My name in books (mostly from google books)

Vaserstein Wasserstein Vasershtein Vasserstein Vaseršteǐn, Waserstein,  Vassershtejn, Васерштейн Вассерштейн

My name in title from Math Reviews

My name in title from other sources

My publications

1969

### Bulletin signalétique: Mathématiques pures et appliquées

1969

Varopoulos, N. T., 1093. Varshavskij, V. I„ 2575. Vasconcelos, W. V., 441, 448. Vasershtejn, L. N"., 305, 609. Vasic, P. M., 14U8, 1755, 1756, 1948, 1949, 1950, 1951, 1953. Vasilescu, F.-H., 822. Vasil'ev, V. G., 2394. Vasquez, A. T., 2128.

Автоматика и телемеханика: орган Комиссии автоматики и телемеханики, Volume 30, Issues 9-12 - Page 103

1969

С другой стороны, естественно ожидать, что при е, близких к 7г, система эргодична. Как заметил Л. Н. Вассерштейн, это можно доказать следующим методом, применимым и во многих других случаях.

Советско-японский симпозюм по теории вероятностей,  Хабаровск, август, 1969 г, Volume 1- Page 30

Akademia nauk SSSR. - 1969

Л И Т В Р- А Т У Р . А 1. Добрушин Р. Л. 2. Вассерштейн Л.Н. 3. Аверинцев М., 4. Досадшин Р. Л. 5. V.;;- . п Р. Л. 6. Беляев Ю.К. Малышев В. А. Громак Ю.И. 7. Ставе кая О.Н. Пятецкий-Шапиро 8. Шнирман М.Г. 9. Тоом А. Л. 10.

### Recueil mathématique de la Société mathématique de Moscou - Page 422, 424, 463

1969

2. Н. В аз з, Л. МПпог апй Л.-Р. Зегге, 5о1иИоп сГ 1Ье сопдгиепсе виЬдгоир ргоЬ- 1ет !ог 51„ (л>3) апй 5Р2п (л^2), РиЫ. МаШ., 33 (1967), 59—137. 3. Л. Н. Васерштейн, Кртеория и конгруэнцпроблема, Матем. заметки, 5, вып. 2 (1969) ...

### Книжная летопись: Дополнительный выпуск - Page 13

1969

... А. А. 14881 Варлинский Н. Н. 17339 Вартанян В. арм 16430 Вартанян В. А. 15173 Васадзе Б. И. 18127 Васенев С. А. 16501 Васерштейн Л. Н 10925 Василевич А. П. 14882 Василенко В. В. 17340 Василенко Е. Д. 15435 Василишин ...

1970

Consultants Bureau  Faraday Press, 1970

Vasershtein

Automation express - Volume 12 -International Physical Index., 1970  Page 16, 37

Vasershtein

Экономика и математические методы - Volume 18, Issues 1-3 - Page 287

1982

Л.: Машиностроение, 1970. 2. Васерштейн Л. Н., Шерман Э. Б. О формировании вариантов в дискретных задачах оптимального отраслевого планирования. — Экономика и матем. методы, 1975, т. XI, вып. 4. 3. Васерштейн Л. П.

1970

... понижению степени матриц в конгруэнц-проблеме. Обычно задачу удается свести к 81,(3, о) и 5/7 (4, о). Сюда относятся работы [10, 14, 194]. Л. Н. Васерштейн [12, 13, 15] с помощью ортогональных и 84.

Васерштейн Л. Н., /Сртеория и конгруэнц-проблема, Мат заметки 1969, 5, No 2, 233—244 (РЖМат, 1969, 7А330) Ю. — , Конгруэнцпроблема для унитарной группы ранга, большего или равного 2. Мат. сб., 1968, 76, No 3, 362—367 ...

1971

Arithmetic groups - Page 117

James E. Humphreys   Courant Institute of Mathematical Sciences, New York University, 1971 - 121 pages ISBN: 0387099727

Vaserstein

MR0339966 \cyr Matematika: Periodicheskiĭ sbornik perevodov inostrannykh stateĭ. Tom 15 (1971), \cyr vyp. 6. (Russian) [Mathematics: Periodical collection of translations of foreign articles.

Vol. 15 (1971), no. 6] Izdat. Mir'', Moscow, 1971. 166 pp. 00A10

\cyr Matematika: Periodicheskiĭ sbornik perevodov inostrannykh stateĭ 15, vyp. 1. (Russian) [Mathematics: Periodical collection of translations of foreign articles

15, no. 1] Izdat. Mir'', Moscow, 1971. 160 pp. 00A10

Модули - Issues 1-4 - Page 4

Институт математики (Академия наук СССР. Сибирское отделение)

9А28в) 14. БУРБАКИ Н. Коммутативная алгебра. М, 'Мир', 1971. 707 с. 15. ВАССЕРШТЕЙН Л.Н. О стабилизации в алгебраической К-те- ории. - 'Функцион. анализ и его прил.', 1989, т. 3, вып. 2, с. 85-88. (РЖМат, 1989, 10А215) 18.

### Introduction to Algebraic K-theory - Page vii

John Willard Milnor - 1971

86 (1967), 16-73 R. Swan, Algebraic K-theory, Lecture Notes in Math. 76, Springer 1968- R. Swan (with E. G. Evans), K-theory of finite groups and orders, Lecture Notes in Math. 149, Springer 1970. L. N. Vaserstein, On the stabilization of the ...

1972

Séminaire de probabilités VI: Université de Strasbourg  1971/72, Volume 11 -  Page 286, 290

Springer - 1972 - 253 pages Lecture Notes in Mathematics 258

References. M. DOBRUSIN, R. L. : Description of a random field by means of conditional probabilities and conditions of its regularity. ... WASSERSTEIN, L. N. : Probl. peredaci informacii 5,3 (1969), 64-73.

Introduction to Algebraic K-Theory  By JOHN W AUTOR MILNOR  Princeton University Press 1972 - Page viii

Vaserstein

MR0352037  \cyr Osnovy teorii chisel. (Russian) [Fundamentals of number theory] Translated from the English by L. N. Vasseršteĭn and A. N. Paršin.

Edited by I. I. Pjateckiĭ-Šapiro. Izdat. Mir'', Moscow, 1972. 408 pp. 12-XX

Челябинская областная универсальная ...

Методы решения задач развития и размещения производства [Текст] / Л. Н. Вассерштейн, В. И. Геминтерн, Э. Б. Шерман. - М. : Информэлектро, 1972.

Вассерштейн Л. Н., Геминтерн В. И., Шерман Э. Б

### Тезисы докладов - Volume 6 - Page 28, 149

1972

АЛГЕБРАИЧЕСКИХ МНОГООБРАЗИИ Л. Н. ВАСЕРШТЕЙН (Москва) ОСНОВЫ АЛГЕБРАИЧЕСКОЙ /С-ТЕОРИИ О различных определениях Кп -функторов и свяаях между ними. А. И. ВЕКСЛЕР (Ленинград) О РАЗЛОЖИМОСТИ ...

1973

Hermitian K-theory and geometric applications: -  Page 125, 156, 212

proceedings of the  conference held at the Seattle Research Center of the Battelle Memorial Institute, from August 28 to September 8, 1972 Hyman Bass - 1973 - 572 pages

Vaserstein

Séminaire de probabilités VII: Université de Strasbourg 1971/72 - Page 286

Paul André Meyer - 1973 - 322 pages Lecture Notes in Mathematics 321

idea of WASSERSTEIN

David H. Sattinger Springer-Verlag, 1973 - - 190 pages

Vaserstein

Proceedings of the Conference on Orders, Group Rings and Related Topics / Edition 1 by J. S. Hsia (Editor), M. L. Madan (Editor), T. G. Ralley (Editor)

1973 - Springer       Institute in Seattle, Washington, August 28- September 8, 1972).

Stability for K 2 R Dennis

[14] LN Vaserstein, On the stabilization of the general linear grOup over

a ring~ Mat. Sbornik 79 (1969), 405-424 (Amer. Math. Soc. Translation v. 8, 383-4oo. ) ...

### Conference on Commutative Algebra, Lawrence, Kansas, 1972 - Page 89

James W. Brewer, ‎Edgar A. Rutter - 1973

Dubriel-Pisot. t. l4 , 1960-l96l, no. 2 . Seshadri, C. [Ses] "Triviality of Vector Bundles over the Affine Space K^" Proc. Nat. Acad. Sci. 44(l958), 456-458. Vaserstein, L. [Vas] "Stable Rank of Rings and Dimensionality of Topological Spaces?

### Итоги науки и техники: Техническая кибернетика - Page 343

1973

11971, No 10, 95 — 107 143. Докл. II Всес. совёщ. по статиетич. методам теории управл. Ташкент, 1970. М., «Наука», 1970 144. Реф. докл. V Всес. совещ. по проблемам управл. М., «Наука», 1971 145. Васерштейн Л. Н. Марковские ...

1974

1974

The definitive form (above) of (b) is due to Vasserstein [Va] . It is by far the most difficult of the results I shall discuss here. Its proof is too long and technical to give in detail within the scope of these lectures. The proof of (a), which is quite easy, ...

Bulletin signalétique:   - Page 291, 312

Informatique, automatique, recherche opérationnelle, gestion, Volume 35, Issues 1-7061

distance de Wasserstein

Introduction to some methods of algebraic K-theory - Page 8

Hyman Bass, Conference Board of the Mathematical Sciences - 1974 - 68 pages

Volume 20 of Regional Conference series in mathematics

The definitive form (above) of (b) is due to Vasserstein [Va] . It is by far the most difficult of the results I shall discuss here. Its proof is too long and technical to give in detail within the scope of these lectures.

Lecture notes on discrete Markov systems - Page 57, 70

Volume 10 of Carleton mathematical lecture notes

D. A. Dawson - Carleton University, 1974 - 144 pages

Vasserstein metric

Snirman, Vasserstein, Leontovich and others have shown that li^pi £ 2 . Furthermore there exists 6 ...

cyr Matematicheskie metody v èkonomicheskikh issledovaniyakh. (Russian) [Mathematical methods in economic research] Supplement to Èkonom. i Mat. Metody.

Edited by E. G. Golʹšteĭn. \cyr Seriya "\cyr Optimalʹnoe Planirovanie i Upravlenie''. [Optimal Planning and Control Series] Izdat. Nauka'', Moscow, 1974. 172 pp. 90-06

развития, специализации и размещения производства в электротехнической промышленности - Kazakevich, David Moiseevich. Page 4, 114

Moskva : OVNIIĖM (Informėlektro), 1974.

13. Березин А. А. Факторы, влияющие на размещение подотраслей электротехнической промышленности. — «Электротехн. пром-сть. Сер. Общеотраслевые вопросы», 1972, вып. 378. 14. Вассерштейн Л. Н., Геминтерн В. И., ...

### Algebraic Geometry, Arcata 1974 - Page 111, 112, 114

Robin Hartshorne - 1974

Suslin-Vaserstein all announced important progress, The detailed history is very well portrayed in Bass' paper [2]; the reader may also find there a very complete exposition of the new results, (The material exposed here comes, in fact, from ...

1975

Limit theorems of probability theory - Page 152, 162

Volume 11 of (Colloquia mathematica Societatis János Bolyai)

North-Holland Pub. Co., 1975 IEEE, 1975 - 420 pages

Wasserstein - distance

APPLICATIONS (a) The Wasserstein metric.

IEEE transactions on communications: Volume 23

Vasershtein

Computer and information systems: Volume 14  1975 Cambridge Scientific Abstracts.

conference held January 7, 8, 9, 1975 Western Periodicals Co.2975 ,

The mismatch bound is in terms of a measure of the distance between random variables which is a generalization of the Vasershtein

distance [ 1, 2] and a special case of the P distance between random processes [ 3] .

Algebraic Geometry: Arcata 1974 - Page 111, 112, 114

edited by Robin Hartshorne, American Mathematical Society 1975

Suslin-Vaserstein all announced important progress.

Vsesoiuznyĭ algebraicheskiĭ simpozium: 30- iiunia - 2 ...

Вассерштейн Л.Н.Стабильный рант колец и размерность топологических пространств, Функц. анализ, 1971,5,12,17-27. 4. Вассерштейн Л.Н.,Суслин А.А. Проблема Серра о проективных модулях над кольцами многочленов и ...

Issue 42 of Queen's papers in pure and applied mathematics - Page 1, 3, 45, 59

A. V. Geramita editor

Kingston, Ont. Queen's University 1975 268 pages

### Peterson's Annual Guides/graduate Study - Page 424

Charles Granade - 1975

Amitai Regeu, Ph.D., Hebrew of Jerusalem. Ring theory, combinatorics. Donald C. Rung, Ph.D., Notre Dame. Analysis, complex variables. Stephen G. Simpson, Ph.D., MIT. Logic, recursion theory. Leonid N. Vaserstein, Ph.D., Moscow. Algebra ...

1976

Introduction to ergodic theory: - Page 15

- Princeton University Press 1976 - 144 pages

Wasserstein

Coupling methods for Markov processes - Page 24, 45, 71

David Scott Griffeath - 1976 - 158 pages

Once again, straightforward computations show that (l6) leads to a coupling, the version for Markov processes of a more general construction due to

Vasershtein; call it the Vasershtein coupling.

Soviet electrical engineering: Volume 46, Issues 7-12  1976. Page 103, 104, 111

1975 Allerton Press, 1976

PARAIEETRIC NODELS FOR OPTII-'IIZING FUTURE INDUSTRY-WIDE PLANNING

L. N. Vasershtein, Yu. A. Rudnev, and E. B. Sherman Eiektrotekhnika, V01. 46, No. T1, pp. 57-59, T975 UDC 65.0T2.2 Fundamentally new parametric models ...

Proceedings of the 1975 IEEE-USSR Joint Workshop on Information Theory, December 15-19, 1975, Moscow, USSR  - Page 48, 49, 63

The V distance can also be interpreted as a natural adaptation of the Vasershtein distance [22] to random processes.

convergence of laws on metric spaces, with a view to statistical testing

Wasserstein norm

University of Wisconsin--Madison, 1976 - John David Prange - 402 pages

The basic result used in the dual operator approach is due to Vasershtein and ...

Geometric algebra over local rings - Page 415

Bernard R. McDonald M. Dekker, 1976 - 421 pages

Vaserstein

Algebraic K-theory: proceedings of the conference held at Northwestern University, Evanston, January 12-16, 197677, 78, 153

Michael R. Stein Springer-Verlag, 1976 - 409 pages

Vaserstein

### Proceedings of symposia in pure mathematics - Volume 28 - Page 47, 49

1976

L. N. Vaserstein and A. A. Suslin, Serre's problem on projective modules over polynomial rings and algebraic K-theory (announcement) (to appear) (Russian). X. Finite groups (M. Asbacher). The major problem in the theory of finite groups is ...

### Annual report - Page 12

In 1973, following a period of intense activity, three young Soviet mathematicians, A. A. Roitman, V. N. Suslin, and L. N. Vaserstein contributed significantly to important extensions, including the cases n ^ 4. Some of this work extends ...

### Newsletter - Volumes 11-15 - Page 181

In l973, following a period of intense activity, three young Soviet mathematicians, A. A. Roitman, V. N. Suslin, and L. N. Vaserstein contributed significantly to important extensions, including the cases n < 4. Some of this work extends ...

### Soviet Electrical Engineering - Volume 46 - Page 104

1976

PARAIEETRIC NODELS FOR OPTII-'IIZING FUTURE INDUSTRY-WIDE PLANNING L. N. Vasershtein, Yu. A. Rudnev, and E. B. Sherman Eiektrotekhnika, V01. 46, No. T1, pp. 57-59, T975 UDC 65.0T2.2 Fundamentally new parametric models ...

1977

Avtomatizatsiia planovykh raschetov

by Romanenko, Il'ia Pavlovich 1977

# Wilhelm Krelle zum 60. Geburtstag

Wilhelm Krelle, ‎Horst Albach, ‎Ernst Helmstädter - 1977

auf £ und eine stetige Funktion / auf £ gilt nach einem Lemma von Vasser- stein \ifdß-ifdv\^liPa(f)\na(l)-y.(l)\. amA Dabei ist Pa(f) = s\ip\f(x)-f(y)\, x.y X~y und x~y bedeutet x(b) = y(b) für alle b4=a; (Vasserstein [1969]). Wenn wir das auf die ...

ACM Guide to Computing Literature - 1977 - 1695 pages

Robert M. Gray, Lee D. Davisson - 1977 - 387 pages

As suggested by Kailath (1973), p" can be interpreted as the Vasershtein distance (Vasershtein (1969)) between [is and // with ... Hence Theorem 1 demonstrates the equivalence of the p distance with the appropriate Vasershtein distance.

The Annals of probability: Volume 5 - 1977 - Page 678, 692

Vasershtein

Controlled spin-flip systems - 1977 - 104 pages - Page 52

Vasershtein

Department of Electrical Engineering and Computer Sciences, Johns Hopkins University, 1977

Abstract The Bhattacharyya, l—divergence, Vasershtein, variational and Levy distances are evaluated, compared and used for the reduction of n data to one feature.

Annales: Calcul des probabilités et statistique - Volume 13 - Page 157

Institut Henri Poincaré - Gauthier-Villars., 1977

A. L. Toom, Nonergodic multidimensional systems of automata. Problemy Peredachi Informatsii, t. 10, no. 3. 1974. p. 229-246. [12] L. N. Vasershtein, A. M. Leontovich, Invariant measures of certain Markov operators describing a homogeneous ...

Cornell University - 1977

... Fall Term Vaserstein, Leonid Academic Year Villareal, Ruben L 2/1/79- 12/21/79 Vietorisz, Thomas 1/10/80-5/31/80 Vladeck, Judith 10/18/79-6/16/80 Voight, K 6/25/80-8/8/80 Wagner, Cyrus H Academic Year Ward, Larry D Academic Year ...

Modular functions of one variable: - Page 192

# proceedings international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976, Volume 2

Jean Pierre Serre, ‎Don Bernard Zagier - 1977

This theorem is proved in [4] and depends on Vaserstein's theorem cited above [12]. The proof being long and very technical will not be reproduced here. However in the particular case q = 1 it can be proved rather shortly. Let us now put ...

Итоги науки и техники: - Volume 15 - Page 63

1977

О суммах модулей коэффициентов некоторых модулярных форм. Сообщ. АН ГрузССР, 1955, 16, No 7, 497—502 (РЖМат, 1956, 3620) 22. Васерштейн Л. Н., О группе З1-2 над дедекиндовыми кольцами арифметического типа.

Методы погружения в задачах оптимизации - Page 153

Абрамов В. В., Крумм Л. А., Мурашко Н. А. Комплексная оптимизация режима и состава работающего оборудования сложных ... Моисеев Н. Н. Нелинейное программирование. ... 43. Васерштейн Л. Н., Чмиль В. И., Шерман Э. Б. 153.

1977

Мальцев В.Н. .Аветисян А. Г. Информационные следящие системы в планировании и управлении. -"Пром- сть Армении", Ереван, ... Васерштейн Л.Н.,Шерман Э.Б. Проблемы формирования вариантов развития и специализации ...

### Летопись журнальных статей - Issues 5-7 - Page 24

1977

23321. Васерштейн Л. Н. Основы алгебраической К-теорнн. — Успехи мат. наук, 1976, т. 31, вып. 4 ©, с. 87—149. Список лит.: 126 назв. 23322. Васин В. В. Метод невязки и конечномерная аппроксимация приближенных решений ...

1977

### Москоу, Volume 102; Volume 144 - Page 550, 598

1977

Васерштейн Л. Н. Конгруэяцпроблема для унитарной группы ранга, большего или равного 2, 76(113) (1968), 362— 367. Васерштейн Л. Н. О группе над дедекиндовыми кольцами арифметического типа, 89(131) (1972), 313—322.

### Экономика и математические методы - Page 821, 1021, 1132

1977

Л. Н. Васерштейн, Ю. А. Руднев, 9. Б. Шерман. Сущность и основные направления параметрического подхода к задачам развития и размещения производства. В сб. Проблемы оптимизации перспективного планирования в ...

1978

Application of mathematical methods and computers in social sciences : international bibliographical index, 1975-1977

by European Coordination Centre for Research and Documentation in Social Sciences  1978

### Matekon - Volume 15 - Page 64

1978

L. N. Vasershtein and E. B. Sherman, "O formirovanii variantov v ... 11, no.

Studies in probability and ergodic theory    Page 14, 26, 39

Gian-Carlo Rota - Academic Press, 1978 - 293 pages -

Note that the classical coupled process is "weaker" than the Vasershtein coupled process since the former moves from (x, y) $A ... In fact, the Vasershtein coupling is characterized by the property that at each step it sends us to the diagonal as ... Locally interacting systems and their application in biology: - Page 55, 112 proceedings of the School-Seminar on Markov Interaction Processes in Biology, held in Pushchino, Moscow Region, March 1976 R. L. Dobrushin, V. I. Kriukov, A. L. Toom - Springer-Verlag, 1978 - 202 pages Vasershtein L.N., Markov processes on a conutable space product describing large automata systems, Problemy Peredaci Informacii, 5_, (1969) , vyp. 3, 64-72. MR0536824 (81e:60003) Szulga, Alicja On the Wasserstein metric. Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, pp. 267--273, Reidel, Dordrecht-Boston, Mass., 1978. (Reviewer: V. J. Paulauskas) 60B05 (90A05) Ergodic theory and information - Page 129 Patrick Billingsley - 1978 Книжная летопись: Дополнительный выпуск - Issues 10-12 - Page 31 1978 24 с.; 20 см. — 17 к. 1.500 экз. — [78-37466] оп 389.1:620.9(083.131) ч 23.1.1 Экономика энергетики 12763. Васерштейн Л. Н. и др. Параметрические модели развития и размещения производства / {Васерштейн Л. Н., Руднев Ю. А., ... Новая советская литература по общественным наукам: 1978 116-122. Задачи календарного планирования. 185. Васерштейн Л. Н., Руднев Ю. А. .Шерман Э.Б. Параметрические модели развития и размещения производства. -"Экономика и мат. методы" , 1977 ,т . 13. вып. 5 ,с. 1008- 1021. 186 ... 1979 14 books proceedings, University of Waterloo, Canada, 12-16 June 1978 Springer-Verlag, 1979 - Lecture Notes in Mathemstics 734 352 pages For example, if X is a topological space, Vaserstein [26] has proved that s. r. (A) = 1+dim X for A the ring of continuous functions on X. H. C. P. Berbee - 1979 - 223 pages Vasershtein The stochastic time evolution of Gaussian interacting systems - Page 91 Cheng-tan Hsiao Cornell University, Aug., 1979 - Mathematics - 182 pages Wasserstein Distance Vallander, S. S., Calculation of the Waser stein Distance Between Sūri kagaku kōkyūroku: Volumes 371-374 - Page 124 Wasserstein By Joseph J. Rotman Academic Press 1979 R. Treger told me of Vaserstein's proof of Suslin's solution of Serre's problem, and was kind enough to translate it for me from the Russian. Remarkably, the problem was solved simultaneously, in January 1976, by Quillen in the United States and Suslin in the Soviet Union. We first present Vaserstein's version of Suslin's proof ; afterwards, we shall outline Qui1len's solution. Additive and cancellative interacting particle systems - Page 106 David Griffeath - 1979 L. N. Vasershtein (1969). Markov processes over denumerable products of spaces IEEE International Symposium on Information Theory - Page 135 THE VASERSHTEIN DISTANCE AS THE STABILITY CRITERION IN ROBUST ESTIMATION, P. Papantoni-Kazakos (School of Engineering, U-l57, University of Connecticut, Storrs, Connecticut 06268). In the models used by Hampel as well as Commutative rings whose finitely generated modules decompose - Page 28, 46, 105, 106 Willy Brandal - 1979 L. N. Vasershtein (1969). Markov processes over denumerable products of spaces, describing large systems of automata, Problemy Peredachl Informatsll 5 (3), 64-73. L. N. Vasershtein and A. M. Leontovlch (1970). Invariant measures of ... ### Lecture Notes in Mathematics 733 - Page 329, 333, 338 Albrecht Dold, ‎Frederick Bloom - 1979 For example, if X is a topological space, Vaserstein [26] has proved that s . r . (a) = 1+dim X for A the ring of continuous functions on X. The connection between stable rank and more traditional concepts of dimension is given by the following ... ### Homological Group Theory - Page 136 C. T. C. Wall. [6°] [61] Notes in Math. 386, Springer-Verlag (1974). J. Tits. On buildings and their applications, Proc. Int. Congress _Mgth_., Vancouver (1974), t. 1, 209-20. L. Vaserstein. On the group SL2 over Dedekind rings of arithmetic type, ... ### London Mathematical Society lecture note series 1979 Notes in Math. 386, Springer-Verlag (1974). J. Tits. On buildings and their applications, Proc. Int. Congress Math. , Vancouver (1974), t. I, 209-20. L. Vaserstein. On the group SL2 over Dedekind rings of arithmetic type, Math. USSR Sbornik 18 ... ### The Soviet Review - Volume 20 - Page 44 1979 18. Matematiko-ekonomicheskie metody i modeli (biblio- graficheskii ukazatel'), Leningrad, "Nauka" Publishers, 1968. 19. W. Zassman and E. Kummerow, Produktsionplanopti- mierung, Berlin, Verlag die Wirtschaft, 1977. 20. L. N. Vasershtein ... ### Preprint Series: Mathematics - Issues 1-5 - Page 50 [50] L.N. VASERSHTEIN: "Markov Processes over a Countable Product Space describing large Systems of Automata". Prob. in Trans of Information, Vol. 5, no 3, 64-72 (1969) (Enlish translation) [51] M. LOEVE: "Probability Theory" . Van No ... ### Planovo stopanstvo - Volume 34 - Page 48 1979 Васерштейн, В. А. Руднсв и др., Параметрнческие молели развития и размещения производства, „Зкономика и математические методи", т. XIII, кн. 5, 1977 г.: Кр. Радева, Б. Данкова, Оптимално райониране на производствените ... 1980 13 books ### Einführung in die kommutative Algebra und algebraischeGeometrie - Page 105 Ernst Kunz - 1980 ... Homomorphismus M(r x t; R[X]) -* M(r x t; Rs [X]) in die Nullmatrix über. Es gibt daher nach III.4.1 ein s G S, welches alle Koeffizienten der Matrix annulliert. Dann ist aber Ai(sX)A2(sX)-A3(sX) = 0. Satz 1.18: (Vaserstein) A G M(r x s; ... Quantum fields: algebras, processes - Page 297 Ludwig Streit - 1980 We have thus shown: Theorem (3.5) Under (D) the unique Gibbs state P € G(tt) has the global Markov property. Remark (3.6) The same argument holds if we define agfc in terms of a Wasser- stein distance and replace (D) by conditions (5.2), ... Vasershtein The Soviet review: Volumes 20-21 1980 - Page 44  LN Vasershtein and EB Sherman, "O formirovanii variantov v diskretnykh zadachakh optimal'nogo otraslevogo planirovaniia," Ekonomika i matematicheskie metody, 1975, vol. 11, no. 4. 21. Multicomponent random systems Page 58, 468, 502, 574 R. L. Dobrushin, Akov Grigorʹevich Sinaĭ, David Griffeath - Marcel Dekker, 1980 - 606 page SK1 von Schiefkörpern:, Martin Kneser - Springer-Verlag, 1980 - 123 pages - Page 108 Markov random fields and their applications - Page 141 Ross Kindermann, James Laurie Snell, American Mathematical Society, 1980 - 142 pages Vasershtein, L.N. (l969) : "Markov processes over ... Publications - Volumes 25-27 - Page 30, 40 Wasserstein distance Biological growth and spread: - Page 144 mathematical theories and applications : proceedings of a conference held at Heidelberg, July 16-21, 1979 Willi Jäger, Hermann Rost, Petre Tăutu Springer-Verlag, 1980 - Science - 511 pages Vasserstein Wasserstein Экономика и математические методы - Volume 16 - Page 745 1980 Многоуровневые системы отраслевой оптимизации. Новосибирск, «Наука», 1975. 5. Л. Н. Васерштейн, В. И. Геминтерн, Э. Б. Шерман. Методы решения задач развития и размещения производства. М., 1972 (Информэлектро) . ### ALGEBRA, TEORIJA ČISEL I ICH PRILOŽENIJA - Page 267 Sergei Mikhailovich Nikol'skii - 1980 L. N. Vaserstein and A. A. Suslin, Serre's problem on projective modules over polynomial rings, and algebraic K-theory, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), 993-1054; English transl. in Math. USSRIzv. 10(1976). 7. Richard G. Swan and ... ### Летопись журналńых статей - Issues 10-18 - Page 65 1980 ... 56271 Варшавский В. Я. 44490 Варшавский П. Т. 39039 Варшавский Ю. С. 47136 Варшавчик М. А. (42456) Варшал Б. Г. 56283 Варшалович Д. А. 54854 Варюхин В. А. 37218 Васев А. В. 52043 Ваоенков Н. В. 37854 Васерштейн Л. 1981 17 books ### Research Publications and Professional Activities - Page 164 Proc. Am. Math. Soc. 75:23l-234 (l979): Singh, S. An R-Stable ANR Which Is Not FR-Stable. Fund. Math. lD3:l77- l34 .(l979). Vaserstein, L. N. On Systems of Particles with Finite-Range and/or Repulsive Interactions. Commun. Math. Phys. ### Algebra Omologica in “Enciclopedia Italiana - V Appendice” – Treccani Enciclopedia Italiana - V Appendice (1991) ..... teorema furono date successivamente da A. A. Suslin (maggio 1976), e da L. N. Vaserstein nello stesso anno. Random fields: - Page 250, 367, 369, 371 rigorous results in statistical mechanics and quantum field theory, Issue 27, Volume 1 J. Fritz, Joel Louis Lebowitz, D. Szász - North-Holland Pub. Co., 1981 1111 pp rigorous results in statistical mechanics and quantum field theory J. Fritz, Joel Louis Lebowitz, D. Szász ... Assume that a uniform Dobnishin — Wasserstein condition (15) a = sup 21 a (/, A:) < 1 holds, and that the dependence in P on the ... Vaserstein American Mathematical Society Translation - Page 11 1981 Vaserstein [4], for example, proved s.r. R[XU . . . , Xn] = n + 1; however for the field C topological methods allow us to establish the inequality s.r. C[Xv . . . , X„] > 1 + n/2. The pi value of the stable rank of a polynomial ring of two variables is ... Statistical theory and method abstracts - Volume 22 ... the corresponding versions of the Blackwell-Orey equivalence, and to prove criteria of Dobrushin-Wasserstein type. ... and the probability of ultimate extinction is approximated using a diffusion approximation with the backward diffusion ... Proceedings of the Conference on Probability Theory Page 140, 149, 152, 159 The Vasershtein metric, which we denote by Ar, is defined by Ar(n, v) = inf U S(x, y)p(dx, dy) where the infimum is taken over all couplings p. of ^ and ... For more facts about the Vasershtein metric see Vasershtein (1969) and Dobrushin (1970). Dobrushin uniqueness techniques and the decay of correlations in continuum statistical mechanics - Page 1, 19, 20, 67 David Michael Klein Cornell University, Aug., 1981 - Science - 134 pages Following Gross [6] and Vasershtein [17], we manipulate these inequalities in matrix form. Eight lectures delivered at the Inernational Congress of Mathematicians in Helsinki By G. S. Makanin, Lev IAkovlevich - Page 11 Algebraic K-Theory. Evanston 1980: Proceedings of the Conference Held at Northwestern University Evanston, March 24-27, 1980 - Page 247, 465 Eric M. Friedlander Springer, May 26, 1981517 pages Inst. Steklov (LOMI) 64^ (1976), 131-152. (Russian). [13] L.N. Vaserstein, On the group ... Methods of representation theory- Page 77, 81, 82, 129, 941, 947 with applications to finite groups and orders Volume 2 1987 Charles W. Curtis Wiley, 1981 - 951 pages In (44.17), we shall prove: (40.44) Injective Stability Theorem (Bass, Vaserstein). If the ring A has stable range d, then EH(A) = GL„(A)r\E(A) < GLn(A) for n>d+\, and there is an isomorphism The map GLn{A)-*Kx(A) is obviously surjective for n ... Abstracts of papers presented to the American Mathematical Society - Volume 3 - Page 164 (Received January 11, 1982 ) 793-20-70 L. N. VASERSTEIN, Department of Mathematics, PennijlTania State UniTersity, University Park, PA 16802. Cluneal groupt over rinjt. • The classical groups over rings include the general linear groups Analele științifice ale Universității "Al. I. Cuza" din Iași: - Page 211 Matematică, Volumes 27-28 H. Dayton, E. M. Friedlander & B. Parshall, H. Gillet, D. R. Grayson, D. Guin- Walerv &".J. -L. Lodav, W. van der Kallen, C. Kassel, J. -L. Loday, R. J. MiUram, R. Oliver, S. Priddy, C. Sherman, C. Soule (2), J. Stienstra, L. N. Vaserstein, C. A. ... Revue roumaine de mathématiques pures et appliquées - Volume 26, Issues 6-10 - Page 1090 ... coupling and since Vasershtein seems to have been the first to construct this coupling we call it Vasershtein's diagonal coupling [63]. We shall usually denote it by fe. The next little lemma is basic in the theory of couplings. Lemma 3.1. ### Lecture notes in mathematics - Issue 882 - Page 268 Albrecht Dold - 1981 106, 1977, 599-612. 11 R. G. Swan, Projective modules over group rings and maximal orders, Ann, of Hath. 76, No. 1, 1962, 55-61. 12 L. K. Vaserstein, On the stabilization of the general linear group over a ring, Hath. USSR, Sbornik 8, 1969, ... ### American Mathematical Society translations - Volume 117 - Page 12 L. N. Vaserstein, 77ie stable rank of rings and the dimension of topological spaces, Funkcional. Anal, i Prilozen. 5 (1971), no. 2, 17-27; English transl. in Functional Anal. Appl. 5 (1971). 5. , On the stabilization of the general linear group over a ... ### Integral representations and applications: - Page 278 # proceedings of a conference held at Oberwolfach, Germany, June 22-28, 1980 Klaus W. Roggenkamp - 1981 Volume 882 of Lecture notes in mathematics 106, 1977, 599-612. 11 R. G. Swan, Projective modules over group rings and maximal orders, Ann, of Math. 76, No. 1, 1962, 55-61. 12 L. N. Vaserstein, On the stabilization of the general linear group over a ring, Hath. USSR, Sbornik 8, 1969, ... ### Экономико-организационные основы отраслевого управления ... долгосрочного плана развития промышленных узлов в Литовской ССР. — Экономика и математические методы, 1975, т. XI, вып. 4. 29. Бусленко И. П. Моделирование сложных систем. М.: Наука, 1968. 30. Васерштейн Л. 1982 16 books Informatsionnaia baza perspektivnogo planirovaniia v OASU by Kuznetsov, S. A 1982 The arithmetic theory of algebraic groups by VP Platonov - 1982 The major part of Humphrey's book [149] concerns the congruence problem, which is ...... Linear algebraic groups, W.A. Benjamin Inc., New York 1969. ... [17] L.N. Vasershtein, The group SL2 over Dedekind rings of arithmetic type, Mat. Sb. MR0662823 (83e:00003) Dieudonné, Jean Alexandre A panorama of pure mathematics. As seen by N. Bourbaki. Translated from the French by I. G. Macdonald. Pure and Applied Mathematics, 97. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. x+289 pp. ISBN: 0-12-215560-2 00A05. p.181 (L. Wasserstein), p,259 (P.Vaserstein). IEEE transactions on information theory: Volume 28 Jean-Michel Bismut, L. Gross, Klaus Krickeberg - 1982 - 313 pages - Chetan Prakash - 1982 - 298 pages - Definition of Vasershtein Matrices Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin: - Page 88 proceedings, Paris 1981 (34ème année) Units in Whitehead groups of finite groups , Robert Oliver, Leonid Vaserstein Matematisk Inst., Univ., 1982 - 56 pages Units in Whitehead groups of finite groups. (English) Prepr. Ser., Aarhus Univ. 27, 56 p. (1982). MSC2000: *18F25 16E20 16S34 Algebraic K-theory - Page 73 proceedings of a conference, held at Oberwolfach, June 1980 Wasserstein Espacios simplécticos sobre [beta]-anillos y anillos de Hermite, tra[n]svecciones simplécticas - Page 39, 68 Vaserstein MR0697232 American men and women of science: The physical and biological sciences, Volume 7; Volume 15, Issue 7 Bowker, 1982 Page 297 Wasserstein Итоги науки и техники: - Volume 20 - Page 71, 131 1982 ЛИТЕРАТУРА. 1. Бейлинсон А. А., Высшие регуляторы и значения /.-функций кривых. Функц. анализ и его прил., 1980, 14, No 2, 46—47 (РЖМат, 1980, 1 1А457) 2. Васерштейн Л. Н., К\ -теория и конгруэнцпроблема. Матем. заметки ... ### Информационная база перспективного планирования в ОАСУ Новосибирск: Наука, 1979. 4. Васерштейн Л. Н, Шерман Э. Б. Проблемы формирования вариантов развития и специализации производственных объектов в задачах оптимального отраслевого планирования. М.: Информ- электро ... ### Летопись журнальных статей - Issues 1-9 - Page 67 1982 Вараксин А. А. 20229 Варвак А. П. 8101 Варвак Л. П. 8101 Варвак П. М. 8101-02, 8759-61 Варвянский С. М. 7680 ... Васекина В. Ф. 25422 Васенин А. П. 6402 Васенин В. Л. 30369 Васенков Н. В. 16864 Васерштейн 3648 Василев В. А. 1983 14 books Probability Theory and Mathematical Statistics: - Page 97 Proceedings of the Fourth USSR-Japan Symposium Held at Tbilisi, USSR, August 23-29, 1982 Kiyosi Itō, ‎Uriĭ Vasilʹevich Prokhorov, ‎Jurii V. Prokhorov - 1983 Let 3V - {u*ZV : u^v, min |u- v| < k} v £V — be the boundary of a set V c Z . We denote by |w| the distance in some translation The term Vasserstein distance used in [4] is not justified by the history of the problem. V V V invariant metric on Z ... Abstracts of papers presented to the American Mathematical Society - Volume 4 - Page 526, 632 Samuel J. Lomonaco, Jr., American Mathematical Society - 1983 B. Magurn, R. Dliver and L. Vaserstein, "Units in Whitehead groups of finite groups", (to appear). 17. R. Dliver, "SK. for finite group rings I", Invent. Math. 57 (1gBD), 1B3-2D4. 1B. R. Dliver, "SK, for finite group rings II", Math. Scand. 47 (1gBD) ... Introduction to robust and quasi-robust statistical methods - Page 205, 226 William J. J. Rey - 1983 - 236 pages Vasershtein distance Alexander S. Kechris, D. A. Martin, Yíannis N. Moschovakis - 1983 - 284 pages Lecture Notes in Mathematics, Issues 1019-1021 Vasserstein distance Low Dimensional Topology: Proceedings of the Special Session - Page 162 special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981. B. Magurn, R. Dliver and L. Vaserstein, "Units in Whitehead groups of finite groups", (to appear). 1 Semi-infinite programming and applications: - Page 77, 82 an international symposium, Austin, Texas, September 8-10, 1981 Anthony V. Fiacco, K. O. Kortanek Springer-Verlag, 1983 - 322 pages Wasserstein distance Étude et calcul de quelques distances en probabilités et statistique et applications séparation asymptotique des chaînes de Markov Bernard Garel Université scientifique et médicale de Grenoble, Institut national polytechnique de Grenoble, 1983 - 169 pages On étudie la distance de Prokhorov, la distance de Geffroy et la distance de Fortet-Mourier-Wasserstein. Lond Mathematical Society Lecture Note Series. 81 , Skew Fields - Page 172 SL (D) = [ A* ,A*] c z ( A) if n — I n ^ 2 (the case n = 1 is covered by Vaserstein's Lemma). Indeed, if the latter were false, Lemma 1 would imply that Ej(A) D SLn(D) is a proper normal subgroup of SLn(D), hence (see Theorem 2 in §21.) ET(A) fl ... MR0696937 Draxl, P. K. Skew fields. London Mathematical Society Lecture Note Series, 81. Cambridge University Press, Cambridge, 1983. ix+182 pp. ISBN: 0-521-27274-2 (Reviewer: Jean-Pierre Tignol) 16A39 (12E15 18F25) Экономико-математические модели в системе управления предприятиями - Page 171 Оптимизационные и экономико-статистические методы в перспективном отраслевом планировании. Новосибирск: Наука, 1975. 18. Васерштейн Л. Н., Шерман Э. В. Проблемы формирования вариантов развития и специализации ... Очерки развития математики в СССР: - Page 742 ... 692 Васильев В. А. 424 Васильев В. В. 459 Васильев В. Г. 352, 702 Васильев О. Ф. 731 Васильев Ф. П. 366, 499, 558, 712 Васильев Ю. Л. 547 Васильева А. Б. 296, 345, 577, 701, 726 Васпп В. В. 705 Вассерштейн Л. Н. 211 Ватажин ... ### Skew Fields - Page 172 P. K. Draxl - 1983 SLn(D) = [A*,A*]EZI(A) if n z 2 (the case n = l is covered by Vaserstein's Lemma). Indeed, if the latter were false, Lemma 1 would imply that ZI(A) fi SLn(D) is a proper normal subgroup of SLn(D), hence (see Theorem 2 in §21.) z (A) n SL (D) c ... ### Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980 - Page 168, 197, 332, ... R. Keith Dennis - 1983 L. N. Vaserstein, On the stabilization of the general linear group over a ring, Mat. Sb. 79 (UV) ( 1969). No. 3 , 405-424 = Math. USSR Sb. 8 (1969) , No. 3, 383-400. 23. L. N. Vaserstein, Stabilization for classical groups over rings, Mat. Sb. 93 ... ### Introduction to robust and quasi-robust statistical methods - Page 226 William J. J. Rey - 1983 Papantoni-Kazakos P., The Vasershtein distance as the stability criterion in robust estimation, IEEE Trans. Inform. Theory, IT-26 (1980) 620-625. Papantoni-Kazakos P. and Kazakos D., Nonparametric Methods in Communication, Electrical ... ### Annales scientifiques de l'Université de Clermont-Ferrand II.: # Probabilites et applications, Volumes 1-5 1983 1 - RAPPELS SUR LA DISTANCE DE FORTET-MOURIER Soit (X,D) un espace métrique séparable que l'on ... Cette définition est souvent attribuée à Wasserstein quoique elle soit plus ancienne [11] ; en fait cette distance fut d'abord ... 1984 18 books Dinamika proizvodstvennykh obʺedineniĭ i modeli planirovaniia ikh deiatelʹnosti by Modin, Anatoliĭ Andreevich 1984 ### Reviews in number theory 1973-83: as printed in Mathematical Reviews - Page 305 ### Richard K. Guy, ‎American Mathematical Society - 1984 ### Another aim is a generalization of VaserStein's computation of G/E to certain subrings B of A and ideals /,,/, of B. A typical result is as follows: If B is an order in a totally imaginary ... 327(1981), 156-183. , Colin J.; Reiner, Irving nations for /. ### Thermodynamic Formalism: # The Mathematical Structures of Classical Equilibrium Statistical Mechanics David Ruelle - 1984 Cambridge University Press, 1984 - Science - 183 pages This book is aimed at mathematicians interested in such topics as ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. Atti Del ... Congresso Internazionale Dei Matematici ... - Volume 1 - Page 385 S. D. Chatterji Springer-Verlag, 1984 The vast literature on the Serre conjecture contains many negative and a few special positive results on the problem of extending to vector bundles on X for X regular: one may consult the articles of Horrocks, Swan, Murthy, Vasserstein, Bass, ... Ola Bratteli, Palle E. T. Jørgensen - 1984 - 188 pages Vasershtein proceedings of a workshop organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 Jürgen Franke, Wolfgang Härdle, Douglas Martin - 1984 - 286 pages Vasershtein Vortex methods in two-dimensional fluid dynamics - Page 36, 46 Carlo Marchioro, Mario Pulvirenti - 1984 - 137 pages Vasershtein Quadratic and Hermitian Forms: 1983 - Page ix, 131, 140 By Carl R. Riehm, Ian Hambleton, Natural Sciences and Engineering Research Council of Canada, McMaster University 1984 L.N.Vaserstein, Stabilization in algebraic K-theory and the congruence subgroup problem, Thesis, Moscow State Univ. 1968 (see Funk. ... L.N.Vaserstein, On the normal subgroups of GL over a ring, in Lecture Notes in Math. #854,456-465. Linear algebra over commutative rings - Page 51 By B R McDonald Vaserstein, On K -theory of topological ... Recently, K. 0ennis, B. Magurn, and L. Vaserstein (Generalized Euclidean Group Rings, to appear in J. reine Angev. Math.) ... Introduction to Commutative Algebra and Algebraic Geometry - Page 100 By Ernst Kunz Vaserstein Report PM - Issues 101-110 Penn State, Department of Mathematics Vaserstein Positive Semigroups of Operators and Applications - Page 384, 390 O. Bratteli, P.E.T. Jørgensen - 1984 Vasershtein, L. N.: 'Processes over Denumerable Products of Spaces Describing proceedings of the international conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982 Springer 1984 Volume 1046 of Lecture notes in mathematics [6] L.N. Vasershtein, "Stabilization for the Milnor ... Vaserstein Kinetic Theories and the Boltzmann Equation - Page 63 Lectures Given at the 1st 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Montecatini, Italy, June 10-18, 1981, Issue 1048 Centro Internazionale Matematico Estivo Springer-Verlag, 1984 - 243 pages LNM 1048 II) Dobrushin and Braun-Hepp used the Wasserstein-metric p, ... Cellular automata: - Page 50, 51 proceedings of an interdisciplinary workshop, Los Alamos, New Mexico 87545, USA, March 7-11, 1983 Vasershtein Stochastic analysis and applications: - Page 37 proceedings of the international conference held in Swansea, April 11-15, 1983 Aubrey Truman, David Williams - 1984 Dobrushin later extended this theorem, replacing the total variation by the Vasserstein distance between probability ... If we take the usual metric |c-n| on the real line, the Vasserstein distance of two probability measures n1 , ir„ on <3 (F) can Динамика производственных объединений и модели планирования их деятельности - Page 122, 227 Анатолий Андреевич Модин, ‎Николай Васильевич Махров, ‎Вâчеслав Иванович Данилин - 1984 -1; Васерштейн Л. Н., Шерман Э. В. Проблемы формирования вариантов развития и специализации производственных объектов в задачах оптимального отраслевого планирования. М., 1977; Оптимизация развития и размещения ... ### Abstracts of Papers Presented to the American Mathematical Society - Page 219 1984 Let P and Q be probabilities on R . Their Wasserstein distance is W2 (P, Q) - inf | | |x - y| |2 dy (x, y) >/2 , k k the infimum being taken over all u on R x R with marginals P and Q . Suppose that P and Q are Gaussion with means m and n and ... 1985 14 books Tezisy dokladov = Abstracts of communications by International Conference on Probability Theory and Mathematical Statistics Vilnius, Lithuania 1985 ### Statistics and control of stochastic processes - Volume 2 - Page 377 Nikolaĭ Vladimirovich Krylov, ‎Robert Shevilevich Liptser, ‎Anatoliĭ Aleksandrovich Novikov - 1985 METRIC DISTANCES BETWEEN COUNTING PROCESSES 1. ... Moreover, we get an upper bound also for the corresponding Wasserstein distance and for the total variation distance between one- dimensional distributions. We start by giving ... Aug. 29 - Sept. 4, 1982, Braşov, Romania Marius Iosifescu, Tiberiu Postelnicu, Serban Grigorescu - 1985 - 674 pages Vallender, S.S. , Calculation of the Wasserstein distance between probability distributions on the line. Theory Probab. Appl., 18, 784- 786 (1973). 15. Wasserjtein, L.N., Markov processes with countable state space describing large systems of ... Time series in the time domain - Page 125 Edward James Hannan, Paruchuri R. Krishnaiah, Malempati Madhusudana Rao - 1985 - 490 pages Papantoni-Kazakos and Gray (1979) proposed the use of the Vasershtein distance on P(X"). The Vasershtein distance utilizes a so-called 'per-letter' metric d = d{xt, Thomas Milton Liggett - 1985 - 488 pages Vasershtein, L. N. 1969 Markov processes over denumerable products of spaces, describing large systems of automata. Problems ... Vasershtein, L. N. and Leontovich, A. M. 1970 Invariant measures of certain Markov operators describing a Margrete Siebert Klein, Floyd James Rutherford - 1985 - 231 pages Reviews in K-theory, 1940-84: as printed in Mathematical reviews Page 12, 108, 775 Bruce A. Magurn - 1985 - 811 pages Topology proceedings - Volume 10 - Page 140, 150 Auburn University Mathematics Department and the Institute for Medicine and Mathematics at Ohio University, 1985 Vaserstein Statistics and control of stochastic processes - Volume 2 - Page 377 Chetvertaia Mezhdunarodnaia Vilʹniusskaia konferentsiia po teorii veroiatnosteĭ i matemeticheskoĭ statistike, Vilʹnius, 24-29 iiunia 1985: A-Z [rom - Page 320, 321 Wasserstein metric Time series in the time domain - Page 125 Vasershtein distance Cancer treatment reports - Volume 69, Issues 9-12 - Page 1066 A convenient class of distance functions are the so-called LP Wasserstein metrics, p > 1, which can be motivated as follows. ... If Fz and Fw are two such distributions functions, then their LP Wasserstein distance is the minimum of computed for ... Quantization - Page 202 Peter F. Swaszek Van Nostrand Reinhold, 1985 - 335 pages Wasserstein distance On the Distance between Mixed Poisson and Poisson Distributions Dietmar Pfeifer Defense Technical Information Center, 1985 - 20 pages Estimations and asymptotic expansions for several distances between mixed Poisson and Poisson distributions are given, such as the total variation distance, the Kolmogrov distance and a specific Wasserstein distance (Fortet-Mourier distance). As an example, the author generalizes and improve results of Vervaat (1969) on the total variation distance between negative binomial and Poisson 1986 19 books ### Oeuvres: Collected Papers - Page 715, 724, 725 Jean Pierre Serre - 1986 Springer 2088 pages 553.2 L. Vaserstein a démontré un résultat plus précis: rA 724. ### Oeuvres - Collected Papers: Volume 3: 1972 - 1984 - Page 534 Volume 3: 1972 - 1984 Jean-Pierre Serre. Springer, 1986 731 pages Notes in Math. 386, Springer-Verlag (1974). [52] J. Tits. On buildings and their applications, Proc. Int. Congress Math. , Vancouver (1974), t. I, 209-20. [53] L. Vaserstein. On the group SL? over ... Regression trees based on rank statistics - Page 22 Mark Robert Segal - Stanford University, 1986 146 pp Instead of using two-sample statistics, their splitting criteria utilizes Wasserstein metrics. Mathematical Methods in Computer Vision University of Minnesota. Institute for Mathematics and Its Applications - 1986 - 394 pages Wasserstein metric Stewart N. Ethier, Thomas G. Kurtz - Willey 1986, 2005 - 534 pages online The notion of duality given by (4.36) was developed first in the context of infinite particle systems by Vasershtein (I969), Vasershtein and Leontovitch (I970), proceedings of AMS Special Session held August 8 - 10, 1983 Kondagunta Sundaresan, Srinivasa Swaminathan, American Mathematical Society Cont Math 54, - 1986 - 122 pages It is not difficult to show that relative to the Vasershtein metric (see, e.g., [BF] for definition and basic properties), proceedings of the Research Conference held June 17 - 23, 1984 Joel E. Cohen, Harry Kesten, Charles Michael Newman - 1986 - 358 pages AMS Cont Math 50 It is not difficult to show that relative to the Vasershtein metric (see, e.g., [BF] for proceedings of an International symposium held in Beijing, Aug. 27-Sep. 8, 1984 Tuan Hsio-Fu Springer, 1986 - 403 pages [59] L. Vaserstein, Stabilization of unitary and orthogonal groups over a ring with involution, Math. USSR Sbornlk, Vol. ... USSR Sbornlk 22, (1971), 271-303- [61] L. Vaserstein, Foundations of algebraic K-theory, Russian Math. Surveys, 31:1 ... 1986 L.N. Vaserstein collection of survey papers : on the 50th anniversary of the institute, Volume 168 Ivan Matveevich Vinogradov American Mathematical Society, 1986 - Mathematics - 266 pages L.N. Vaserstein By Lev IAkovlevich Leĭfman Izv. 6 (1972). Translated by L. N. VASERSTEIN (2) Vol. 128. 1986 On Algebraic Geometry and Its Applications: - Page 226 Tpуды Ордена Ленина Математического Института Имени В.А.Стеклова (Proceedings of the Steklov Institute of Mathematics) by S. M. Nikolskii and E. A. Volkov (Oct 1986) Translated by L.N. Vaserstein proceedings of the US-Japan seminar, Kyoto, July 1983 Huzihiro Araki, Edward G. Effros Longman Scientific & Technical, 1986 - 439 pages If t denotes the algebraic functor (Vaserstein, 1976) then we have Theorem. IC(K) = 0. 2. PROOFS Recall that K is a C -algebra and so has a square root operation (Takesaki, 1979)- As a result we see that Yr = K. Geometric methods in operator algebras. Proceedings of the US-Japan Seminar, Kyoto (Japan), July 1983. (English) Pitman Research Notes in Mathematics Series, 123. Harlow, Essex: Longman Scientific \& Technical. Copubl. in the U.S. with John Wiley \& Sons, Inc., New York. VII, 439 p.; \sterling 27.00 (1986). MSC2000: *00B25 46-06 Automation and remote control - Volume 47; - Page 692 L. N. Vasershtein and E. B. Sherman, "Problems of forming variants in development and specialization of industrial plants in problems of optimum industrial planning," Review information, TS-30. Economic-mathematical modeling [in Russian], ... Galen R. Shorack, Jon A. Wellner Wiley, May 7, 1986 - 938 pages Wasserstein distance Mathematical programming study - Issues 26-30 - Page 182 North-Holland Publishing Company, 1986 Wasserstein metric Duality in stochastic linear and dynamic programming - Page 218 Willem K. Klein Haneveld Springer-Verlag, 1986 - Business & Economics - 295 pages Wasserstein metric Probability and mathematical statistics - Volumes 7-9 - Page 113 Państwowe Wydawnictwo Naukowe, 1986 Wasserstein Итоги науки и техники: - Volume 21 - Page 115 1988 Ананасов Б. Н., Дискретные группы преобразований и структуры много* образий. Новосибирск: Наука, 1983, 242 с. 2. Боревич 3. И., Шафаревич И. Р., Теория чисел. 2-е изд., М.: Наука, 1972, 495 с. 3. Вассерштейн Л. Н., Группы, ... 1987 13 books VIII International Congress on Mathematical Physics: - Page 723 July 16-25, 1986, Marseille, France M. Mebkhout, R. Sénéor - 1987 L.N. Vasershtein, Prob. Inform. Transm. 5, 64 (1969); O.E. Lanford III, in Statistical Mechanics and Mathematical Problems (Lecture Notes in Physics #20), ed. A. Lenard (Springer, Berlin, 1973). 39. M. Aizenman and R. Theory of Linear Operations: S. Banach ; English Translation by F. Jellett Elsevier, 1987 - 237 pages Yuri I Lyubich, Leonid N Vaserstein - 1993 - Geometriae Dedicata ... Linear Algebra Serge Lang Springer, Jan 26, 1987 - 296 pages Vaserstein Introduction to signals and systems Edward W. Kamen Macmillan Pub. Co., Jan 1, 1987 - 634 pages Vaserstein Carleton University, Mathematics and Statistics, 1987 - 15 pages Vaserstein Probability, random variables, and random signal principles Peyton Z. Peebles McGraw-Hill, 1987 - 349 pages Vaserstein Statistical data analysis based on the L1-norm and related methods - Page 181 Yadolah Dodge - 1987 - 464 pages It has origins in the papers of Kantorovich [lo] and Vasershtein [23] and it was introduced to mathematical statistics by Sudakov [17] and Zolotarev [24] ... The status of Soviet civil science: - Page 38 proceedings of the Symposium on Soviet Scientific Research, NATO Headquarters, Brussels, Belgium, September 24-26, 1986 Craig Sinclair - M. Nijhoff, 1987 -- 289 pages Vasershtein Harry Kesten - 1987 - 323 pages Thus (Y£(t))t>0 is Cauchy in distribution (in, say, the Vasserstein norm based on the Skorohod metric on path space) and hence converges in distribution to a process which we denote by Y(t). (In fact, it is not difficult to simultaneously realize all ... Number theory :- Page 357 proceedings of the 1985 Montreal conference held June 17-29, 1985 H. Kisilevsky, J. Labute, Canadian Mathematical Society - 1987 - 466 pages Vaserstein's theorem Statistics & decisions: Volume 5 Akademische Verlagsgesellschaft, 1987 New perspectives in theoretical and applied statistics - Page 447 Madan Lal Puri, José Pérez Vilaplana Wiley, Mar 12, 1987 - 544 pages Wasserstein distance edited by E. F. Robertson, Colin Matthew (London Mathematical Society Lecture Note Series 121) Cambridge University Press (February 27, 1987) USSR Izvestia I\_ (l977), 22l-238. 23. L.N. Vaserstein, Kj-theory and the congruence problem. Math. iJotes 5 (l969) , l4l-l48. 24. L.N. Vaserstein, On the stabilization of the general linear group over a ring, Math. USSR Sb. jl (l969), 383-400. 1988 23 books Perspektivnoe planirovanie v ugolʹnoĭ promyshlennosti by Romashkin, I. P 1982 Encyclopaedia of Mathematics: C - Page ii Michiel Hazewinkel - 1988 ... F. Takens, R. J. Takens, N. M. Temme, S. H. Tijs, B. Trakhtenbrot, L. N. Vaserstein, M. L. J. van de Vel, F. D. Veldkamp, P. M. B. Vitanyi, N. J. Vlaar, H. A. van der Vorst, J. de Vries, F. Waldhausen, B. Wegner, J. J. O. O. Wiegerinck, J. Wiegold, ... Classical Dirichlet forms on topological vector spaces Closability and a Cameron-Martin Formula Sergio Albeverio, Michael Röckner - 1988 - 53 pages Contractions in the 2-Wasserstein Length Space and Thermalization ... José A Carrillo, Robert J McCann, Cédric Villani - 2006 - Archive for Rational Mechanics and Analysis Normal subgroups of gauge groups L. N. Vaserstein Max-Planck-Inst. f. Mathematik, 1988 - 26 pages Normal subgroups of symplectic groups over rings L. N. Vaserstein Max-Planck-Inst. f. Mathematik, 1988 - 34 pages Annual report - Page 33, 37, 43 An introduction to linear programming and game theory Paul R. Thie Wiley, Mar 8, 1988 - 396 pages Vaserstein Zbl 0691.60031 Fiebig, Doris Über very weak Bernoulli-Prozesse mit schnellen Raten. (On very weak Bernoulli processes with fast rates). (German) Göttingen: Univ. Göttingen, Math.-Naturwiss., Diss. 77 S. (1988). MSC2000: *60G10 28D05, Reviewer: E.Slud Wasserstein distance Zbl 0659.60044 Kirschfink, Heribert Konvergenz von Verteilungen von Summen abhängiger Zufallsvariablen in verschiedenen Wahrscheinlichkeitsmetriken mit Ordnungen. (Convergence of distributions of sums of dependent random variables in different probability metrics with order). (German) Aachen (FRG): Technische Hochschule Aachen, Mathematisch- Naturwissenschaftliche Fakultät, viii, 121 S. (1988). MSC2000: *60F05 60B10 60B05, Reviewer: L.Hahn Wasserstein metric MR0978631 Karpilovsky, Gregory Unit groups of classical rings. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1988. xiv+370 pp. ISBN: 0-19-853557-0 (Reviewer: Carl Riehm) 20C05 (11R27 11R33 12E15 16A25) Robert M. Gray - Springer-Verlag, 1988 295 pp ISBN0387966552, 9780387966557 In the optimal transportation literature, the German spelling of Vasershtein, Wasserstein, also caught on as a suitable name for the Monge/Kantorovich distance and remains so. The Monge/Kantorovich optimal cost provides a distortion or ... Probability, random processes, and ergodic properties. (English) New York etc.: Springer-Verlag. xvi, 295 p. DM 98.00 (1988). MSC2000: *60A10 94A15 60-02, Reviewer: U.Krengel On a formula for the L_p Wasserstein metric between messures on Euclidean and Hilbert spaces Matthias Gelbrich Humboldt-Univ., Sekt. Mathematik, 1988 - 26 pages École d'été de probabilités de Saint-Flour XV-XVII, 1985-87 - Page 193 Persi Diaconis, David Elworthy, Paul-Louis Hennequin - 1988 - 459 pages For two probability measures n and v on S « C[0,1] , let iJfdn-Jfdv) R(M,w) = sup denote the Vasserstein distance as in Ch. I (2.18); Persi Diaconis Institute of Mathematical Statistics, 1988 - 198 pages Wasserstein… metric North Holland, 1988 Wasserstein metric as printed in Mathematical reviews, Volume 1 American Mathematical Society - 1988 - 3998 pages Funaki, Tadahisa (J-NAGO) A certain class of diffusion processes associated with nonlinear parabolic equations. ... op(ui,uj) is a Wasserstein type metric between U|,uj using pth moments and k(r) is a function with / dr/fc2(\/f) divergent at zero. Encyclopedia of statistical sciences: Volume 9 Samuel Kotz, Norman Lloyd Johnson, Campbell B. Read - 1988 Logarithmic Descriptions of Whitehead Groups and Class Groups for p-Groups - Page 96 By Robert Oliver, Larry Taylor Memoirs of the American Mathematical Society 1988; 97 pp; softcover Volume: 76 Operator Algebras and Applications: Structure theory, K-theory, Geometry and Topology - Page 54 edited by David E. Evans, Masamichi Takesaki Vaserstein Whitehead Groups of Finite Groups - Page 34, 35, 56, 241, 343, 349 By Robert Oliver Vaserstein Ring theory. 2 (1988) - Page 26 By Louis Halle Rowen Vaserstein Memoirs of the American Mathematical Society - Volumes 392-397 - Page 96 MR0938472 Oliver, Robert; Taylor, Laurence R. Logarithmic descriptions of Whitehead groups and class groups for$p$-groups. Mem. Amer. Math. Soc. 76 (1988), no. 392, vi+97 pp. (Reviewer: Bruce A. Magurn) 18F25 (19A22 19A31 19B28) Vaserstein Итоги науки и техники: - Volume 21 - Page 115 1988 Апанасов Б. Н., Дискретные группы преобразований и структуры много- образий. Новосибирск: Наука, 1983, 242 с. 2. Боревич 3. И., Шафаревич И. Р., Теория чисел. 2-е изд., М.: Наука, 1972, 495 с. 3. Вассерштейн Л. Н., Группы, ... 1989 21 books ### Numerical Analysis and Parallel Processing: - Page 122 # Lectures given at The Lancaster Numerical Analysis Summer School 1987 Peter R. Turner - 1989 At present, it is not clear whether further modifications of our method will produce more information about the structure gap off the real axis. 3. We report on some joint work with F. Grunewald and L. Vaserstein, which belongs to unstable ... Annual Report - Page 13 If d=3, the Vasserstein symbol was shown to yield an isomorphism of the group of unimodular 3-vectors modulo elementary operations with the symplectic elementary Witt group. Vector bundles of rank at least n—l over the complements, in the ... Lp-Wasserstein-Metriken [Lp-Wasserstein-Metriken] und Approximationen stochastischer Differentialgleichungen Matthias Gelbrich, Matthias Gelbrich - 1989 J. F. Jardine, Victor Percy Snaith - 1989 - 550 pages Algebraic K-Theory and Algebraic Number Theory: Proceedings of a Seminar held Januaey 12 -16, 1987- Page 449 AMS Cont Math 83 By Michael R. Stein, R. Keith Dennis Classical Groups and Related Topics: Proceedings of a Conference .in Honor of L.K. Hua - Page 198 AMS Cont Math 82 R.K. Dennis, B. Magum and L.N. Vaserstein, 0eneralized Euclidean group rings, J.Reine Ang. Math. 35l (l9s4), ll3-l2s ... Report PM - Issues 71-80 Penn State, Department of Mathematics, 1989 Springer Science & Business Media, 1989 L.N. Vaserstein Theory of statistical inference and information - Page 10, 98, 111 - 1989 - 432 pages Kantorovich — Vasershtein distance and related functions of measures In this section we apply Theorem (4.35) and other results of Sec. 4 to convex functions of measures defined by means of certain distances of measures. Theory of statistical inference and information. Transl. from the Slovak by the author. (English) Theory and Decision Library, Series B: Mathematical and Statistical Methods, 11. Dordrecht etc.: Kluwer Academic Publishers. 432 p. Dfl. 305.00; \$ 149.00; \sterling 95.00 (1989). MSC2000: *62B10 62-01, Reviewer: J.Virtanen

Christian U. Jensen, Helmut Lenzing - 1989 - 443 pages

[189] A. A. Suslin and L. N. Vasershtein. Serre's problem on projective modules over polynomial rings and algebraic K-theory. Izv. Akad. Nauk. SSSR,

Stochastic analysis, path integration, and dynamics: - Page 57

emanations from "Summer Stochastics", Warwick 1987

K. D. Elworthy, Jean-Claude Zambrini - 1989 - 265 pages

Wasserstein distance

Dynamical systems and ergodic theory - Page 40

Karol Krzyżewski, Instytut Matematyczny (Polska Akademia Nauk) - 1989 - 479 pages

Wasserstein distance

Probability and mathematical statistics - Volumes 10-11 - Page 312

Wasserstein distance

Stability Problems for Stochastic Models:  - Page 170

Proceedings of the 11th International Seminar Held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept. 25-Oct. 1, 1987, Issue 1412

Wasserstein distance

Technical report series of the Laboratory for Research in Statistics and Probability - Issues 131-140 - Page 3

Laboratory, Carleton University, 1989

Wasserstein distance      First International Conference on Stochastic Geometry,

Representation Theory, Group Rings, and Coding Theory:  - Page 347

Papers in Jonor of S.D. Berman (1922-1987)

Irving Martin Isaacs - 1989 AMS Cont Math 93

L. N. Vaserstein, The structure of classic arithmetic groups of rank greater than one, Math. USSR Sbornik 20 (1973), 465-492.

1989 ISBN0521369193, 9780521369190

Vaserstein

The classical groups and K-theory - Page 161, 177, 519

We point out that Vaserstein's theory

; O'Meara, O. Timothy The classical groups and $K$-theory. With a foreword by J. Dieudonné.

Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 291. Springer-Verlag, Berlin, 1989. xvi+576 pp. ISBN: 3-540-17758-2 (Reviewer: James E. Humphreys) 20-02 (11E57 19-02 20G15 20H25)

IMS bulletin - Volume 18, Issues 102-107 - Page 86

... Uniform large deviation property of the empirical process of a Markov chain R. ARRATIA & M.S. WATERMAN: The ... urn models Juan Antonio CUESTA: Notes on the Wasserstein metric in Hilbert spaces Articles STATISTICAL SCIENCE a ...

MR0999391 Proceedings of Research Symposium on $K$-Theory and its Applications. Held at the University of Ibadan, Ibadan, August 10–15, 1987. Edited by A. O. Kuku and C. Weibel. $K$-Theory 2 (1989), no. 5. This is a Historical Journal, Ann Arbor, MI, 1989. pp. i–ii and 557–673. 18-06 (19-06)

MR0991972  Algebraic $K$-theory and algebraic number theory. Proceedings of the seminar held in Honolulu, Hawaii, January 12–16, 1987. Edited by Michael R. Stein and R. Keith Dennis. Contemporary Mathematics, 83. American Mathematical Society, Providence, RI, 1989. xiv+488 pp. ISBN: 0-8218-5090-3 18F25 (19-06)

1990   19 books

Matematicheskie bilʹardy : bilʹardnye zadachi i smezhnye voprosy matematiki i mekhaniki

by Galʹperin, G. A; Гальперин, Г. А 1990

Ergodic Theory and related topics, III (1990)

Lecture Notes in Math. 1514

L . N. Vaserstein, On Systems of particles with finite - range and/or repulsive

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

S.T. Rachev and R.M. Shortt.  google books

Warszawa : Państwowe Wydawn. Naukowe, 1990. 39 pp  ISBN 8301099704 9788301099701

Zbl 0718.60057 Gelbrich, Matthias  L${}\sp p$-Wasserstein-Metriken und Approximationen stochastischer Differentialgleichungen. $(L\sp p$

Wasserstein metrics and approximations of stochastic differential equations). (German)  Berlin: Humboldt-Universität Berlin, Mathematisch- Naturwissenschaftliche Fakultät,

Diss. 77 S. (1990). MSC2000: *60H10 60B10, Reviewer: M.Gelbrich

Probability theory and mathematical statistics:  - Page 142, 388

proceedings of the fifth Vilnus conference: Volume 1

Bronius Grigelionis - 1990 - 646 pages

Now we define the so-called Vasershtein metric between two probability measures

Number-Theoretic Analysis Seminar, Vienna, 1988-89 - Page 6, 17, 18

Edmund Hlawka, Robert F. Tichy - 1990 - 220 pages

We so get the rate of convergence of a sample path to with regard to the Vasserstein metric cf. [14]: The Vasserstein distance ...

System modelling and optimization - Page 690, 695, 696

proceedings of the 14th IFIP-Conference, Leipzig, GDR, July 3-7, 1989

Hans-Jürgen Sebastian, K. Tammer, International Federation of Automatic Control - 1990 - 960 pages

Wasserstein

Séminaire de mathématiques Rouen: Comptes rendus des séances: - Page 105

septembre 1988-juin 1989

Université de Rouen. Laboratoire d'analyse et modèles stochastiques - 1990 - 180 pages ISBN2877750175, 9782877750172

Wasserstein

Centre de Recherches Mathématiques, Université de Montréal, 1990

Wasserstein distance

Uppsala abstracts:  - Page 143

abstracts of papers presented in Uppsala, Sweden, 13-18 August 1990

The Institute of Mathematical Statistics and the Bernoulii Society for Mathematical Statistics and Probability, 1990 - Mathematics - 216 pages

Wasserstein distance

Bulletin / Institute of Mathematical Statistics - Volume 19 - Page 412

1990

Wasserstein distance

1990

Cette distance, dite ici de Wasserstein, se généralise aux espaces lP par d(P,Q) - a IX-YI ...

proceedings of the 14th IFIP-Conference, Leipzig, GDR, July 3-7, 1989

Hans-Jürgen SebastianSpringer-Verlag, 1990 - 960 pages

Wasserstein distance

Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis - Page 179, 182

By R. L. Dobrushin, V. I. Kriukov, A. L. Toom Manchester University Press, 1990 - 541 pages

Vaserstein

Centre for Mathematical Sciences (Trivandrum, India) Centre for Mathematical Sciences, 1990  - 129 pages

Vaserstein

Weizmann Science Press of Israel, 1990  MR1159095

Vaserstein

Topology and combinatorial group theory - Page 90

proceedings of the Fall Foliage Topology Seminars, held in New Hampshire 1986-1988

Springer-Verlag, Oct 18, 1990 - 207 pages

Also I want to thank Leonid Vaserstein for

his interest and encouragement, and George Bergman for his helpful correspondence.

Festschrift in Honor of I.I. Piatetski-Shapiro on the Occasion of His Sixtieth Birthday:

Papers in representation theory

Vaserstein

В.Л Макаров, ‎Валентин Давыдович Маршак, ‎Сергей Матвеевич Анцыз - 1990

Васерштейн Л. Н., Шерман Э. Б. О формировании вариантов в дискрет- пых задачах оптимального планирования ... Васерштейн Л. Н. Проблема формирования вариантов развития и специализации производственных объектов в ...

1991    18 books

Moscow University Computational Mathematics and Cybernetic  - Page 58, 60, 61

Moskovskiĭ gosudarstvennyĭ universitet im. M.V. Lomonosova

Allerton Press, 1991

13) it is stated that the maximal coupling in Markovian case {i.e., each component is Markovtan with identical transition probabilities and different initial aistributions) cannot be {Griff eath's) Markovian. Theorem 2. Wassershtein's coupling is ...

Algebraicheskie gruppy i teoriia chisel

by Platonov, V. P. 1939 1991

Discrete Subgroups of Semisimple Lie Groups - Page 268

In particular, in case rankK G ^ 2, this was proved by Vasserstein [Va 2] for all classical groups and by Raghunathan [Rag 7] for all G. In [Va 2] some results on normal subgroups were also announced, e.g., in case G is a K'-rank 1 classical ...

Ergodic theory and dynamical systems: Volume 11, Issues 3-4

University Press, 1991

École d'été de probabilités de Saint-Flour XIX, 1989 - Page 173, 176

Donald L. Burkholder, Étienne Pardoux, Alain-Sol Sznitman - 1991 - 259 pages

Vaserstein metric, Vasershtein metric

Svetlozar Todorov Rachev - 1991 - 494 pages

... f |x( - yt\ x, yeM" i=i (13.2.3) see (3.2.2), (3.3.3) and (5.2.18). Remark 13.2.2. Dobrushin (1970) called £x the Vasershtein (Wasserstein) distance.

Dall'aglio, G.; Kotz, S.; Salinetti, G. (Eds.)  1991, XVIII, 232 p. 5 illus.

Limit theorems and some applications in statistical physics - Page 135

Boris Nahapetian - 1991 - 244 pages

If the sequence of distributions Pa converges to P in a sense of Kantorovich-Vasershtein metric,

Statistics: Volume 22   Taylor & Francis, 1991

Vasershtein

Singularity Theory and Its Applications: Geometric aspects of Singularities - Page 176

Warwick 1989  David Mond, James Montaldi, Mark Roberts - 1991 - 408 pages

Vasershtein

Stochastic orders and decision under risk - Page 310

edited by Karl C. Mosler, Marco Scarsini

Wasserstein distance

Comparison of Statistical Experiments - Page 664

By Erik Torgersen

Wasserstein distance

Svetlozar Todorov Rachev Wiley, May 13, 1991 - 494 pages

Wasserstein metric, Wasserstein norm

Adriano Barlotti Kluwer Academic, 1991 - 447 pages

Using the Dennis-Vaserstein results, the bounds in [20] can be greatly improved for large n.

Thirteen Papers in Algebra, Functional Analysis, Tipology and Probability - Page 192

translated by V. Valentin Senderovich Afraimovich AMS 1991

Vaserstein

Groups St Andrews 1989: - Page 375

edited by C. M. Campbell, E. F. Robertson

Vaserstein

Oxford University Press, Nov 7, 1991 - 157 pages

Vaserstein

Proceedings of the International Congress of Mathematicians, ... - Volume 1 - Page 385

Ichirō Satake - University of Toronto Press, 1991

The vast literature on the Serre conjecture contains many negative and a few special positive results on the problem of extending to vector bundles on X for X regular: one may consult the articles of Horrocks, Swan, Murthy, Vasserstein, Bass, ...

1992   24 books

### Publications du Centre international de rencontres mathématiques, Issue 2 - Page 198

1992

... sont fournies par des solutions au problème de Tarry- Escott, sauf deux d'entre elles, dues à Rao et Vaserstein. ... notions de déterminants non commutatifs (déterminant quantique, Bérézinier, déterminant de Dieudonné) à la théorie des ...

continuous approximation schemes for stochastic programs - Page 12

john r. birge, liqun qi - 1992

We next use the assumptions to obtain bounds on the Wasserstein metric. ..

Proceedings of a Us-French Workshop, Rutgers University, New Brunswick, N.J., April 29-May 2, 1991

Ioannis Karatzas, Daniel Ocone - 1992

Cuesta J.A. and Matran C. (1989) Notes on the Wasserstein metric in Hilbert spaces. ... Kantorovich, L.V. and Rubinstein G. Sh. (1958) On the space of completely additive functions, Vestnik LGU, Ser. Mat. ... The distance between two 260.

Abstracts of papers presented to the American Mathematical Society - Volume 13 - Page 332

Exact convergence rates for the bounded law of the Iterated logarithm in Hilbert space. ... Rate of Convergence of Empirical Measures in the Wassersfein Metric. ... observations from an i.i.d. sequence of rvs in with underlying law P, and let W be the Wasserstein distance (of order 2) between Pn and P. Then, under very mild ...

Lectures on the Coupling Method - Page 177

Torgny Lindvall - 1992  The Vasershtein coupling.

Carlo Marchioro, Mario Pulvirenti - 1993

It can be proved that the topology induced by the metric (3.8) is equivalent to the topology of the weak convergence of the measures.

This metric is called the Kantorovich-Rubistein (K-R) distance (sometimes called the Vasershtein distance).

Atti del Seminario matematico e fisico dell'Università di Modena - Volume 40 - Page 98

... R. Herman - L. N. Vasershtein, The stable range of C*-algebras, Invent. Math., 77 (1984), 553-555. [13] E. Hewitt - K. Ross, Abstract harmonic Analysis I, Springer Verlag, Berlin, Heidelberg, New York, 1963. [14] K. Hoffman, Lectures on sup ...

Poisson approximation, Lars Holst, Svante Janson - 1992 - 277 pages - Page 17, 254, 274

Wasserstein distance Suppose that the state space is a separable metric space (X,d) equipped with its Borel c-field, and ...

proceedings of the eighth international conference, [held at Bowdoin College in summer 1991]

Richard M. Dudley, Marjorie G. Hahn, James Kuelbs - 1992 - 510 pages

Wasserstein distance

Mufa Chen - 1992 - 550 pages

Givens, C. R. and Shortt, R. M.(1984), A class of Wasserstein metrics for probability distributions, Mishigan Math. J. 31 ...

Stochastic approximation and optimization of random systems - Page 56

Lennart Ljung, Georg Ch Pflug, Harro Walk - 1992 - 113 pages

Wasserstein-metric

Stochastic optimization:  - Page 118

numerical methods and technical applications : proceedings of a GAMM/IFIP-workshop held at the Federal Armed Forces University Munich, Munich, FRG, May 29-31, 1990

Kurt Marti, Hochschule der Bundeswehr München - 1992 - 182 pages

Wasserstein metric

Automata, languages, and programming: - Page 410

19th International Colloquium, Wien, Austria, July 13-17, 1992. Proceedings

Werner Kuich - 1992 - 719 pages

The resulting general metric between functions is known as the Kantorovich-Rubinstein distance or the Wasserstein ...

Numerical solution of stochastic differential equations - Page 607

Peter E. Kloeden, Eckhard Platen - 1992 - 632 pages

If- Wasserstein-Metriken und Approximation stochastischer Differentialgleichungen. Ph. D. thesis, Dissert

[2] M. Gelbricht, On a formula for the L1 Wasserstein metric between measures on euclidean and Hilbert spaces, Math. Nachr. ...

Algebraic K-Theory, Commutative Algebra, and Algebraic Geomey - Page 196

Proceedings of the U.S.-Italy Joint Seminar Held June 18-24, 1989 at Santa Margheri (Google eBook)

L. N. Vaserstein, The stable range of rings and the dimension of topological spaces. Funk. Anal. 5:2 (1971) ... L. N. Vaserstein, Normal subgroups of the general linear groups over Banach algebras, J. Pure Appl. Algebra 41:1 (1986), 99-112. 6.

Topology '90 - Page 459

Boris Apanasov, Walter D. Neumann, Alan W. Reid - 1992

... Transform Approach - D. Thakur: On Gamma Functions for Function Fields - A. Thiery: Indépendance Algébrique des Périodes et Quasi-périodes d'un Module de Drinfeld - L. Vaserstein: Ramsey's theorem and Waring's problem for algebras ...

proceedings of a Conference in honor of Goro Azumaya's seventieth birthday : proceedings of a Conference held May 23-27, 1990 with support from the National Science Foundation .

Replacing 6rj by 6'^6rj we see that P w ©Pj where PI is of rank 1 and Pi for i > 1 is the pullback of (4) and hence isomorphic to A. It remains to prove the lemma. We will deduce it from the following well known result of Vaserstein [V]. LEMMA ...

Fuchsian Groups - Page x

Svetlana Katok - 1992

I wish to express my appreciation to Peter Sarnak and Leonid Vaserstein for discussions on arithmetic groups. I would like to thank Ozlem Umamoglu and Yves Martin, graduate students from my class at the University of California at Santa ...

Simeon Ivanov - 1992

... where the degree of the group is sufficiently large in comparison with the stable rank of the ring, these formulas and even the more precise one were proved by Bass and Vaserstein. The first of the formulas is equivalent to the normality of £(<

L. N. Vaserstein, Stabilization of unitary and orthogonal groups over a ring with involution. Mat. Sb. 81 (1970), no. 3, 328-351; English transl. in Math. USSR-Sb. 10 (1970). Institute of Mathematics Academy of Sciences of the Belorussian SSR ...

Cyclic homology - Page 352, 376, 443

Jean-Louis Loday - 1992

11.2.14 Theorem. For any ring A the connected space X(A) is acyclic (H.(X(A)) = 0) and is simple in dimension > 2. Proof (absence of). The original proof is due to Volodin [1971], see also Vaser- stein [1976]. We refer to Suslin [1981] for a short ...

Sensitivity analysis and optimization of discrete event systems - Volume 39, Issues 1-4 - Page 179

Søren Asmussen, Reuven Y. Rubinstein, Alexander Shapiro - 1992

We introduce the Wasserstein distance for probability measures Vi and v2 on the Borel a- algebra of (R, r): r(Vi, V2) :=sup{ < G, Vi ) - < G, v2 > : G is a real function on /? with £(G) ^ 1 } . There is no ambiguity in denoting the distance in R and the ...

MR1196508 The arithmetic of function fields. Proceedings of the workshop held at The Ohio State University, Columbus, Ohio, June 17–26, 1991. Edited by David Goss, David R. Hayes and Michael I. Rosen. Ohio State University Mathematical Research Institute Publications, 2. Walter de Gruyter & Co., Berlin, 1992. viii+482 pp. ISBN: 3-11-013171-4 11-06 (11G09 11R58)

1993  16 books

### Resenhas Do Instituto de Matemática E Estatística Da Universidade de São Paulo, Volumes 1-3 - Page 121

1993

In fact, it is a result of Bass-Milnor-Serre-Vaserstein that (i) and (ii) always hold if rij > 3 and for n,- = 2 they hold provided that Di ^ Q or imaginary quadratic or a definite quaternion algebra. We shall further assume that if n, = 1 then D, is a totally ...

### Subgroup growth - Page 46, 397

Alexander Lubotzky - 1993

[MaSh] A. Mann, A. Shalev, Maximal subgroups of finite simple groups and positively finitely generated groups, preprint [MVW] C.R. Matthews, L.N. Vaserstein, B. Weisfaler, Congruence properties of Zariski dense subgroups I, Proc. Lond.

### Dissertation Abstracts International: The sciences and engineering. - Page 2531

Adviser: Leonid N. Vaserstein Order Number DA9326805 The problem of writing matrices as products of involutory matrices has been investigated over fields by many people. In this thesis, we investigate this problem when the base ring ...

Report PM - Issues 151-160

Herbert Schröder - 1993

... and L. Vaserstein [HrV] have shown that sr(>4) and tsr(.4) coincide if A is a C*-algebra. Although the condition of 1.6.2 guarantees weak stability, the size of the stable range depends on far subtler properties of the C*-algebra in question.

Mathematical Theory of Incompressible Nonviscous Fluids - Page 184

Carlo Marchioro, Mario Pulvirenti - 1993

It can be proved that the topology induced by the metric (3.8) is equivalent to the topology of the weak convergence of the measures. This metric is called the Kantorovich-Rubistein (K-R) distance (sometimes called the Vasershtein distance).

Shape recognition using metrics on the space of shapes

David Spotts Fry - 1993

O. V. Gulinsky, A. Yu Veretennikov - 1993 - 186 pages

Vaserstein, L. N. Markov processes over denumerable products of spaces, describing large systems of automata. Problems of Information Transmission (1969) 5, 47-52. Veretennikov, A. Yu. Bounds for the mixing rate in the Bibliography 185.

Cellular automata and cooperative systems - Page 453

Nino Boccara - 1993 - 546 pages

Gazette - Australian Mathematical Society: Volumes 20-21

Encyclopaedia of Mathematics (9) - Page ii

Michiel Hazewinkel - 1993

... L. Streit, K. Stromberg, L. G. Suttorp, D. Tabak, F. Takens, R. J. Takens, N. M. Temme, S. H. Tijs, B. Trakhtenbrot, L. N. Vaserstein, M. L. J. van de Vel, F. D. Veldkamp, P. M. B. Vitanyi, N. J. Vlaar, H. A. van der Vorst, J. de Vries, F. Waldhausen, ...

a symposium in honor of John Milnor's sixtieth birthday, Volume 3

Early results of the author [HB2, 3] and Vaserstein [Vasl] showed, under suitable "finite dimensionality" assumptions on A, ... It was later shown by Suslin and Vaserstein that, for A a finitely generated Z(/4)-module, (1) and (2) hold for all n > 3.

Units in integral group rings. With an appendix by Al Weiss. Pitman Monographs and Surveys in Pure and Applied Mathematics, 69. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. xii+357 pp. ISBN: 0-582-23081-0 (Reviewer: E. Jespers) 16U60 (16-02 16S34 20-02 20C05 20C07 20C10 20C12)

On Lower Bounds for the L2-Wasserstein Metric in a Hilbert Space

J. A. Cuesta-Albertos, Carlos Matrán Bea, Universidad de Cantabria - 1993

### Commutative Ring Theory - Page 67, 70, 73

Cahen - 1993

Wilson in [11], for n > 3 hy Borevich and Vavilov in [2,3], and generalized and finalized hy Vaserstein in [10]. The main tool in this characterization is the notion of the level ideal of a matrix in GL(n, A). lfX = [ay] is in GL(n, A), the level ideal f(X] of ...

### Algebraic Groups and Number Theory - Page 606

Vladimir Platonov, ‎Andrei Rapinchuk, ‎Rachel Rowen - 1993

Vasserstein L. N. [1] “On SL2 over an arithmetic Dedekind ring,” Mat. Sb. 89 2 (1972), 313-322. [2] “On full subgroups of Chevalley groups,” Tohéku Math. J. 37 4 (1985), 423-454. [3] “On arithmetic subgroups of simple algebraic groups,” Linear ...

1994  16 books

### Encyclopaedia of Mathematics (set) - Page ii

Michiel Hazewinkel - 1994 - ‎Mathematics

ENCYCLOPAEDIA OF MATHEMATICS Managing Editor M. Hazewinkel ... Takens, N. M. Temme, S. H. Tijs, B. Trakhtenbrot, L. N. Vaserstein, M. L. J. van de Vel, ...

### Partial Differential Equations of Elliptic Type: Cortona, 1992 - Page 132

Angelo Alvino, ‎E. B. Fabes, ‎Giorgio Talenti - 1994

Remark 1 We can define the Kantorovich-Wasserstein distance (see [RR] for example) between po and p\ by setting x (5)

### Probability Theory and Mathematical Statistics:  - Page 90

Proceedings of the Sixth Vilnius Conference (1993) : Vilnius, Lithuania, 28 June-3 July, 1993

Bronius Grigelionis - 1994

Another approach is connected with the property of "contraction" of transition probabilities (see (Dobrushin, 1970)). It means that Kantorovich-Wasserstein distance R(P(xi,-),P(x2,-)) between P(XI,-) and P(x2,-) has to be less than p(x\,x2), />(*,.) ...

Translations. Ser. 2, 161. Selected papers on analysis,Probability, and Statistics

Katsumi Nomizu - AMS 1994 ISBN0821875124, 9780821875124

The Vasserstein distance for two probability distributions fi\, fi: on 5, is defined as 2) = sup Also, the oscillation at a coordinate / of a function / on the product space g" is defined as follows S/(/ ) = sup{|/(**) - /(>'*)|/r(.v;,>'*);x* = >** except at the ...

K-theory: Strasbourg, 1992 - Page 412, 414

A beautiful theorem of L. N. Vaserstein [SV, Corollary 7.4], identifies Um.z(A)/Ez(A), the coset space of unimodular 3-vectors Umz{A) modulo action of the Elementary matrices E${A), with the Symplectic Elementary Witt group We(A) when ... The Vaserstein symbol V = Va : Umz{A) / E$(A) — WE(A) is the map [(a,b,c)]~[V(v,w)], where v = (a,b,c), w = (a',b',d) with aa' + bb' + cd = 1. In [SV, Theorem 5.2], L. N. Vaserstein has shown that this map is well defined (i.e. it is independent of ...

MR1297782 (95d:52002)  First International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures.

Proceedings of the conference held in Palermo, April 25–May 2, 1993. Edited by M. I. Stoka. Rend. Circ. Mat. Palermo (2) Suppl. No. 35 (1994). Circolo Matematico di Palermo, Palermo, 1994. pp. 1–358.

52-06 (60-06)

Juan A. Cuesta-Albertos [Juan Antonio Cuesta] and Carlos Matrán-Bea [Carlos Matrán], Stochastic convergence through Skorohod representation theorems and Wasserstein distances (89–113);

Analysis, Algebra, and Computers in Mathematical Research:  - Page 127

Proceedings of the Twenty-First Nordic Congress of Mathematicians

Mats Gyllenberg, Lars Erik Persson - CRC Press 1994  408 pp

[22] D.W. Stroock and S.R.S Varadhan, "Multidimensional Diffusion Processes". Springer- Verlag, Berlin, 1979. [23] A. Szulga, On the Wasserstein metric, Trans. 8th Prague Conference, B, D. Reidel Publishing Company, Dordrecht, Holland, ...

Probability theory and mathematical statistics:  - Page 30, 90, 130, 142, 190

Proceedings of the Sixth Vilnius Conference (1993) : Vilnius, Lithuania, 28 June-3 July, 1993

Bronius Grigelionis - VSP 1994 - 742 pages ISBN9067641782, 9789067641784

Wasserstein, L.N. (1969). Markov processes on a countable product

Thus, this coupling means that at each step, the components maintain the same length of jumps with the biggest possible rate. In the time-discrete case, the classical coupling and the basic coupling are due to Doeblin (1938) and Wasserstein ...

Collected works of Pere Menal - Page 245, 435, 436

Pere Menal, Manuel Castellet, Warren Dicks - 1994 - 639 pages

INTRODUCTION Let R be a ring and let I be an ideal of R. In [ 5 ] Vasershtein proves that ...

Carlo Marchioro, Mario Pulvirenti - 1994 - 283 pages

Vasershtein distance

Kybernetika: Volume 30 - Page 85

Vasershtein distance

Algebraic Groups and Number Theory - Volume 139 - Page 606

Vasserstein L. N. [1] “On SL2 over an arithmetic Dedekind ring,” Mat. Sb. 89 2 (1972), 313-322. [2] “On full subgroups of Chevalley groups,” Tohéku Math. J. 37 4 (1985), 423-454. [3] “On arithmetic subgroups of simple algebraic groups,” Linear ...

Appendix by Jonathan D. Rogawski (Google eBook)

Alex Lubotzky - 1994

To be more precise, Kazhdan announced it only for rank > 3, but it was very quickly realized by Wang [Wanl], Delaroche-Kirillov [DKi] and Vaserstein [Vs] that the same holds for rank > 2 and over every local field. Some of the R-rank one real ...

Commutative ring theory:  - Page 67, 70, 73

Proceedings of the Fès International Conference

Paul-Jean Cahen - CRC Press, 1994 - 256 pages

Klingenherg, Lineare Gruppen iiher lokalen Ringen, Amer. J. Math. 83(1961), 137-153. [9] N. H. J. Lacroix, Two-dimensional linear groups over local rings, Canad. J. Math. 21(1969), 106-135. [10] L. N. Vaserstein, On the normal suhgroups of ...

Lecture notes in pure and applied mathematics - Volume 153 - Page 73

Cahen - 1994

J. Math. 83(1961), 137-153. [9] N. H. J. Lacroix, Two-dimensional linear groups over local rings, Canad. J. Math. 21(1969), 106-135. [10] L. N. Vaserstein, On the normal subgroups of GLn over a ring, L. N. S. 854, Springer (1981), 456-465.

[24] Cuesta-Albertos, J. A., MatrAn, C. and Tuero-Diaz, A. (1993) Optimal maps for the Z. 2 -Wasserstein distance. Preprint. ... (to appear) [26] Cuesta-Albertos, J. A., Ruschendorf, L. and Tuero-Diaz, A.

(1993) Optimal coupling of multivariate distributions and stochastic processes. ... [35] GELBRICH, M. (1990) On a formula for the L2-Wasserstein metric between measures on Euclidean and Hilbert spaces.

1995  14 books

### Exercises in classical ring theory - Page 16

Tsit-Yuen Lam - 1995

Comment. This interesting exercise is a special case of a result of L. N. Vaserstein in algebraic if-theory (see his paper "Stable rank of rings and dimensionality of topological spaces", Funct. Anal. Appl. 5 (1971), 102- 110). The above solution is ...

# Proceedings of a Conference at the Department of Mathematics, Uppsala University, May 1993 : Organizer, Matts Essén

Lennart Carleson, ‎Yngve Domar, ‎Anders Vretblad - 1995

[Roy80] G. Royer, Croissance exponentielle de produits markoviens de matrices alea- toires, Ann. Inst. Henri Poincar6, Probability et Statistique 16 (1980), 49-62. [V69] L. Vaserstein, Markov processes over denumerable products of spaces ...

### Panoramas of mathematics: colloquia 93-94 - Page 80, 87

Bronisław Jakubczyk, ‎Stanisław Janeczko, ‎Bogdan Ziemian - 1995

Lyubich, L. Vaserstein, Isometric imbeddings between classical Banach spaces, cubature formulas, and spherical designs, Geom. Dedicata 47 (1993), 327-362. [M] V. Milman, A few observations on the connections between local theory and ...

CUP Archive, 1995  SBN0521227291, 9780521227292   345 pp

L. Vaserstein

James Laurie Snell - 1995 - 380 pages

[42] Vaserstein, Leonid, Markov Processes over Denumerable Products of Spaces, Describing Large Systems of Automata, ... [43] Vaserstein, Leonid and Leontovitch, Andrei, Invariant Measures of Certain Markov Operators Describing a ...

Handbook of incidence geometry: buildings and foundations - Page 1084, 1371

Francis Buekenhout - 1995 - 1420 pages

Canadian Mathematical Society, Peter A. Fillmore - 1995 - 286 pages

.. denotes the Vasserstein metric. (Mf(Rd),do) is a Polish space and do

Second International Conference on Algebra:  - Page 14

Dedicated to the Memory of A.I. Shirshov

Leonid A. Bokut, Alekseĭ Ivanovich Kostrikin, Semen Samsonovich Kutateladze - 1995

The theorem over general commutative rings has been investigated by many mathematicians and in particular by L. N. Vaserstein [38, 39]. For the Chevalley groups, some partial solutions have been given by E. Abe [1], E. Abe and K. Suzuki ...

L. N. Vaserstein, On the Normal Subgroups of GLn over a Ring, Lecture Notes in Math., 854, Springer, 1980, pp. 454-465.

Groups '93 Galway/St Andrews: - Page 402, 605

C. M. Campbell, E. F. Robertson, T. C. Hurley - 1995

The theorem of Dennis and Vaserstein also applies to many other groups such as Q = li_m Aut(F,,) where F,, is the free group of rank n. Is every element of Q a single commutator? Keith Dennis Problem 16. Let {1,p°, . . . ,p'} be a set of powers ...

Number Theory: Fourth Conference of the Canadian Number Theory Association - Page 91

Acknowledgement: I am grateful to the referee for providing the references [7], [8], to Koyama, and the reference to Conn and Vaserstein [3], who discover the solution 416396113 + (-41531726)3 + (-8241191)3 = 84. REFERENCES 1. APECS

Acknowledgement: I am grateful to the referee for providing the references [7], [8], to Koyama, and the reference to Conn and Vaserstein [3], who discover the solution 416396113 + (-41531726)3 + (-8241191)3 = 84. REFERENCES 1. APECS

A Primer of Algebraic D-Modules - Page 30

S. C. Coutinho - 1995

This follows an idea of L. Vaserstein and V. Katz; see [Bass, Connell and Wright 82, p.297]. The next section is a digression on results about derivations that will be required in §4. 3.

Different Aspects of Coding Theory:  - Page 201, 205

American Mathematical Society Short Course, January 2-3, 1995, San Francisco, California

Robert Calderbank - 1995

Y. I. Lyubich and L. N. Vaserstein, Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs, Report PM 128, Penn. State Univ., Philadelphia PA, 1992. [57] A. L. Mackay, The ...

Columbia University number theory seminar: New York, 1992 - Page 171

Columbia University Number Theory Seminar (, Dorian Goldfeld, Columbia University - 1995

That such questions are topical is clear from the recent work of Batyrev, Duke, Fomenko, Franke, Golubeva, Heath-Brown, Hooley, Iwaniec, Manin, Moroz, Rudnik, Sarnak, Schulze-Pillot, Silverman, Tschinkel, Vaserstein, and others (cf.

Analysis of censored data:  - Page 61, 62, 63, 64, 65

Proceedings of the Workshop on Analysis of Censored Data, December 28, 1994-January 1, 1995, University of Pune, Pune, India

Hira L. Koul, J. V. Deshpande, Institute of Mathematical Statistics - 1995 - 291 pages ISBN0940600390, 9780940600393

Wasserstein metrics, Wasserstein statistics

1996   17 books

### Rings and Radicals - Page 98, 104

Proceedings of the International Conference, Shijiazhuang '94

R. Wiegandt, ‎J.W. Gardner, ‎Shao-Xue Liu - CRC Press, 1996

... cancellation of modules (esp., of projective modules) comes from the well-known Serre's conjecture. In this paper, we will give a brief survey of some works of Evans, Goodearl, Menal, Vaserstein and Warfield, etc, on this area of research.

In 1980, Warfield [20] characterized the module M such that EndR(M) G srl : EndR(M) G srl iff M satisfies substitution property. In 1971, Vaserstein [18] studied srl condition and obtained the following results: srl condition is left-right symmetric;

We first follow Jensen (1993b) and give a precise definition of the the metric r and the Vasserstein metric R introduced in Section 3. Let p\ be the discrete metric on ft, i.e, p\{t,s) = 1 if i / s and zero otherwise. Define the symmetric metric p? on ft ...

DISCRETIZATION FOR STOCHASTIC DIFFERENTIAL EQUATIONS, Lp WASSERSTEIN METRICS, AND ECONOMETRICAL

MR1485518 (98g:60004) Distributions with fixed marginals and related topics. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Distributions with Fixed Marginals,

Doubly Stochastic Measures and Markov Operators held in Seattle, WA, August 1–5, 1993. Edited by Ludger Rüschendorf, Berthold Schweizer and Michael D. Taylor.

Institute of Mathematical Statistics Lecture Notes—Monograph Series, 28. Institute of Mathematical Statistics, Hayward, CA, 1996. xx+364 pp. ISBN: 0-940600-40-4, 60-06 (62-06)

Volume 76 of Lecture Notes in Statistics

David J. Aldous, Robin Pemantle - Springer-Verlag GmbH, 1996 -  225 pages ISBN 0387946233, 9780387946238

Sergio Bittanti, Giorgio Picci, North Atlantic Treaty Organization. Scientific Affairs Division -   1996 - 552 pages

Wasserstein distance

Stochastic modelling in physical oceanography - Page 276, 277

Robert J. Adler, Peter Müller, Boris Lʹvovich Rozovskiĭ - 1996 - 466 pages

Wasserstein metric, Wasserstein case

Mathematics in St. Petersburg - Page 128, 129, 139

Andrej A. Bolibruch, A. S. Merkur'ev, N. Yu Netsvetaev - 1996

L. Vasserstein, On the stabilization of the general linear group over a ring, Mat. Sb. 79 (1969), 405-424; English transl., Math. USSR-Sb. 8 (1969), 383-400. 13. M. Wodzicki, Excision in cyclic homology and in rational algebraic K-theory, Ann.

1996

[24] Cuesta-Albertos, J. A., MatrAn, C. and Tuero-Diaz, A. (1993) Optimal maps for the Z. 2 -Wasserstein distance. Preprint. [25] Cuesta-Albertos, J. A., MatrAn, C. and Tuero-Diaz, A. (1993) On lower bounds for the L2-Wasserstein metric in a Hilbert space. J. Theor. Prob. (to appear)

[26] Cuesta-Albertos,J.A.,ROschendorf,L. and Tuero-Diaz, A. (1993) Optimal coupling of multivariate distributions and ...

Group Theory in China - Page 44, 46, 47, 48, 52, 53, 54

Zhexian Wan, Sheng-Ming Shi - 1996

[39] Magum, B., Van der Kallen, W. and Vaserstein, L., Absolute stable rank and Witt cancellation for non-commutative rings, Inv. Math., 91 (1988), 525-543. [40] O'Meara, O.T., The automorphisms of the orthogonal groups fln(V) over fields, ...

Interaction between functional analysis, harmonic analysis, and probability - Page 286

Nigel J. (Nigel John) Kalton, Elias Saab, Nigel Kalton Elias Saab Stephen Montgomery-Smith - 1996

One can find results on Banach spaces with polynomial norms and on the structure of suhspaces of L^* with fc € N in the papers Reznick (1979), Lyuhich and Vaserstein (1993), Konig (1994). Let us formulate the result of Proposition 6 in the

Masters abstracts - Volume 34, Issues 1-2 - Page 770

Adviser: Richard Arratia Order Number MA1376449 We discuss the coupon collector's problem: Coupons are of m ... R we compute approximations for the total variation distance d-rv (£(T), £(T')) and the Wasserstein distance dw(£(T), £(r')).

# Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Montecatini Terme, Italy, May 22-30, 1995, Issue 162

Carl Graham, ‎Denis Talay, ‎Luciano Tubaro - 1996

Q-*°0<t<T t-a<,<t+a Then we have convergence in probability of the flow (/x?)t>o to (Qt)t>o *» E)([0,T],V(M )) endowed with the uniform topology. Proof. Let p be the Vaserstein distance on JR . We have to prove that suPo<i<TP(At?, Qt) tends in ...

### Progress in algebraic combinatorics - Page 310

Eiichi Bannai, ‎Akihiro Munemasa - 1996

In the present Section 4 this is put into the natural framework of isometric linear maps from real spaces with the 2-norm into real Banach spaces with the g-norm, following Reznick and Lyubich- Vaserstein. This leads to the main Theorem 4.4 ...

### Dissertation Abstracts International: The sciences and engineering - Page 5145

1996

Adviser: Leonid N. Vaserstein Order Number DA9600144 The goal of this paper is to introduce a game theoretic modeling framework which allows the inclusion of empirically observable human tendencies other than rationality, and which ...

### Memòria d'activitats: curs 1994-1995 - Page 183, 264

1996

L. Vaserstein, de la Universitat de l'Estat de Pennsilvania, EUA: «Products of conjugacy classes». Febrer de 1995. J. M. Burgués, de la Universitat Autonoma de Barcelona: «El problema de Neumann a dominis estrictament pseudoconvexos ...

# Ecole D'été de Probabilités de Saint-Flour XXIV, 1994

R. L. Dobrúshín, ‎P. Groeneboom, ‎Michel LeDoux - 1996

For example, in applications to Markov interaction processes the Kantorovich distance is often called the Vasserstein distance. Below we discuss the main properties of the Kantorovich distance, but omit nontrivial proves of the facts which will ...

### Simulation of Random Processes and Rate-Distertion Theory - IEEE Xplore Abstract

by Y Steinberg - ‎1996

Jan 15, 1996 - Prohorov and other distances of the Kantorovich-Vasershtein type, we show that the finite-precision resolvability is equal to the rate-distortion function with a fidelity criterion derived from the accuracy measure. This connection leads to new ...

1997   19 books

### Computational Science for the 21st Century - Page 7

Marie Odile Bristeau, ‎Garret J. Etgen, ‎W. Fitzgibbon - 1997

The Wasserstein distance, [12], between two probability measures u,, and m on R is dOi,,^)2 = inf J I x - y I2 dp(x,y), ... The variational problem (3.4) is an example of a Monge-Kantorovich mass transference problem with the cost function c(x,y) ...

### Geometry of Cuts and Metrics - Page 34, 161

M. Deza, ‎Monique Laurent - Springer, 1997 ISBN 354061611X, 9783540616115  587 pages

Isometric embeddings among the Lp-spaces. There is a vast literature on the topic of isometric embeddings among the various Lp-spaces; see, e.g., Wells and Williams [1975], Dor [1976], Ball [1987] , Lyubich and Vaserstein [1993].

... among them, the following are based on the Li-metric: q The usual Li-metric between the random variables: ) = E(\X -Y\)= \x(u) - y Jn • The Monge-Kantorovich-Wasserstein metric (i.e., the Lj-metric between the distribution functions): k(X,Y)= I ...

Model Theory of Groups and Automorphism Groups - Page 90

David M. Evans - 1997

... 0 lemmas relating simplicity properties of an algebraic group G to its restriction G(F) to a pseudofinite field F (§6); 0 a fast though non-effective model-theoretic proof of a result of Matthews, Vaserstein and Weispfeiler on reduction at primes ...

Abstracts of papers presented to the American Mathematical Society - Volume 18 - Page 390

On the connections between the Wasserstein metric and diffusions.

Samuel Kotz, Campbell B. Read, David L. Banks - 1997 - 582 pages

Differential equations and applications: - Page 109, 117, 118, 120

proceedings of the US-Chinese conference, held in Hangzhou, June 24-29, 1996

P. W. Bates - 1997 - 363 pages

The Wasserstein metric is equivalent to a topology on the ... Finally, we offer an observation about the Tsallis entropy, [37] recently introduced to investigate Levy like super-diffusion and fractal generation.

Geometry of cuts and metrics - Page 34, 161

, Monique Laurent - 1997 - 587 pages

Wasserstein

Gaussian Hilbert spaces - Page 207

Svante Janson - 1997 - 340 pages

Wasserstein distance

Malempati Madhusudana Rao - 1997 - 393 pages

Wasserstein metrics

Gordon and Breach Science Publishers, 1997

Thirty-one invited addresses at the International Congress of Mathematicians in Moscow, 1966  - Page 196

Volume 70 of American Mathematical Society Translations Series 2

M. A. Aizerman, D. V. Anosov, V. I. Arnold - 1997  ISBN0821817701, 9780821817704  266 pp

3) F is the group of integral points of a spinor group connected with a quadratic form, in which the number of negative squares, and also the number of positive squares, is not less than two (L. N. Waserstein, in press). In all the cases ...

Modern Theory of Summation of Random Variables - Page 400

Vladimir M. Zolotarev - 1997

Givens, GR, and Schorff, R.M. (1984). A Class of Wasserstein Metrics for Probability Distributions. Dept. Math. ... A generalization to Ornstein's distance with applications to information theory. Ann. Probab. 3, 315-318. Grigorevskii, N.V. (1986).

1996 Ams-Siam Summer Seminar in Applied Mathematics, June 17-22, 1996, Williamsburg,Virginia

Volume 33 of Lectures in applied mathematics, v. 33

G. George Yin, George Yin Qing Zhang -  AMS 1997 ISBN0821807552, 9780821807552 399 pp

Wasserstein metric

In fact one may base a distance concept on the existence of couplings: We define the Wasserstein distance r for inner regular probability measures ^i and /i2 on a general metric space (R, r): r(^1,^2) = inf{E(r(Xi,X2)) : (Xi,Xi) is a bivariate ...

Strassen.s construction suggests the close relation between distances of probability measures and coupling constructions. In fact one may base a distance concept on the existence of couplings: We define the Wasserstein distance r for inner regular probability measures ^i and /i2 on a general

metric space (R, r): r(^1,^2) = inf{E(r(Xi,X2)) : (Xi,Xi) is a bivariate random variable (2) with given marginals Xi ...

Stochastic Differential and Difference Equations - Page 336

I Csiszár, György Michaletzky - 1997

[KMW] G. Kallianpur, I. Mitoma and R. L. Wolpert, Diffusion equation in duals of nuclear spaces, Stochastics, 29 (1990), 1-45. [EK] S. ... [Sz] A. Szulga, On the Wasserstein metric, Transactions of the 8th Prague Conference, (1978), 267-273.

Surender Kumar Jain, S. Tariq Rizvi - 1997

The following lemma is due to Vaserstein M. Let us note that if i, j and k are pairwise distinct integers, and a, b are in our ring, then the commutator [/ + aEij,I + 6F/j^] is equal Lemma 2.2. Let W be any nonzero ideal in (n. Then, for any natural

Satya Mandal - 1997

Theorem 5.1.1 (Suslin) En(j4) is a normal subgroup of GLn(A) for any integer n > 3. We need the following lemmas to prove Theorem 5.1.1. Lemma 5.1.2 (Vaserstein) Let a be an r x s -matrix and 0 be an 8 x r-matrix. Suppose I + a/3 is in GLr(A) ...

Cyclic Homology - Page 356

Jean-Louis Loday - 1997

The original proof is due to Vaserstein [1976] and Wagoner [1977]. We refer to Suslin [1981] for a short proof of this technical and important result. D 11.2.15 Corollary. The Volodin space fits into a natural homotopy fibration

Memòria d'activitats: curs 1994-1995 - Page 264

... 175 Vaquero, T. 205 Vaserstein, L. 183 Vayreda, J. 204, 207 Vázquez i García, Merce 119 Veciana Tormo, Robert 144 Veerman, J. J. P. 176, 193 Vegara i Carrió, Josep M. 142 Velickovic, B.

Multivariate approximation: recent trends and results :  - Page 26

Proceedings of the 2nd International Conference on Multivariate Approximation Theory Held at Witten-Bommerholz, Germany, September 29-October 4, 1996

Werner Haussmann, K. Jetter, Manfred Reimer - Akademie Verlag, 1997   ISBN3055017706, 9783055017704

Lyubich, L. Vaserstein: Isometric imbeddings between classical Banach spaces, cubature formulas, and spherical designs, Geom. Dedicata 47 (1993), 327-362. [10] B. Reznick: Sums of even powers of real linear forms, Memoirs Amer. Math.

1998 16 books

### Proceedings of the International Colloquium on Lie Groups and Ergodic Theory, Mumbai, 1996  - Page 157

S. G. Dani, ‎Tata Institute of Fundamental Research - 1998 - ‎Snippet view - ‎More editions

We remark that this result was previously obtained by Vaserstein in the case of classical simple groups for a number field K and 5-arithmetic subgroups with K- rank > 2 (1973) and by Tits in the case of Chevalley groups (1976). This result ...

Probability Toward 2000 - Page 337

Luigi Accardi, C. C AUTOR HEYDE - 1998

[10] Cuesta, J. A. and Matran, C. (1994). Stochastic convergence through Skorohod representation theorems and Wasserstein distances. ... The impossible coupling: on hidden variables models in quantum mechanics. Proceedings of the 51st ...

K-Theory for Operator Algebras - Page 36, 290

Bruce Blackadar - 1998

... and Vaserstein 1984] R. H. Herman and L. N. Vaserstein, "The stable range of C*-algebras", Invent. Math. 77:3 (1984), 553-555. [Higson 1983] N. Higson, On Kasparov Theory, M.a. thesis, Dalhousie University, Halifax, 1983. [Higson 1988] ...

David E. Evans, Yasuyuki Kawahigashi - 1998

(Herman and Vaserstein 1984) have shown that (for C* -algebras) topological stable rank is the same as Bass stable rank and (Villadsen (preprint 1997)) has shown that for each n € N, there is a simple C* -algebra of topological stable rank n.

1998

... (x,y) = A^(y,x) pm(y) Pm(z)' and apply the previous results. We omit details. Proposition 6.3 is proved. The Vaserstein distance. For any x and x' in [0, £] we set (7.1) and then we define the Vaserstein distance D,t(<m(n, u) of. 70 A. De Masi, ...

Mass Transportation Problems: Volume I: Theory - Page 404, 436, 442, 464, 469, 481

Svetlozar Todorov Rachev, Ludger Rüschendorf - 1998 - 508 pages

Wasserstein norm

llUllu U#(<P) (separable) metric space 92 333 shift operator 65, 390 SkorohodI Lebesgue metric 34 97 dual form of SP(P1> P2) 97 measure space 36 392 ... optimal value 252 total variation distance in X(IRd) 134 optimal value of the dual problem 253 absolute pseudomoment

194 105 Brownian motions 278 LP-Wasserstein metric / LP-Kantorovich metric 40 354 transposed function 172 “output” fiow 71 ...

On a formula for the L2-Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr., 147:185— 203, 1990.

Peter Armitage, Theodore Colton - 1998 - 690 pages

Microsurveys in discrete probability: DIMACS workshop, June 2-6, 1997 - Page 32, 39

David J. Aldous, James Propp - 1998 - 220 pages

Springer, Lecture Notes in Mathematics, vol. 1117. [3] Arratia, R. (1996) Independence of small prime factors: total variation and Wasserstein metrics, insertions ...

Vesselin S. Drensky, A. Giambruno, Sudarshan K. Sehgal - 1998 - 314 pages

[97] L.N. Vaserstein, On the group SLo over Dedekind rings of arithmetic type, Math. USSR Sbornik 18 (1972), 321-332.

[98] L.N. Vaserstein, The structure of classic arithmetic groups of rank greater than one, Math. USSR Sbornik 20 (1973),

Daniel Bump  1998 - 574 pages It is a deep theorem of Vaserstein (1972) that the Hilbert modular group is always generated by these elements, so this ...

Although we cannot prove Vaserstein's result in these notes, we will show that it is true for K = Q(\/5) (Exercise 1.10.1), ...

Variational problems in transport theory with mass concentration. (English)

Tesi. Scuola Normale Superiore Pisa (Nuova Serie) 4. Pisa: Edizioni della Normale; Pisa: Scuola Normale Superiore (Dissertation). xxxii, 198~p. EUR~18.00/net; SFR~30.00; \$~24.95; \sterling~14.00 (2007). MSC2000: *35-02 90B20 49N60, Reviewer: Giuseppe Buttazzo (Pisa) Wasserstein distances Alberto Facchini - 1998, 2012 - 285 pages Then sr(C(X)) = sr(C(X)) = dim(X) + 1 [Vasershtein]. Hence the stable range of the [Vasershtein] L. N. Vasershtein, Stable rank of rings and dimensionality of topological spaces, Funct. Anal. Appl. 5 (1971), 102I110. [Warfield 69a] R. B. Warfield, ... ### Cyclic Homology - Page 356, 380, 497 Jean-Louis Loday - 1998 The original proof is due to Vaserstein [1976] and Wagoner [1977]. We refer to Suslin [1981] for a short proof of this technical and important result. D 11.2.15 Corollary. The Volodin space fits into a natural homotopy fibration X(A) -> BGL(A) ... ### Proceedings of the International Congress of Mathematicians: - Page 298, 676 # August 18-27, 1998, Berlin, Germany, Volume 2 Gerd Fischer, ‎Ulf Rehmann - 1998 Phys., 124, No.2, 217-227, 1989. [Th-Sa] W.Thurston, G.Sandri. Classical hard sphere 3-body problem. Bull. Amer. Phys. Soc, 9, 386, 1964. [Va] L.N.Vaserstein. On systems of particles with finite range and/or repulsive interactions. Comm. ### Wavelet Applications in Signal and Image Processing - Page 149 Andrew Laine, ‎Michael A. Unser, ‎Akram Aldroubi - 1998 K. Dennis, B. Magurn, and L. Vaserstein, "Generalized euclidean group rings," J. reine angew. Math. 351, pp. 113-128, 1984. 15. M. Nelson, "Data compression with the Burrows- Wheeler transform," Dr. Dobb's Journal , September 1996. 16. ### Charlemagne and his heritage - Volume 2 - Page 360 Paul Leo Butzer, ‎Max Kerner, ‎Walter Oberschelp - 1998 [22] Lyubich,Y.I., Vaserstein.L.N.: Isometric Embeddings between Classical Ba- nach Spaces, Cubature Formulas, and Spherical Designs; Geometriae Dedicata. 47(1993),327-362. [23] Schreiber,P.: Zur Geschichte des sogenannten Steiner- ... 1999 21 books 1999 ... marginal distributions are, respectively, P and Q. Another form of mass transport problem, formulated by Kantorovich (cf. ... and phrases: Monge-Kantorovich transportation problem, optimal coupling, cyclic monotonicity, Levy-Wasserstein ... Seminaire de Probabilites XXXIII - Page 379, 386 J. Azema, M. Emery, M. Ledoux - 1999 Nachr., 147:185-203, 1990. Givens, C. R., and Shortt, R. M . A class of Wasserstein metrics for probability distributions. Michigan Math. J., 31:231-240, 1984. GOLDSTEIN, S. Maximal coupling. Z. Wahrscheinltchkeitstheor. Verw. Geb., 46:193- ... Monge Ampere Equation: Applications to Geometry and Optimization : - Page 2, 4, 82, 87, 95, 96, 102, 103 NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University Luis A. Caffarelli, Mario Milman - AMS 1999 - 172 pages ISBN0821809172, 9780821809174 More precisely they show that the heat equation is the gradient flow of the Dirichlet integral with respect to the L2 distance as well as the gradient flow of the entropy with respect to the Wasserstein distance. A weighted combination of these ... Surgery on Compact Manifolds - Page 297 CTC Wall, A Ranicki - 1999 - C. T. C AUTOR WALL, A. A AUTOR RANICKI - 1999 - [VI] VASERSTEIN, L. Stability of the unitary and orthogonal groups over rings with involution. Math. S6. 81 (1970), 328-351. based on "Structures métriques des variétés Riemanniennes" Gromov Springer, Springer, 1999 - 585 pages ISBN0817638989, 9780817638986 Contractions in the 2-Wasserstein Length Space and Thermalization Raoul Bott, Arthur Jaffe, S. T. Yau - 1999 diffusion. An interesting emerging theme in much current research is the interplay between Monge-Kantorovich mass transform ... Preparatory to describing this procedure, let us first define for the functions /+, /" € V the Wasserstein distance ... Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem - Issue 653 - Page 4 Lawrence C. Evans, Wilfrid Gangbo - 1999 The resulting distance and its variants are called the Monge-Kantorovich-Rubinstein-Wasserstein-etc. metrics; see Rachev [R] ... We can consequently interpret the limit of (1.21) as p — » oo as an "infinitely fast/infinitely slow" diffusion limit (cf. Shape recognition via Wasserstein distance - Page 1, 5, 9,34, 35 Wilfrid Gangbo, Robert J. MacCann - 1999 - 34 pages Abstract. The Kantorovich-Rubinstein-Wasserstein metric ... Jacques Azéma, M. Emery, Michel Ledoux - 1999 - 418 pages [2] Abdellaoui, T., et Heinich, H. Sur la distance de deux lois dans le cas vectoriel. C. R. Acad ... 3] Aldous, D. J. Shift-coupling. ... 6] Cuesta-Albertos, J. A., and Matran, C. Notes on the Wasserstein metric in Hilbert spaces. ... J. A., Matran, C, and Tuero-Diaz, A . On lower bounds for the i2-Wasserstein metric in a Hilbert space. Stochastic dynamics - Page 402, 427, 440 Hans Crauel, Matthias Gundlach - 1999 - 440 pages This extension will be achieved by a combination of Wasserstein metric and weighted Sobolev norm estimates. René Carmona, Boris Rozovskii - 1999 - 334 pages - Let Lip(Rd) = {/ : Rd -> K : \f(*)-f(v)\ < k-y|, l/MI < i, v*,y e Rd}. if w e MF(Rd), d^v) = sup{ \n(f)-v(f) I : / £ Lip(Ud)} denotes the Vasserstein metric. Monge Ampère equation: applications to geometry and optimization : - Page 2, 4, 82, 87, 95, 96, 102, 103 Applications to Geometry and Optimization : NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University Luis A. Caffarelli ISBN0821809172, 9780821809174 -Interpolation of the L2 and the Wasserstein distances. When two densities P0 and pr must be compared, it is very natural to use the Wasserstein distance. However, sometimes, the simpler L2 distance : (1-18) d/Xpo, Pr)2 = j \po(x) - pr(x)fdx ... Heping Zhang, Burton Singer - 1999 - 226 pages Wasserstein distance RAIRO.: Modélisation mathématique et analyse numérique : - Page 837, 838, 849, 860 M2N. Mathematical modelling and numerical analysis, Volume 33, Pages 651-1319 We can introduce a Wasserstein metric for this purpose. ... is the metric we shall introduce (the Wasserstein metric). ... is the classical convection diffusion Algebra, K-Theory, Groups & Education: - Page 112, 124, 216, 237 On the Occasion of Hyman Bass's 65th Birthday Hyman Bass, T. Tsit-Yuen Lam, Andy R. Magid - 1999 88, Birkhauser, 1990, pp. 247-435. [Va69] L. Vaserstein, On the stabilization of the general linear group over a ring, Math. USSR- Sb. 8 (1969), 383-400. [Va71] L. Vaserstein, The stable range of rings and the dimension of topological spaces, ... Looking forward, Bass' stable range results were improved in [Bass] and again in Vaserstein's work [Va69] [Va71] A. Pott, P. Vijay Kumar, Tor Helleseth - 1999 While constructing the isometric embedding ^ _> gNW+W (see Lyubich and Vaserstein (1993)) he augmented the set of N2/2 lines from Cameron and Seidel (1973) by the standard coordinate frame. This did not increase the set of prescribed Surgery on Compact Manifolds - Page 297 [VI] VASERSTEIN, L. Stability of the unitary and orthogonal groups over rings with involution. Math. S6. 81 (1970), 328-351. [Wl] WAGONER, J. B. Smooth and piecewise linear surgery. Bull. Amer. Math. Soc. 73 (1967), 72-77. [lY2] WAGONER Introduction to the Theory of Games: Concepts, Methods, Applications - Page 126, 326, 339 Ferenc Forgó, Jeno Szép, Ferenc Szidarovszky - 1999 [17] Byrne, C.C. and Vaserstein, L.N., An improved algorithm for finding sad- ... 48 Vaserstein, 128 veto player, 231 von Neumann, 122, ... Number Theory: - Page 33 Fifth Conference of the Canadian Number Association, August 17-22, 1996, Carleton University, Ottawa, Ontario, Canada A. Bremner, Integer points on a special cubic surface, Duke Math. J. 44 (1977), no. 4, 757-765. 4. W. Conn and L. N. Vaserstein, On sums of three integral cubes, The Rademacher Legacy to Mathematics (University Park, PA, 1992), Contemp. Wolfgang Krull: gesammelte Abhandlungen - Volume 1 - Page 35 Wolfgang Krull, Paulo Ribenboim - 1999 Dabei hat man zum Beweis von (i) nur ganz elementare Schlußweisen der kommutativen Algebra anzuwenden, (ii) benutzt dagegen das Resultat von Q u i 1 1 e n - Suslin-Vaserstein [32], [40], 1976: Jeder projektive Modul über einem ... Number theory in progress: - Volume 2 - Page 1128 proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in honour of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997. Elementary and analytic number theory, Volume 2 Andrzej Schinzel, Kálmán Györy, Henryk Iwaniec - 1999 [A96] Arratia, R., Independence of small prime factors of a uniformly distributed integer : total variation and Wasserstein metrics. Manuscrit, 1996. [AS97] Arratia, R., Stark, D., A total variation distance invariance principle for primes, ... 2000 20 books On Dobrushin's Way: From Probability Theory to Statistical Physics - Page 237 R. Robert Adolfovich Minlos, ‎S. B.. Chlosman, ‎Yu. M. Suhov - 2000 Leonid Vaserstein. Nikolai Vassiliev and others). ... The talk quickly turned to a dispute between Dobrushin and Pyatecky 's group, and at a certain point somebody (I think it was Vaserstein) said, addressing his colleagues. "Let's postpone the ... Hard Ball Systems and the Lorentz Gas - Page 26, 27, 34, 48, 88, 126, 143 L.A. Bunimovich, D. Szasz - 2000 [Se-Va] A. Semenovich, L. Vaserstein. Uniform estimates on the number of collisions in particles' systems. preprint. [St-1] L. Stojanov. An estimate from above of the number of periodic orbits for semi-dispersed billiards. Comm. Math. Phys. 124 Units in Skew Fields - Page vii, 32, 78 By Ernst Kleinert 2000 Maximal Subgroups of infinite index in finitely generated linear groups, J. of Algebra 69 (1981) 1-23 [MOV] Magurn, B., R. Oliver and L. Vaserstein. Units in Whitehead Groups of Finite Groups, J. of Algebra 84 (1983) 324-360 [MVW] Matthews, ... Svetlozar Todorov Rachev, S. Mittnik - 2000 The methods employed are based on the evaluation of drift and diffusion coefficients over grid points. ... method by replacing the increments of the Wiener process by other "simpler" i.i.d. random variables: He uses Lf- Wasserstein metrics Skorokhod's ideas in probability theory - Page 318 and let (Xt) and (Xi) be two diffusion processes with L and L as their generators. We show thai the Kantorovich- Wasserstein's distance of these two processes is dominated by C{log[2 + log" (||.4 -.4||L2 )]}-> where 7 and C are positive ... Algebra colloquium - Volume 7 - Page 161, 189, 196 [66] L.N. Vaserstein, Stabilization of unitary and orthogonal groups over a ring, Math. USSR Sbornik 10 (1970) 307-326. [67] L.N. Vaserstein, On normal subgroups of GL„ over a ring, in: Algebraic K-Theory, Lecture Notes in Mathematics, Polynomial Automorphisms: And the Jacobi Conjecture - Page 263 A R P Van Den Essen - 2000 A first relationship with rings of differential operators was found by Vaserstein and Kac. They observed that if every ^-endomorphism of the n-th Weyl Algebra A„ is surjective, then JC(k, n) follows! It was later remarked by the author that in fact ... Algorithmic Number Theory: - Page 62, 63 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000 Proceedings Volume 1838 of Lecture Notes in Computer Science Wieb Bosma - 2000 [CV] Conn, W., Vaserstein, L.N.: On sums of integral cubes. Pages 285-294 in The Rademacher legacy to mathematics (University Park, 1992), Contemp. Math. 166, AMS 1994. [PV] Payne, G., Vaserstein, L.N.: Sums of three cubes. Pages 443-454 in The Arithmetic of Function Fields, de Gruyter, 1992. [S] Stahlke, C: Algebraic curves over (Q) with many rational points and minimal automorphism group. Lnternational Advances in Steiner Trees - Page 13 Ding-Zhu Du, J.M. Smith, J. Hyam Rubinstein - 2000 17] Y.I. Lyubich and L.N. Vaserstein, Isometric Embeddings between Classical Banach Spaces, Cubature Formulas, and Spherical Designs, Geome- triae Dedicata, 47(1993), pp. 327-362. 18] CM. Petty, Equilateral sets in Minkowski space, ... An Introduction to Superprocesses - Page 130 Alison Etheridge - 2000 The Wasserstein metric on MF (R . ) is given by , v) = sup {|{0, ft)-(4,,v}\:4,€ Lip (Rd) } . REMARK 7.3. For any metric space, (S,d), we can define the corresponding Wasserstein metric on Mp(S) in an obvious way. The topology induced on Mp(S) ... Sorting: a distribution theory - Page xi, 161, 164, 174, 191, 192, 343, 345, 385, 394 Hosam Mahmoud Mahmoud - 2000 - 394 pages Alison Etheridge - 2000 - 187 pages Wasserstein metric Wasserstein distance Galen R. Shorack - Springer 2000 - 585 pages ISBN0387989536, 9780387989532 Exercise 3.4 (Wasserstein distance) For k = 1 or 2, define Fk {F : F is a df, and ... MR1764176 (2001m:60043) Graf, Siegfried; Luschgy, Harald Foundations of quantization for probability distributions. Lecture Notes in Mathematics, 1730. Springer-Verlag, Berlin, 2000. x+230 pp. ISBN: 3-540-67394-6 (Reviewer: Kalev Pärna), 60E99 (60F25 62H05 94A12) Coupling, stationarity, and regeneration - Page 56 Hermann Thorisson - 2000 - 517 pages Information theory: 50 years of discovery: Volume 1 - Page 37, 49, 739 Sergio Verdú, Steven W. McLaughlin, IEEE Information Theory Society - 2000 Vasershtein Development of mathematics 1950-2000 - Page 1299 Jean-Paul Pier - 2000 - 1372 pages Vasershtein L.N., Foundations of algebraic K-theory, 89-156. Ilʹia Iosifovich Piatetskiĭ-Shapiro, James Wesley Cogdell, S. Semen Grigor'evich Gindikin - 2000 is the group of integral points of a spinor group connected with a quadratic form, in which the number of negative squares, and also the number of positive squares, is not less than two (L. N. Waserstein, in press). In all the cases considered ... Amenable groupoids - Page 85 [L-V] Lyubich, Y.I. and L.N. Vasserstein. Isometric embeddings between classical Banach spaces, cubature formulas and spherical designs. Geom. Dedicata 47 (1993), 327-362. [M] Martinet, J. Les reseaux parfaits des espaces euclidiens. 2001 21 books ### Réseaux euclidiens, designs sphériques et formes modulaires - Page 85 Boris Borisovich Venkov, ‎Jacques Martinet - 2001 Symmetric squares and lattice minima. Preprint, Essen. [L-V] LYUBICH, Y. I. and L.N. VASSERSTEIN. Isometric embeddings between classical Banach spaces, cubature formulas and spherical designs. Geom. Dedicata 47 (1993), 327-362. ### Social Economics - Page 623, 643 Jess Benhabib, ‎Matthew O. Jackson, ‎Alberto Bisin - 2010 Topa, G., 2001. Social Interactions, Local Spillover and Unemployment. The Review of Economic Studies 68, 261–295. Vasserstein, L.N., 1969. Markov Processes over Denumerable Product of Spaces Describing large Systems of Automata. ### Variational and Level Set Methods in Computer Vision: - Page 30, 31, 33 # Proceedings : IEEE Workshop on Variational and Level Set Methods in Computer Vision : 13 July, 2001, Vancouver, Canada 2001 1 Finding an Initial Mapping We will now propose an explicit algorithm to solve the Monge—Kantorovich problem. So we want to minimize the L2 KantorovichWasserstein distance functional over MP functions from (fl0,#0) to (Q1,#1). ### VLSM - Volume 1 - Page 30, 31, 33 mt #(1--)=u1- (22) It is shown in [3] that this infimum is attained for some am," and z;,,,,~,,, and that it is equal to the L2 KantorovichWasserstein distance between no and ,u1. Further, the flow X = X(:c.t) corresponding to the minimizing velocity ... Jürgen Herzog, Gaetana Restuccia - 2001 As mentioned, the special case of Theorem 6 for free commutative monoids is due to Suslin [8] (the case of a trivial monoid being the Bass-Vaserstein classical results on surjective KI stabilizations, see Ch. 5, §4 in [1] and [11]). In [4] we have Ramanujan: Essays and Surveys - Page 224, 253 Bruce C. Berndt, Robert A. Rankin - 2001 R. Gar-el and L. Vaserstein, On the Diophantine equation a3 + b3 + c3 + d3 = 0, J. Number Thy. (to appear). Codes On Euclidean Spheres - Page 533 T E O Ericson, Victor Zinoviev - 2001 Y.I. Lyubich and L.N. Vaserstein, Isometric embeddings between classical Banach spaces, cubature formulas and spherical designs, Geom. Dedic., Vol. 47, pp. 327-362, 1993. A.L. MacKay, The packing of three-dimensional spheres on the ... Tsi-Yuen Lam - 2001 If we assume the result of Vaserstein in Ex. ( 1 .25), it will follow that left and right stable range 1 are equivalent properties. ... To show that it is not essential here to assume Vaserstein's result, we shall continue to work with the notion of left ... Large deviations and idempotent probability - Page 74, 266, 472, 496, 497 Anatolii Puhalskii - Taylor & Francis, 2001 - 500 pages ISBN 1584881984, 9781584881988 Wasserstein Eighth International Conference in Magdeburg, February/March 2000, Volume 1 Michael Fey, Heinrich Freistühler, International Conference on Hyperbolic Problems - Springer 2001 - 472 pages Springer, 2002 ISBN 3764367091, 9783764367091 Wasserstein distance Ch. A. Charalambides, Markos V. Koutras, N. Balakrishnan - 2001 - 624 pages establishing asymptotic results is the Kolmogorov distance (instead of the Wasserstein or the total variation distance). G. Kallianpur, Takeyuki Hida - 2001 - 410 pages ISBN0817641378, 9780817641375 Wasserstein metric Stochastic processes: theory and methods - Page 102, 106 D. N. Shanbhag, Calyampudi Radhakrishna Rao - 2001 - 967 pages John C. McConnell, James Christopher Robson, Lance W. Small - 2001 - 636 pages 8.5 (a) A good source for the topics in the first half of the section is [Suslin 81] where it is noted that 5.8(h) is due to Vaserstein, (b) The second half, concerning matrices, originates from [Vaserstein 71] where, in particular, 5.17 appears. Universite de Paris VII publications mathematiques: Volume 92 Research in stochastic programming - Page 69, 70, 72 John R. Birge, N. C. P. Edirisinghe, W. T. Ziemba - 2001 - 306 pages Wasserstein distance Festschrift for Willem R. Van Zwet Mathisca de Gunst, Chris Klaassen, A. W. van der Vaart - 2001 - 616 pages Wasserstein distance ### Noncommutative Noetherian Rings - Page 443, 618 8.5 (a) A good source for the topics in the first half of the section is [Suslin 81] where it is noted that 5.8(h) is due to Vaserstein, (b) The second half, concerning matrices, originates from [Vaserstein 71] where, in particular, 5.17 appears. ### Ring Theory And Algebraic Geometry - Page 209, 210 A. Granja, ‎J.A. Hermida Alonso, ‎A Verschoren - 2001 1 (1999) 178-184. II] A. A. Suslin, On the structure of the special linear group over polynomial rings, Math. USSR Izv. 11 (1977) 221-238. [12] L.N. Vaserstein and A. A. Suslin, Serre's Problem on Suslin's Stability Theorem for IV,,...,',,.) 209. ### Handbook of the Geometry of Banach Spaces - Volume 1 - Page 989 William B. Johnson, ‎Joram Lindenstrauss - 2001 ... 793, 831 [50] Vaaler, J.D. 175, 194 [38] van Dulst, D. 515, 529 [50] van Mill, J, 603, 669 [I65] van Rooij, A.C,M. 91, 121[II8];121[119] Vanderwerff, J. 434 [36]; 828, 835 [I72] Varga, R. 555, 559 [41] Vargas, A. 222, 231 [44] Vaserstein, L. 916, ... ### SIAM Journal on Control and Optimization - Page 144 Boris Borisovich Venkov, ‎Jacques Martinet - 2001 Symmetric squares and lattice minima. Preprint, Essen. [L-V] LYUBICH, Y. I. and L.N. VASSERSTEIN. Isometric embeddings between classical Banach spaces, cubature formulas and spherical designs. Geom. Dedicata 47 (1993), 327-362. 2002 20 books Partial Differential Equations: Mark Vishik's Seminar - Page 162 M. I. Vishik, M. S. Agranovič, M. Mikhail Aleksandrovich Shubin - 2002 KPS01] the author of this paper and his collaborators developed a coupling approach to study the systems under ... acting in the space of probability measures, given the Kantorovich(-Wasserstein) metric, defines a contraction of this space. Handbook of Mathematical Fluid Dynamics - Volume 1 - Page 194, 279 S. Friedlander, D. Serre - 2002 For instance, if W stands for the Wasserstein distance (244), then solutions of (273) satisfy ∫ +∞1 W ( f(t),f S(t) ) dt = +∞. ... Quantum kinetic theory Very recently, Lu [328], Escobedo, and Mischler [210,211] have begun to apply the techniques ... Bruce A. Magurn - 2002 The theorem (10.15) of Vaserstein. presented below, shows these are isomorphisms for n > sr(R). As with the surjective stability theorem of Bass, we only present a special case of Vaserstein "s theorem here. The general form of hoth theorems ... Proceedings of the ... International Conference on Information Fusion, Volume 5 Conclusions In this paper we have borrowed the concept of Wasserstein distance from theoretical statistics to introduce what we believe is the first comprehensive L,type theory of distance metrics for ... Carlos María Cuadras, Josep Fortiana, José A. Rodríguez-Lallena - 2002 - 244 pages 1996) that the square of the L2-Wasserstein distance between two probabilities is greater than or equal to the sum of the squares of the distances ... Tarpey, T. and B. Flury (1996), 'Self-Consistency: A Fundamental Concept in Statistics'. Statist. Real analysis and probability - Page 425 , 438, 553 Richard M. Dudley - 2002 - 555 pages Wasserstein distance Catherine Huber-Carol - 2002 - 507 pages - Wasserstein distance Contemporary combinatorics - Page 29, 40, 42, 43, 49, 88 Béla Bollobás - 2002 - 301 pages Springer, Lecture Notes in Mathematics, vol. 1117. R. ARRATIA* How much dependence is there in the prime factorization of a random integer distributed uniformly from 1 to n? ... respect to total variation distance, considering only small components, and with respect to a Wasserstein distance, considering ... of changes — insertions and deletions — needed to change the dependent system into an independent system. ... A corollary of this construction is the first metric bound on the distance to the Poisson-Dirichlet in Billingsley's 1972 ... Proceedings of the International Congress of Mathematicians: - Volume 1 - Page 185 # August 20-28, 2002, Beijing, Volume 1 Daqian Li - Higher Education Press, 2002 - 2439 pages - a) It was pointed out by Otto, that the Wasserstein metric can be used to describe , M. S. Agranovich, Mikhail Aleksandrovich Shubin - 2002 - 278 pages Wasserstein Handbook of stochastic analysis and applications - Page 264 Kannan, V. Lakshmikantham - 2002 - 763 pages Wasserstein metric Numerical methods and stochastics: Volume 1999 - Page 56 T. J. Lyons, Thomas Stephenson Salisbury - 2002 - 121 pages Wasserstein distance ' Claude Greengard, Andrzej Ruszczyński - 2002 - 154 pages Wasserstein dis- Torgny Lindvall - 2002 - 272 pages Vasershtein coupling Lectures on probability theory and statistics: - Page 307 Ecole d'Ete de Probabilites de Saint-Flour XXIX - 1999 Erwin Bolthausen, Edwin Arend Perkins, A. W. van der Vaart - 2002 - 466 pages Lecture notes in mathematics, 1781 ISBN: 978-3-540-43736-9 (Print) 978-3-540-47944-4 (Online) Statistical Publishing Company, 2002 Geometric Analysis and Nonlinear Partial Differential Equations - Page 483 Stefan Hildebrandt, Hermann Karcher - 2002 The Dobrushin approach is based on a comparison of these measures for different boundary conditions in the Kantorovich(- Ornstein-Rubinstein-Vasserstein) metric Higher Franz-Reidemeister Torsion - Page 4 Kiyoshi Igusa - 2002 It is a theorem of Wagoner and Vasserstein best explained by Suslin [SusS1], [Sus82] that the higher Volodin A'-theory of R also gives the usual algebraic A'-theory groups of R as defined by Quillen. Algebra - Page 846 Serge Lang - 2002 We give here a simplification of Suslin's proof b> Vaserstein, also using a previous result of Horrocks. MR1878556 Lang, Serge Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002. xvi+914 pp. ISBN: 0-387-95385-X 00A05 (15-02). Lang.djvu 7MB Нерешенные вопросы теории групп: Коуровская тетрадь - Page 163 2002 4.2, 4.5, 7.1, 7.3, 13.34, А: 1.24, 1-63, 1.82, 2.13, 2.15, 2.39, 3.9, 4.1, 4.3-5, 7.2, 7.2 Азаров Д. Н. А: 11.10 АлеевР. ... Е. А: 3.29 Васильев А.Ф. 14.28-29, 15.38-39, А: 11.21, 11.24, 12.7 Вассерштейн Л. Н. 14.15 Вдовин Е. П. 3.62, 15.40, ... 2003 30 items Recent advances in group theory and low-dimensional topology / edited by Jung Rae Cho and Jens Mennicke. - Page 136, 140 Heldermann, 2003. ### Handbook of the Geometry of Banach Spaces - Page 1846 William B. Johnson, ‎J. Lindenstrauss - 2003 - ‎Mathematics ... 1514 [115]; 1639, 1641–1643, 1646, 1647, 1649–1652, 1654–1658, ... N.Th. 1363, 1423 [95] Vašák, L. 1764, 1770, 1815 [325] Vaserstein, L. 916, 917, 938 ... ### Oeuvres: Collected Papers - Volume 2 - Page 55, 715 Jean Pierre Serre - 2003 ... plus ou moins complets ont été obtenus entre 1973 et 1975 par M. P. Murthy, M. Roitman, A. Suslin, R. Swan et L. N. Vaserstein. ... clos lOl.i Le cas d'un corps résiduel non algébriquement clos est traité dans la thèse de M. Hazewinkel. Peut-être donnerai-je aussi la démonstration du théorème de Matthews- Vaserstein-Weisfeiler et Nori : si F est un sous-groupe Zariski dense de type fini de Sp2n(Q), son adhérence dans le groupe adélique H Sp2n(Qf) est ouverte, i.e. F a la ... ### Topics in Optimal Transportation - Page 368 Cédric Villani - 2003 differentiability of Wasserstein distance, 262 differential cost, 144 Dirichlet boundary condition, 127 Dirichlet form, 278, ... convexification trick, 51, 60 duality for c-concave functions, 33, 87 Kantorovich, 19 Legendre-Fenchel-Rockafellar, 24, 56, ... ### Communications in Applied Analysis - Page 488 2003 THE MONGE-KANTOROVICH-WASSERSTEIN DISTANCE It is simply to verify that S)(/ilt Hi) :=(2.8) defines a distance on the set of probability measures on M. Analogously, reseating in (2.8) one could obtain a distance on the set of Radon ... ### Medical Image Computing and Computer-Assisted Intervention - Page 279, 280 Randy E. Ellis, ‎Terry M. Peters - 2003 Hence, the KantorovichWasserstein metric may be thought of as the cost associated with transporting, via u, a distribution of material given by μ0. 线性规划导论 书覆盖了线性规划的基本主题, 时包含许多高级主题。通过不同难易程度的习题, 为学生提供逐步提高的机会, 并使优秀的学生完成更具挑战性的任务. Subgroup Growth - Page 392, 397, 441, 453 Alexander Lubotzky, Dan Segal - 2003 However, different versions of this important result have been proved in [Nori 1 987] , [Mathews, Vaserstein k, Weisfeiler 1984], [Weisfeiler 1984] and [Hrushovski & Pillay 1995], and we would like to illustrate three quite different ways of ... Записки научных семинаров ПОМИ: - Volumes 304-307 - Page 224 W. van der Kallen, B. Magurn, and L. N. Vaserstein, Absolute stable rank and Witt cancellation for non-commutative rings. — Invent. Math. ... L. N. Vaserstein, Normal subgroups of orthogonal groups over commutative rings. — Amer. J. Math. Seventh International Conference on P-Adic Funcional Analysis, June 17-21, 2002, University of Nijmegen, The Netherlands Volume 319 of Contemporary mathematics - American Mathematical Society Wilhelmus Hendricus Schikhof, C. Pérez García, Alain Escassut - 2003 ISBN0821833200, 9780821833209 422 pp ( abc)-Theorems for entire functions and polynomials In [34] and [37] Mason and Vaserstein considered the afec-problem for polynomials. In [26] P. C. Hu and C.-C. Yang gave a solution to the abc-problem in the set of p-adic entire functions in ... J. C. Misra - 2003 ... by W^A) and W(A) respectively. Moreover, the surjective map W^A) to W(A) is a group homomorphism. Keeping the above notation in mind, we state the following beautiful theorem of Vaserstein ([S-V], Theorem 5.2 (d)) which says that if dim ... Mathematical Methods in Computer Vision - Page 69, 85 Peter J. Olver, Allen Tannenbaum - 2003 D. Fry, Shape Recognition Using Metrics on the Space of Shapes, Ph.D. Thesis, Harvard University, 1993. ... W. Gangbo and R. McCann, "Shape recognition via Wasserstein distance," Technical Report, School of Mathematics, Georgia ... Ying Lü, Ji-Qian Fang - 2003 Use of the difference I begin the introduction of splitting rules with the use of Wasserstein metrics to measure the between-nodes distributional ... Exercises in Classical Ring Theory - Page 17 T.Y. Lam - 2003 Ex. 1.2,'i. (Vaserstein) Let a, b, c be such that ab + c = 1 in a ring R. If there exists x C R such that a + ex C U(/?), show that there exists y € /? such that; 6 + T/c C Solution. Write u = a + ex C U(/?). We claim that the element y : = (1 - 6x)u-1 works, Introduction to linear programming This book makes Linear Programming easily accessible to any reader, regardless of his or her mathematical background. Logarithmic combinatorial structures: -- Page ix, 5, 67, 68, 185, 279, 359 IBN3037190000, 9783037190005 Wasserstein distance Logarithmic combinatorial structures: A probabilistic approach. (English) EMS Monographs in Mathematics. Zürich: European Mathematical Society (EMS). xi, 363~p. (2003). MSC2000: *60-02 05-02 05A05, Reviewer: Hsien-Kuei Hwang (Taipei) Review in MR 2032426 (2004m:60004) Wasserstein distances Cédric Villani - 2003 - 370 pages Kinderlehrer, D., and Walkington, N. J. Approximation of parabolic equations using the Wasserstein metric. M2AN Math. Model. Numer. Anal. 33, 4 (1999), 837–852. Eberhard Bänsch - 2003 - 285 pages Wasserstein Mathematical aspects of evolving interfaces: - Page 2, 5, 16, 28, 49 Lectures Given at the C.I.M.-C.I.M.E. Joint Euro-Summer School Held in Madeira, Funchal, Portugal, July 3-9, 2000, Issue 1812 (Google eBook) Kantorovich-Wasserstein distance Cavity and Mean Field Models, Volume 46 Michel Talagrand - 2003 - 586 pages ISBN3540003568, 9783540003564 Sergiy Butenko, Robert Murphey, Panos M. Pardalos - 2003 - 364 pages The Mohammed Dahleh Symposium 2002 Laura Giarré, Bassam Bamieh, Mohammed A. Dahleh - 2003 - 229 pages W. Gangbo and R. McGann, “Shape recognition via Wasserstein distance,” Technical Report, School of Mathematics, Georgia ... Optimal transportation and applications: - Page v, 44, 45, 59, 64, 65, 67, 68, 70, 71, 74, 80, 83, 88 Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 2-8, 2001, Issue 1813 Luigi Ambrosio, Luis A. Caffarelli, S. Salsa - 2003 - 171 pages Volume 1813 of Lecture Notes in Mathematics ISBN354040192X, 9783540401926 Wasserstein metric Christian Miehe - 2003 - 478 pages Wasserstein metric Applications to Physics, Industry, Life Science and Economics : Eveq2000 Conference in Levico Terme (Trenton, Italy) October 30-November 4, 2000 (Google eBook) Mimmo Iannelli, Günter Lumer - 2003 - 423 pages Wasserstein distance Stefan Hildebrandt, Hermann Karcher - 2003 - 673 pages - Michael G. Akritas, Dimitris N. Politis - 2003 - 512 pages theorems for the Wasserstein distance between the empirical and the true distributions, Markus Kirkilionis - 2003 - 419 pages The author uses the Wasserstein metric. He gets an evolution ... M2N.. Mathematical modelling and numerical analysis, Volume 37, Pages 1-556 One of these metrics is known as the Vasershtein distance [19,32]. ... The Vasershtein distance between n and v can be rewritten as the L2-distance of the Handbook of Algebra - Volume 3 - Page 196, 540 Michiel Hazewinkel - 2003 L. Vaserstein, On the stabilization of the general linear group over a ring, Math. USSR-Sb. 8 (1969), 383–400. L. Vaserstein, The stable range of rings and the dimension of topological spaces, Funktsional. Anal. i Prilozhen. 5 (1971), 17–27 (in 2004 33 books ### Recent Advances in the Theory and Applications of Mass Transport - Page 16, 17, 24, 97 Summer School on Mass Transportation Methods in Kinetic Theory and Hydrodynamics, September 4-9, 2000, Ponta Delgada, Azores, Portugal Volume 353 of Contemporary mathematics - American Mathematical Society Maria da Conceicao Vieira de Carvalho, ‎José-Francisco Rodrigues - 2004 P. Seppechere, Shape Optimization Solutions via Monge- Kantorovich, C.R.Acad.Sci. Paris ... Partial differential equations and Monge-Kantorovich mass transfer. ... [16] W. Gangbo, R.J. McCann, Shape recognition via Wasserstein distance. Interacting Particle Systems - Page 486 Thomas M. Liggett - 2004 Vasershtein, L. N. 1969 Markov processes over denumerable products of spaces, describing ... When I wrote this book twenty years ago, it was 486 Bibliography. Contractivity of Wasserstein-type distances: - Page title asymptotic profiles, equilibration rates and qualitative properties. File Format: PDF/Adobe Acrobat José A. Carrillo. Institucio Catalana de. Recerca i ... Paris 2004 Stochastic analysis and related topics in Kyoto: - Page 51 in honour of Kiyosi Itô Kiyosi Itō, H. Kunita, Shinzō Watanabe - 2004 to Ito Calculus, hence also to the problems originating from Physics, quantum chemistry, large deviations, etc. ... Note that inf { J(0) : 0 € E(p, v)} is the square of Wasserstein metric dj{(p,v) with respect to the Cameron-Martin space H. Any ... Markov processes and related fields - Volume 10 - Page 446 2004 The canonical choice for a d-sensitivity matrix is: C,j{f) = sup — , j<i, (4.11) and Cij(f) = 0 otherwise. Here || • ||d is the Vasserstein- Kantorovich- Rubin- o stein distance and ft ( • | £) is the restriction of each singleton measure to If d is the discrete ... 1 in terms of the law of the process Xt by introducing the Wasserstein distance Wk, k being a positive integer (see [1]). For k = 1, the Wasserstein distance W\ between two measures \i and v can be defined as the dual of the \.]\iP-norm: Wx{n,u) ... Remark 3.3 (Convergence in the Wasserstein distance Wk, k > 1). We can state the result of Proposition 3. 1 in terms of the law of the process Xt by introducing the Wasserstein distance Wk, k being a positive integer (see [1]). For k = 1, the ... Stochastic inequalities and applications - Page v, 33, 34, 278, 279 , 281, 283, 285, 287, 289, 293, 295 Evarist Giné, Christian Houdré, David Nualart - Springer, 2004 - 365 pages ISBN3764321970, 9783764321970 In the present paper we modify d(Fn, F) into a finite quantity for all F by an adaptation of the notion of trimming from statistics, and study the asymptotic distributions of these trimmed Wasserstein distances for appropriate classes of distribution ... Partial Differential Equations and Inverse Problems: - Page v, 144, 145, 147, 160, 161, 162, 163, 164, 170, 172, 186 Pan-american Advanced Studies Institute On Partial Differential Equations, Nonlinear Analysis And Inverse Problems, January 6-18, 2003, Santiago, Chil Issue 362 of Contemporary Mathematics Series Carlos Conca - American Mathematical Soc., 2004 - 410 pages ISBN0821834487, 9780821834480 More precisely, one can estimate the Wasserstein distance by computing directly the equation for the pseudo-inverse of the distribution function. This technique has been recently applied to general diffusion equations (see the review paper ... From Markov chains to non-equilibrium particle systems - Page 8, 173, 223, 542, 578, 586, 595 - 2004 - 597 pages 2nd edition Vallender, S. S.(1973), Calculation of the Wasserstein distance between probability distributions on line, Theory Prob. Ansgar Jüngel - 2004 - 192 pages Commun Math Phys 203: 667-706 [26] Vasershtein LN (1969) Markov processes on countable product space describing large systems of automata (in Russian). Summer School On Mass Transportation Methods In Kinetic Theory And Hydrodynamics, September 4-9, 2000, Ponta Delgada, Azores, Portugal Volume 353 of Contemporary Mathematics Series Maria da Conceição Vieira de Carvalho, José-Francisco Rodrigues - American Mathematical Soc., 2004 - 109 pages ISBN0821832786, 9780821832783 Wasserstein distance, Wasserstein metric Invited Talks from the ICIAM 2003 Congress James M. Hill, Ross Moore - SIAM, 2004 - 413 pages ISBN0898715598, 9780898715590 ... dissipative equations (porous medium equations, lubrication equations, limited flux diffusion equations, granular flow equations,...) were discovered to be gradient flows of some suitable functionals with respect to the Wasserstein distance. A modern treatment of this problem was initiated by Kantorovich in 1942, based on a probabilistic approach to reduce it to an infinite dimensional linear program. ... and the related concept of Wasserstein distance, as referred, for instance, in the recent book by Rachev and Riischendorf. Numerical mathematics and advanced applications: proceedings of Enumath 2003 - Page 574, 577 Miloslav Feistauer - 2004 - 863 pages Wasserstein distance Pierluigi Colli, Claudio Verdi, Augusto Visintin - 2004 - 346 pages Selected Papers of the International Conference on Operations Research (Or 2003) Heidelberg, September 3-5 2003 (Google eBook) Dino Ahr, Roland Fahrion, Marcus Oswald - 2004 - 490 pages Wasserstein metric Proceedings of the First JAMS Conference, Discrete Geometric Analysis, December 12-20, 2002, Sendai, Japan (Google eBook) Motoko Kotani, Tomoyuki Shirai, Toshikazu Sunada - 2004 - 258 pages Wasse rstein distance Dimacs Workshop, Unusual Applications of Number Theory, January 10-14, 2000, Dimacs Center (Google eBook) Melvyn B. Nathanson - 2004 - 264 pages Wasserstein Young measures on topological spaces: with applications in control theory and probability theory. (English) - Page vii, 77 Charles Castaing, Paul Raynaud de Fitte, Michel Valadier - 2004 - 320 pages Young measures on topological spaces. With applications in control theory and probability theory. (English) Mathematics and its Applications (Dordrecht) 571. Dordrecht: Kluwer Academic Publishers. xii, 320~p. (2004). MSC2000: *28-02 28A33 28C15, Reviewer: Riccardo De Arcangelis (Napoli) Parametrized Lévy-Wasserstein distances The space Lip^ef) can be ... 3.4. PARAMETRIZED LEVY-WASSERSTEIN DISTANCES 77. Balakrishnan, Calyampudi Radhakrishna Rao - 2004 - 795 pages Wasse rstein distances Functional analysis and its applications: - Page 46 Proceedings of the International Conference on Functional Analysis and Its Applications, Dedicated to the 110th Anniversary of Stefan Banach, May 28-31, 2002, Lviv, Ukraine, Issue 197 ladimir M. Kadet͡s͡, Wiesław Żelazko, Stefan Banach - Elsevier, 2004 - 326 pages ISBN0444513736, 9780444513731 Wasse rstein distances , Wolfgang Härdle, Yuichi Mori - 2004 - 1070 pages Australian Research Counci Centre of Excellence for Mathematics and Statistics of Complex Systems Anual Report 2004 pdf - Page 48 IMPROVED RESULTS ON POISSON PROCESS APPROXIMATION IN JACKSON NETWORKS Aihua Xia (Chief Investigator), Tim Brown (Australian National University) and Mark Fackrell (The University of Melbourne) Carl Clifton Faith - 2004 - 475 pages This answered a question of Handelman and Vasershtein, and the proof required a theorem of Vasershtein [71]. Mu-Fa Chen - 2004 When 7 is a distance, EX.y7(X«, Yt) is nothing but the Wasserstein metric W = W\ with respect to 7 of the distributions at time t. Discrete Geometric Analysis: - Page 147 The First JAMS Conference, Discrete Geometric Analysis, December 12-20, 2002, Sendai, Japan Motoko Kotani, Tomoyuki Shirai, Toshikazu Sunada - 2004 ISBN0821833510, 9780821833513 Let (X,d) be a crystal lattice with the graph distance d. ... 2-Wasserstein distance. Gakkōtosho, 2004 1.2 Gradient flow and Wasserstein distance The notion of gradient flow, or steepest descent, only has meaning when an appropriate metric is defined on the manifold. Consequently, a certain evolution problem can be given different gradient Otto proves in [21] that dm is equivalent to the Wasserstein distance of order two defined on M. We recall the definition of the Wasserstein distance of order p > 1 as found in [19]. For this purpose we introduce P(ui,U2) := < nonnegative Borel ... Dynamics and Randomness - Page 152, 193 Alejandro Maass, Servet Martínez, Jaime San Martín - 2004 We endow C^ with the uniform metric and P(C^) with the Vaserstein metric ( f i, v) = inf < / d(x, y) A l)R(dx, dy)\ R has marginals // and compatible with the topology of the weak convergence. Hence By Proposition 4.13, and (4.32) lim E (d (((T1, ... Seminar of Mathematical Analysis: - Page 117 proceedings, Universities of Malaga and Seville (Spain), September 2003-June 2004 Genaro López Acedo, Rafael Villa Caro - 2004 Lyubich, L. Vaserstein, Isometric imbeddings between classical Ba- nach spaces, cubature formulas, and spherical designs, Geom. Dedic. , 47 (1993), 327-362. 16] V.D. Milman, A Group Theory: Selected Problems - Page 30 B. Sury - 2004 ASIDE This proof is due to Vaserstein. Geometric Aspects of Functional Analysis: Israel Seminar 2002-2003 - Page 192 Vitali D. Milman, Gideon Schechtman - 2004 I., Vaserstein, L.N.: Isometric embeddings between classical Banach spaces, cubature formulas and spherical designs. Geom. Dedicata, 47, 327-362 (1993) [M] Milman, V.D.: A few observations on the connections between local theory and ... Richard Guy - 2004 Barry Cipra, Science, 239(1988) 464; and James Glieck, New York Times, 88-04-17. Rachel Gar-el k. Leonid Vaserstein ... Proceedings of the International Conference on Algebraic Groups and Arithmetic, Mumbai, 2001 - Page 30 S. G. Dani, Gopal Prasad, Tata Institute of Fundamental Research - 2004 Following the ideas of Bass, Milnor and Serre, L. Vaserstein proved this, by a case-by-case analysis, for most of the classical groups. In his first, and very important, paper [17] on the congruence subgroup problem, Raghunathan proved the ... 2004 and only if R/JCR) satisfies stable range one (see Vaserstein [7]) . Thus a ring R is u- nit semiregular if and only if R is a weakly unit-regular ring and idempotents can be lifted modulo J(i?) . The following lemma dues to [3, Lemma 3. 2005 27 items ### MICCAI 2005: - Page 153 James Duncan, ‎Guido Gerig - 2005 In the present work, the pure L2 Kantorovich-Wasserstein functional is proposed as the similarity measure. A modified energy functional penalizing the intensity change can also be implemented [12]. Other types of distance measures, e.g. ... ### Acta Academiae Aboensis: Mathematica et physica - Page 7, 18, 27 2005 A commonly used metric in the theory of iterated function systems is the so-called Wasserstein metric (Hutchinson metric, Kantorovich ... Definition 3 Define the generalized Wasserstein distance dw,a, 0 < a § 1 by dW',n(/1'1”) =52? fdll—/fd,\] ... ### Proceedings of the Twentieth National Conference onArtificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference - Page 934, 935 2005 Instead, we measure the difference in the spatial distributions of region projections using a higher dimensional metric, the Kantorovich-Wasserstein distance dw- Consider the reverse projections for two regions in SA: "<0 = "„,,,(•*») and tf(r,) ... New Trends in Mathematical Physics : In Honour of the Salvatore Rionero 70th Birthday Proceedings of the International Meeting Naples, Italy 24 - 25 January 2003 (2005, Hardcover) World Scientific Publishing Company, Incorporated ISBN-10: 9812560777 | ISBN-13: 9789812560773 J.A. Carrillo, G. Toscani, Wasserstein metric and large--time asymptotics of nonlinear diffusion equations, New Trends in Mathematical Physics, (In Honour of the Salvatore Rionero 70th Birthday), 234-244, 2005. Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré - 2005 V.Bogachev kindly pointed out to us that the correct spelling of the name Wasserstein should be “Vasershtein” [124] and that the attribution to Kantorovich and Rubinstein is much more correct. We kept the attribution to Wassertein and the Gradient flows in metric spaces and in the space of probability measures. (English) Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser. vii, 333~p. EUR~34.24 (2005). MSC2000: *35-02 49-02 49J40, Reviewer: Giuseppe Buttazzo (Pisa) Operator Algebras: Theory of C*-Algebras and von Neumann Algebras - Volume 13 - Page 501 Bruce Blackadar - 2005 Birkhauser Verlag, Basel, 2002. [Vas69] L. N. Vaserstein. On the stabilization of the general linear group over a ring. Math. USSR-Sb., 8:383-400, 1969. [vD82] Alfons van Daele. Celebration of Tomita's theorem. In Operator References 501. Joint International Meeting of the American Mathematical Society and the Indian Mathematical Society on Commutative Algebra and Algebraic Geometry, Bangalore, India, December 17-20, 2003 Vaserstein, LN..; Suslin, A.; Serre's problem on projective modules over polynomial rings, and algebraic A'-theory. L.N. Vaserstein also gave an alternative approach to the Local-Global analysis by a ... Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians - Page 211 Steven George Krantz - 2005 One need only imagine the three of them, often fully clothed, laid out side by side. j/Wathematician Leonid Vaserstein ... One day there was a seminar being given by a mathematician who had heard nothing of Vaserstein's emigration; but the ... Current trends in potential theory: - Page 60 conference proceedings, Bucharest (Romania), September 2002 and 2003 Dominique Bakry - 2005 measurable pseudometric, ... We also mention the deep study [10] of the L2 -Wasserstein metric on abstract Wiener spaces related to transportation ... Kinetic methods for nonconservative and reacting systems - Page 169, 225, 234 Gíuseppe Toscani - 2005 The decay of Wasserstein metric for 7 > 0 We will start the analysis of ... Eigenvalues, inequalities, and ergodic theory - Page 23, 28, 35, 171 , 215, 220, 221, 222 Mufa Chen - Springer 2005 - 228 pages ISBN1852338687, 9781852338688 Wasserstein distance Michel Denuit - 2005 - 440 pages 9.6 Wasserstein distance Haim Brézis, Catherine Bandle - 2005 - 470 pages RN) as follows: for any number p > 0 we define the Wasserstein distance dp between two probability measures Mi, ^ by the ... Edward C. Waymire, Jinqiao Duan - 2005 - 262 pages Jean-Dominique Deuschel, Andreas Greven - 2005 - 450 pages The space P(M) will always be equipped with the Lθ-Wasserstein distance. . Seminaire de Probabilites: Volume 38 - Page 320, 322, 324, 333 M Emery, Michel Ledoux, Marc Yor - 2005 - 392 pages Wasserstein distance A. D. Barbour, Louis Hsiao Yun Chen - 2005 - 225 pages However, no "magic factors" as good as those in Theorem 2.3 are known. If the total variation distance is replaced by the Wasserstein ^-metric ... ... being of order 0(1) (Arratia, Goldstein & Gordon 1989; Barbour, Hoist & Janson 1992, p. 203). With respect to a more natural Wasserstein distance between point processes, uniform bounds of order 0(X~1cx) for the second differences can ... Séminaire sur les équations aux dérivées partielles - Page VE-17 la fonctionnelle H de Boltzmann : H(fi) = / / log / dvol, où f est la densité de H par rapport au volume ; - la distance de Wasserstein quadratique : W^^i, u) = \/C^JJi^ Giannessi, A. Maugeri - 2005 - 1184 pages Kinderlehrer, D. and Walkington, N. (1999) Approximation of parabolic equations based upon Wasserstein's variational ... , W. T. Ziemba - 2005 - 709 pages Philpott, Henderson, and Teirney [13] discuss an alternative approach based on Vasershtein coupling (see [10]), but this is shown to produce unrealistic weather Applied combinatorics on words: Volume 105 - Page 351, 352 M. Lothaire - 2005 - 610 pages Wasserstein distance Friedrich Ischebeck, Ravi A. Rao - Springer 2005 - 336 pages ISBN3540230327, 9783540230328 4.5 Vaserstein's Proof of Serre's Conjecture Quillen's proof of Serre's conjecture does not use the fact that projective ... But using this fact and Quillen's ideas, one obtains a remarkably short proof of Serre's conjecture, as L.N. Vaserstein wrote ... 4.5 Vaserstein's Proof of Serre's Conjecture Quillen's proof of Serre's conjecture does not use the fact that projective ... But using this fact and Quillen's ideas, one obtains a remarkably short proof of Serre's conjecture, as L.N. Vaserstein wrote ... Anastasios Mallios - 2005 - 293 pages Remark] as well as L.V. Vaserstein [1]) can be applied instead, all these spaces having the desired property (viz. the Serre-Swan theorem is in force) as before. V.Bogachev kindly pointed out to us that the correct spelling of the name Wasserstein should be “Vasershtein” [124] and that the attribution to Kantorovich and Rubinstein is much more correct. We kept the attribution to Wassertein and the Gradient flows in metric spaces and in the space of probability measures. (English) Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser. vii, 333~p. EUR~34.24 (2005). MSC2000: *35-02 49-02 49J40, Reviewer: Giuseppe Buttazzo (Pisa) Wasserstein metric - Page title [PDF] from psu.eduF Otto… - 2005 - Citeseer Abstract. We consider the porous medium equation on a compact Riemannian manifold and give a new proof of the contraction of its semigroup in the Wasserstein distance. This proof is based on the insight that the porous medium equation does not increase the size of ... Methods and applications of analysis - Volume 12 - Page 203 Project Euclid - 2005 This sequence converges weakly, because our distance functional is stronger than the Kantorovich-Waserstein metric which induces the topology of weak convergence on spaces of measures. Therefore, fi„ — UNIQUENESS FOR THE ... 2006 36 books ### Recent Trends in Partial Differential Equations: - Page 17, 19, 31 UIMP-RSME Santaló Summer School, July 12-16, 2004 Universidad Internacional Menéndez Pelayo, Santander, Spain Juan Luis Vazquez, ‎Xavier Cabré, ‎José Antonio Carrillo - 2006 Optimal transport and Wasserstein distance ### Eigenvalues, Inequalities, and Ergodic Theory - Page 172, 215, 220, 221, 228 Mufa Chen - 2006 Uniqueness of Gibbs states and the L2-convergence of infinite-dimensional reflecting diffusion processes. Sci. Sin. Ser (A) ... On order preservation for couplings of multidimensional diffusion processes. Chinese J. ... L. N. Wasserstein. Markov ... Ischia Group Theory 2004: Proceedings of a Conference in Honor of Marcel Herzog, March 31-April 3, 2004, Naples, Italy - Page 209 Israel mathematical conference proceedings, ISSN 0792-4119EditorsZvi Arad, Marcel HerzogEditionillustrated Publisher American Mathematical Soc., 2006 ISBN0821887033, 9780821887035 263 pages Proofs using Coupling Techniques A. Coupling Lemma For each fixed x, y € X, let ps(-|x, y) be an optimal coupling of the update rules pg( |x) and ps(-|y) that achieves the Wasserstein distance W(pB(-|x),pB(-|y))- We call the family {ps( |x,y)} the ... Problems on Mapping Class Groups and Related Topics - Page 36 Benson Farb - 2006 ... useful ingredient is a theorem of Grunewald-Mennike-Vaserstein [GMV] which gives free quotients of arbitrarily high rank for the group SL2(Z[i]) and the group SL2(A'[s,i]), where K is an arbitrary finite field. Since we know for g > 3 that Ig is ... Tutorials in Operations Research: Models, Methods, and Applications for Innovative Decision Making I N F O R M S: Institute for Operations Research & the Management Sciences, Michael P. Johnson, Bryan Norman - 2006 ... for Innovative Decision Making I N F O R M S: Institute for Operations Research & the Management Sciences, Bryan Norman Michael P. Johnson ... Wasserstein (Kantorovich) Metric Suppose Q is a metric space with metric d. dw(P,P) = sup< ... ISBN1877640204, 9781877640209 Encyclopedia of Actuarial Science Hermann Thorisson Published Online: 15 SEP 2006 Coupling - Wiley Online Library Compstat 2006 - Proceedings in Computational Statistics 17th Symposium Held in Rome, Italy, 2006 Alfredo Rizzi, Maurizio Vichi ISBN: 978-3-7908-1708-9 Chapter Dynamic clustering of histograms using Wasserstein metric IRPINO A, VERDE R, LECHEVALLIER Y Dependence in Probability and Statistics - Page 156 Patrice Bertail, Paul Doukhan, Philippe Soulier - 2006 Academic Press, Harcourt Brace Jovanovich Publishers, New York, 1980. Probability and Mathematical Statistics. ... The Wasserstein distance and approximation theorems. Zeitschrift für Wahrscheinligkeits Theorie und Verwandte Gebiete, ... Advances in Database Technology -- EDBT 2006: - Page 866 10 International Conference on Extending Database Technology, Munich, Germany, 26-31 March 2006, Proceedings (Google eBook) Yannis Ioannidis, Marc H. Scholl, Joachim W. Schmidt - 2006 ISBN3540329609, 9783540329602 Earlier works (e.g., [6,7]) call it the match distance, and statistics literature uses Mallows or Wasserstein ... Quantum probability - Page 199, 206 Marek Bożejko, Wojciech Młotkowski, Janusz Wysoczański - 2006 and the Wasserstein distance are useful distances between measures. . Ph. Biane and D. Voiculescu, A free probabilistic analogue of the Wasserstein metric on the trace-state space, Geom. John Clark - 2006 , 2008 Some of the basic properties of stable range 1 appear first in [35], in Vaserstein's [350], [351], and in notes by Kaplansky [187]. The proof of the symmetry of the condition in 15.4 is taken from Goodearl's [129] and, as he says, is adapted from ... T.Y. Lam - 2006 Our exposition of Vaserstein's elementary proof follows the lecture notes of Ferrand's Bourbaki talk [Ferrand: 1976]. ... In the literature, this proof of Serre's Conjecture has sometimes been fondly referred to as "Vaserstein's 8-line proof" (see, ... Topics on Concentration Phenomena and Problems with Multiple Scales - Page 291 Andrea Braides, Valeria ChiadÚ Piat - 2006 Ambrosio, L.; Gigli, N.; Savare, G. Gradient flows in metric spaces and in the Wasserstein spaces of probability measures, Birkhaüser, 2005. 2. ... X. Generation and propagation of interfaces for reaction-diffusion equations, J. Diff. Eq. 96 ... Analysis, Modeling and Simulation of Multiscale Problems - Page 361 Alexander Mielke - 2006 Semiconductor simulations using a coupled quantum drift-diffusion Schrödinger-Poisson model. SIAM J. Appl. Math. ... A fourth-order nonlinear PDE as gradient flow of the Fisher information in Wasserstein spaces. In preparation, 2006. Diffusion, quantum theory, and radically elementary mathematics - Page 243 William G. Faris - 2006 ... 28 optimal, 141-154 Trotter product formula, 76, 85 twelve-tone row, 215 ultracontractive, 59 variance, 36 Wasserstein distance, 144 Wasserstein space, 149 wave function, 6, 1 1 8 Wick power, 20, 26, 39, 82 Wick product, 39 Wiener bridge, ... DCDS-B - Volume 6, Pages 1-649 - Page 311 Weak topology implicit schemes based on Monge-Kantorovich or Wasserstein metrics have become prominent for their ability to solve a variety of diffusion and diffusion-like equations. They are very flexible, encompassing a wide range of ... Functional Inequalities Markov Semigroups and Spectral Theory - Page 292 Fengyu Wang - 2006 ... inf dn, 1( ) 7r€(€(/H/) EXEP which is well-known in probability theory as the L1-Wasserstein distance between /.7 and 1/. ... In the smooth case the Dirichlet form of the diffusion process generated by div(AV) + AVV, which is symmetric in L2(p), Groups, Rings And Group Rings - Page 136 L.N. Vaserstein, The structure of classic arithmetic groups of rank greater than One, Math. USSR Sbornik 20 (1973), Markov processes and related fields: Volume 12 Polymat, 2006 Handbooks in Operations Research And Management Science: Shane G. Henderson, Barry L. Nelson - 2006 - 678 pages Wasserstein metric Recent trends in partial differential equations: - Page vii, 1,2, 11, 16, 17, 18, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32 UIMP-RSME Santaló Summer School, July 12-16, 2004 Universidad Internacional Menéndez Pelayo, Santander, Spain Juan Luis Vázquez ISBN0821838911, 9780821838914 The Wasserstein distance arises as a powerful tool to analyze the asymptotic behaviour of solutions of PDE's of diffusion type, to obtain new general proofs of geometric and functional inequalities and to characterize solutions of shape ... Nonsmooth mechanics and analysis: theoretical and numerical advances - Page 14 , 16, 18, 19, 20, 320 Alart, O. Maisonneuve, R. Tyrrell Rockafellar - 2006 - 320 pages Wasserstein distance Michael J. P. Cullen - Imperial College Press, 2006 - 259 pages ISBN186094518X, 9781860945182 Ching-Zong Wei, Hwai-Chung Ho, Ching-Kang Ing - 2006 - 294 pages To measure the error of approximation, we use Wasserstein pseudo-metric which has the advantage of allowing us to lift the carrier space to a bigger carrier space. Of course, other metrics such as the total variation distance can also be ... Dictionary of distances - Page 29, 98, 188, 267, 384, 391 M. Deza Elena Deza, - 2006 - 391 pages he state space of any unital C *-algebra) of the Kantorovich— Mallows—Monge—Wasserstein metric defined as the Lipschitz ... Let the commutator [D, f] for f G A be the Clifford multiplication by the gradient V f so that its operator norm ||. Gianni Dal Maso, Antonio DeSimone, Franco Tomarelli - 2006 - 159 pages ... path functionals over Wasserstein spaces, variational approaches to quasi- … systems Giuseppe Buttazzo (Universit`adiPisa) Path functionals over Wasserstein spaces Antonin Chambolle Data science and classification - Page , 183, 189, 191, 355 International Federation of Classification Societies. Conference, Vladimir Batagelj - Springer 2006 - 358 pages ISBN3540344160, 9783540344162 Wasserstein based 17th Symposium Held in Rome, Italy, 2006 lfredo Rizzi, Maurizio Vichi - 2006 - 537 pages Wasserstein metric Peter Topping - 2006 - 113 pages Wasserstein metric Giuseppe Da Prato, Luciano Tubaro - 2006 - 347 pages In Section 12.5, the results from previous sections are applied to stochastic reaction- diffusion equations. ... norm intermediate between the total variation metric and Wasserstein metric has been obtained for stochastic Navier–Stokes equation. Handbook of differential equations: evolutionary equations - Page v, 1, 4, 5, 6, 7, 8, 13, 14, 29, 30, 38, 40, 45, 46, 52, 55, 58, 80, 81, 104, 105, 106, 107, 109, 113, 115, 116, 117, 120, 122, 123, 131, 134, 135, 136, 634, 638 Constantine M. Dafermos, Eduard Feireisl - Elsevier, 2006 - 652 pages ISBN0444528482, 9780444528483 J.A. Carrillo, R.J. McCann and C. Villani, Contractions in the 2-Wasserstein space and thermalization of granular media, Arch. Ration. Mech. Anal. (2006). In this way we recover in a more general framework the Riemannian interpretation of the Wasserstein distance developed by Otto in [74] (see also [57,73]) and used to study the long time behavior of the porous medium equation. In the original ... Journal de mathématiques pures et appliquées Joseph LiouvilleGauthier-Villars, 2006 Wasserstein DCDS-B: Volume 6, Pages 1-649 - Page 311, 313, 325 Wasserstein metric, Wasserstein space 44th Annual Allerton Conference on Communication, Control, and Computing 2006 Proceedings: Volume 44, Part 2 - Page 913, 915, 917 Wasserstein coupling 3rd SUMMER SCHOOL ON ''METHODS AND MODELS OF KINETIC THEORY'' (M&MKT 2006) Porto Ercole (Grosseto, Italy) June 4-10, 2006 Large time asymptotics for nonlinear diffusion and kinetic equations José A. Carrillo The main goal of this course is to give an overview of the recent ideas of contractivity of Wasserstein and Fourier-type distances applied to the asymptotic behavior of nonlinear diffusion, scalar conservation laws and granular flow models based on kinetic equations with inelastic interactions. Program: 1. Basics of the Wasserstein distance & Model equations: nonlinear diffusions and homogeneous inelastic kinetic equations; description of models and main formal properties of their solutions; contractivity for 1-D models: consequences on qualitative properties of the solutions. 2. Gradient flows for the euclidean Wasserstein distance: asymptotic behavior for nonlinear diffusions and simplified homogeneous inelastic kinetic models; formal ideas behind gradient flows; contractivity in several dimensions; quantified displacement convexity and decay rates; entropy method versus mass transportation method for large time asymptotics. 3. Large time asymptotics for general nonlinear diffusion equations and scalar conservation laws: asymptotic profiles and identification of universal behavior; applications to the large time asymptotics of scalar conservation laws with integrable bounded positive initial data and decay rates towards N-waves. 4. Contractivity for the inelastic Boltzmann equation: Wassertein and Fourier-based metrics: conditions for being "equivalent"; contractivity of Wasserstein and Fourier-based distances for the inelastic homogeneous Boltzmann operator in the maxwellian approximation; existence, uniqueness, nonlinear asymptotic stability and decay rates for diffusive equilibria and homogeneous cooling states. Lecture 1: Main Models & Basics of Wasserstein Distance File Format: PDF/Adobe Acrobat - Quick View Presentation of models. Wasserstein Distance: Basics. Contractivity in 1D. Lecture 1: Main Models & Basics of. Wasserstein Distance. J. A. Carrillo ... 2007 29 books ### Financial optimization - Page 262, 265, 266 Hercules Vladimirou - 2007 3.2 Kolmogorov-Smirnov (Uniform) distance Besides the moment matching method, a common approach is to ... 3.3 Wasserstein distance and the facility location problem Due to the Kantorovich-Rubinstein theorem (Section 2.2.1) the problem ... ### Variational Analysis and Applications - Page 498 F. Giannessi, ‎A. Maugeri - 2007 The novelty in our development is that the dynamical process is set in a weak topology as described by a Kantorovich-Wasserstein metric. This owes in part to a result of Brenier and Benamou, [3]. It illustrates the feasibility of mesoscale ... On Conformal Field Theories, Discrete Groups and Renormalization, Volume 2 of Frontiers in Number Theory, Physics, and GeometryEditorsPierre Cartier Publisher Springer, 2007ISBN3540303081, 9783540303084 817 pages Entropy Methods for the Boltzmann Equation: - Page 47 Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001, Issue 1916 Fraydoun Rezakhanlou, Cédric Villani, François Golse - Springer 2007 in particular ^2(Q+(/, /),M) < W(/,M). Here VK2 is the (improperly called) Wasser- stein distance with exponent 2 W2(f ... 0(e-(A-°)*). (A = spectral gap of the Discrete and continuous dynamical systems: Series B. - Volume 8, Pages 529-1026 - Page 877 [11] U. Gianazza, G. Savar6 and G. Toscani, The Wasserstein gradient flow of the Fisher information and the quantum drift- diffusion equation, Preprint, Universita di Pavia, Italy, (2006). [12] M. P. Gualdani, A. Jiingel and G. Toscani, A nonlinear ... Topological algebras and applications: - Page 7, 8, 14 5th International Conference on Topological Algebras and Applications, June 27-July 1, 2005, Athens, Greece, Volume 10 Volume 427 of Contemporary mathematics - American Mathematical Society Anastasios Mallios, Marina Haralampidou - 2007 ISBN0821838687, 9780821838686 442 pp Amer. Math. Soc. 105 (1962), 264-277. [13] L. N. Vaserstein, Vector bundles and projective modules, Trans. Am. Math. Soc. 294 (1986), no. 2, 749-755. OPERATIONS RESEARCH, jilid 1 - Page 71 Operation Research jilid 1 / Siswanto -- Jakarta , Erlangga , 2007. xii , 428 hal; 26 cm. ISBN, : 9789797818357. Lokasi, : Perpustakaan Kementerian Keuangan ... Vaserstein, Leonid Nison, Introduction to Linear Programming, Prentice Hall, New Jersey 2003. Certain Number-Theoretic Episodes In Algebra - Page v R. Sivaramakrishnan - 2007 He has also extended this result to a residue class ideal of a number ring. Mn(Z) denotes the ring of n×n matrices with entries from Z. L. N. Vaser- stein has shown that given an integer p and A M2(Z), one can find matrices X,Y M2(Z) such ... Алгебра и анализ: - Volumes 1-3; Volume 19 - Page 50 Paris Ser. A-B 283 (1976), A693-A695. Vaserstein L. N., On the normal subgroups of the GL„ over a ring, Algebraic ... Vaserstein L. N., Normal subgroups of orthogonal groups over commutative rings, Amer. J. Math. 110 (1988), no. 5, 955-973. First International Conference, SSVM 2007, Ischia, Italy, May 30 - June 2, 2007 : Proceedings Fiorella Sgallari, A Murli, Nikos Paragios - ISBN3540728236, 9783540728238 931 pp To overcome this issue, we propose to use the Wasserstein distance (Monge-Kantorovich distance) to compare ... Gröbner Bases in Control Theory and Signal Processing - Page 105 L. N. Vaserstein and A. A. Suslin, Serre's Problem on projective modules over polynomial rings and algebraic if-theory, Math. USSR Izviestija ... Combinatorics and Probability - Page 82 Graham Brightwell, Imre Leader, Alex Scott - 2007 References [1] Arratia, R. (1996) Independence of prime factors: total variation and Wasserstein metrics, insertions and deletions, and the ... 51 800–832. [14] In Honor of the 65th Birthday of Antonio Greco, Palermo, Italy, 5-7 June 2006 Tommaso Ruggeri, Marco Sammartino - 2007 - 216 pages Eustasio Del Barrio, Paul Deheuvels, Sara A. Geer - 2007 - 254 pages 5. Tests based on Wasserstein distance Dirk Blömker - World Scientific, 2007 - 126 pages ISBN9812706372, 9789812706379 E. Diday, Paula Brito, Patrice Bertrand - 2007 - 634 pages Surveys in differential geometry: metric and comparison geometry - Page 233, 237, 240 Jeff Cheeger, Karsten Grove - 2007 - 347 pages Wasserstein distance Juan Luis Vázquez - 2007 - 624 pages The idea proposed by F. Otto [413] sees the HE, the PME and other nonlinear diffusion equations as gradient flows in a space of measures endowed with a convenient metric given by the Wasserstein distance, a tool developed in probability ... Madrid, August 22-30, 2006, Volume 1 Marta Sanz Solé - 2007 - 4500 pages Amer Mathematical Society If we replace the exponent 2 by p e [1 , oo] in the Wasserstein formula (13), we get the Wasserstein non-quadratic distances. ... Wasserstein distance Fabio Ancona - 2007 - 404 pages Wasserstein-metric-based, Wasserstein distance Michael Griebel, Marc Alexander Schweitzer - 2007 - 306 pages Wasserstein distance Festschrift in Honor of Giorgio Picci on the Occasion of His Sixty-Fifth Birthday Alessandro Chiuso, Augusto Ferrante, Stefano Pinzoni - 2007 - 355 pages celebrating Béla Bollabás's 60th birthday Papers presented at the conference "Combinatorics in Cambridge," held in Cambridge, Aug. 4th-7th, 2003 edited by Graham Brightwell, Imre Leader, Alex Scott, Andrew Thomason - Cambridge University Press, 2007 - 633 pages ISBN0521872073, 9780521872072 Wasserstein distance, Wasserstein metrics Dynamics in models of coarsening, coagulation, condensation and quantization - Page 39 Weizhu Bao, Jian-Guo Liu - 2007 - 294 pages Applications to Gases, Semiconductors, Photons, and Biological Systems Carlo Cercignani, Ester Gabetta - 2007 - 271 pages Perspectives in nonlinear partial differential equations: in honor Haïm - Page 482 Henri Berestycki - 2007 - 495 pages . L. Ambrosio, N. Gigli, G. Savare, Gradient Flows in Metric Spaces and in the Wasserstein Spaces of Probability Measures, Birkhaiiser, (2005). . August GutzmerGeorg Reimer, 2007 Handbook of Linear Algebra - Page 49-18 ... Holmes and T. Y. Tarn 68-1 69 Nonassociative Algebras Murray R. Bremner, Lucia I. Murakami, and Ivan P. Shestakov 69- 1 70 Lie Algebras Robert Wilson 70-1 Applications to Optimization 50 Linear Programming Leonid N. Vaserstein 50- MR2279160 (2007j:15001) Handbook of linear algebra. Edited by Leslie Hogben. Associate editors: Richard Brualdi, Anne Greenbaum and Roy Mathias. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2007. xxx+1370 pp. ISBN: 978-1-58488-510-8; 1-58488-510-6, 15-00 (00A20) Vladimir Igorevich Bogachev - 2007 - 575 pages 52, 455] [1919] Vasershtein L.N. Markov processes over denumerable products of spaces describing large system of automata. Probl. Peredaˇci Inform. 1969. 2008 35 books ### COMPSTAT 2008: Proceedings in Computational Statistics - Page vii, 76, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88, 89, 561 Paula Brito - 2008 Comparing Histogram Data Using a Mahalanobis–Wasserstein Distance ### Scenarios for Risk Management and Global Investment Strategies - Paga x, xvii, 256, 270, 273, 315 Rachel E. S. Ziemba, ‎William T. Ziemba - 2008 Figure 26.4 Approximation of a t-distribution with a Kolmogrov-Smirnov distance on the left and the Wasserstein distance measure on ... ### Kazhdan's Property (T) - Page 465 Bachir Bekka, ‎Pierre de la Harpe, ‎Alain Valette - 2008 [Vaser–68] L.N. Vaserstein. Groups having the property (T). Funct. Anal. Appl., 2:174, 1968. [Vaser–88] L.N. Vaserstein. Reduction of a matrix depending on parameters to a diagonal form by addition operators. Proc. Amer. Math. Soc, 103:741– ... ### Proceedings - Volume 11 - Page 37, 39 Association for Computing Machinery, 2008 Finally, we compare fixed-PRR links of the various simulation methods to the Kantorovich-Wasserstein distance on conditional packet delivery functions (CPDFs). CPDFs describe packet delivery probability given n consecutive successes or ... The Essence of Ricci Curvature - Page 15 Colin Douglas Hinde - 2008 Let W2(M,m) = (W2(M,m),dw) be the L2-Wasserstein space of probability measures on M absolutely continuous with respect to m ... If no, fii E W2{M, m) the distance between them has ^(^0,^1) = fMxMd2(p,q)du where u, an optimal coupling, ... Abstracts of papers presented to the American Mathematical Society - Volume 29 - Page 507 Some probabilistic and topological properties of the free quantum orthogonal group A0(n). The free ... Our proof involves obtaining an Otto-Villani type estimate on the Biane-Voiculescu-Wasserstein distance for free diffusion starting at the ... Efficient Transient Noise Analysis in Circuit Simulation - Page 144 Thorsten Sickenberger - 2008 A class of Wasserstein metrics for probability distributions. Michigan Math. ... Sixth quantum 1/F noise and other low frequency fluctuations in electronic devices, volume 371 of AIP conference proceedings, Woodbury, 1993. American Institute ... Finite Fields and Applications: - Page 61, 77 Eighth International Conference on Finite Fields and Applications, July 9-13, 2007, Melbourne, Australia Gary L. Mullen, Daniel Panario, Igor E. Shparlinski - 2008 Volume 461 of Contemporary mathematics - American Mathematical Society [22] L.N. Vaserstein. Waring's problem for algebras over fields, J. Number Theory 26 (1987). 286-298. [23] L.N. Vaserstein, Ramsey's Theorem and Waring's Problem, in The Arithmetic of Function Fields (eds D. Goss and al), de Gruyter. Intro To The Theory Of Numbers 6E - Page 449 Godfrey Harold Hardy, Edward M. Wright, David Rodney Heath-Brown - 2008 Vaserstein has shown that ν(8) 28 (J. Number Theory 28 (1988), 66–68), and A. Choudhry has proved that ν(7) 12 (J. Number Theory 81 (2000), 266–9). Both conclusions depend on the existence of remarkable polynomial identities too ... Variational PDE-based image segmentation and inpainting with Applications in Computer Graphics, 35 Kang-Yu Ni, University of California, Los Angeles - ProQuest, 2008 120 pp ISBN0549980636, 9780549980636 The optimal transport distance, commonly called the Wasserstein distance with exponent p, is Wp(p, v) = Tp(n, v)1/p. ... The goal of this work is to understand low-order feature segmentation, which is based on the statistics of image intensity ... Compstat: Proceedings in Computational Statistics 2008 - Page 88 Paula Brito - 2008 Proceedings in Computational Statistics 2008 Paula Brito. of histogram data. The Mahalanobis–Wasserstein distance and the proposed interdependency measures between histogram variables can be considered as new useful tools for ... Wasserstein Space Over the Wiener Space Shizan Fang, Jinghai Shao, Karl-Theodor Sturm - 2008 Séminaire de Probabilités XLI - Page 131, 370 Catherine Donati-Martin, Michel Émery, Alain Rouault - 2008 Wasserstein. distance. F. Bolley Ecole Normale Sup ́erieure de Lyon, A Level-set Method for Solving Elliptic Eigenvalue Problems on Hypersurfaces, And, Finite-time Blow-up of L(infinity) Weak Solutions of an Aggregation Equation - Page 51 Jeremy Brandman - 2008 Global-in-time solutions of (2.1), with the addition of a density-dependent diffusion used to model repulsion, were studied ... by viewing solutions as gradient flows in the Wasserstein metric and long-time behavior of solutions was also studied. Probability theory: a comprehensive course - Page 384 Achim Klenke - 2008 - 616 pages Wasserstein metric , Stephen P. Boyd, Hidenori Kimura - 2008 - 277 pages Wasserstein distance Philippe Blanchard, Dimitri Volchenkov - 2008 - 181 pages Wasserstein distance Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré - 2008 - 334 pages E. A. Carlen and W. Gangbo, Constrained steepest descent in the 2- Wasserstein metric, Ann. of Math. ... Gradient flows in metric spaces and in the space of probability measures. 2nd ed. (English) Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser. vii, 334~p. (2008). MSC2000: *35-02 49-02 49J40 Wasserstein distances; 18th Symposium Held in Porto, Portugal, 2008 Paula Brito, COMPSTAT 18, 2008, Porto, International Association for Statistical Computing - 2008 - 571 pages Wasserstein distance Transition from Microscopic to Macroscopic Equations Peter Kotelenez - 2008 - 458 pages Wasserstein distance Proceedings of an International Workshop Held at Rockefeller Foundation's Bellagio Conference Center, Milan, Italy 2006 Approximation of parabolic equations based upon Wasserstein's variational principle, Statistical advances in the biomedical sciences: - Page 268 Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics Atanu Biswas - 2008 - 582 pages Atanu Biswas, Sujay Datta, Jason P. Fine, Mark R. Segal Wiley, Dec 14, 2007 - 640 pages Bayesian inference and maximum entropy methods in science and engineering - Page 61, 62 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Boracéia, São Paulo, Brazil, 6-11 July 2008 Marcelo de Souza Lauretto, Carlos Alberto de Bragança Pereira, Julio Michael Stern - 2008 - 384 pages Anirban DasGupta - 2008 - 722 pages Kolmogorov's zero-one law, 6 Kolmogorov and Wasserstein metrics, ... 536–537 infinite-order kernels, 537 kernel density estimation consistency of, 533–535 ... Proceedings of the 8th International Flins Conference : Madrid, Spain, 21-24 September2008 Da Ruan, Javier Montero, Jie Lu - 2008 - 1173 pages Ravindra Khattree, Dayanand N. Naik - 2008 - 408 pages Wasserstein metric Proceedings of the 31st Annual Conference of the Gesellschaft für Klassifikation e.V., Albert-Ludwigs-Universität Freiburg, March 7-9, 2007 Christine Preisach, Hans Burkhardt, Lars Schmidt-Thieme - 2008 - 719 pages Last row: Corrected Rand Index (CRI) of the obtained partition compared with the expert partition c L2 Wasserstein Adaptive L2 HausdorffL1 distance ... Mathematical models of granular matter - Page 70 Gianfranco Capriz, Pasquale Giovine, Alain Barrat - 2008 - 212 pages Wasserstein distance Joint Projects Between Universities and Industry 2004-2007 (Google eBook) Willi Jäger, Hans-Joachim Krebs - 2008 - 357 pages Wasserstein metric Peter Mörters - 2008 - 336 pages Wasserstein distance Centro Stefano Franscini, Ascona, May 2005 Robert C. Dalang, M. Dozzi, Francesco Russo - 2008 - 519 pages A stochastic spatial model for invasive plants and a general Theory of Monotonicity for Interaction Map Particle Systems The coupling to follow is essentially the same as the Vasershtein coupling[37] given for spin systems, also known as the basic coupling [23]. An introduction to sequential dynamical systems - Page 242 Henning S. Mortveit, Christian M. Reidys - 2008 - 248 pages 26. L. N. Vasershtein. Markov processes over denumerable products of spaces describing large system of automata. Statistical Models and Methods for Biomedical and Technical Systems - Page 188 Filia Vonta, Mikhail. Nikulin, Nikolaos. Limnios - 2008 We consider the Kantorovich metric (one of the most-used Vasserstein metrics) /c(/ii, H2) [see Kantorovich (1942)], Алгебра и анализ - Volumes 4-6; Volume 20 - Page 161 2008 Сходным образом в случае нерасщепимых классических групп над кольцами Васерштейн [28, 29] определил элементарную подгруппу как подгруппу, порождённую всеми трансвекциями Эйхлера-Зигеля-Диксона. 2009 33 books ### DCDS-A - Volume 24, Pages 1-651 - Page 66 2009 3.1. Wasserstein distances. Let us denote by P(RN) the set of probability measures. Given two probability measures f,g & P(RN), the Euclidean Wasserstein Distance is defined as W2(f,g)= inf •(// \v-x\2<m(v,x)\ ' (25) where II runs over the set of ... ### Differential Equations - Geometry, Symmetries andIntegrability: - Page 49, 51, 57 The Abel Symposium 2008 Boris Kruglikov, ‎Valentin Lychagin, ‎Eldar Straume - 2009 By construction, when Prob (resp. Diff) is endowed with the Otto (resp. Arnol'd) metric, the map Vi becomes a Riemannian submersion (see e.g. [C-E75, pp. 65-68], [FIP04] and references therein). 3.5 The L2 Wasserstein Distance Given (y, v) e ... ### Probability, Random Processes, and Ergodic Properties - Page 272 Robert M. Gray - 2009 The problem of (9.3) is widely known as the Monge/Kantorovich optimal transportation or transport problem, and when the ... of Vasershtein, Wasserstein, also caught on as a suitable name for the Monge/Kantorovich distance and remains so. The 12th International conference on information fusion Seatle 6-9 July 2009 Information Fusion, 2009. FUSION '09. 12th International Conference on IEEE Conference Publications 2009 Wasserstein distance for the fusion of multisensor multitarget particle filter clouds [PDF] from isif.orgD Danu, T Kirubarajan… - Information Fusion, 2009. …, 2009 - ieeexplore.ieee.org 12th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 2009 Abstract In a multisensor multitarget tracking application, the evaluation of the cost of assigning particle filter clouds of different sensors as being estimates of the same target is an essential part in the particle cloud association. This paper treats the problem of ... Modern Differential Geometry in Gauge Theories: Yang-Mills Fields - Volume 2 - Page 107 Anastasios Mallios - 2009 481, Theorem 4.2], as well as L.N. Vaser- stein [1]. Yet, setting (5.28) A CAX in (5.27), one then obtains, by the very definitions, (5.29) CMn(A)X = Mn(CAX) Mn(A), so that we can still write (5.27) in the form (5.30) EfA(X)EfMn(A)(X), ... Jul 16, 2009 – This book is devoted to the theory of probabilistic information measures and their application ...... Breiman's and Billingsley's approach requires the martingale convergence theorem ...... Levenshtein [95] and Vasershtein [146] ... - Page 846 on Computational and Mathematical Methods in Science and Engineering Gijón (Asturias), Spain June 30, July 1-3, 2009 . Editor J. Vigo-Aguiar The Kantorovich-Wasserstein distance between ρ0 and ρ1 verifies: d2(ρ0,ρ1) = ... Transport Equations for Semiconductors - Page 273 Ansgar Jüngel - 2009 The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. To appear in Arch. Rat.Mech. Anal., 2009. 263 24. A. J ̈ungel With Applications to Financial Mathematics and Risk Theory Dmytro Gusak, Alexey Kulik, Yuliya Mishura - 2009 -Springer, 2010- 375 pages ISBN0387878629, 9780387878621 Wasserstein metric Probability, Random Processes, and Ergodic Properties - Page x, xxxiii, 272, 315 - 2009 - 322 pages - In the optimal transportation literature, the German spelling of Vasershtein, Wasserstein, Differential equations: geometry, symmetries and integrability : - Page , iii, vii, viii, 1, 2, 9, 19, 20, 21, 22, 23, 25, 26, 27, 28, 37, 40, 42, 47, 48, 49, 52, 72, 73, 75, 77, 105, 106, 107, 151, 158, 159, 160, 161, 162, 163, 164, 165, 167, 169, 170. ... Proceedings of the Fifth Abel Symposium, Tromsų, Norway, June 1722, 2008 Boris Kruglikov, Valentin Lychagin, Eldar Straume - Springer, 2009 - 386 pages ISBN3642008739, 9783642008733 The Otto distance do coincides on Prob with the L2 Wasserstein distance W2. ... a distance. Moreover, recalling the definition of the Arnol'd metric, we may Differential Geometric Heuristic 57 3.4 The Otto Metric 3.5 The L2 Wasserstein Distance. Optimal transport: old and new - Page xxi, 32, 93, 94, 95, 96, 97, 98, 106, 110, 926, 941 Cédric Villani - 2009 - 973 pages ... (b) the explicit definition of this distance is not so easy to find in Wasserstein's work; and (c) Wasserstein was only interested in the case p = 1. By the way, also the spelling of Wasserstein is doubtful: the original spelling was Vasershtein. Springer 2008 ISBN 3540710507, 9783540710509 MR2459454 (2010f:49001) Villani, Cédric Optimal transport. Old and new. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 338. Springer-Verlag, Berlin, 2009. xxii+973 pp. ISBN: 978-3-540-71049-3 (Reviewer: Dario Cordero-Erausquin), 49-02 (28A75 37J50 49Q20 53C23 58E30) Zbl 1156.53003 Villani, Cédric Optimal transport. Old and new. (English) Grundlehren der Mathematischen Wissenschaften 338. Berlin: Springer. xxii, 973~p. EUR~99.95/net; SFR~166.00; \$~159.00; \sterling~79.00 (2009). MSC2000: *53-02 49-02 90-02, Reviewer: Mihail Voicu (Iaşi)

(6) The Wasserstein distances,

Empirical Processes with Applications to Statistics - Page xii, 23

Galen R. Shorack, Jon A. Wellner - 2009 - 948 pages

Wasserstein Distance, 62 Definition of Wasserstein distance d2; Mallow's

Sergio Albeverio - European Mathematical Society, 2009 - 379 pages ISBN3037190701, 9783037190708

Wasserstein distance

Olivier Thas - 2009 - 353 pages

Calculation of the Wasserstein distance between probability distributions on the line. Theory of Probability ...

Encyclopedia of Distances - Page 51, 147, 253, 254, 571, 580, 590

Michel M. Deza, Elena Deza - Springer 2009 - 590 pages ISBN 364200234X, 9783642002342

fLip≤1 ∫ If μ and ν are probability measures, then it is the Kantorovich–Mallows–Monge-Wasserstein metric (cf. Chap. 14).

Random Matrices: High Dimensional Phenomena - Page 437

... 150 symmetric powers 374 symmetric diffusion semigroup 381 symmetric group, infinite 352 symmetric tensor powers ... Wallis's product 29 Wasserstein metric 100 Wasserstein metric dual form 101 Wasserstein metric in

MR2566878 Blower, Gordon Random matrices: high dimensional phenomena. London Mathematical Society Lecture Note Series, 367. Cambridge University Press, Cambridge, 2009. x+437 pp. ISBN: 978-0-521-13312-8 (Reviewer: Michael Stolz), 60B20  page 100

Wahrscheinlichkeitstheorie - Page 386

Achim Klenke - 2009 - 624 pages

With a Chapter on Coupling from the Past by James G. Propp and David B. Wilson

David Asher Levin, Yuval Peres, Elizabeth Lee Wilmer - 2009 - 371 pages

Vasershtein, L. N. 1969. Markov processes over denumerable products of

American Mathematical Society, United States. Office of Naval Research - 2009 - 231 pages

... Stochastic convergence through Skorohod representation theorems and Wasserstein metrics, Suppl. Rendic. Circolo Matem. Palermo II, 35 (1994), 89-113.

Boris A. Khesin, Robert Wendt - 2009 - 304 pages

Marc Bernot, Vicent Caselles, Jean-Michel Morel - 2009 - 200 pages

Michael Drmota - Springer, 2009 - 458 pages ISBN3211753575, 9783211753576

Wasserstein metric

MR2484382 (2010i:05003) Drmota, Michael Random trees. An interplay between combinatorics and probability. SpringerWienNewYork, Vienna, 2009. xviii+458 pp. ISBN: 978-3-211-75355-2 (Reviewer: Lyuben R. Mutafchiev), 05-02 (05C80 60-02 60C05 68P05 68P10 68W40)

Operations research proceedings 2008:  - Page 352

Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), University of Augsburg, September 3-5, 2008 (Google eBook)

Bernhard Fleischmann, Karl-Heinz Borgwardt, Robert Klein - Springer, 2009 - 580 pages ISBN3642001424, 9783642001420

Wasserstein metric

Large random matrices: lectures on macroscopic asymptotics :  - Page 275

École D'Été de Probabilités de Saint-Flour XXXVI – 2006 (Google eBook)

Alice Guionnet - 2009 - 294 pages Lecture notes in mathematics (Springer-Verlag) ; 1957

Necessary optimality conditions for geodesics in weighted Wasserstein spaces.

Pierre L'Écuyer, Art B. Owen - 2009 - 672 pages

Since the latter two quantities can equivalently be defined in terms of the Wasserstein distance on the space of Borel

15Th Annual International Conference, Cocoon 2009 Niagara Falls, Ny, Usa, July 13-15, 2009: Proceedings

Hung Q. Ngo - 2009 - 540 pages

Wasserstein metric

B. Mohammadi, Olivier Pironneau - 2009 - 304 pages

Wasserstein

- 2009 - 199 pages

Vaserstein (or Wasserstein) metric

Séminaire de Probabilités XLII - Page 130

Catherine Donati-Martin, Michel Émery, Alain Rouault - 2009

Non-monotone Convergence in the Quadratic Wasserstein Distance Walter Schachermayer1, Uwe 130 L. Miclo.

MR2599203 (2010h:60007) Séminaire de probabilités XLII. [Seminar on Probability Theory XLII] Edited by Catherine Donati-Martin, Michel Émery, Alain Rouault and Christophe Stricker. Lecture Notes in Mathematics, 1979.

Springer-Verlag, Berlin, 2009. xiv+449 pp. ISBN: 978-3-642-01762-9, 60-06

Zbl 1213.60002 Andres, Sebastian Diffusion processes with reflection. (English)

Berlin: TU Berlin, Fakultät II, Mathematik und Naturwissenschaften (Diss.). 114~p. (2009). MSC2000: *60-02 60J60

whose associated empirical measure process converges weakly to the Wasserstein diffusion in the high-density limit

MR2547644 (2011a:20055) Segal, Dan Words: notes on verbal width in groups. London Mathematical Society Lecture Note Series, 361. Cambridge University Press, Cambridge, 2009. xii+121 pp. ISBN: 978-0-521-74766-0 (Reviewer: Benjamin Klopsch), 20E10 (20-02 20F10 20F12 20G25 20G35 20M05)

Scaling limits in statistical mechanics and microstructures in Continuum Mechanics -, 91, 93, 94, 95, 97, 240, 242, 247, 361, 367, 368, 369, 370, 377

Errico Presutti - Springer 2009 - 467 pages  ISBN3540733051, 9783540733058

Vaserstein. distance. The theory is much more general than the applications to statistical mechanics that we discuss in this book, as a general reference see the book by Villani [208]. This is Part I because our presentation continues in Sect.

Zbl 1156.82001    Presutti, Errico   Scaling limits in statistical mechanics and microstructures in continuum mechanics. (English)

Theoretical and Mathematical Physics. Berlin: Springer (ISBN 978-3-540-73304-1/hbk). xvi, 467 p. EUR 69.95/net; SFR 116.50; £ 52.50; $109.00 (2009). Wasserstein 2010 49 books Anatolii Puhalskii - CRC Press, 2010 - 520 pages ISBN 420035800, 9781420035803 Wasserstein ### Geodesic Methods in Computer Vision and Graphics - Page 166, 175, 196 Gabriel Peyré, ‎Mickael Pechaud, ‎Renaud Keriven - 2010 In order to take into account the position of the index in the descriptors, one can use the Wasserstein distance, also called the earth mover's distance [246] which is more complicated to compute. The lp Wasserstein distance is defined as a ... ### Serre's Problem on Projective Modules - Page 374 T. Y. Lam - 2010 Amer. Math. Monthly 85, 357–359. 216. Gustafson, W. H.; Moore, M. E.; Reiner, I. (1981): Matrix completions over Dedekind rings. Lin. ... MR 1125204 (Reviewers: L. N. Vaserstein and E. R. Wheland) 224. Hinson, E. K. (1991b): Word length in ... ### Control Theory and Systems Biology - Page 251, 252 Pablo A. Iglesias, ‎Brian P. Ingalls - 2010 Figure 12.2 (a) Graphical interpretation of the Wasserstein pseudometric as the area between two inverse cumulative .. ### Probability and Partial Differential Equations in Modern Applied Mathematics Edward C. Waymire, ‎Jinqiao Duan - 2010 This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering. Studies in Classification, Data Analysis, and Knowledge Organization - Page 41, 42 Data Analysis and Classification: from Exploration to Confirmation (Google eBook) Francesco Palumbo Springer, 2010 482 pages ISBN3642037399, 9783642037399 Clustering linear models using Wasserstein distance Wasserstein. Distance. Antonio Irpino and Rosanna Verde Abstract This paper deals with the clustering of complex data. ... We show the properties of the proposed metric and an application to real data using a dynamic clustering algorithm. ... is a set of probability distributions associated with the sample space S, while a parameterized statistical model is a parameter set Θ together with a function Data Analysis and Classification: Proceedings of the 6th Conference of the Classification and Data Analysis Group of the Società Italiana di ... Data Analysis, and Knowledge Organization) Francesco Palumbo (Editor), Carlo Natale Lauro (Editor), Michael Greenacre (Editor) Springer; 1st Edition. edition (December 17, 2009) 504 pp ISBN-10: 3642037380 ISBN-13: 978-3642037382 MR2664206 (2011b:62004) Data analysis and classification. Proceedings of the 6th Conference of the Classification and Data Analysis Group of the Società Italiana di Statistica (CLADAG) held in Macerata, September 12–14, 2007. Edited by Francesco Palumbo, Carlo Natale Lauro and Michael J. Greenacre. Studies in Classification, Data Analysis, and Knowledge Organization. Springer-Verlag, Berlin, 2010. xxii+482 pp. ISBN: 978-3-642-03738-2, 62-06 Measure Theory: Sigma-Algebra, Cantor Set, Measure, Dirac Delta Function, Measurable Function, Null Set, Borel-cantelli Lemma Books, LLC, Books Group - 2010 Metric Geometry: Metric Space, Complete Metric Space, Cauchy Sequence, Euclidean Distance, Triangle Inequality, Curve, Hausdorff Dimension Books, LLC General Books, 2010 1156531802, 9781156531808 332 pages 26Th Southern Biomedical Engineering Conference Sbec 2010, April 30 - May 2, 2010, College Park, MD - Page 353 Keith E. Herold, Jafar. Vossoughi, William E. Bentley - 2010 ... approach to digital pathology that relies on measuring the optimal transportation (Kantorovich-Wasserstein) metric between pairs of ... Comparing distributions - Page 341, 348 Olivier Thas - 2010 See 2009 An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes. Journal of Statistical Computation and ... Calculation of the Wasserstein distance between probability distributions on the line. Theory of Probability ... Probability Theory: Doomsday Argument Source Wikipedia, Books Llc, Books Group - 2010 ISBN1156574188, 9781156574188 Control Theory and Systems Biology - Page 246, 252, 253, 259 Pablo A. Iglesias, Brian P. Ingalls - 2010 minimize the Wasserstein pseudometric W1dðP1;P3ðk1;k2ÞÞ, where P3ðk1;k2Þ is the probability measure generated by the simple reaction network in figure 12.1a. This algorithm is an extension of the standard gradient descent method that ... Probabilistic Approach to Geometry Motoko Kotani, Masanori Hino, Takashi Kumagai - 2010 ISBN4931469582, 9784931469587 On Wasserstein Geometry of Gaussian Measures (A Takatsu) Entropic Measure and Wasserstein Diffusion Max von Renesse Technische Universit¨at Berlin European Congress of Mathematics, Amsterdam, 14-18 July, 2008 - Page 15 André Ran, H. J. J. te Riele, Jan Wiegerinck - 2010 J. A. Carrillo, R. J. McCann, and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular ... (Monge-Kantorovich-Wasserstein) The Poisson-Dirichlet Distribution and Related Topics: - Page 209, 210 Models and Asymptotic Behaviors Shui Feng - Springer 2010 ISBN3642111947, 9783642111945 Wasserstein metric The logarithmic Sobolev inequality for the Wasserstein diffusion. Probab. Theory Relat. Otmar Scherzer - 2010 - 1607 pages Gromov–Wasserstein Distances. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani - 2010 - 438 pages Carrillo, J.A., McCann, R., Villani, C.: Contractions in the 2-Wasserstein length space and thermalization of granular media. Wasserstein distance is O(δ). ... interpreted as an explicit Euler discretization in time of a gradient flow on the Wasserstein space, at least for sufficiently smooth motion mappings, cf. [1,38,50]. Therefore, the Wasserstein metric may be ... Kac equation, Tanaka [301] introduced into kinetic theory the concept of a metric nowadays known by the German version of the name of the Russian mathematician L.N. Vasershtein, who introduced it independently in a different field [325]. Herbert Edelsbrunner, John Harer - 2010 - 241 pages Wasserstein stability. Although a general stability result like the one for the bottleneck distance is out of reach, we get stability under the Wasserstein distance for a reasonably large class of functions. Let X be a metric space, that is, ... MR2572029 (2011e:00001) Edelsbrunner, Herbert; Harer, John L. Computational topology. An introduction. American Mathematical Society, Providence, RI, 2010. xii+241 pp. ISBN: 978-0-8218-4925-5 (Reviewer: Andrzej Kozlowski), Michel Talagrand - 2010 - 485 pages Wasserstein distance Heping Zhang, Burton H. Singer - 2010 - 259 pages Wasserstein distance Shapes and Diffeomorphisms - Page 252 , 429, 434 Laurent Younes - 2010 - 434 pages Wasserstein distance Vassili N. Kolokoltsov - 2010 - 400 pages Another convenient way to metricize the weak topology of measures is using Wasserstein–Kantorovich distances. H. Holden, Kenneth Hvistendahl Karlsen - 2010 - 389 pages Before that, let us remind the reader the definition of the euclidean Wasserstein distance Stochastic Analysis 2010 - Page 227 Dan Crisan - 2010 - 390 pages ... coefficients (diffusion, drift and L ́evy measure) depending Lipschitz continuously on its parameters generates a Markov semigroup, where the measures are metricized by the Wasserstein–Kantorovich metrics Wp. The analysis of SDE driven A Joint Framework for Cauchy Problems in and Beyond Vector Spaces, Issue 1996 (Google eBook) Thomas Lorenz - 2010 - 509 pages Wasserstein distance Constantine M. Dafermos - 2010 - 708 pages Asymptotics in terms of the Wasserstein metric is discussed by Carrillo, DiFrancesco and Lattanzio [1]. Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws. J Thorsten Hens, Marc Oliver Rieger - 2010 - 373 pages Wasserstein metric Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao - 2010 - 405 pages Wasserstein distance The State of the Art in Honor of George B. Dantzig George B. Dantzig, Gerd Infanger - 2010 - 362 pages Wasserstein distances 21st International Conference, ALT 2010, Canberra, Australia, October 6-8, 2010. Proceedings (Google eBook) Marcus Hutter, Frank Stephan, Vladimir Vovk - 2010 - 421 pages Wasserstein Distances Wasserstein Distances  Mathematics In Industry / the European Consortium for Mathematics In Industry: Janne Roos, Luis R. J. Costa - 2010 - 588 pages Wasserstein metric Christian Borgelt, Gil González Rodríguez, Wolfgang Trutschnig - 2010 - 644 pages Catherine Donati-Martin, Antoine Lejay, Alain Rouault - 2010 - 503 pages This includes all Wasserstein distances with respectto the time- dependent Riemannian metric generated by the symbol of the ... Alexander Lubotzky - 2010 - 208 pages Vaserstein Collected Papers of John Milnor: V. Algebra - Page 317 John Milnor, Hyman Bass, T. Y. Lam - 2011 - 408 pages The result was extended to all split (Chevalley) groups by Matsumoto [18]. Some nonsplit isotropic groups of classical types were treated by L.N. Vaserstein. A proof of Serre's conjecture for general isotropic groups was given by Raghunathan ... Theory and Applications: Ninth International Conference Finite Field and Applications, July 13-17, 2009, Dublin, Ireland Gary McGuire, Gary L. Mullen, Daniel Panario - 2010 - 384 pages Vaserstein Mathematics, Metric (mathematics), Measure (mathematics), Metric Space, Computer Science, Earth Mover's Distance, Radon Measure, Conditional Probability, Expected Value Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken -Betascript Publishing, 2010 - 100 pages ISBN 10: 6130361807 ISBN 13: 9786130361808 Susanne Boll, Qi Tian, Lei Zhang - 2010 - 806 pages Wasserstein distance 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings Kostas Daniilidis, Petros Maragos, Nikos Paragios - 2010 The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. ... It is possible to replace the geodesic distance by a diffusion distance [15] computed by solving a linear Poisson PDE. 5th International Workshop, MIAR September 19-20, 2010, Beijing, China Hongen Liao, P. J. Edwards, Xiaochuan Pan - 2010 - 573 pages he Earth Mover's Distance The Earth Mover's Distance, also called Kantorovich-Wasserstein distance, can be visualized as Keith E. Herold, Jafar Vossoughi, William E. Bentley - 2010 - 1000 pages, Wasserstein Eckhard Platen, Nicola Bruti-Liberati - 2010 - 856 pages Discretization for stochastic differential equations, Lp Wasserstein metrics, and econometrical models. In Distributions with fixed ... Vladimir I. Bogachev - 2010 - 501 pages Sturm K.-T. Entropic measure and Wasserstein diffusion. Fang S., Shao J., Sturm K.-Th. Wasserstein space over the Wiener space. Areski Cousin, Stéphane Crépey, Olivier Guéant - 2010 - 359 pages Wasserstein space Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini - 2010 - 77 pages AMS Mem MR2808856 Gangbo, Wilfrid; Kim, Hwa Kil; Pacini, Tommaso Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Mem. Amer. Math. Soc. 211 (2011), no. 993, vi+77 pp. ISBN: 978-0-8218-4939-2, 37Kxx (53Dxx 58Axx). Zbl 1221.53001 Wasserstein space, Wasserstein theory MR2605602 (2010m:58002) Probabilistic approach to geometry. Papers from the 1st Conference of the Seasonal Institute of the Mathematical Society of Japan held at Kyoto University, Kyoto, July 28–August 8, 2008. Edited by Motoko Kotani, Masanori Hino and Takashi Kumagai. Advanced Studies in Pure Mathematics, 57. Mathematical Society of Japan, Tokyo, 2010. xvi+514 pp. ISBN: 978-4-931469-58-7, 58-06 (58J65 60-06) Vasserstein and Vasershtein 2010 7 books -3 Daniel Alpay, Victor Vinnikov - 2010 - 389 pages The second result we need is due to Vasershtein ([14], Theorem 3) Theorem 5.4. Given a ring A with stable rank k, let Mn(A) denote the ring of nxn matrices with An Outline of Ergodic Theory - Page 67 Steven Kalikow, Randall McCutcheon - 2010 The dbar distance is closely related to various distance metrics that have been around for a long time, going by the names Vasershtein distance, Monge–Kantorovich transportation metric, earth mover's distance, etc. Quantum Mechanics and Path Integrals: Emended Edition Jess Benhabib, Alberto Bisin, Matthew O. Jackson - Newnes, 2010 ISBN0444537139, 9780444537133 1600 pp Random Fields and Interacting Particle Systems. Providence: Mathematical Association of America, 1971. G. Topa. Social Interactions, Local Spillover and Unemployment. The Review of Economic Studies. 2001;68:261-295. L.N. Vasserstein. Vaserstein 2010 13 items ### European Congress of Mathematics, Amsterdam, 14-18 July, 2008 - Page xxv André C. M. Ran, ‎H. J. J. te Riele, ‎Jan Wiegerinck - 2010 ... and Villani obtained a new characterization of Riemannian manifolds with bounded Ricci curvature from below, in terms of convexity of the Boltzmann entropy with respect to optimal transportation (Monge-Kantorovich-Wasserstein) metrics. Complex Analysis - Page 131, 143, 144 Several Complex Variables and Connections With Pde Theory and Geometry Peter Ebenfelt, Norbert Hungerbühler, Joseph J. Kohn - Springer 2010 - 340 pages ISBN3034600097, 9783034600095 Every null-homotopic holomorphic map f : X B = SLm (C) admits a continuous lifting F : X E for a suitably chosen N N (Vaserstein [31]), and the goal is to deform F to a holomorphic lifting G = (G1 ,...,G N ): X E. Collected Papers of John Milnor: Algebra - Page 317 John Willard Milnor, Hyman Bass, T. Y. Lam - 2010 - 425 pages Some nonsplit isotropic groups of classical types were treated by L.N. Vaserstein. A proof of Serre's conjecture for general isotropic groups was given by Raghunathan ... Alexander Lubotzky - 2010 - 208 pages Vaserstein Finite fields: theory and applications : Ninth International Conference - Page 160 Gary McGuire, American Mathematical Society - 2010 - 384 pages L. N. Vaserstein, Quantum (abc)-theorems, J. Number Theory 81, 2000, pp. 351 – 358. Ideals and Reality: Projective Modules and Number of Generators of Ideals , Ravi A. Rao - 2010 - 350 pages A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Marián Fabian, Petr Habala, Petr Hajek - Springer 2010 - 820 pages J. Lukeš and J. Malý, Measure and integral, Matfyzpress, Prague 1994. Y. Lyubich and L. N. Vaserstein, Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs, Geom. Dedicata 47 (1993), 327–362. 2010 ISBN3642092438, 9783642092435 Springer 2010 580 pp There is a vast literature on the topic of isometric embeddings among the various Lp-spaces; see, e.g., Wells and Williams [1975], Dor [1976], Ball [1987] , Lyubich and Vaserstein [1993]. Lee Johnson, R. Dean Riess, Jimmy T. Arnold - 2010 This book's flexible table of contents makes it suitable for students majoring in science and engineering as well as students who want an introduction to mathematical abstraction and logical reasoning. Vaserstein Encyclopedia of business information sources - Volume 2 - Page 553 Virgil L. Burton - 2010 Leonid N. Vaserstein and others. Prentice Hall. ' 2002.$8l.0O. Publisher: "...enables those with little mathematical background to learn to use linear programming in their respective fields (business. economics. operations research. etc.).".

This book covers all aspects of linear programming from the two-dimensional LPs and their extension to higher dimensional LPs, through duality and sensitivity analysis and finally to the examination of commented software outputs.

This text provides up-to-date information on how good project management and effective use of software can help you manage projects, especially information technology projects.

This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications.

ISBN3642092438, 9783642092435 728 pp

Wasserstein 2011  68 books

Centro Stefano Franscini, Ascona, May 2008

Robert C. Dalang, Marco Dozzi, Francesco Russo, editors. Basel : Birkhäuser, 2011. 492pp

ISBN 9783034800204 (alk. paper) 3034800207 (alk. paper) 9783034800211 (ebk.)  3034800215 (ebk.)

We give an alternative representation of the Wasserstein Dirichlet form that was introduced by von Renesse and Sturm in [7]. Based on this ... Recall that the Wasserstein distance is compatible with the weak topology. In order to give the ...

Functional Inequalities for the Wasserstein Dirichlet Form / W. Stannat

### Handbook of Mathematical Methods in Imaging: Vol. 1 - Page 1430

Otmar Scherzer - 2011

32.5.1.4 Wasserstein Distances Let the sets X and Y be further equipped with measures μ X and fly, respectively. ... (32.39) r relso(Z) Wasserstein distances are intimately related to Monge–Kantorovich optimal transportation problems.

### - Page 3, 10

Zhenyu Mao - 2011

It is the extension to general distortion measures of Ornstein's d (d-bar) distance (which is based on the the Hamming distortion) or, equivalently, the extension of the classic Monge/Kantorovich/Wasserstein (or Vasershtein) distance [43, 31, 61] ...

### Handbook of Differential Equations: Evolutionary Equations: - Page 4, 7, 30, 107, 134, 135, 136, 634

C.M. Dafermos, ‎Eduard Feireisl - 2011

E.A. Carlen and W. Gangbo, Constrained steepest descent in the 2-Wasserstein metric, Ann. of Math. (2) 157 ... E. Chasseigne and J.L. Vazquez, Theory ofextended solutionsforfast-diffusion equations in optimal classes of data. Radiation from ...

Handbook of Empirical Economics and Finance - Page 268

Aman Ullah, David E. A. Giles - 2011

In the case of Wasserstein, the distance is defined in the Lj norm and in the Mallows in the Li norm. When considering Equation 10.34, D(hXl, fiXj) will be calculated by implementing the Wasserstein or Mallows distance. By using the definition ...

Image Processing (ICIP), 2011 18th IEEE International Conference on

Date: 11-14 Sept. 2011 Rabin, J. CMLA, ENS de Cachan, Cachan, France

Peyre, G. Wasserstein regularization of imaging problem 1541 - 1544

Studies In Classification, Data Analysis, and Knowledge Organization - Page 370

Classification and Multivariate Analysis for Complex Data Structures

Bernard Fichet - Springer, 2011 473 pp ISBN3642133126, 9783642133121

Irpino, A., Verde R., Lechevallier Y.: Dynamic clustering of histograms using Wasserstein metric. In: Rizzi, A., Vichi, M. (eds.) ...

Energy Minimization Methods in Computer Vision and Pattern Recognition - Page 74, 81, 86

8th International Conference, EMMCVPR 2011, St. Petersburg, Russia, July 25-27, 2011, Proceedings

We present comparisons of the un-normalized model (3), our new normalized model (5), CV and LBF models (12), using the 1-D Wasserstein distance ...

Proceedings of the International Congress of Mathematicians 2010  (ICM 2010) (in 4 Volumes) - Vol. I:, 92

Plenary Lectures and Ceremonies, Vols. II-IV: Invited Lectures

Rajendra Bhatia, Arup Pal - 2011

In a study of nonlinear heat equations, F. Otto [38] defined a formal Riemannian structure on P2 (M) and interpreted these equations as gradient flows on the Wasserstein space P2 (M) with this formal Riemannian structure.

Wasserstein geodesic

Hisham Sati, Urs Schreiber - 2011

In the “probabilisticapproach (see a good review in [L], or original proofs in [LV], [St]) one uses the ideas of optimal transport (different point of view is presented in [AGS]). ...

More precisely the space P(X) carries a family Wp ,p ≥ 1 of the so-called Wasserstein metrics. ... on C(X) discussed in the Introduction, thus making a connection with Connes's approach to noncommutative Riemannian geometry.

Nonlinear PDE’s and Applications: C.I.M.E. Summer School, Cetraro,, Italy - Page 80

Unlike the critical fast diffusion equation that came discussed in Sect.2, this fast diffusion equation is particularly nice: Both terms in the entropy are “displacement convex” – convex along geodesics in the Wasserstein space – and the second ...

Hamiltonian Systems and the Calculus of Differential Forms on the  Wasserstein space

Hwa Kil Kim - Proquest, Umi Dissertation Publishing, 2011 - 90 pages  ISBN1244090794, 9781244090798

This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in [2]. We regularize H via Moreau-Yosida approximation to get Htau and denote by mutau a solution of system with the new Hamiltonian Htau. Suppose Htau converges to H as tau tends to zero. We show mutau converges to mu and mu is a solution of a Hamiltonian system which is corresponding to the Hamiltonian H. At the end of first part, we give a sufficient condition for the uniqueness of Hamiltonian systems. In the second part, we develop a general theory of differential forms on the Wasserstein space. Our main result is to prove an analogue of Green's theorem for 1-forms and show that every closed 1-form on the Wasserstein space is exact. If the Wasserstein space were a manifold in the classical sense, this result wouldn't be worthy of mention. Hence, the first cohomology group, in the sense of de Rham, vanishes.

Achim Klenke - 2011 - 624 pages

Für zwei W-Maße P und Q auf (E,B(E)) schreiben wir K(P,Q) C M\{E x E) für die Menge der Kopplungen von P und Q. Wir können dann einen Abstand, die so genannte Wasserstein Metrik, auf M.\(E) definieren durch dw(P,Q):=mi(J

05 Wasserstein Metrik

Variational Pde-Based Image Segmentation and Inpainting with Applications to Computer Graphics

Kang-Yu Ni,   BiblioBazaar, 2011 - 142 pages  ISBN1243579633, 9781243579638

 This dissertation explores the applications of variational PDE models to image processing, computer vision, and computer graphics, and also to building efficient numerical algorithms and schemes. In particular, the areas of contributions are segmentation, inpainting, and matting. There are three separate topics in segmentation. The first is unsupervised segmentation, in which we propose and analyze a nonparametric region-based active contour model for segmenting cluttered scenes. The novelty is the use of the Wasserstein distance in segmentation,

Geometric Approach to Evolution Problems in Metric Spaces : Product Formulas in CAT(0) Spaces Fokker-Planck Equation Maximal Monotone Operators on Wasserstein Spaces

Igor Stojkovi - 2011 - 240 pages

This PhD thesis contains four chapters where research material on a range of different topics is presented.

Michael Demuth, Bert-Wolfgang Schulze, Ingo Witt - 2011 - 342 pages

The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Arch. Ration. Mech. Anal., 194:133–220, 2009. [55] J. Glimm. Solutions in the large for nonlinear hyperbolic systems of equations. Commun.

nternational Joint Conference, VISIGRAPP 2009, Lisboa, Portugal, February 5-8, 2009. Revised Selected Papers (Google eBook)

Alpeshkumar Ranchordas, Joao Madeiras Pereira, Hélder J. Araújo - 2011 - 369 pages

Ni, K., Bresson, X., Chan, T., Esedoglu, S.: Local histogram based segmentation using the Wasserstein distance. In: Scale ... Rousson, M., Brox, T., Deriche, R.: Active unsupervised texture segmentation on a diffusion based feature space.

Bir Bhanu, Chinya V. Ravishankar, Amit K. Roy-Chowdhury - Springer  2011 - 485 pages

Wasserstein distance

Zbl 1213.62027 Chen, Louis H. Y.; Goldstein, Larry; Shao, Qi-Man  Normal approximation by Stein's method. (English)  Probability and Its Applications. Berlin: Springer. xii, 405~p. (2011). MSC2000: *62E20 62-02 60-02, Reviewer: Thorsten Dickhaus (Berlin)

W Gangbo, HK Kim… - 2011

MR2808856  Gangbo, Wilfrid; Kim, Hwa Kil; Pacini, Tommaso Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Mem. Amer. Math. Soc. 211 (2011), no. 993, vi+77 pp. ISBN: 978-0-8218-4939-2 (Reviewer: Koji Kikuchi) 37K25 (58B20 58D05)

Stochastic Optimization Methods in Finance and Energy - Page xii, 333, 353, 354, 357, 359, 360, 363, 368, 387, 388, 390, 392, 394, 397, 400, 401, 402, 406, 407, 414, 415, 474

New Financial Products and Energy Market Strategies

Series: International Series in Operations Research & Management Science, Vol. 163

Bertocchi, Marida; Consigli, Giorgio; Dempster, Michael A. H. (Eds.) Springer, 2011 ISBN1441995862, 9781441995865

2012, 2011, XXIII, 474 p. 133 illus., 65 in color.

Energy Minimazation Methods in Computer Vision and Pattern Recognition - Page 74, 75, 76, 79, 80, 81, 82, 83, 84, 85, 86, 88

Yuri Boykov, Victor Lempitsky, Frank R. Schmidt - 2011 - 450 pages

Wasserstein distance

Passing to the limit in a Wasserstein gradient flow: from Diffusion to Reaction

Issue 1593 of Preprint PublisherWIAS, 2011 32 pages

General Relativity, Geometry, and PDE

Mark Agranovsky, Matania Ben-Artzi, Greg Galloway - 2011 - 284 pages

The Wasserstein space P2 (X) is defined as (3.4) P2(X) = { μ P(X) ∫ X d(

Random Finite Sets for Robot Mapping and SLAM:  - Page 49

New Concepts in Autonomous Robotic Map Representations

John Stephen Mullane, Ba-Ngu Vo, Martin David Adams - 2011 - 148 pages

Wasserstein construction, Wasserstein distance

Markov Processes, Semigroups and Generators - Page 41, 42, 240, 430

Vassili N. Kolokoltsov - 2011 - 430 pages

Wasserstein metric

Bernard Fichet, Domenico Piccolo, Rosanna Verde - 2011 - 473 pages

Wasserstein

Computer Analysis of Images and Patterns:  Part 1 - Page 256

14th International Conference, CAIP 2011, Seville, Spain, August 29-31, 2011, Proceedings

Ainhoa Berciano, VARIOS AUTORES, Daniel Diaz-Pernil - 2011 - 611 pages -

Wasserstein distance

Advances in Swarm Intelligence: Part 2 - Page 490

Second International Conference, ICSI 2011, Chongqing, China, June 12-15, 2011, Proceedings

Ying Tan, Yuhui Shi, Yi Chai - 2011 - 587 pages -

Wasserstein distances

Amit Gefen - 2011 - 560 pages

Wasserstein distance

Camillo De Lellis, Emanuele Nunzio Spadaro - 2011 - 79 pages

Wasserstein

Michael Demuth, Bert-Wolfgang Schulze, Ingo Witt - 2011 - 341 pages

Wasserstein

Video Tracking: Theory and Practice, Andrea Cavallaro - 2011 - 292 pages

Wasserstein distance is an evaluation metric for multi-target algorithms and has been used to evaluate trackers based on the RFS framework [

Wiener Chaos: Moments, Cumulants and Diagrams: A Survey with computer implementation - Page 203

Giovanni Peccati, Murad S. Taqqu - 2011 - 200 pages

Wasserstein distance

Anirban DasGupta - 2011 - 641 pages

Wasserstein metric

Sergio Albeverio, Ruzong Fan, Frederik Herzberg - 2011 - 284 pages

Entropic measure and Wasserstein diffusion.

Karen Yeats - 2011 - 82 pages

Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

On Systems of Equations Over Free Partially Commutative Groups - Page 157

Montserrat Casals-Ruiz, Ilya Kazachkov - 2011 - 153 pages

Wasserstein space

Positive Definiteness of Functions With Applications to Operator Norm Inequalities - Page 84

Hideki Kosaki - 2011 - 80 pages

Wasserstein space

Dynamics, Games and Science, in Honour of Maricio Peixoto and David Rand - Page 242

Conference Dyna 2008, September 8-12, 2008, Universidade Do Minho, Braga, Portugal

Maurício Matos Peixoto, Alberto Adrego Pinto, David A. J. Rand - 2011 - 830 pages

Wasserstein metric

Random perturbation of PDEs and fluid dynamic models:  - Page 166, 175

École D'été de Probabilités de Saint-Flour XL-2010

Franco Flandoli - 2011 - 176 pages

Wasserstein distance, Wasserstein control

Iwasawa Theory, Projective Modules, and Modular Representations - Page 189

Ralph Greenberg - 2011 - 185 pages

Wasserstein space

Valuations and Differential Galois Groups - Page 72

Guillaume Duval - 2011 - 68 pages

Wasserstein space

Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence - Page 137

Leonid Positselski - 2011 - 133 pages Memoirs of the American Mathematical Society Series ISBN0821852965, 9780821852965

Wasserstein space

Man Chun Leung - 2011 - 99 pages -

Iterated Function Systems, Moments, and Transformations of Infinite Matrices - Page 109

Palle E. T. Jorgensen, Keri A. Kornelson, Karen L. Shuman - 2011 - 105 pages

ations of Infinite Matrices

ISBN0821852485, 9780821852484

Michael Handel, Lee Mosher - 2011 - 104 pages

Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ...

Multicurves and Equivariant Cohomology - Page 121

N. P. Strickland - 2011 - 117 pages

David Bourqui - 2011 - 151 pages

Zbl 05954668           Franek, Marzena Magdalene          Variational methods using transport metrics and applications.

(English)  Münster: Univ. Münster, Mathematisch-Naturwissenschaftliche Fakultät, Fachbereich Mathematik und Informatik (Diss.). 183 p. (2011).

Furthermore, the connection to the gradient flow theory is developed in this thesis and several evolution equations are identified as Wasserstein gradient flow equations.

Zbl 1213.62027       Chen, Louis H. Y.;           Goldstein, Larry;                  Shao, Qi-Man

Normal approximation by Stein's method. (English)   Probability and Its Applications. Berlin: Springer (ISBN 978-3-642-15006-7/hbk; 978-3-642-15007-4/ebook). xii, 405 p.

(in Wasserstein ($L^1$) and Kolmogorov ($L^\infty$) distances)

Seminar on Stochastic Analysis, Random Fields and Applications VI:  - Page vi, 109, 116, 244, 245, 246, 247, 249, 251, 253, 256, 260, 262, 265, 276, 277

Centro Stefano Franscini, Ascona, May 2008

Robert Dalang, Marco Dozzi, Francesco Russo - 2011 - 492 pages

Keywords. Wasserstein diffusion,

We give an alternative representation of the Wasserstein Dirichlet form that was introduced by von Renesse and Sturm ... definition of the Wasserstein Dirichlet form let us first recall an alternative description of the Wasserstein space over I that ...

books.google.comAri Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh - 2011 - 335 pages

Wasserstein

Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees - Page 109

Lee Mosher, Michah Sageev - 2011 - 105 pages

Wasserstein

Parabolic Systems with Polynomial Growth and Regularity - Page 122

MR2866816  Duzaar, Frank; Mingione, Giuseppe; Steffen, Klaus Parabolic systems with polynomial growth and regularity.

Mem. Amer. Math. Soc. 214 (2011), no. 1005, x+118 pp. ISBN: 978-0-8218-4967-5 (Reviewer: Luca Lorenzi) 35K40 (35B65 35D30 35K59 35K92)

forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ...

Numerical Analysis of Multiscale Computations:  - Page 316

Proceedings of a Winter Workshop At the Banff International Research Station 2009

Björn Engquist, Olof Runborg, Yen-Hsi Richard Tsai - 2011 - 420 pages

Wasserstein distance

Stochastic Optimization Methods in Finance and Energy:  - Page 394

New Financial Products and Energy Market Strategies

Giorgio Consigli, Marida Ida Bertocchi, Michael A. H. Dempster - 2011 - 474 pages

Fundamentals of Object Tracking - Page 261

Subhash Challa, Mark R. Morelande, Darko Mušicki - 2011 - 392 pages

Probability for Statistics and Machine Learning:  - Page 506, 693, 782

Fundamentals and Advanced Topics

Anirban DasGupta - 2011 - 782 pages

Wasserstein metric

Second IFIP WG 5.5/SOCOLNET Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2011, Costa de Caparica, Portugal, February 22-24, 2011, Proceedings

Luis M. Camarinha-Matos - 2011 - 615 page

Wasserstein

On asymptotically optimal source coding and simulation of  Stationary Sources

It is the extension to general distortion measures of Ornstein's d (d-bar) distance (which is based on the the Hamming distortion) or, equivalently,

the extension of the classic Monge/Kantorovich/Wasserstein (or Vasershtein) distance [43, 31, 61] ...

Advances in Computer Science, Environment, Ecoinformatics, and Education: Part 1 - Page 277

, Xiong Huang - 2011 - 664 pages

Wasserstein distance

... has utilized the idea of curvature, which requires contraction of the transportation metric (also known as the Wasserstein distance.) I

10th International IFIP TC 6 Networking Conference, Valencia, Spain, May 9-13, 2011, Proceedings

Jordi Domingo-Pascual, Pietro Manzoni, Sergio Palazzo - 2011 - 381 pages

Wasserstein rank distance

When comparing two users and their ranking of topics, we use the number and distance of permutation steps required to transform one list into the other (the Waserstein rank distance [18]) as a measure of user similarity. A network-wide ...

Tarmo Järvilehto - 2011 - 78 pages  AMS Mem

Wasserstein space

Theo Bühler - 2011 - 97 page

Wasserstein space

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates - Page 82

Steve Hofmann, Guozhen Lu, Dorina Mitrea - AMS  2011 - 78 pages ISBN0821852388, 9780821852385

Wasserstein space

Spectral methods for isometric shape matching and symmetry detection - Page 90

Maksims OvsjanikovsStanford University, 2011

Wasserstein

Vaserstein 2011 10 items

Commutative algebra. Constructive methods. Finite type projective modules. (Algèbre commutative. Méthodes constructives. Modules projectifs de type fini. Cours et exercices.) (French)

Mathématiques en Devenir. Paris: Calvage et Mounet. xxxi, 991~p. EUR~69.00 (2011). MSC2000: *13-01 13C10 13C11, Reviewer: Werner Kleinert (Berlin)

Vaserstein

The Homotopy Principle In Complex Analysis (Google eBook)

Franc Forstneric - 2011 - Springer, Jan 1, 2011 - 489 pages 3642222501, 9783642222504

In this section we outline the solution to Gromov's Vaserstein problem obtained by Ivarsson and Kutzschebauch [272, 273].

[PDF] from tu-darmstadt.deW  Stannat - Seminar on Stochastic Analysis, Random Fields and …, 2011 - Springer ISBN 978-3-0348-0020-4

Abstract We give an alternative representation of the Wasserstein Dirichlet form that was introduced by von Renesse and Sturm in [7].

Computer Vision - ACCV 2010:    Part 2 - Page 487

10th Asian Conference on Computer Vision, Queenstown, New Zealand, November 8-12, 2010, Revised Selected Papers

Ron Kimmel, Reinhard Klette, Akihiro Sugimoto - Springer, May 3, 2011 - 726 pages LNCS 6492-6495

Vaserstein

Hans-Otto Georgii - Walter de Gruyter, May 13, 2011 - 545 pages ISBN3110250292, 9783110250299

... references also deal with the more general case that the total variation distance (8.1) is replaced by the more general Vaserstein-Kantorovich-Rubinstein distance relative to some metric on the state space. (If this metric is the discrete metric, ...

Huanyin Chen - World Scientific, 2011 ISBN9814329711, 9789814329712

Vaserstein

Zbl 1245.16002 Chen, Huanyin Rings related to stable range conditions. (English)

Series in Algebra 11. Hackensack, NJ: World Scientific. xviii, 661~p. \$~148.00, \sterling~92.00; \$~192.00 (2011). MSC2000: *16-02 16D70 16E20, Reviewer: Kenneth R. Goodearl (Santa Barbara)

Aspects of operator algebras and applications:  - Page 70

UIMP-RSME Lluís A. Santaló Summer School, Universidad Internacional Menéndez Pelayo, Santander, Spain, July 21-25, 2008

Pere Ara, Fernando Lledo, Francesc Perera - 2011 - 168 pages ISBN 9780821849057

Vaserstein

Masoud Khalkhali, Guoliang Yu - 2011 - 163 pages

In [36], Suslin extended the Bass–Vaserstein theorem to higher algebraic Ktheory.

Number Theory, Analysis and Geometry: In Memory of Serge Lang - Page 321, 346, 347, 352,

Dorian Goldfeld, Jay Jorgenson, Peter Jones - 2011 - 704 pages

Non-Abelian Fundamental Groups and Iwasawa Theory - Page 114, 1310 131

John Coates, Minhyong Kim, Florian Pop - 2011 - 320 pages

[47] Vaserstein, L. N. On stabilization for general linear groups over a ring. Math. USSR Sbornik, 8:383–400, 1969. [48] Vaserstein, L. N. On the Whitehead determinant for semi-local rings. J. Algebra, 283:690–699, 2005. [49] Venjakob, O.

Marián Fabian, Marián J. Fabian - 2011

J. Lukeš and J. Malý, Measure and integral, Matfyzpress, Prague 1994. Y. Lyubich and L. N. Vaserstein, Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs, Geom. Dedicata 47 (1993), 327–362.

Waserstein 2011

Networking 2011: Part 2 - Page 318

10th International IFIP TC 6 Networking Conference, Valencia, Spain, May 9-13, 2011, Proceedings

Jordi Domingo-Pascual, Pietro Manzoni, Sergio Palazzo - 2011 - 381 pages

Waserstein rank distance

Vasershtein 2011

### MÚSICA, MATEMÁTICA Y CONCERTISMO - Emilio Lluis Puebla pdf

2011 enciclopedia clásica, adecuada para sus volúmenes de textos, se generaliza a la ...... [V] Vaserstein L.N. Vector bundles and projective modules revisited. Trans.

Serguei Y. Novak - 2011 CRC Press, 2012

Estimate of the accuracy of approximation (8.11) in terms of a Vasershtein-type distance is given by Barbour et al. [30].

Robert M. Gray - Springer 2011        ISBN1441979700, 9781441979704  - 409 pages

Monge/Kantorovich/Vasershtein. Distance.

In this formulation the coupling of two random objects by a joint measure is replaced by a deterministic mapping of the first into the ... In the optimal transportation literature, the German spelling of Vasershtein, Wasser- stein, also caught on as a ...

27–30 May 2011, UT Austin    Shannon meets Ornstein

Robert M. Gray   Stanford University el eng

Vasershtein/Wasserstein (1969)

Vaserstein 2012   9 books

### Introduction to Commutative Algebra and Algebraic Geometry - Page 100

Ernst Kunz - 2012

(Vaserstein) A G M (r X s;R[X]) is equivalent to A(O) if and only if A is locally equivalent to A(O) for all m G Max(R). Proof. Let A and A(O) be locally equivalent for all m G Max(R). Let I denote the set of all a G R with the following property: For all f ...

Rational Number Theory in the 20th Century: From PNT to FLT - Page 227, 228, 255, 424, 600, 641, 642

Wladyslaw Narkiewicz - Springer 2012  - 654 pages ISBN0857295322, 9780857295323

15, 389–400 (1953) Vaserstein, L.N.: Waring's problem for commutative rings. J. Number Theory 26, 299–307 (1987) Vaserstein, L.N.: Every integer is a sum or difference of 28 integral eighth powers. J. Number Theory 28, 66–68 (1988) ...

Conn, W., Vaserstein, L.N.: On sums of three integral cubes. ...... Nauk SSSR 30, 687–689 (1941); Márki, L., Steinfeld, O., Szép, J.: Short ...

Issues in Mathematical Theory and Modeling: 2011 Edition - Page 202

Q Ashton Acton, PhD   ScholarlyEditions, 2012 ISBN1464966931, 9781464966934

Vaserstein and colleagues published their study in International Journal of Number Theory (Polynomial ... Additional information can be obtained by contacting L. Vaserstein, Pennsylvania State University, Dept. of Math, University Park, PA ...

Issues in Algebra, Geometry, and Topology: 2011 Edition

Q Ashton Acton, PhD ScholarlyEditions, 2012     ISBN1464966346, 9781464966347

R, Lambda), which is an analog for the results existing in the general linear groups; see [L.N. Vaserstein, The subnormal structure of general linear groups over rings, Math. Proc. Cambridge Philos. Soc., 108 (1990) 219-229; N.A. Vavilov, ...

Noncommutative Iwasawa Main Conjectures Over Totally Real Fields:  - Page 32

Münster, April 2011

John Coates, Peter Schneider, R. Sujatha - 2012

The following result of Vaserstein is very useful. Proposition 2.4. Let R be a semilocal ring. Then the natural inclusion of R D GL1.R/ into GL.

Number Theory, Analysis and Geometry - Page 346,347

In Memory of Serge Lang

D. Goldfeld - 2012 - 704 pages ISBN 10.1007/978-1-4614-1260-1

We may now apply the theorem of Mathews, Vaserstein, and Weisfeller [MVW], to , to conclude that for all sufficiently large l prime to N, say for all

l not in the finite set S, Γ maps onto . For any such l, Γ3 maps onto the image of in , i.e., Γ3 maps ...

[PDF] Stable range adequate Bezout duo-ring- Page 120

I Vasiunyk - International Mathematical Conference, 2012 - mmk.mdu.edu.ua

... Студ., 1998.–9.–№ 2.–С. 115-119. [3] Vaserstein LN The stable rank of rings and dimensionality

of topological spaces// Functional Anal. Appl., 1971.–5.–P. 102-110. [4] Васюник I. С, Забавський

БВ Стабiльний ранг дуо-кiльця Безу та його узагальнення//Прикл. пробл. мех. ...

Vaserstein

- Page 17

P Sarnak - Proceedings of MSRI conference on Thin Groups and … - math.princeton.edu

Page 1. Notes on Thin Matrix Groups Peter Sarnak Prepared for the MSRI hot topics

workshop on superstrong approximation (Feb. 2012). My aim is to give an overview

of the developments in the theory and its applications. ...

L. Vaserstein

### Geometric And Combinatorial Aspects Of Commutative Algebra - Page 224, 225

Jurgen Herzog, ‎Gaetana Restuccia - 2012

As mentioned, the special case of Theorem 6 for free commutative monoids is due to Suslin [8] (the case of a trivial monoid being the Bass-Vaserstein classical results on surjective KI stabilizations, see Ch. 5, §4 in [1] and [11]). In [4] we have ...

Wasserstein 2012  73 books

### Analysis and Numerics of Partial Differential Equations - six pages

Franco Brezzi, ‎Piero Colli Franzone, ‎Ugo Gianazza - 2012

On the other hand, by a result of Benamou and Brenier [3], given two probability densities f*,fon Q, the Wasserstein distance d(f,f*) ... Let us briefly review the notion of Kantorovich-Rubinstein-Wasserstein metric, or simply Wasserstein metric.

### Encyclopedia of Distances - Page 53, 143, 245

Michel Marie Deza, ‎Elena Deza - 2012

11). o KMMW metric Given a metric space (X, d), the Kantorovich-Mallows-Monge-Wasserstein metric, or KMMW metric, for short, or transportation distance, is defined by W1(P1,P2)Iinf1ES[d(X,Y)]Iinf/ d(X, Y)dS(X, Y), 5 (X,Y)GXXX where the ...

### Probability and Partial Differential Equations in Modern Applied Mathematics

Edward C. Waymire - 2012

This volume is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling.

### Survival trees - a new method in innovation theory:  - Page 49, 50

A successful introduction of a method commonly used in survival analysis into the field of innovation diffusion theory

A successful introduction of a method commonly used in survival analysis into the field of innovation diffusion theory ... Graphically, whenp :1, the Wasserstein metrics d1(S1, S2) between two KapIan-Meier curves 8; and S2 is the shaded area ...

### Scale Space and Variational Methods in Computer Vision

This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on Scale Space Methods and  Variational Methods in Computer Vision Location: Ein Gedi, ISRAEL Date: MAY 29-JUN 02, 2011

Book Editor(s): Bruckstein, AM; Romeny, BMT; Bronstein, AM; et al.

Page 435

Author(s): Rabin, Julien; Peyre, Gabriel; Delon, Julie; et al.

Volume: 6667   Pages: 435-446 Published: 2012

Issues in Applied Mathematics: 2011 Edition

... a method for numerical integration of Wasserstein gradient flows based on the classical minimizing movement scheme. ... to the nonlinear fourth-order Derrida-Lebowitz-Speer-Spohn equation, which arises in quantum semiconductor theory.

ScholarlyEditions, 2012

James E. Gentle, Wolfgang Karl Härdle, Yuichi Mori - 2012

There are well established statistics that measure the difference in distribution. In survival analysis, we ... Gordon and Olshen used the so-called Lp Wasserstein metrics, d p .; /;

as the measure of discrepancy between the two survival functions.

A Varian of Kolmogorovian Probability Emerging from Quantum Theory

MF Rosyid - Asian Physics Symposium, 2012 - prosiding.papsi.org

... The metric di defined on Ωi induced the Wasserstein metric W i d on PW(Ωi) through ... Now Let

ˆ ˆ :ε Σ × × Σ D P P W 1 W N A A ( ( )) . be a maping from the set of all density operators into

the product space of Wasserstein spaces ˆ Σ PW i A ( ( )) defined by ...

Scale Space and Variational Methods in Computer Vision:  - Page  xi, 250, 252, 254, 435, 436, 438, 439, 442, 445

Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 -- June 2, 2011, Revised Selected Papers

Alfred M. Bruckstein, Bart Ter Haar Romeny, Alexander M. Bronstein - Springer 2012 - 798 pages 3642247849, 9783642247842

Moreover, W2 is too difficult to handle in problems requiring the optimization of point clouds with functional involving the Wasserstein distance.

To overcome the time complexity involved by the numerical solving of such problem, the original Wasserstein metric is replaced by a sliced approximation over 1D distributions.

Recent Advances in Computer Science and Information Engineering: Volume 5 - Page 325

an, Lei Cao, Weilian Su - 2012 - 766 pages - Google eBook

 The Wasserstein miss-distance is proposed to evaluate the multitarget tracking performance [3]. Fig. 1. Plot of x and y components of position estimates (star) against time, superimposed on ground truth (solid line) (single experiment result) ...

Issues in Statistics, Decision Making, and Stochastics: 2011 Edition - Page 240

Q. Ashton Acton, PhD  ScholarlyEditions, 2012

ISBN 1464967040, 9781464967047 286 pages

 Wuhan University: Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition “Let (X-n)(n >= 1) be a sequence of i.i.d.r.v.'s with values in a Polish space (E, d) of law mu,” investigators in Wuhan, People's Republic of ...

Second Order Analysis on (P2(M), W2) - Page vii, xi, 2, 5, 6, 15, 16, 18, 49, 50, 51, 113, 123, 125, 154, 158

Nicola Gigli - 2012 - 154 pages

MR2344814 (2008j:49113) K.-T. Sturm, M.K. von Renesse, Entropic Measure and Wasserstein Diffusion, Ann. Probab. 37 (2009), pp. 1114–1191.

Robotics: Science and Systems VII - Page 166

e.comHugh Durrant-Whyte, Nicholas Roy, Pieter Abbeel - 2012 - 384 pages

C. Belief space metric To compute distance between beliefs in B (line 11 & 15 of Algorithm 1), GCS uses Wasserstein ... The Wasserstein distance WD(b,b) between two beliefs b,b B is the minimum expected distance in S among all ...

Visual Indexing and Retrieval - Page 25

books.google.comJenny Benois-Pineau, Frédéric Precioso, Matthieu Cord - 2012 - 107 pages - Google eBook

In that case, the EMD is equivalent to the 1st Mallows distance or 1st Wasserstein distance between the two distributions. Recently, Pele and Werman [163] proposed a modified version of EMD extending standard EMD to non-normalized ...

Professional Media Understanding:  - Page 215

The Common Methods of Audio Retrieval, Biosignal Processing, Content-Based Image Retrieval, Face Recognition, Music Classification, Speech Recognition, Text Retrieval and Video Surveillance

books.google.comHorst Eidenberger - 2012 - 256 pages

 M5 inf x sup y mi(x, y) Bottleneck distance. M6 max sup x infy m i (x, y) , sup y ... j mi( ̄xj, yj )c( ̄xj, y j ) K Mallows distance [133] (a.k.a. Wasserstein distance, earth mover's distance), where c() is the cost function weighting the distances. B.3.

Issues in Mathematical Theory and Modeling: 2011 Edition - Page 186

 “We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the ...

Helge Holden, Kenneth H. Karlsen - 2012 - 360 pages

... Wasserstein distance of order 1, W1(μ,ν) = sup: {∫ φdμ − ∫ φdν;φ1-Lipschitz } . Estimates of this sort are found in [95, Chap. 5] and date back to

the 1970s (Dobrushin [48], Braun and Hepp [24], Neunzert [87]).

Gangbo, W.: Hamiltonian ODE's in the Wasserstein space of probability

Foundations of Software Science and Computational Structures:  - Page 451

15th International Conference, FOSSACS 2012, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2012, Tallinn, Estonia, March 24 -- April 1, 2012, Proceedings

Lars Birkedal - 2012 - 484 pages

... 7. van Breugel, F., Worrell, J.: Approximating and computing behavioural distances in probabilistic transition systems. ... (1986) Thorsley, D.,

Klavins, E.: Approximating stochastic biochemical processes with Wasserstein pseudometrics.

Peter G. Casazza, Gitta Kutyniok - 2012

Given any nonzero vectors Φ = {φi }Mi=1, there are two natural embeddings into the space of probability measures, namely 1 ∑Mi=1φi2 M∑ i=1 φi 2 δφi/φi.

The 2-Wasserstein distance between μΦ and μΨ satisfies μΦ= 1 M M∑ i=1δφi and ...

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition - Page 107

ScholarlyEditions, Jan 4, 2012

“The coupling arises from the Stokes drag force exerted by a phase on the other. ... (2010 DEC 7) SISSA, Trieste: Estimates On Path Functionals Over

Wasserstein Spaces “In this paper we consider the class a functionals (introduced in ...

Advances in Dynamic Games:  - Page 44

Theory, Applications, and Numerical Methods for Differential and Stochastic Games

Pierre Cardaliaguet, Ross Cressman - 2012

An example of such a distance could be the classical Wasserstein distance or the Monge–Kantorovich distance between ... additive white Gaussian noise (AWGN) multiple-access channel with N senders with coupled constraints (or actions).

Metric and Differential Geometry: The Jeff Cheeger Anniversary Volume - Page 106

Xianzhe Dai, Xiaochun Rong - 2012

In 2005, Sturm introduced a new distance between metric measure spaces which leads to such limits more naturally and also interacts well with mass transport notions mentioned above [65]. He uses the Wasserstein distance, Wp, to measure

Integrated Tracking, Classification, and Sensor Management: Theory and Applications - Page 93, 94

Mahendra Mallick, Vikram Krishnamurthy, Ba-Ngu Vo - 2012

This distance was termed the Wasserstein metric in [44] because it yields the pth order Wasserstein metric between the empirical distributions of the point patterns Xand Y. The OMAT metric is not necessarily better than the Hausdorff ...

Operator Theory:  - Page 310, 317, 318, 319, 320, 321

Advances and Applications, Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton

Harry Dym, Mauricio C. de Oliveira, Mihai Putinar - 2012

Now noting the characterization of the Wasserstein norm from Equation (16), we see that the steepest gradient direction (with respect to the Wasserstein metric) is given by μt = div(μlogμ)=Δμ, which is the linear heat equation.

Thus inspired by the Benamou and Brenier [4], given two “points,” [14],}11 G D, the geodesic (Wasserstein) distance is: 1 ...

Multi-Scale and High-Contrast PDE: From Modelling, to Mathematical Analysis, toInversion - Page 93, 94

Habib Ammari, Yves Capdeboscq, Hyeonbae Kang - 2012 AMS Cont Math 577

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities as the Wasserstein gradient flow of the total variation.

Here, W2 (u0 Ld,uLd) is the 2–Wasserstein distance between u0Ld and uLd (Ld denotes the Lebesgue measure in Rd, d = 1,2) and defines a distance within the space of probability measures [3, 20, 21, 1, 17]. This minimisation problem can be interpreted as a discrete in time approximation of a solution of the gradient flow (1.1) of E(u) with respect to the L2 Wasserstein metric.

O (a) Prove that the function d2 I d2(F, G), which is known as the Wasserstein metric, is indeed a metric and the space 82 is complete for the metric d2.

e-Study Guide for: Asymptotic Theory of Statistics and Probability for Statistics and Machine Learning: Fundamentals and Advanced Topics by Anirban DasGupta

ISBN 9780387759708, Anirban DasGupta - 2012 - 43 pages

Eigenfunction Cell David V. Hinkley Wasserstein deterministic or essentially probabilistic) which is

analyzable in terr ... one pile into the other, Vi assumed to be the amount of dirt that needs to be moved times the distance it has to be moved

The name 'Wasserstein/Vasershtein distance'

Just the FACTS101 E-Study Guide For: Probability for Statistics and Machine Learning

ISBN 9781441996336, Anirban DasGupta - 2012 - 43 pages

Wasserstein Wasserstein Distance In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of ...

e-Study Guide for: Introduction to Probability and Statistics by William Mendenhall

Cram101 Textbook Reviews - 2012

Wasserstein metric d. Infinite monkey theorem 4. A ______ is a single measure of some attribute of a sample (e.g. its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items comprising the

Cram101 Textbook Reviews - 2012

For tossing two coins, the ______ is {(head,head), (head,tail), (tail,head), (tail,tail)}. a. Sample space b. Subjectivism c. Wasserstein metric d. Christopher Cattan ...

e-Study Guide for: Probability, Statistics, and Stochastic Processes by  Peter Olofsson

Cram101 Textbook Reviews - 2012 -

Standard probability space b. Subjectivism c. Wasserstein metric d. Sample space 5. In mathematics, a ______ is a set with some added structure. Mathematical _________s often form a hierarchy, i.e., one

ISBN 9780321570444

Cram101 Textbook Reviews - 2012

... if the experiment is tossing a coin, the ______ istheset {head, tail}. For tossing two coins, the ______ is {(head,head), (head,tail), (tail,head), (tail,tail)}. a. Standard probabilityspace b. Subjectivism c. Wasserstein metric d. Sample space 3. In.

Cram101 Textbook Reviews - 2012

... (tail,tail)}. a. Standard probability space b. Subjectivism c. Wasserstein metric d.Sample space Chapter 8. Random Variables ANSWER KEY 0. b.

e-Study Guide for: Discrete Calculus: Applied Analysis on Graphs for Computational Science by Leo J. Grady

Cram101 Textbook Reviews - 2012

Total variation c. Typical set d.Wasserstein metric 3. ______ is a class ofmachine learning techniques that make use ofboth labeled and unlabeled data for training typicallya small amount oflabeled data with a large amount ofunlabeled data.

Cram101 Textbook Reviews - 2012

For tossing two coins, the ______ is {(head,head), (head,tail), (tail,head), (tail,tail)}. a. Standard probability space b. Subjectivism c. Wasserstein metric d. Sample space 5.

Cram101 Textbook Reviews - 2012  ISBN147840180X, 9781478401803 47 pp

Wasserstein metric d. Structural equation modeling 5. In mathematics, a ______ is a setwith some added structure. Mathematical _________s often form a hierarchy, i.e., one ______ mayinherit all the characteristics ofa parent ______.

Mats Boij - 2012

... Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ... manifolds and applications, 2011 Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, part

N-Harmonic Mappings Between Annuli: The Art of Integrating Free Lagrangians - Page 110

Tadeusz Iwaniec, Tadeusz Iwaniec and Jani Onninen - 2012  Mem AMS

... Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ... manifolds and applications, 2011 Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, part

General Relativistic Self-Similar Waves That Induce an Anomalous Acceleration Into the Standard  Model of Cosmology - Page 74

Joel A. Smoller, Blake Temple - AMS  2012   69 pp

... Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ... manifolds and applications, 2011 Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, part

The Lin-Ni's Problem for Mean Convex Domains - Page 110

Olivier Druet, Frederic Robert, Juncheng Wei - 2012

... Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ... manifolds and applications, 2011 Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, part

Mark Behrens - 2012

... Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, ... manifolds and applications, 2011 Mark Walsh, Metrics of positive scalar curvature and generalised Morse functions, part

Gap Junctions in the Brain: Physiological and Pathological Roles - Page 276

Ekrem Dere - 2012

Role of olivary electrical coupling in cerebellar motor learning. Neuron 58, 599e612. Vandecasteele ... coupling is required for proper insulin production. J. Cell Biol. 131, 1561e1572. ... Wasserstein, J., 2005. Diagnostic issues for adolescents ...

Springer London, Limited, Jul 31, 2012 - 772 pages

ISBN-13: 9781461293699

Wasserstein

Stochastic Analysis and Related Topics - Page 203, 208

Laurent. Decreusefond, Jamal. Najim - 2012

In the case of Wiener space, we can define a stronger Wasserstein metric using the Cameron–Martin norm as we have already done in [5, 6] as follows: d2H.P;Q/ D

Infinite-Dimensional Representations Of 2-Groups - Page 125

John C. Baez, Aristide Baratin, Laurent Freidel - 2012  Mem AMS

... 2011 Wilfrid Gangbo, Hwa Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, 2011 Ralph Greenberg, Iwasawa theory, projective modules, and modular representations, ...

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations - Page 136

Igor Burban, Bernd Kreuler - 2012

Extended Graphical Calculus for Categorified Quantum Sl(2) - Page 92

Mikhail Khovanov - 2012

... 2011 Wilfrid Gangbo, Hwa Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, 2011 Ralph Greenberg, Iwasawa theory, projective modules, and modular representations, ...

Algebras in the Smooth and Algebraic Category - Page 71

Ernst Heintze, Christian Gross - 2012

... 2011 Wilfrid Gangbo, Hwa Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, 2011 Ralph Greenberg, Iwasawa theory, projective modules, and modular representations, ...

Modular Branching Rules for Projective Representations of Symmetric Groups - Page 128

A S Kleshcheev, Vladimir Shchigolev - 2012

Wasserstein space

The Reflective Lorentzian Lattices of Rank 3 - Page 113

Daniel Allcock - 2012  Mem AMS

Wasserstein space

Elliptic Integrable Systems: A Comprehensive Geometric Interpolation - Page 222

Idrisse Khemar - 2012 Mem AMS

... 2011 Wilfrid Gangbo, Hwa Kil Kim, and Tommaso Pacini, Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems, 2011 Ralph Greenberg, Iwasawa theory, projective modules, and modular representations, ...

Reifenberg Parameterizations for Sets With Holes - Page 106

Guy David, Tatiana Toro - 2012 Mem AMS

Wasserstein space

On L-Packets for Inner Forms of SLn - Page 101

Kaoru Hiraga, Hiroshi Saito - 2012  Mem AMS

Wasserstein space

Dimer Models and Calabi-Yau Algebras - Page 90

Nathan Broomhead - 2012 Mem AMS

Wasserstein space

Chevalley Supergroups - Page 68

MR2918543  Fioresi, R.; Gavarini, F. Chevalley supergroups. Mem. Amer. Math. Soc. 215 (2012), no. 1014, vi+64 pp. ISBN: 978-0-8218-5300-9 14M30 (17Bxx 58A50)

Wasserstein space

Weighted Shifts on Directed Trees - Page 111

Zenon Jan Jablónski, Il Bong Jung, Jan Stochel - 2012 Mem AMS

Wasserstein space

Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates - Page 136

Jun Kigami - 2012  Mem AMS

Wasserstein space

Towards a Modulo $p$ Langlands Correspondence for GL$_2$ - Page 118

Chistophe Breuil, Vytautas Paskunas - 2012   Mem AMS

Wasserstein space