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Eigenvalue Distributions of Beta-Wishart Matrices
Eigenvalue distributions of beta-Wishart matrices The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Edelman, Alan, and Plamen Koev. “Eigenvalue Distributions of Beta- Wishart Matrices.” Random Matrices: Theory and Applications 03, no. 02 (April 2014): 1450009. As Published http://dx.doi.org/10.1142/S2010326314500099 Publisher World Scientific Pub Co Pte Lt Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/116006 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ SIAM J. MATRIX ANAL. APPL. c 2013 Society for Industrial and Applied Mathematics Vol. XX, No. X, pp. XX{XX EIGENVALUE DISTRIBUTIONS OF BETA-WISHART MATRICES∗ ALAN EDELMANy AND PLAMEN KOEVz Abstract. We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart matrices to any β > 0. Key words. random matrix, Wishart distribution, eigenavalue, hypergeometric function of a matrix argument AMS subject classifications. 15A52, 60E05, 62H10, 65F15 DOI. XX.XXXX/SXXXXXXXXXXXXXXXX 1. Introduction. Recently, the classical real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart random matrix ensembles were generalized to any β > 0 by what is now called the Beta{Wishart ensemble [2, 9]. In this paper we derive the explicit distributions for the extreme eigenvalues and the trace of this ensemble as series of Jack functions and, in particular, in terms of the hypergeometric function of matrix argument. -
The Nature of Hellenistic Domestic Sculpture in Its Cultural and Spatial Contexts
THE NATURE OF HELLENISTIC DOMESTIC SCULPTURE IN ITS CULTURAL AND SPATIAL CONTEXTS DISSERTATION Presented in Partial Fulfillment of the Requirements for The Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Craig I. Hardiman, B.Comm., B.A., M.A. ***** The Ohio State University 2005 Dissertation Committee: Approved by Dr. Mark D. Fullerton, Advisor Dr. Timothy J. McNiven _______________________________ Advisor Dr. Stephen V. Tracy Graduate Program in the History of Art Copyright by Craig I. Hardiman 2005 ABSTRACT This dissertation marks the first synthetic and contextual analysis of domestic sculpture for the whole of the Hellenistic period (323 BCE – 31 BCE). Prior to this study, Hellenistic domestic sculpture had been examined from a broadly literary perspective or had been the focus of smaller regional or site-specific studies. Rather than taking any one approach, this dissertation examines both the literary testimonia and the material record in order to develop as full a picture as possible for the location, function and meaning(s) of these pieces. The study begins with a reconsideration of the literary evidence. The testimonia deal chiefly with the residences of the Hellenistic kings and their conspicuous displays of wealth in the most public rooms in the home, namely courtyards and dining rooms. Following this, the material evidence from the Greek mainland and Asia Minor is considered. The general evidence supports the literary testimonia’s location for these sculptures. In addition, several individual examples offer insights into the sophistication of domestic decorative programs among the Greeks, something usually associated with the Romans. -
Matrix Algorithms: Fast, Stable, Communication-Optimizing—Random?!
Matrix algorithms: fast, stable, communication-optimizing—random?! Ioana Dumitriu Department of Mathematics University of Washington (Seattle) Joint work with Grey Ballard, James Demmel, Olga Holtz, Robert Kleinberg IPAM: Convex Optimization and Algebraic Geometry September 28, 2010 Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 1 / 49 1 Motivation and Background Main Concerns in Numerical Linear Algebra Size issues 2 Reducing the flops Stability of FMM Stability of FLA Why Randomize? 3 Reducing communication Why is communication bad? Randomized Spectral Divide and Conquer Communication Costs 4 Conclusions Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 2 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/complexity (how many operations they require, e.g., multiplications). Parallelism (how to distribute the computation to multiple processors in order to optimize speed – if possible). Communication complexity (how to minimize the amount of back-and-forth between levels of memory or processors.) Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 3 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/flops complexity (how many operations they require, e.g., multiplications). -
The Random Matrix Technique of Ghosts and Shadows
The Random Matrix Technique of Ghosts and Shadows Alan Edelman November 22, 2009 Abstract We propose to abandon the notion that a random matrix has to be sampled for it to exist. Much of today's applied nite random matrix theory concerns real or complex random matrices (β = 1; 2). The threefold way so named by Dyson in 1962 [2] adds quaternions (β = 4). While it is true there are only three real division algebras (β=dimension over the reals), this mathematical fact while critical in some ways, in other ways is irrelevant and perhaps has been over interpreted over the decades. We introduce the notion of a ghost random matrix quantity that exists for every beta, and a shadow quantity which may be real or complex which allows for computation. Any number of computations have successfully given reasonable answers to date though diculties remain in some cases. Though it may seem absurd to have a three and a quarter dimensional or pi dimensional algebra, that is exactly what we propose and what we compute with. In the end β becomes a noisiness parameter rather than a dimension. 1 Introduction This conference article contains an idea which has become a technique. Perhaps it might be labeled a conjecture, but I think idea is the better label right now. The idea was discussed informally to a number of researchers and students at MIT for a number of years now, probably dating back to 2003 or so. It was also presented at a number of conferences [3] . As slides do not quite capture a talk, this seemed a good place to write down the ideas. -
Mathematics of Data Science
SIAM JOURNAL ON Mathematics of Data Science Volume 2 • 2020 Editor-in-Chief Tamara G. Kolda, Sandia National Laboratories Section Editors Mark Girolami, University of Cambridge, UK Alfred Hero, University of Michigan, USA Robert D. Nowak, University of Wisconsin, Madison, USA Joel A. Tropp, California Institute of Technology, USA Associate Editors Maria-Florina Balcan, Carnegie Mellon University, USA Vianney Perchet, ENSAE, CRITEO, France Rina Foygel Barber, University of Chicago, USA Jonas Peters, University of Copenhagen, Denmark Mikhail Belkin, University of California, San Diego, USA Natesh Pillai, Harvard University, USA Robert Calderbank, Duke University, USA Ali Pinar, Sandia National Laboratories, USA Coralia Cartis, University of Oxford, UK Mason Porter, University of Califrornia, Los Angeles, USA Venkat Chandrasekaran, California Institute of Technology, Maxim Raginsky, University of Illinois, USA Urbana-Champaign, USA Patrick L. Combettes, North Carolina State University, USA Bala Rajaratnam, University of California, Davis, USA Alexandre d’Aspremont, CRNS, Ecole Normale Superieure, Philippe Rigollet, MIT, USA France Justin Romberg, Georgia Tech, USA Ioana Dumitriu, University of California, San Diego, USA C. Seshadhri, University of California, Santa Cruz, USA Maryam Fazel, University of Washington, USA Amit Singer, Princeton University, USA David F. Gleich, Purdue University, USA Marc Teboulle, Tel Aviv University, Israel Wouter Koolen, CWI, the Netherlands Caroline Uhler, MIT, USA Gitta Kutyniok, University of Munich, Germany -
Roman Literature from Its Earliest Period to the Augustan Age
The Project Gutenberg EBook of History of Roman Literature from its Earliest Period to the Augustan Age. Volume I by John Dunlop This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at http://www.gutenberg.org/license Title: History of Roman Literature from its Earliest Period to the Augustan Age. Volume I Author: John Dunlop Release Date: April 1, 2011 [Ebook 35750] Language: English ***START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ROMAN LITERATURE FROM ITS EARLIEST PERIOD TO THE AUGUSTAN AGE. VOLUME I*** HISTORY OF ROMAN LITERATURE, FROM ITS EARLIEST PERIOD TO THE AUGUSTAN AGE. IN TWO VOLUMES. BY John Dunlop, AUTHOR OF THE HISTORY OF FICTION. ivHistory of Roman Literature from its Earliest Period to the Augustan Age. Volume I FROM THE LAST LONDON EDITION. VOL. I. PUBLISHED BY E. LITTELL, CHESTNUT STREET, PHILADELPHIA. G. & C. CARVILL, BROADWAY, NEW YORK. 1827 James Kay, Jun. Printer, S. E. Corner of Race & Sixth Streets, Philadelphia. Contents. Preface . ix Etruria . 11 Livius Andronicus . 49 Cneius Nævius . 55 Ennius . 63 Plautus . 108 Cæcilius . 202 Afranius . 204 Luscius Lavinius . 206 Trabea . 209 Terence . 211 Pacuvius . 256 Attius . 262 Satire . 286 Lucilius . 294 Titus Lucretius Carus . 311 Caius Valerius Catullus . 340 Valerius Ædituus . 411 Laberius . 418 Publius Syrus . 423 Index . 453 Transcriber's note . 457 [iii] PREFACE. There are few subjects on which a greater number of laborious volumes have been compiled, than the History and Antiquities of ROME. -
The Annual MIDAS Network Meeting Takes Place April 3-5, 2018, at the Hyatt Regency Bethesda. Registration and Other Informatio
MIDAS CIDID Newsletter #14 View this email in your browser Issue #14 | February 2018 Welcome to the February 2018 edition of the MIDAS CIDID Newsletter. This is where you can nd Center-wide updates, along with relevant news and highlights. CIDID Website CIDID Twitter The annual MIDAS Network Meeting takes place April 3-5, 2018, at the Hyatt Regency Bethesda. Registration and other information is available on the MIDAS meeting website. The 10th Summer Institute in Statistics and Modeling in Infectious Diseases (SISMID) takes place July 9-25, 2018, at the University of Washington in Seattle. Registration and scholarship information is available on the SISMID website. Seroprevalence of Dengue Antibodies in Three Urban Settings in Yucatan, Mexico AJTMH [pdf] An Assessment of Household and Individual-Level Mosquito Prevention Methods during the Chikungunya Virus Outbreak in the United States Virgin Islands, 2014–2015 AJTMH [pdf] Core pertussis transmission groups in England and Wales: A tale of two eras Vaccine [pdf] Resilience management during large-scale epidemic outbreaks Scientic Reports [pdf] Panel data analysis via mechanistic models arXiv [pdf] Models and analyses to understand threats to polio eradication BMC Medicine [pdf] Comparative epidemiology of poliovirus transmission Scientic Reports [pdf] Silent circulation of poliovirus in small populations Infectious Disease Modeling [pdf] Steve Bellan, Natalie Dean, and Ira Longini contributed to the development of an interactive web-based decision tool, InterVax, to assist in the design of vaccine efcacy trials during emerging outbreaks. This work is part of the ongoing World Health Organization (WHO) Research and Development Blueprint for Action to Prevent Epidemics. CIDID John Drake is a co-author on a paper that will be read at the Royal Statistical Society on March 14, 2018. -
Sonderkarte Bosporos / Goldenes Horn 1: 100 000
TABULA IMPERII BYZANTINI 12/13 - Sonderkarte Bosporos / Goldenes Horn 1: 100 000 29°00 N ATROPARION - Mpuka tu Argyru Rebas Kyaneai/Symplegades- Phanarion Krommyon - n Kilios / Kela o Medeae Pyrgos Re- i Ancyreum ba n - - Kyaneai s a Gypopolis Dotine/Proika H. Isidoros Promontorium P - s ia - - n Ampelodes ik L Myrileion Calograea Limen- Lykion- / Kolpos Myrleiu Aphrodision Dios Akra Uskumru / Skombriköy Coracium Promonturium Ephesion- Limen/Ephesiates- - n o i h c i e t Mauros Molos n C a h P r Pyrgos tu Obidiu y Thimea so - rr Phosphoros Chelae oa Ophru Limen- s - Hieron Romelias Prodromu tu Phoberu Mone- 177 Hieron Milton/Tripiton 280 Kataskepe(?)- n io - - n Skletrinas o - r Panteleemonos y - Simas g Mone Bahçeköy r A Megalu Agru (?) B Kallipolis/Kalos Agros s i r o o Bathys Ryax p a k Bathykolpos s u M 179 - p Dikaia Petra/Brulogenes o r Aietu Rynchos Kleides kai Kleithra / Dialithra os / y c h i a 245 Therapeia/Pharmakias Eudios Kalos/LinonS -o n 323 t Amykos G r enKolpos o Palodes- n Libadion / Pitheku- Limen- Thermemeria- Komarodes/Komaron- - Neapolis / Neochorion- Sycia Barbyses Romanu- - Sosthenion- Kantangeion Philemporion Kolpos Eirenaion- Tria Stauria s olo Akoimeton- - Mone- ab at Oxyrrus K Akra 285 Trivia Phrixu Limen- 115 - - - Gynaikospolis Kyparodes/Kyparisson 109 Sarantakopa us - Cheimarr Phiale Phaidalia 442 Laimokopia Su Neokastron e Potamo - n n a i o Aretae h t n i - -- g Phoneus/Roodes a K Babricum - N Chelai ausi kle Küçüksu Echaia ia Akr. Brochthoi 138 iu K x yda o Mega n ros o d Reuma i A u libe Kagýthane - d y Su E Hestiai/Michaelion a k y n L - Promotu o Nausimachion n 128 a Baka p 228 e Anaplus Barbyses r D Bythias a Kalamos str Chrysokeramos Se- my H.Kallinikos Parabolos H. -
2017-2018 Annual Report
Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2017 – April 30, 2018 Brendan Hassett, Director Mathew Borton, IT Director Jeff Brock, Associate Director Ruth Crane, Assistant Director Sigal Gottlieb, Deputy Director Elisenda Grigsby, Deputy Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Associate Director Jill Pipher, Consulting Associate Director Bjorn Sandstede, Associate Director Homer Walker, Consulting Associate Director Ulrica Wilson, Associate Director for Diversity and Outreach Table of Contents Mission ....................................................................................................................................... 6 Core Programs and Events ......................................................................................................... 6 Participant Summaries by Program Type ................................................................................... 9 ICERM Funded Participants ................................................................................................................. 9 All Participants (ICERM funded and Non-ICERM funded) .................................................................. 10 ICERM Funded Speakers ................................................................................................................... 11 All Speakers (ICERM funded and Non-ICERM funded) ...................................................................... 12 ICERM Funded Postdocs .................................................................................................................. -
MIDAS-CIDID-Newsletter-15-June-2018.Pdf
MIDAS CIDID Newsletter #15 View this email in your browser Issue #15 | June 2018 Welcome to the June 2018 edition of the MIDAS CIDID Newsletter. This is where you can nd Center-wide updates, along with relevant news and highlights. CIDID Website CIDID Twitter The 10th Summer Institute in Statistics and Modeling in Infectious Diseases (SISMID) takes place July 9-25, 2018, at the University of Washington in Seattle. Registration information is available on the SISMID website. CIDID Seminar: Pelton Auditorium, Fred Hutch August 7, 2018, 10:00 - 11:00am Speaker: Adam Lauring Inuenza Evolution... Getting Personal Live video stream and recording available: [link] Transmission-clearance trade-offs indicate that dengue virulence evolution depends on epidemiological context Nature Communications [pdf] Transmissibility of Norovirus in Urban versus Rural Households in a Large Community Outbreak in China Epidemiology [pdf] Quantifying the risk of local Zika virus transmission in the continental US during the 2015-2016 ZIKV epidemic bioRxiv [pdf] How single mutations affect viral escape from broad and narrow antibodies to H1 inuenza hemagglutinin Nature Communications [pdf] Deep mutational scanning of hemagglutinin helps predict evolutionary fates of human H3N2 inuenza variants bioRxiv [pdf] Inuenza A(H7N9) Virus Antibody Responses in Survivors 1 Year after Infection, China, 2017 Emerging Infectious Diseases [pdf] The impact of past vaccination coverage and immunity on pertussis resurgence Science Translational Medicine [pdf] High dimensional random walks can appear low dimensional: Application to inuenza H3N2 evolution Journal of Theoretical Biology [pdf] Spatio-temporal coherence of dengue, chikungunya and Zika outbreaks in Merida, Mexico PLoS Neglected Tropical Diseases [pdf] Design of vaccine trials during outbreaks with and without a delayed vaccination comparator Annals of Applied Statistics [pdf] Modeling and Inference for Infectious Disease Dynamics: A Likelihood- Based Approach Statistical Science [pdf] Nextstrain continues to expand its repertoire of pathogens. -
ANNOUNCEMENT of WINNERS of the Seventy-Ninth Competition Held on December 1, 2018
ANNOUNCEMENT OF WINNERS of the seventy-ninth competition held on December 1, 2018 WINNING TEAMS Rank School Team Members (in alphabetical order) 1 HARVARD UNIVERSITY Dongryul Kim, Shyam Narayanan, David Stoner 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Junyao Peng, Ashwin Sah, Yunkun Zhou 3 UNIVERSITY OF CALIFORNIA, LOS ANGELES Ciprian Mircea Bonciocat, Xiaoyu Huang, Konstantin Miagkov 4 COLUMBIA UNIVERSITY Quang Dao, Myeonhu Kim, Matthew Lerner-Brecher 5 STANFORD UNIVERSITY David Kewei Lin, Hanzhi Zheng, Yifan Zhu The institution with the first-place team receives an award of $25,000, and each member of the team receives $1,000. The awards for second place are $20,000 and $800; for third place, $15,000 and $600; for fourth place, $10,000 and $400; and for fifth place, $5,000 and $200. In each of the following categories, the listing is in alphabetical order. THE PUTNAM FELLOWS — THE FIVE HIGHEST RANKING INDIVIDUALS Each receives an award of $2,500. DONGRYUL KIM Harvard University SHYAM NARAYANAN Harvard University DAVID STONER Harvard University YUAN YAO Massachusetts Institute of Technology SHENGTONG ZHANG Massachusetts Institute of Technology THE NEXT TEN HIGHEST RANKING INDIVIDUALS Each receives an award of $1,000. MURILO CORATO ZANARELLA Princeton University JIYANG GAO Massachusetts Institute of Technology ANDREW GU Massachusetts Institute of Technology JAMES LIN Massachusetts Institute of Technology MICHAEL MA Massachusetts Institute of Technology ASHWIN SAH Massachusetts Institute of Technology KEVIN SUN Massachusetts Institute of Technology DANIELLE WANG Massachusetts Institute of Technology HUNG-HSUN YU Massachusetts Institute of Technology YUNKUN ZHOU Massachusetts Institute of Technology THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION ELIZABETH LOWELL PUTNAM PRIZE The winner receives an award of $1,000. -
On the Lion Harbour and Other Harbours in Miletos: Recent Historical, Archaeological, Sedimentological, and Geophysical Research*
On the Lion Harbour and other Harbours in Miletos: recent historical, archaeological, sedimentological, and geophysical research* HELMUT BRÜCKNER, ALEXANDER HERDA, MARC MÜLLENHOFF, WOLFGANG RABBEL & HARALD STÜMPEL Καλοὶ δὲ Μιλησίων εἰσὶ λιμένες “But beautiful are the harbours of the Milesians” (Chariton, Chaireas and Kallirhoë 4.1.5) 1. Introduction from its strategic role as one of the closable war harbours The Lion Harbour was Miletos’ most prominent harbour of Archaic and later times. Its central position in the Ar- during antiquity. It can be envisaged as the heart of the chaic insula street grid, lining the agora and the main city Ionian metropolis in western Asia Minor. Originally situ- sanctuary of Apollo Delphinios, made it a gate through ated in a bay of the “(I-)Karian Sea”, Miletos is now fully which, so to speak, gods and humans entered the city; incorporated into the plain of the Maeander river, today’s it was also the point from which Milesians left the city Büyük Menderes. to start their sailing seasons or found their many colo- In this article we combine results from historical and nies. The Lion Harbour is likely to be identified with the archaeological research with those from palaeo-geography “Harbour of Dokimos” mentioned by the 1st century AD and geophysics. This geoarchaeological approach offers novelist Chariton (Chaireas and Kallirhoë 3.2.11) new insights into the dynamic evolution of the harbour The commercial relevance of the Lion Harbour, how- basin from the time of the marine transgression in the ever, was quite limited in antiquity. Miletos had a series early Bronze Age (c.