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1. On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere

Author

Eduard Gorbunov, Alexander Gasnikov, Evgeniya Vorontsova, Moscow Institute of Physics and Technology [Moscow] (MIPT), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Far Eastern Federal University (FEFU)

Subjects
Unit sphere, Concentration of measure, General Mathematics, 010102 general mathematics, Mathematical analysis, MathematicsofComputing_GENERAL, 02 engineering and technology, 16. Peace & justice, равномерно распределённый насфере вектор, 01 natural sciences, Measure (mathematics), Upper and lower bounds, 020303 mechanical engineering & transports, 0203 mechanical engineering, Optimization and Control (math.OC), Phenomenon, Euclidean geometry, FOS: Mathematics, Mathematics::Metric Geometry, концентрация меры, 0101 mathematics, [MATH]Mathematics [math], Mathematics - Optimization and Control, Mathematics
Abstract

We considered the problem of obtaining upper bounds for the mathematical expectation of the $q$-norm ($2\leqslant q \leqslant \infty$) of the vector which is uniformly distributed on the unit Euclidean sphere. We finish the paper with numerical experiments illustrating our results., Comment: in Russian, 10 pages, 2 figures

Published
2019

2. Partial orders based on inverses along elements

Author

Alexander Guterman, Pavel Shteyner, Xavier Mary, Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Lomonosov Moscow State University (MSU), and ANR-11-LABX-0023,MME-DII,Modèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions(2011)

Subjects
Statistics and Probability, Pure mathematics, Applied Mathematics, General Mathematics, 010102 general mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], 0211 other engineering and technologies, 021107 urban & regional planning, 02 engineering and technology, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Order (group theory), 0101 mathematics, Element (category theory), ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

The paper introduces and investigates partial orders that are finer than the minus partial order and are based on inverses along an element and other specific outer inverses. It turns out that in this way a number of classical partial orders can be equivalently defined.

Published
2017

3. A structural pattern based method for automated morphological analysis of word forms in a natural language

Author

Andrey Chepovskiy, Elena Egorova, Alexei Lavrentiev, Interactions, Corpus, Apprentissages, Représentations (ICAR), École normale supérieure de Lyon (ENS de Lyon)-Université Lumière - Lyon 2 (UL2)-INRP-Ecole Normale Supérieure Lettres et Sciences Humaines (ENS LSH)-Centre National de la Recherche Scientifique (CNRS), Department of Applied Mathematics - State University Higher School of Economics, State University Higher School of Economics, Les auteurs remercient le LABEX ASLAN (ANR-10-LABX-0081) de l'Université de Lyon pour son soutien financier dans le cadre du programme 'Investissements d'Avenir' (ANR-11-IDEX-0007) de l'Etat Français géré par l'Agence Nationale de la Recherche (ANR)., ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-INRP-Ecole Normale Supérieure Lettres et Sciences Humaines (ENS LSH)-Centre National de la Recherche Scientifique (CNRS), and ANR-11-IDEX-0007,Avenir L.S.E.,Advanced Studies on Language Complexity(2011)

Subjects
Statistics and Probability, алгоритм выделения основ, General Mathematics, computer.software_genre, 01 natural sciences, 010305 fluids & plasmas, word structural pattern, 0103 physical sciences, анализ текстов на естественном языке, 0101 mathematics, natural language processing, [SHS.LANGUE]Humanities and Social Sciences/Linguistics, алгоритм морфологического разбора, Mathematics, business.industry, Applied Mathematics, 010102 general mathematics, French, morphological analysis algorithm, Word formation, language.human_language, stemming algorithm, French language, Morphological analysis, language, algorithms of morphological analysis, Artificial intelligence, структурная схема слова, business, Algorithm, computer, Natural language, Word (computer architecture), Natural language processing
Abstract

International audience; http://mech.math.msu.su/~fpm/ps/k14/k143/k14303.pdfIn this paper, a computerized model for morphological analysis of languages with word-formation based on affixation processes is proposed. The main idea consists in defining structural patterns of words and corresponding lists of suffixes. First, a detaileddescription of a stemming algorithm, its modification, and the technique of determining grammatical characteristics of word-forms are given. The next part of this work focuses on the application of the proposed algorithms for the French language. Finally, some results of execution of these algorithms are provided.; http://mech.math.msu.su/~fpm/ps/k14/k143/k14303.pdfВ работе предлагается метод структурных схем в качестве модели морфологического анализа словоформ естественного языка с развитым аффиксальным словообразованием и словоизменением. Дано описание алгоритма выделения псевдоосновы, его модификация, а также алгоритм восстановления грамматических характеристик словоформ. Описано применение предложенного метода для анализа словоформ французского языка. Представлены результаты работы предложенных алгоритмов.

Published
2015