)
#
def init(self):
pass
#
def initial_integrate(self, vflag):
pass
#
def final_integrate(self):
pass
#
def initial_integrate_respa(self, vflag, ilevel, iloop):
pass
#
def final_integrate_respa(self, ilevel, iloop):
pass
#
def reset_dt(self):
pass
Any classes implementing new atom motion functionality have to be derived from the LAMMPSFixMove class, overriding the available methods as needed.
Examples for how to do this are in the examples/python folder.
Restart, fix_modify, output, run start/stop, minimize info:
No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
## Restrictions
This pair style is part of the PYTHON package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
| 2020-06-01T15:27:22 |
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|
https://www.usgs.gov/node/278781
|
# Naturally Occurring Uranium in Groundwater in Northeastern Washington State
May 27, 2020
Uranium is a radioactive element (radionuclide) that occurs naturally in rock, soil, and water – usually in low concentrations. Radionuclides are unstable atoms with excess energy and as radionuclides decay, they emit radiation. The uranium decay sequence also includes other radionuclides of concern such as radium and radon (DeSimone and others, 2014).
| 2023-01-29T03:58:15 |
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|
https://www.zbmath.org/authors/?q=ai%3Ahutchinson.kevin
|
# zbMATH — the first resource for mathematics
## Hutchinson, Kevin
Compute Distance To:
Author ID: hutchinson.kevin Published as: Hutchinson, K.; Hutchinson, Kevin External Links: MGP · Wikidata
Documents Indexed: 23 Publications since 1990 Reviewing Activity: 74 Reviews
all top 5
#### Co-Authors
15 single-authored 4 Tao, Liqun 1 Bustamante, Miguel D. 1 Lvov, Yuri V. 1 Onorato, Miguel 1 Ryan, Dermot 1 Vlasenko, Masha 1 Wendt, Matthias
all top 5
#### Serials
5 Journal of Number Theory 4 Journal of Pure and Applied Algebra 3 Acta Arithmetica 2 Journal of Algebra 1 Communications in Algebra 1 Transactions of the American Mathematical Society 1 $$K$$-Theory 1 Algebra Colloquium 1 Documenta Mathematica 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Homotopy and Related Structures 1 Journal of $$K$$-Theory
all top 5
#### Fields
19 $$K$$-theory (19-XX) 12 Group theory and generalizations (20-XX) 9 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Ordinary differential equations (34-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX)
#### Citations contained in zbMATH
19 Publications have been cited 90 times in 48 Documents Cited by Year
The third homology of the special linear group of a field. Zbl 1187.19002
Hutchinson, Kevin; Tao, Liqun
2009
The 2-Sylow subgroup of the wild kernel of exceptional number fields. Zbl 1012.11102
Hutchinson, Kevin
2001
A new approach to Matsumoto’s theorem. Zbl 0725.19001
Hutchinson, Kevin
1990
A Bloch-Wigner complex for $$\mathrm{SL}_{2}$$. Zbl 1284.19003
Hutchinson, Kevin
2013
On tame and wild kernels of special number fields. Zbl 1082.11076
Hutchinson, Kevin
2004
On the low-dimensional homology of $$\mathrm{SL}_2(k [t, t^{- 1}])$$. Zbl 1310.19004
Hutchinson, Kevin
2015
A refined Bloch group and the third homology of $$\mathrm{SL}_2$$ of a field. Zbl 1281.19003
Hutchinson, Kevin
2013
Homology stability for the special linear group of a field and Milnor-Witt $$K$$-theory. Zbl 1216.19005
Hutchinson, Kevin; Tao, Liqun
2010
Étale wild kernels of exceptional number fields. Zbl 1163.11074
Hutchinson, Kevin
2006
The third homology of $$\mathrm {SL}_2$$ of local rings. Zbl 1444.20029
Hutchinson, Kevin
2017
A note on Milnor-Witt $$K$$-theory and a theorem of Suslin. Zbl 1205.19007
Hutchinson, Kevin; Tao, Liqun
2008
Hilbert symbols as maps of functors. Zbl 1067.19003
Hutchinson, Kevin; Ryan, Dermot
2004
Norm groups of global fields. Zbl 0822.11074
Hutchinson, Kevin
1995
The third homology of $$\mathrm{SL}_2$$ of fields with discrete valuation. Zbl 1357.19003
Hutchinson, Kevin
2017
On the third homology of $$\mathrm{SL}_2$$ and weak homotopy invariance. Zbl 1330.20069
Hutchinson, Kevin; Wendt, Matthias
2015
Conditions under which $$K_2(\mathcal O_F)$$ is not generated by Dennis-Stein symbols. Zbl 0936.11066
Hutchinson, Kevin
1999
Hecke actions on the $$K$$-theory of commutative rings. Zbl 0863.19001
Hutchinson, Kevin
1996
Milnor-Witt $$K$$-theory and tensor powers of the augmentation ideal of $$\mathbb Z[F^\times]$$. Zbl 1282.19006
Hutchinson, Kevin; Tao, Liqun
2013
On relative integral bases for unramified extensions. Zbl 0815.11054
Hutchinson, Kevin
1995
The third homology of $$\mathrm {SL}_2$$ of local rings. Zbl 1444.20029
Hutchinson, Kevin
2017
The third homology of $$\mathrm{SL}_2$$ of fields with discrete valuation. Zbl 1357.19003
Hutchinson, Kevin
2017
On the low-dimensional homology of $$\mathrm{SL}_2(k [t, t^{- 1}])$$. Zbl 1310.19004
Hutchinson, Kevin
2015
On the third homology of $$\mathrm{SL}_2$$ and weak homotopy invariance. Zbl 1330.20069
Hutchinson, Kevin; Wendt, Matthias
2015
A Bloch-Wigner complex for $$\mathrm{SL}_{2}$$. Zbl 1284.19003
Hutchinson, Kevin
2013
A refined Bloch group and the third homology of $$\mathrm{SL}_2$$ of a field. Zbl 1281.19003
Hutchinson, Kevin
2013
Milnor-Witt $$K$$-theory and tensor powers of the augmentation ideal of $$\mathbb Z[F^\times]$$. Zbl 1282.19006
Hutchinson, Kevin; Tao, Liqun
2013
Homology stability for the special linear group of a field and Milnor-Witt $$K$$-theory. Zbl 1216.19005
Hutchinson, Kevin; Tao, Liqun
2010
The third homology of the special linear group of a field. Zbl 1187.19002
Hutchinson, Kevin; Tao, Liqun
2009
A note on Milnor-Witt $$K$$-theory and a theorem of Suslin. Zbl 1205.19007
Hutchinson, Kevin; Tao, Liqun
2008
Étale wild kernels of exceptional number fields. Zbl 1163.11074
Hutchinson, Kevin
2006
On tame and wild kernels of special number fields. Zbl 1082.11076
Hutchinson, Kevin
2004
Hilbert symbols as maps of functors. Zbl 1067.19003
Hutchinson, Kevin; Ryan, Dermot
2004
The 2-Sylow subgroup of the wild kernel of exceptional number fields. Zbl 1012.11102
Hutchinson, Kevin
2001
Conditions under which $$K_2(\mathcal O_F)$$ is not generated by Dennis-Stein symbols. Zbl 0936.11066
Hutchinson, Kevin
1999
Hecke actions on the $$K$$-theory of commutative rings. Zbl 0863.19001
Hutchinson, Kevin
1996
Norm groups of global fields. Zbl 0822.11074
Hutchinson, Kevin
1995
On relative integral bases for unramified extensions. Zbl 0815.11054
Hutchinson, Kevin
1995
A new approach to Matsumoto’s theorem. Zbl 0725.19001
Hutchinson, Kevin
1990
all top 5
#### Cited by 43 Authors
13 Hutchinson, Kevin 5 Mirzaii, Behrooz 4 Jaulent, Jean-François 4 Wendt, Matthias 3 Soriano-Gafiuk, Florence 2 Burciu, Sebastian M. 2 Caputo, Luca 2 Cathelineau, Jean-Louis 2 Movahhedi, Abbas 2 Pauli, Sebastian 2 Pohst, Michael E. 2 Tao, Liqun 1 Asok, Aravind 1 Banaszak, Grzegorz 1 Cohen, Henri 1 Diaz y Diaz, Francisco 1 Dorbidi, Hamid Reza 1 Elbaz-Vincent, Philippe 1 Essert, Jan 1 Fallah-Moghaddam, R. 1 Fasel, Jean 1 Fleck, Norman A. 1 Gille, Stefan G. 1 Hutchinson, R. G. 1 Knudson, Kevin P. 1 Kolster, Manfred 1 Mahdavi-Hezavehi, M. 1 Mazzoleni, Amedeo 1 Michel, Alexis 1 Mokari, Fatemeh Y. 1 Olivier, Michel 1 Rahm, Alexander Daniel 1 Ryan, Dermot 1 Schlichting, Marco 1 Scully, Stephen 1 Stepanov, Alexeĭ Vladimirovich 1 Stern, Leonid 1 Symons, D. D. 1 Vavilov, Nikolaĭ Aleksandrovich 1 Weibel, Charles A. 1 Werner, Nicholas J. 1 Williams, Ben 1 Zhong, Changlong
all top 5
#### Cited in 23 Serials
9 Journal of Number Theory 9 Journal of Pure and Applied Algebra 4 Journal of Algebra 3 Journal of $$K$$-Theory 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Algebra Colloquium 2 Journal of Homotopy and Related Structures 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Mathematics of Computation 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Transactions of the American Mathematical Society 1 Journal of Symbolic Computation 1 $$K$$-Theory 1 Journal de Théorie des Nombres de Bordeaux 1 Journal of Mathematical Sciences (New York) 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
all top 5
#### Cited in 12 Fields
33 $$K$$-theory (19-XX) 23 Group theory and generalizations (20-XX) 17 Number theory (11-XX) 6 Algebraic geometry (14-XX) 4 Associative rings and algebras (16-XX) 4 Category theory; homological algebra (18-XX) 3 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Geometry (51-XX) 1 Mechanics of deformable solids (74-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-25T17:37:21 |
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|
http://dlmf.nist.gov/35.11
|
§35.11 Tables
Tables of zonal polynomials are given in James (1964) for $|\kappa|\leq 6$, Parkhurst and James (1974) for $|\kappa|\leq 12$, and Muirhead (1982, p. 238) for $|\kappa|\leq 5$. Each table expresses the zonal polynomials as linear combinations of monomial symmetric functions.
| 2016-10-01T20:40:24 |
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|
https://www.usgs.gov/center-news/photo-and-video-chronology-k-lauea-may-20-2021
|
# Photo and Video Chronology – Kīlauea – May 20, 2021
Release Date:
Kīlauea's summit eruption continues on the Island of Hawai‘i; Halema‘uma‘u west vent erupts lava into the lava lake, which was 229 m (751 ft) deep this morning, May 20. Gas emissions and seismic activity at the summit remain elevated. HVO field crews—equipped with specialized safety gear—monitor the eruption from within the closed area of Hawai‘i Volcanoes National Park with NPS permission.
HVO scientists collect detailed data to assess hazards and understand how the eruption is evolving at Kīlauea's summit, all of which are shared with the National Park Service and emergency managers. Access to this hazardous area is by permission from, and in coordination with, Hawai‘i Volcanoes National Park.
### May 19, 2021 — Kīlauea
The area of active surface lava has diminished over the past month in Halemaumau crater, at the summit of Kilauea. Yesterday, active surface lava was limited to a small pond, about 20 meters (yards) long. The pond surface was normally covered with a stationary crust, but occasionally resurfaced. This video shows crustal foundering during a resurfacing event. A gust of wind shakes the camera at the start of the video.
Matt Patrick, USGS Hawaiian Volcanoes Observatory
(Public domain.)
### Active surface lava limited to a small pond in Halema‘uma‘u
This comparison of thermal images taken from the south rim of Halema‘uma‘u, at the summit of Kīlauea, show the diminishing area of active lava on the surface over the past month. Yesterday, active lava was limited to a small pond, about 20 meters (yards) long, near the western fissure. USGS images by M. Patrick.
(Public domain.)
Active surface lava in Halema‘uma‘u, at the summit of Kīlauea, is now limited to a small lava pond near the western fissure. Normally the lava pond is covered in a stationary crust, as shown by the image on the left. Occasionally, the pond abruptly resurfaces with fluid lava, with foundering of crustal plates and abundant bubbling, shown by the image on the right. The resurfacing process takes just a few minutes. USGS photos by M. Patrick.
(Public domain.)
### Thermal timelapse of summit lava lake
The lava lake in Halemaʻumaʻu crater, at the summit of Kīlauea, remains active but has diminished in area and vigor over the past month. This thermal timelapse sequence shows the changes in the lake activity over the past month. In mid-April the area of active surface lava in the lake was approximately 7.5 acres (3 hectares). By mid-May the area was about 0.5 acres (0.2 hectares). Taken from the automated camera (F1cam).
(Public domain.)
| 2021-06-17T17:26:16 |
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|
https://par.nsf.gov/biblio/10067116-cloaking-mechanism-mitigate-market-manipulation
|
A Cloaking Mechanism to Mitigate Market Manipulation
We propose a cloaking mechanism to deter spoofing, a form of manipulation in financial markets. The mechanism works by symmetrically concealing a specified number of price levels from the inside of the order book. To study the effectiveness of cloaking, we simulate markets populated with background traders and an exploiter, who strategically spoofs to profit. The traders follow two representative bidding strategies: the non-spoofable zero intelligence and the manipulable heuristic belief learning. Through empirical game-theoretic analysis across parametrically different environments, we evaluate surplus accrued by traders, and characterize the conditions under which cloaking mitigates manipulation and benefits market welfare. We further design sophisticated spoofing strategies that probe to reveal cloaked information, and find that the effort and risk exceed the gains.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10067116
Journal Name:
Twenty-Seventh International Joint Conference on Artificial Intelligence
Page Range or eLocation-ID:
541-547
5. Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call scoring rule markets'' (SRMs), in which traders predict the value of arbitrary statistics of the random variables, provided these statistics can be elicited by a scoring rule. Surprisingly, despite active recent work on prediction markets, there has not yet been any investigation into more general SRMs. To initiate such a study, we ask the following question: in what sense are SRMs markets''? We classify SRMs according to several axioms that capture potentiallymore »
| 2022-07-06T06:30:26 |
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https://datasciencecampus.ons.gov.uk/supporting-healthcare-guidance-recommendations-using-natural-language-processing/
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# Supporting healthcare guidance recommendations using natural language processing
The Data Science Campus ‘Enable’ programme is aimed at strengthening data science capability across the public sector, and you can read about more of our work on the data science accelerator, graduate programme and much more in our capability pages. This work includes supporting public sector organisations to use data science tools and techniques in their daily operations, to go faster, improve quality, and reduce costs.
This article describes our work with the National Institute for Health and Care Excellence (NICE) to identify documents and recommendations that are relevant to guidance that is under review by NICE. The project was carried out in three major parts:
• data-engineering, where the existing recommendations and guidance data were web-scraped from NICE’s application programming interface (API) and put into a structured JSON data format
• natural language processing (NLP) exploratory research, which evaluated several models and data augmentation methods
• putting project deliverables into a production environment on NICE servers for live use
The project was successful in delivering significant and proven improvements to NICE’s surveillance operations in both accuracy and processing time.
This report describes the technical work and design choices made during the exploratory and delivery phases of the work.
## 1. Introduction
The National Institute for Health and Care Excellence (NICE) provide national guidance and advice to improve health and social care practices, organised as guidance products. These guidance products were stored in HTML format with no clear distinction between the text sections within guidelines. The data records described must be kept up to date with state-of-the-art healthcare practices, which evolve daily through new research. Our research project used state-of-the-art natural language processing (NLP) practices to help NICE build a mechanism to query related recommendations throughout their dataset given an input recommendation.
#### Motivation
In NICE, the surveillance team is responsible for assessing whether any new evidence impacts on the existing guideline recommendations. With over 300 guidelines, each containing hundreds of recommendations as well as other textual information, this is no small task. One key element of the guideline review process is the identification of overlapping content. NICE needs to make sure that it is consistent in its recommendations and there are no contradictions between guidelines. Checking related guidelines is a manual, time-consuming task as content is stored on the website. For any given guideline, up to a week of an analyst’s time may have been spent checking other guidelines for overlaps. This task was challenging primarily because NICE did not have a searchable structured database of its recommendations for a keyword search.
##### Figure 1: A screenshot of NICE’s website showing a guidance page.
The rest of this report is structured into three categories, including:
• data: a section describing the data and the data-engineering phase of the project
• methods: a section describing the NLP models evaluated in this project as well as the benchmarking mechanism employed to rank them
• results and discussion: a section listing our best results as well as comments
## 2. Data description for the National Institute for Health and Care Excellence
When developing a guideline, the National Institute for Health and Care Excellence (NICE) uses Microsoft Word files as the main publishing software for guideline documents. A guideline can amount to thousands of pages when including all the methods, analysis and interpretation of the evidence leading to the recommendations. These long and complex documents are generally converted to PDF format and hosted on the guideline webpages (see Figure 1 for an example). The recommendations and other key information are converted directly from a Word file to HTML for display on the NICE website.
When searching for existing recommendations, NICE staff used the NICE website to search for relevant guidelines or recommendations. Although a keyword search within the NICE website was available, this returned webpages rather than specific recommendations. Analysts needed to read through or use a “browser find” function to search to find the specific recommendations of interest. They also needed to manually record their findings.
This method was inefficient in many ways. An analyst needed to read potentially thousands of recommendations to find a few relevant recommendation relationships. The number of recommendations per guidance product ranges from 417 to 4,891 at the time of publication, with 17 out of 19 topics consisting of more than 1,000 recommendations. A breakdown of the guidance products per topic is presented in Figure 2. The website keyword searching would not capture all synonyms or changes in terminology over time, so results could be incomplete. Similarly, the searches would be influenced by an individual’s pre-existing knowledge of the topic area, so results could be expected to differ depending on who did the searches. Finally, decisions about which recommendations were considered to be related could differ between individuals and so were not entirely objective, and the recording of findings was subject to human error.
## 3. Data engineering
To perform any cutting-edge natural language processing (NLP) methods, we needed to apply structure to the data, because we only needed the recommendation text out of each guideline. Unfortunately, the recommendation text inside guidelines was not structured in a consistent way. We (Data Science Campus at the Office of National Statistics)worked with the National Institute for Health and Care Excellence (NICE) to find patterns for certain guideline groups so that we could extract most of the recommendations using web scraping, creating a state machine to map text to structure.
During this process, we aimed to give a unique index (ID) to each section inside a guideline, creating a hierarchical JSON structure, as depicted in Figure 3. Every guideline listed recommendations, and every recommendation listed sections, and every section listed of paragraphs and/or sections, and every paragraph contained the underlying text. This underlying text we now refer to as the actual recommendation.
Note that the depth of the hierarchy varies depending on the structure of the individual guideline – some had sections and some had sub-sub-sections, all with slightly different formatting. These recommendations were then given a unique ID, so that our matching algorithm could return their IDs, rather than their text. Out of this JSON file, we extracted only the recommendations for our modelling work, and each recommendation had a composite key, namely <guideline ID, paragraph ID>. We need to mention here that the paragraph ID consisted of three parts, which are the recommendation ID, the section ID and the paragraph ID, as depicted in Figure 3.
We performed quantitative and qualitative tests to measure the success of this operation, and both estimated it to be over 95%. The test criteria were the number of guidance products and recommendations successfully web-scraped and appended into our structured dataset compared to the total number of guidance products and recommendations that were estimated by NICE. A reporting mechanism was applied to our web-scraping data-engineering process to report when there were issues with the process, such as text that could not be extracted and missing paragraphs, for example. Manual random sampling was also used to ascertain the accuracy of the process, as explained in the Data Testing section. The outcome of this random sampling was taken into consideration when applying the necessary changes to the web-scraping code to further improve the completeness of the resulting structured dataset.
##### Figure 3: Example dataset structure on completion of our data engineering phase.
JSON element Types of content Examples Guidance product Title Heading ID List of Chapters of Recommendations Fractures (non-complex): assessment… NG38 Chapters of Recommendations Heading ID Preamble List of Chapter Sections Initial pain management 1 ‘preamble text prior to each chapter section’ [optional] Chapter Section Heading ID Preamble List of Recommendations List of Chapter Subsections Pain assessment 1.2 ‘preamble text prior to each chapter subsection’ [optional] [optional] Chapter Subsection Heading List of Recommendations List of Chapter Subsubsections Pain assessment [optional] Chapter Subsubsection Heading List of Recommendations Pain assessment Recommendation ID Text 1.2.1 or 1.1.1.3 We recommend that…
## 4. Data testing
Testing by inspection was conducted to ensure the data extraction was accurate. This testing involved comparing the recommendation content extracted using the data-engineering approach described above with the guideline content on the National Institute for Health and Care Excellence (NICE) website. A random sample of 10% of all recommendations (n=2,077) were inspected manually by domain experts. On evaluating the errors, only 70 error reports were classed as true errors and generally fit into four broad categories. A major issue identified at this stage was that older public health guidelines had a different structure, which meant that extra code was needed to split and number individual recommendations. The remaining three broad categories of errors identified were headings missed because of a non-standard structure in the source guidance, non-recommendation paragraph text being included, and table content identified inconsistently.
The feedback from this manual inspection was used to apply any necessary changes to the data-engineering approach. Because the error rate was so low in the first analysis, no further systematic validation of the data-engineering output was needed.
## 5. Methods
### Verification and validation plan
Once the data-engineering work was complete, we were faced with a plethora of algorithms and models that could help with this task, including:
The question at this point was: which one? There were several publications comparing the above, however each corpus and task can be different. We decided to create a verification and validation (V&V) framework to assess several models that we considered fit for this task. The process of creating this V&V file for each of the two recommendation link tasks included the following steps:
• we asked the National Institute for Health and Care Excellence (NICE) to provide a set of surveillance queries (<=100) using their existing methods; we will refer to this as phase 1 of the process
• each query would have their associated recommendation results and we would use this file as a standard (we will refer to it as the “NICE Standard” set) to assess several algorithms and models
• next, we used our models to score all the recommendations in our dataset, once for each query against the NICE standard set; then, for each query, we ranked the results from the highest to the lowest score
• we then scored the models by the number of (known) true positives that they were able to recover on their top-200 recommendation links for each query, and then picked the outputs from our best model and sent the results back to domain experts; he known true positives were annotated with a flag (1) to indicate that they belonged to the NICE standard
• the domain experts would, in turn, annotate the newly retrieved true positives with the label ‘2’; we called this phase 2 of the process, and these would be true positives that were recovered by the model, but not from experts on their initial evaluation
• the union between the new set of labels and the old ones from the NICE standard would become our new “Gold Standard”; this new set would be the basis for further algorithm evaluations, and these new true positives would have been missed by the existing manual process
### Verification and validation implementation
This section explains how the verification and validation (V&V) sample was constructed, including phase 1 (National Institute for Health and Care Excellence (NICE) Standard) and phase 2 (Gold Standard).
#### Phase 1
A convenience sample of surveillance queries was selected to provide data for model testing. Data were collated to test two user cases, which were keyword searching and recommendation searching.
Surveillance subject-matter experts were allocated guidelines and asked to randomly select keywords and recommendations related to their allocated guidelines. To ensure broad coverage of topic areas, one person was responsible for allocations and distributed guideline products across the team. They ensured that all guidance products were in the sample – namely, clinical and public health guidelines, technology appraisals, diagnostic guidance and interventional procedure guidance.
For keyword searches, the relevant term was searched on the NICE website and relevant recommendations, including that keyword, were identified. Data including keyword and output recommendations was recorded in a spreadsheet. For recommendation relationships, the full input recommendation, or keywords from the recommendation, was searched on the NICE website. All data were quality assured by two independent domain experts responsible for surveillance. This dataset was then used by as a basis to evaluate several models.
#### Phase 2
Model data provided by the Office for National Statistics (ONS) were validated by domain experts responsible for surveillance. Recommendation relationships identified by the model were provided to the National Institute for Health and Care Excellence (NICE) in a spreadsheet. Using pre-specified criteria, relationships between input and output recommendations identified by the model were manually determined as a real relationship or not and decisions were recorded. All manual decisions were independently verified by a second reviewer and any disagreements discussed to reach a consensus. Manual data were fed back to the Data Science Campus to further adjust the model rankings and explore further possibilities. The newly retrieved data by the model were given a label 2 to record that they were recovered by the model but not from NICE in phase 1. The verification and validation workflow is shown in Figure 5.
### Figure 5: The verification and validation workflow.Methods employed
#### Data augmentation
After the data engineering phase of the project, we inspected the data prior to making decisions on the search algorithms. It quickly became apparent that there were two main issues. The first issue was that some recommendations were extremely short and relied upon context from neighbouring recommendations. The second issue was that some recommendations did not mention the subject matter; this was assumed from the heading.
We investigated these issues and came up with solutions described in the following sections.
We attempted to resolve this issue by grouping small recommendations (whose word count fell below a certain threshold) that belong to the same parent section. This way we could ensure that contextless recommendations would inherit context from a richer paragraph in word count and appear in search results. We used this method to compare against non-load-balanced datasets and then pick the best performing one. Different levels of load balancing were tried, with thresholds of [50, 100, 150] word counts and with groupings on section level and on recommendation level.
The grouping was done using a greedy algorithm approach. This means that, for every given level, (such as chapter-of-recommendations, chapter-of-sections and recommendations), we sorted the recommendations text by word length. Then starting from the top recommendation (pivot point – highest word count), we would construct and probe groupings of recommendations below it (including self) and keep the grouping closest to the given threshold. The groupings would be assessed with the score of the pivot recommendation on its own, too. This is because, in some cases, such as group on recommendation level with threshold 50, most recommendations would not require grouping. Once the top scoring grouping was found, the constituent recommendations were removed from the pool and merged into the processed data frame, along with the necessary information to decompose at a later stage.
An alternative method of adding context to the recommendations was by prefixing each recommendation with the guidance product title, and any headings or preambles that logically precede each recommendation within the hierarchy structure of the guidance product.
Figure 6 shows the word length distributions of load balancing on different section levels and different thresholds. The reason why the datasets suffixed with “lemma” have a smaller variance compared to their non-lemmatized equivalents is because these datasets have kept nouns only from each sentence, hence the lesser word-count. The dataset preceded by ‘_cn’ is the one augmented with header and pre-amble information. This plot helps understanding of the impact of load balancing on the data by looking at the shift of the wordcount distributions compared to plain recommendations, as shown on the first boxplot on the graph. For example, if we look at the chaptersOfRecommendations-level data (one before last) along with its load-balanced sets (lb_50_ chaptersOfRecommendations and lb_150_ chaptersOfRecommendations), we can see how our load balancing has shifted the distributions of the word lengths around the target threshold (150 and 50 words respectively).
### Modelling approaches
#### Word vectors (bio-embedding intrinsic)
The bio-embedding intrinsic model is trained using the word2vec algorithm on PubMed data, hence we will also be referring to it as bio-word2vec. This was the best performing model during phase 1 amongst several others like Word2Vec, TF-IDF, GloVe and doc2vec (table 1). We need to mention that, at that stage, BERTs were not widely available as BERT was released mid-way through the project. Hence, the BERT models were mainly evaluated on phase 2.
Initial attempts with this model averaged the word vectors of each recommendation document. By “recommendation document”, we refer to either a single recommendation document or a merged recommendation document in the case of a load-balanced dataset. We then hypothesised that including all the words in a document could skew the vectors – the “signal” words would become averaged out with “noise” words. Our next idea was to keep only the nouns from every document, as we thought that those would be the strongest features in each document, and average those instead of the whole document. The results were consistently better using this technique, hence we settled for it. Finally, this model was working best when using the load-balanced set of documents with a threshold of 150 and at a chapter-of-sections level (tables 1 and 2).
#### BERT and friends
The BERT language model (and related transformer models) triggered a step-change in natural language processing and triggered a whole new family of language models (BERT, RoBERTA, ALBERT, StructBERT, et al). These models are initially trained on massive datasets (such as the 2.5G word English Wikipedia dataset and 800M word BooksCorpus) and then made available. The models can then be refinement trained to perform specific tasks.
One task-specific refinement is Semantic Textual Similarity (STS), part of the SemEval benchmark suite. With BERT, two tokenised sentences are supplied, which are then compared by BERT. BERT responds with a score from 0 to 5, semantically different to the same meaning. However, to compare a sentence against N other sentences, this means we must compute N passes through BERT, which is relatively slow if a CPU is used (minutes rather than seconds). Given that the National Institute for Health and Care Excellence (NICE) prefer not to use specialist hardware (namely, just CPUs), this is not viable.
An alternative approach is to convert the sentence to a vector embedding and then use vector similarity to compare sentences. Unfortunately, BERT is not designed for this – you can add the last layer’s weights as an embedding, but that produces worse results than GloVe.
We also trialled Sentence-BERT, which utilises a Siamese network. This consists of two interlinked BERT networks to generate embeddings directly from sentences. This enabled vector embeddings to be created for each recommendation in advance and stored for late rapid comparison (through, for example, cosine similarity). We used the Hugging Face transformers library, which provides simple, open-source access to many pre-trained models and is used to build Sentence-BERT from pretrained BERT models. We tested the presented models.
Since completing this work, Sentence-BERT has further improved and is now hosted on the Sentence Transformers website. It now includes tutorials on semantic similarity and semantic search, which may be of interest to the user.
Although Sentence-BERT provides a model to embed sentences to n-dimensional vectors, this cannot be used straight out of the box. This is because BERT is used for several mainstream tasks like semantic textual similarity (STS), question answering, General Language Understanding Evaluation (GLUE), for example. To fine tune the BERT weights for a specific task, like STS in our case, sBERT needs to be refine trained. There are two different ways to do so. One is with a natural language inference dataset (NLI), which has labelled sentence pairs with three labels: contradiction, entailment, and neutral. The other is with an STS benchmark dataset, which provides sentence pairs to the Siamese neural network, along with scores ranging from one to five.
#### Refine-trained Bio-BERT sentence transformers with the Med-NLI and MedSTS datasets
We tried several medical-domain-specific BERT models trained with PubMed data and/or clinical discharge notes. These models would not work well out of the box, for reasons explained previously, but once refined, they could be trained with medical natural language inference (NLI) datasets and med-sts datasets that we obtained from MIMICII and Mayo Clinic respectively. We also obtained BIOSSES [14] and fused it with medical NLI, which gave us slightly better results. Both our fused NLI and STS datasets were small (just 500 records of the fused NLI and 1380 of the med- STS), hence we feel that the results we demonstrate by refine train medical sBert variants could be improved by larger datasets created in the future.
#### Bio-embedding augmented TFIDF
In this approach, the frequency of words or phrases (terms) in each recommendation are counted to form a recommendation – term count matrix (term frequency TF). The term column values in this matrix are then adjusted according to how rare each term is in the overall corpus of recommendations, which is known as inverse document frequency (IDF). Similarity between recommendations may then be calculated as the cosine between the normalised recommendation term vectors.
For the results reported here, TFIDF was augmented in two ways. Firstly, the vocabulary of terms, up to five grams, was filtered by Wikipedia article titles. Secondly, the TFIDF recommendation vectors were enriched with up to 10 terms from nearby bioword2vec embeddings (enriched terms weighted at 20% of original terms). Other operations included lowercasing, tokenisation, and removal of stop-words (unigrams, bigrams only). The BM25 variant of TFIDF was also employed.
## 6. Results and discussion
When carrying out the model evaluations, we treated this as a classification problem where, given a particular recommendation, we needed to determine the related recommendations. This means that related is a “positive” result and not related is a “negative” result. We will describe the metrics used for evaluation. Tables 1 and 2 summarise our results for the best performing models.
#### Metrics used for the benchmarks
Classifications can be examined with a Receiver Operating Characteristic (ROC) curve, which plots the true-positive rate against false-positive rate. An example is shown in Figure 7.
##### Figure 7: Example ROC curve demonstrating results coming from the ClinicalBert_dish model (clinical BERT trained with discharge notes). The curve represents the true positive against false positive rate for several similarity threshold cutoffs ranging from maximum to minimum, which are not included in the graph.
The curve represents the performance of the model when using different thresholds to determine when to assign a result as a “related” (positive) or “unrelated (negative) recommendation. An ideal model would show a curve that is near to the “perfect point” at the top-left of the graph (100% positive results with 0% false positives). The “area under curve” (AUC) summary value for a ROC curve shows 0.5 as a “pure chance” result (represented by the blue diagonal line), with 1.0 being a “perfect” result. A “perfect” result is akin to the probability that a randomly chosen “related” recommendation will be ranked higher than a randomly chosen “unrelated” one. In our case, ROC curves and AUC would represent the ability of the model to rank results by a similarity score. A perfect curve with 1.0 AUC would assign scores to recommendation pairs such that the matching ones would be
Average precision
However, due to our dataset being heavily unbalanced (of approximately twenty thousand recommendations, fewer than 10 will be a positive match), the ROC curve can be overly sensitive to changes in the small number of correct predictions. As a result, our ROC curve may present an overly optimistic view of the performance. A precision-recall (PR) curve was presented to help detect this, plotting precision, which is true positives / (true positives + false positives), versus recall, which is true positives / (true positives + false negatives). The curve is created for a range of increasing thresholds, not visible to the graph, similar to ROC curves. An example is presented in Figure 8.
##### Figure 8: Example precision-recall curve for the same model we used for the ROC curves above (ClinicalBERT_disch). The curve represents precision versus recall at increasing matching thresholds (not shown in the graph).
The precision-recall curve can be summarised with “average precision” (AP). Note that, compared with a reasonable ROC curve and AUC score, the PR curve drops off very rapidly with recall, producing a low AP. This helped us recognise when models were not as strong as the AUC first suggested.
Weighted mean reciprocal rank
Finally, as we are performing an information-retrieval task, we used a range of ranking metrics that would reward high-ranked results throughout the experiments samples.
Specifically, Top N is how many related recommendations were returned in the top 200 similarity scores, and Top N recall is calculated as how many related recommendations were in the top 200 divided by the total number of related recommendations. N was chosen to be 200 as this was demonstrated by NICE to be a manageable number of results to review.
Another metric worth looking at is the mean reciprocal rank, which gives us a score of the ranking ability of the model for the whole corpus. We decided to use a weighted mean reciprocal rank to account for the fact that our queries varied in the number of true positives assigned to them; hence, the formula for our metric was:
$$WMRR = \frac{1}{Q} \sum_{k=1}^{Q} \left( \frac{1}{n}\sum_{i=1}^{n} \frac{1}{rank_i} \right)$$
Where Q is the number of sample queries, n is the number of samples on our dataset and rank_i is the rank of the true positive i.
### Results
#### Phase 1
We now present our top results from phase 1 (“National Institute for Health and Care Excellence (NICE) standard”) in Table 1, sorted by Top N. “NICE standard” consists of 246 TPs out of 74 sample queries. The record in bold (bio-embedding intrinsic, with the 150 CoR nouns only – lemmatized data processing) was the best performing model at the time, which we forwarded to domain experts for manual investigation of its results.
##### Table 1 Phase 1 (“NICE standard”) shows results for a selection of our best models, sorted by Top N. Data augmentation (“Data Aug”) notes how we adapted the data before processing, namely N=Nouns only, L=Lemmatized, and S=Stemmed. “LB” is Load Balancing, and 150 CS means Chapters Sections were merged with a target word count of 150. Similarly, CoR is Chapter of Recommendations, whereas CN means context added.
Model Data Aug AUC Mean Prec WMRR Top N Top N Recall Load Balancing Bioembedding Augmented TFIDF CN 0.943 0.067 0.156 141 0.573 – Bioembedding Augmented TFIDF – 0.942 0.083 0.172 138 0.561 – micros_sbert_refined_sts CN 0.93 0.06 0.115 133 0.54 – bio_embedding_intrinsic CN N L 0.931 0.02 0.102 122 0.496 – GloVe-840B-300d CN N 0.913 0.018 0.108 119 0.494 – BERT-large-uncased CN N L 0.883 0.031 0.064 115 0.467 – GloVe-6B-300d CN N 0.915 0.013 0.076 114 0.463 – GloVe-42B-300d CN N 0.924 0.012 0.088 113 0.459 – BioWordVec pubmed MIMIC III CN N L 0.935 0.019 0.099 111 0.451 – BERT-base-uncased CN N L 0.863 0.032 0.076 111 0.451 – bio_embedding_intrinsic – 0.899 0.012 0.056 111 0.451 150 CoR Biobert v1.1 pubmed CN N L 0.887 0.042 0.104 107 0.435 _ BioWordVec pubmed MIMIC III CN N L 0.887 0.025 0.091 106 0.431 – Biobert v1.1 pubmed – 0.896 0.024 0.085 102 0.415 – bio_embedding_intrinsic – 0.857 0.012 0.044 97 0.394 150 CoR BERT-base-uncased – 0.849 0.023 0.054 89 0.362 – BioWordVec pubmed MIMIC III – 0.836 0.011 0.032 82 0.333 150 CoR GloVe-42B-300d – 0.811 0.024 0.087 68 0.276 – GloVe-6B-300d – 0.806 0.021 0.079 64 0.260 – NICE – N/A N/A N/A 277 N/A N/A
Note that we have recorded the base and top scores for each model, where the base score is the raw recommendations, and the top score from all variants of load balancing, grouping and context addition. Interestingly, context-added variants were better than all forms of load balancing in this table.
#### Phase 2
Additional labels were provided by the National Institute for Health and Care Excellence (NICE) as part of phase 2 (using potential additional true positives flagged by bio_embedding_intrinsic), forming the “Gold Standard”, which consisted of 875 TPs in total out of 74 queries in total. The models were then re-run and top results presented in Table 2. Results are again sorted by Top N, using the same naming convention as Table 1.
##### Table 2 Phase 2 (“Gold standard”) shows results for a selection of our best models, sorted by Top N. Data augmentation (“Data Aug”) notes how we adapted the data before processing, namely N=Nouns only, L=Lemmatized, and S=Stemmed. “LB” is Load Balancing, and 150 CS means Chapters Sections were merged with a target word count of 150. Similarly, CoR is Chapter of Recommendations, whereas CN means context added.
Model Data Aug AUC Mean Prec WMRR Top N Top N Recall LB bio_embedding_intrinsic N L 0.932 0.091 0.181 702 0.802 150 CoR Bioembedding Augmented TFIDF CN 0.980 0.275 0.231 675 0.771 – BioWordVec pubmed MIMIC III N L 0.933 0.090 0.173 674 0.770 150 CoR Bioembedding Augmented TFIDF – 0.977 0.255 0.206 650 0.743 – micros_sbert_refined_sts CN 0.96 0.21 0.226 641 0.732 – micros_sbert_refined_sts – 0.97 0.13 0.167 633 0.723 150 CoR micros_sbert_refined_sts_x_sentsplit CN 0.96 0.05 0.157 618 0.706 – dmis_bio_nli_fused – 0.97 0.17 0.155 600 0.686 50 CoR bio_embedding_intrinsic CN 0.936 0.116 0.203 583 0.666 – GloVe-840B-300d N L 0.904 0.083 0.163 583 0.666 150 CoR BioWordVec pubmed MIMIC III CN N 0.935 0.073 0.198 573 0.655 – bio_embedding_intrinsic – 0.906 0.087 0.165 564 0.645 150 CoR micros_sbert_refined_sts_x – 0.95 0.07 0.171 561 0.641 150 CoR BioWordVec pubmed MIMIC III N L 0.911 0.065 0.169 548 0.626 150 CoS GloVe-840B-300d CN 0.897 0.077 0.194 522 0.597 – microsoft biobert – 0.890 0.116 0.116 506 0.578 – Biobert v1.1 pubmed – 0.926 0.062 0.108 506 0.578 – WordCount N S 0.953 0.071 0.159 503 0.575 150 CoR GloVe-840B-300d – 0.860 0.063 0.154 496 0.567 150 CoR GloVe-840B-300d N L 0.878 0.045 0.125 495 0.566 – GloVe-840B-300d N 0.878 0.042 0.126 485 0.554 – ClinicalBERT_disch_20200120 – 0.916 0.081 0.102 481 0.550 – scibert_scivoca – 0.907 0.060 0.100 470 0.530 – bio_embedding_intrinsic – 0.870 0.065 0.127 462 0.528 – BERT-large-uncased – 0.881 0.083 0.144 410 0.469 150 CoR BioWordVec pubmed MIMIC III – 0.857 0.059 0.125 410 0.469 – BERT-large-uncased – 0.884 0.055 0.093 396 0.453 – BERT-base-uncased – 0.890 0.051 0.083 395 0.451 – GloVe-840B-300d – 0.814 0.039 0.122 397 0.454 – ALBERT xlarge v2 – 0.796 0.058 0.135 328 0.375 150 CoR ALBERT xlarge v2 – 0.793 0.020 0.068 308 0.352 – NICE – N/A N/A N/A 277 N/A N/A
#### Discussion
The results in table two show the best models sorted by their performance in the top-200 ranked results. Also, we have used bold to highlight numbers models that performed at the top in other areas like mean reciprocal rank. There are a few remarks to make on the results of table two.
The bio-embedding intrinsic appears to be the best performing model, but we must take into consideration that this model’s results have been manually evaluated by domain experts, hence all its true positives in the top-200 ranks have been revealed. This is not the case for all other models as there is a likelihood that many unknown true positives are hiding in their top-200 ranked results. Table 1 results, which were produced for that purpose, show that several models like the refine-trained sentence bioBERT and the augmented TFIDF model performed better on the phase 1 the National Institute for Health and Care Excellence (NICE) standard. However, these models were not available at phase 1 as BERTs were invented at a later stage and the augmented TFIDF technique, as well as the context-added data augmentation method, were discovered during phase 2.
With that in mind, our recommendation is that Augmented TFIDF and Microsoft’s sentence BERT, which is refine trained with medical NLI and STS data, should not be underestimated. Especially for the latter, we saw a big improvement in scores when training it with medical NLI and STS data. It feels as if the NLI and STS datasets we had in hand were small, but when larger medical datasets will be available then of course there should be another evaluation of the model.
Models were evaluated as a combination of all the metrics in the tables. This helped to overcome the question of whether the top n metric might be sensitive to the number of true positives in each query. Data load balancing and augmentation is something that worked very well, as demonstrated through our benchmarks with all our top-20 model results in the table having used either load-balancing or context-enhancement variants of the data.
Considering the results in Tables 1 and 2 and their running times, we concluded that our best models were the refine-trained bio-sBERT (both as sentence transformers and cross autoencoders) and the bioword2vec ones (bioembedding intrinsic and MIMIC III models). We decided to test these further by looking more closely at some normalised density plots for these models run with the context-added augmentation method.
Figure 9 depicts normalised density plots for the similarity scores found in true positives and true negatives. The plots were normalised as there was a difference in magnitudes for the two curves as the true negatives account for almost the whole corpus. The plots come from two of our best models, namely bioword2vec and several variants of bioBERT. We can see that in all plots a large part of the orange curve overlaps the blue. If we consider that the total for the orange curve is approximately 20,000 recommendation documents, it is apparent that, if we wished to recover most of the known true positives, we would have needed to include thousands of true negatives too in our results, which is rather impractical. That goes to show that, although our models have almost doubled NICE’s capacity to recover linked recommendations, there is still plenty of room for improvement and plenty of potential for better models to be uncovered in the future!
Taking a closer look at Figure 9, we can see that the score distributions of refine-trained variations of BERT at the bottom row look less overlapping and their peaks are more spaced apart. It is also interesting to see the Cross-encoders distributions on the bottom right-hand plot. It seems that the true negative scores are well distributed in the range of values [0,3], but true positives span the whole spectrum of values between zero and one with enough overlap on the TN curve. In theory, cross encoders should be performing better than sentence encoders when both are refine-trained, but we did not see that in our case. However, cross encoders are significantly slower than sentence transformers (>10x slower), and their training and evaluation would not allow as much experimentation as we could do with other models because of time constrains. Our intention was to explore the possibility of using the sentence transformer models to shortlist 1,000 – 2,000 recommendations and then use cross encoders to re-rank them. But since we did not get the significantly better results that we expected, we dropped the idea, but that prospect should be revisited in the future.
## 7. Deployment of the proposed method
#### Outline of proposed proof of concept
The model assessed as the best performing to meet the National Institute for Health and Care Excellence’s (NICE) needs was the bio_embedding_intrinsic using the lemmatized nouns only chapter of recommendations at 150 words level. The reason for this choice was that BERTs would need a GPU to execute at reasonable pace, and the TFIDF augmentation method was not developed at the time. Also, this model could be used out of the box for keyword to recommendation searches too. A sentence BERT would not function as well with an input of one or two keywords as sentence transformers were not built for that purpose. The next step was to produce a proof of concept that would be deployed on NICE infrastructure and allow users to interact, query and make use of this method.
The proposed implementation of the proof of concept is as follows:
1. Package core methods that came out of the methodology and model comparison into a set of python functions as part of a package that then will underpin the server defined in point 2.
2. Create a python web server able to process incoming requests containing keywords or recommendation IDs and able to then use the chosen machine-learning model (as well as an index of all recommendations) to predict nearest matches. This can serve as both an API for direct programmatic access as well as a back end for a more usable UI.
3. Create a UI that allows colleagues in NICE to input recommendation IDs and keywords, which then will get sent to and processed by the server described previously. This UI also then displays the response containing all the matching recommendations to the user.
Therefore, it follows a similar pattern to the “model view controller” pattern, where the server is the model underpinning the logic, and containing the machine-learning model element, and the UI is then both the controller and the presentation layer. Figure 10 illustrates the proposed interactions:
##### Figure 10: Simplified diagram of the final interactions between the UI and Norma. Norma sits as the underpinning library for the server, and the server works to enable the translation between the user interface and Norma.
A simplification of the outlined proposal can be achieved by merging the python server and the python package steps into one step (and consequentially one codebase). However, the decision was made to keep them separate to allow greater modularity when deploying on the users’ infrastructure and to allow easy in-place replacements of either component because of minimal coupling.
#### Implementation details
After consulting the National Institute for Health and Care Excellence (NICE) on the previous outline for a proposed proof of concept, work started to implement the distinct parts. Each part was split into a separate repository prefixed by the project name (norma, norma-server and norma-ui).
## 8. Python package (Norma)
To develop the python package, the experimental code developed as part of the model benchmarking exercise was assessed and relevant parts extracted, reviewed and refactored. The package was then documented, core parts of it were tested and this was fed into the next stage of work – creating the server.
Server
The server was built in python using flask as the main tool to translate HTTP requests into python commands. The implementation and codebase are fairly lightweight, consisting of mainly one API endpoint that is able to accept post requests with a given JSON body containing all the information required to find matching recommendations.
It is worth noting that for the server to provide matches it needs to have a dataset of recommendations that will serve as the core look up for any recommendation-matching requests. This means that, upon starting the server, a dataset and model are loaded into memory, and these two components are key to the process of providing recommendation matches. Note that, upon delivery of the proof of concept to NICE, the data was loaded from static files. However, it was built in a way that would allow the end user of this server to tweak the ingestion functions so that these data could be drawn from a database instead. This would allow the decoupling of the server and the recommendation in the future which, in turn, would provide matches that were always up to date.
The core of the server is one web endpoint performing the translation of requests to the python code. This endpoint expects a POST request with a body similar to the following JSON snippet:
{
“query”: [“keyword1”, “keyword2”, “…”],
“type”: “keywords”,
“topn”: “200”,
“threshold”: “0.98”
}
Each field parametrises the python code and dictates the results that will be sent back. Namely, the type parameter switches between exact word search across documents, semantic keyword matching and recommendation-to-recommendation matching. The “query” then contains either the keywords required for exact or semantic keyword matching or a string containing the recommendation ID in the case of recommendation-to-recommendation lookups. The “topn” and “threshold” parameters dictate how many maximum results to return and what the lowest score is to return.
The response is then of shape:
[
{
“rec_id”: “CG104.4”,
“score”: 0.32,
“text_snippet”: “Some text from the recommendation”,
“guidance_title”: “Vitamin d…”
},
]
Simply put, it will contain a list where each entry is a recommendation that matched against the specific query and some other metadata and sample text.
#### UI
The final component of the deployed Norma is the presentation and interaction UI, which would allow users to send queries and view the results. This component was built as a single-page React.js application. It does not use any formal state management, like Redux, and is fairly simple in its features.
To expedite the process of building the proof-of-concept UI, the popular Material UI framework was chosen to provide components such as buttons, bars and inputs. Using these components, a simple layout consisting of a single input field and a few customisation options was built (see Figure 10 A screenshot from the NORMA interface). This allows users to provide either keywords or recommendation names in the input and set a few parameters. All these inputs simply correspond to the API specification show above and are passed on to the server upon submission.
There were a few challenges to overcome, mainly because of specific stakeholder requirements relating to the user experience. That said, most of these were trivial to solve and were mainly focused on things such as making the input box more accepting of varying ways to input recommendation IDs.
## 9. Conclusions
This report summarises our efforts to improve the National Institute for Health and Care Excellence’s (NICE) surveillance operations using state-of-the-art data science and natural language processing (NLP). The project outcomes were successful and that was evident even at early stages of the project when our initial results brought a 2.5x improvement in accuracy over the existing surveillance at the time. In addition, it reduced the time lag of finding related recommendations from weeks to hours. This means that updates in healthcare recommendation can now be addressed by NICE without the previous week-long time lag. Given the ease and speed of use, significantly more updates can also be done in a given timeframe, which in turn would reduce any potential backlogs significantly. This is not only good for NICE’s operations but for the public in general.
#### Recommendation for use and future improvements
Our recommendation is that the National Institute for Health and Care Excellence (NICE) uses the new tool in such a way that it can accommodate future improvements. Natural language processing (NLP) is fast evolving and a two-to-three-yearly tech refresh on models would be a good option. The top-200 results coming out of queries could be scored by experts in such a way that there is a score between 1.0-5.0 between recommendation pairs, along with a label (entailment, contradiction and neutral) on the returned Excel files. This way, NICE can build a domain-specific training sample to refine train sentence transformers in the future, either on its own or fused with the existing ones we hold.
There have been discussions between DSC and NICE with regards to what happens with the unique recommendation IDs when there is an update. Our recommendation is that there should be a new Boolean field added to the JSON structure <live>, which will be true if the recommendation is live and false if not. New recommendations will then be assigned a new unique ID by simply incrementing the last available ID number by one. For example, if the recommendation of product x, with ID 1.2.6.13, is replaced by a new one, and the last ID of the recommendations section was 1.2.6.18, then the recommendation that replaces 1.2.6.13 would get an ID of 1.2.6.19 and its <live> switch would be assigned a true value, whereas the 1.2.6.13 recommendation’s <live> Boolean would be turned to false. This way, NICE will also keep a good track of the history of its dataset, and of course more data will be available to train new models in the future.
| 2022-10-03T01:09:10 |
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|
https://par.nsf.gov/biblio/10349600-recent-lmcsmc-collision-timing-impact-parameter-constraints-from-comparison-gaia-lmc-disk-kinematics-body-simulations
|
This content will become publicly available on March 1, 2023
The Recent LMC–SMC Collision: Timing and Impact Parameter Constraints from Comparison of Gaia LMC Disk Kinematics and N-body Simulations
Abstract We present analysis of the proper-motion (PM) field of the red clump stars in the Large Magellanic Cloud (LMC) disk using the Gaia Early Data Release 3 catalog. Using a kinematic model based on old stars with 3D velocity measurements, we construct the residual PM field by subtracting the center-of-mass motion and internal rotation motion components. The residual PM field reveals asymmetric patterns, including larger residual PMs in the southern disk. Comparisons of the observed residual PM field with those of five numerical simulations of an LMC analog that is subject to the tidal fields of the Milky Way and the Small Magellanic Cloud (SMC) show that the present-day LMC is not in dynamical equilibrium. We find that both the observed level of disk heating (PM residual rms of 0.057 ± 0.002 mas yr −1 ) and kinematic asymmetry are not reproduced by Milky Way tides or if the SMC impact parameter is larger than the size of the LMC disk. This measured level of disk heating provides a novel and important method to validate numerical simulations of the LMC–SMC interaction history. Our results alone put constraints on an impact parameter ≲10 kpc and impact timing <250 Myr. When more »
Authors:
; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10349600
Journal Name:
The Astrophysical Journal
Volume:
927
Issue:
2
Page Range or eLocation-ID:
153
ISSN:
0004-637X
3. ABSTRACT Within lambda cold dark matter ($\Lambda$CDM), dwarf galaxies like the Large Magellanic Cloud (LMC) are expected to host numerous dark matter subhaloes, several of which should host faint dwarf companions. Recent Gaia proper motions confirm new members of the LMC system in addition to the previously known SMC, including two classical dwarf galaxies ($M_\ast$$\gt 10^5 M_{\odot }; Carina and Fornax) as well as several ultrafaint dwarfs (Car2, Car3, Hor1, and Hyd1). We use the Feedback In Realistic Environments (FIRE) simulations to study the dark and luminous (down to ultrafaint masses, M_\ast$$\sim$6$\times 10^ {3}$ M$_{\odot }$) substructure population of isolated LMC-mass hosts ($M_{\text{200m}}$ = 1–3$\times 10^ {11}$ M$_{\odot }$) and place the Gaia + DES results in a cosmological context. By comparing number counts of subhaloes in simulations with and without baryons, we find that, within 0.2 $r_{\text{200m}}$, LMC-mass hosts deplete $\sim$30 per cent of their substructure, significantly lower than the $\sim$70 per cent of substructure depleted by Milky Way (MW) mass hosts. For our highest resolution runs ($m_\text{bary}$ = 880 M$_{\odot }$), $\sim 5\!-\!10$ subhaloes form galaxies with $M_\ast$$\ge 10^{4}$ M$_{\odot }$ , in agreement with the seven observationally inferred pre-infall LMC companions. However, we find steeper simulated luminosity functions than observed, hinting at observation incompleteness at the faintmore »
| 2022-12-08T20:20:42 |
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https://ecoursesonline.icar.gov.in/mod/page/view.php?id=125561
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## Lesson 24.
24.1 Consider a pulley 1 driving the pulley 2. The pulley 1 is called driver and pulley 2 is called driven. So velocity ratio may be defined as the ratio of speed of driven to that of driver or ratio of diameter of driver to that of driven.
Mathematically the equation is:
$\frac{{{{\text{N}}_{\text{2}}}{\text{ }}}}{{{{\text{N}}_{\text{1}}}}} = \frac{{{{\text{D}}_{\text{1}}}}}{{{\text{ }}{{\text{D}}_{\text{2}}}}}$
N1 = Speed of driver pulley in rpm
N2 = Speed of driven pulley in rpm
D1 = Diameter of driver pulley in mm
D2 = Diameter of driven pulley in mm
When the thickness of the belt (t) is considered, then velocity ratio is given by
$\frac{{{{\text{N}}_{\text{2}}}}}{{{{\text{N}}_{\text{1}}}}} = {\text{ }}\frac{{\left( {{{\text{D}}_{\text{1}}} + {\text{ t}}} \right){\text{ }}}}{{\left( {{{\text{D}}_{\text{2}}} + {\text{t}}} \right)}}$
24.2 SLIP OF BELT DRIVES
The forward motion of the driver without carrying the belt with it is called slip of the belt and is generally expressed in percentage. For slippage velocity ratio is given by
$\frac{{{{\text{N}}_{\text{2}}}}}{{{{\text{N}}_{\text{1}}}}}={\text{}}\frac{{\left({{{\text{D}}_{\text{1}}}+{\text{t}}}\right){\text{}}}}{{\left({{{\text{D}}_{\text{2}}} + {\text{t}}} \right)}}\times {\text{ }}\left( {{\text{1}} - \frac{{\text{S}}}{{100}}} \right)$
Where S= S1+S2 (total percentage of slip)
S1 = Percentage slip between driver and the belt and
S2= Percentage slip between belt and the follower
24.3 Length of open belt drive
Consider an open belt drive; both the pulleys rotate in the same direction as shown in the figure 5.7
Let r1 and r2 be radii of larger and smaller pulley
X= distance between the centres of two pulleys i.e. (C1, C2)
L= Total length of the belt
Fig. 5.7 Length of open belt drive
Let the belt leaves the larger pulley at A and C and smaller pulley at B and D. Through C2 draw C2G parallel to AB.
From the figure, C2G will be perpendicular to C1A.
We know that length of belt is given by
L= Arc CEA+AB+Arc BFD+DC
=2(Arc AE+AB+Arc BF)
From the figure,
AB= GC2= [(C1C2)2 – (C1G) 2]1/2= [x2-(r1-r2)2]1/2
Expanding by binomial theorem
Substituting the values of arc AE from equation, arc BF and AB from equations we get
24.4 Ratio between belt tensions
A driven pulley rotating in clockwise direction is shown in figure 5.8
Let T1 = Tension on tight side of the belt
T2 = Tension on slack side of the belt
θ = Angle of contact of belt with pulley in radians
µ = Coefficient of friction between the belt and pulley.
Considering a small portion of belt XY in contact with the pulley. X makes angle δθ at the centre of the pulley. Let T be the tension in the belt at X and (T + δT) be the tensions in the belt at Y.
Fig 5.8 Ratio of driving tensions
The belt portion XY is in equilibrium under the action of following forces:
1. Tension T in belt at X.
2. Tension T + δT in belt at Y.
3. Frictional reaction R at U.
4. Frictional force µR between belt and pulley.
Now again solving the forces expression in horizontal direction
µR = (T + δT) cos (δθ / 2) - T cos (δθ / 2)
Since δθ is very small
cos (δθ / 2) = 1
µR + T = (T + δT)
µR = δT …(1)
and resolving the force is vertical reaction.
R = T sin (δθ / 2) + (T + δT) sin (δθ/2)
Since, δθ is very small, so
R = T δθ/2 + (T + δT) δθ/2 = T δθ …(2)
From equations (1) and (2)
µ(T δθ) = δT (neglecting δT. δθ / 2 )
δT / T = µ δθ
On integration, we get
T2T1 δT/T = ∫oθ µdθ
loge T1 / T2 = µθ
T1 / T2 = (e)µθ
24.5 Power transmitted by belt drive
Power transmitted, P = (T1 - T2) V (Watt)
V is the velocity of the belt = $= \frac{{{\text{ }}{{\text{D}}_{\text{1}}}{{\text{N}}_{\text{1}}}}}{{60}}$ (m/sec)
24.6 Tension in the belts
The initial tension (T0) ensures that the belt would not slip under designed load. Belts are mounted on the pulleys with a certain amount of tension T0. At rest, the forces acting on the two sides of belts are equal. As the power is transmitted, the tension on the tight side increases and tension on the slack side decreases.
Fig 5.8 (b) Pulleys Working
Mathematically Initial tension is given by
Where T1 and T2 are tensions on tight side and slack side and Tc is the centrifugal tension given by
Tc=mv2
Where m= mass of belt per unit length and V=Velocity of belt in m/s
24.7 Condition for the transmission of Maximum power
Power transmitted by belt drive is given by
P= (T1-T2) V…………………………….(1)
Where T1= Tension in the belt on tight side
T2= tension in the belt on slack side
V= velocity of belts
Also $\frac{{{{\text{T}}_{\text{1}}}}}{{{{\text{T}}_{\text{2}}}}} = {{\text{e}}^\mu }^\theta$
Substituting the value of T2, we get
$= ({{\text{T}}_{\text{1}}}--{\text{ }}\frac{{{{\text{T}}_{\text{1}}}{\text{ }}}}{{{{\text{e}}^{\mu \theta }}}}){\text{V}} = {\text{ }}{{\text{T}}_{\text{1}}}({\text{1}} - \frac{{\text{1}}}{{{{\text{e}}^{\mu \theta }}}}){\text{V}} = {{\text{T}}_{\text{1}}}.{\text{V}}.{\text{Z}}$ ……………… (2)
Where
${\text{Z}} = {\text{1}} - \frac{{{\text{1 }}}}{{{{\text{e}}^{\mu \theta }}}}$
Also maximum tension (T) in the belt considering centrifugal tension (Tc) is given by
T=T1+Tc
Substituting the value T1 in equation (2)
P= (T-Tc) V.Z= (T.V-mV3) Z
Differentiating with respect to V for maximum power and equate to zero
| 2018-02-23T04:06:01 |
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|
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