Essentials Of Tropical Combinatorics
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Essentials Of Tropical Combinatorics
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Author : Michael Joswig
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-08
Essentials Of Tropical Combinatorics written by Michael Joswig and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.
Surveys In Combinatorics 2022
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Author : Anthony Nixon
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Surveys In Combinatorics 2022 written by Anthony Nixon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Introduction To Tropical Geometry
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Author : Diane Maclagan
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-15
Introduction To Tropical Geometry written by Diane Maclagan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-15 with Mathematics categories.
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature.
Discrete Mathematics Days 2022
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Author : Luis Felipe Tabera Alonso
language : en
Publisher: Ed. Universidad de Cantabria
Release Date : 2022-07-04
Discrete Mathematics Days 2022 written by Luis Felipe Tabera Alonso and has been published by Ed. Universidad de Cantabria this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-04 with Mathematics categories.
El congreso Discrete Mathematics Days (DMD20/22) tendrá lugar del 4 al 6 de julio de 2022, en la Facultad de Ciencias de la Universidad de Cantabria (Santander, España). Este congreso internacional se centra en avances dentro del campo de la Matemática discreta, incluyendo, de manera no exhaustiva: · Algoritmos y Complejidad · Combinatoria · Teoría de Códigos · Criptografía · Geometría Discreta y Computacional · Optimización Discreta · Teoría de Grafos · Problemas de localización discreta y temas relacionados Las ediciones anteriores de este evento se celebraros en Sevilla (2018) y Barcelona (2016), estos congresos heredan la tradición de las Jornadas de Matemática Discreta y Algorítmica (JMDA), el encuentro bienal en España en Matemática Discreta (desde 1998). Durante la celebración del congreso tendrán lugar cuatro conferencias plenarias, cuarenta y dos presentaciones orales y una sesión de once pósteres. Abstract The Discrete Mathematics Days (DMD20/22) will be held on July 4-6, 2022, at Facultad de Ciencias of the Universidad de Cantabria (Santander, Spain). The main focus of this international conference is on current topics in Discrete Mathematics, including (but not limited to): Algorithms and Complexity Combinatorics Coding Theory Cryptography Discrete and Computational Geometry Discrete Optimization Graph Theory Location and Related Problems The previous editions were held in Sevilla in 2018 and in Barcelona in 2016, inheriting the tradition of the Jornadas de Matemática Discreta y Algorítmica (JMDA), the Spanish biennial meeting (since 1998) on Discrete Mathematics. The program consists on four plenary talks, 42 contributed talks and a poster session with 11 contributions.
Mathematical Software Icms 2024
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Author : Kevin Buzzard
language : en
Publisher: Springer Nature
Release Date : 2024-07-16
Mathematical Software Icms 2024 written by Kevin Buzzard and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Computers categories.
This book constitutes the proceedings of the 8th International Conference on Mathematical Software, ICMS 2024, held in Durham, UK, during July 22–25, 2024. The 37 full papers presented were carefully reviewed and selected from 46 submissions. The papers are organized in subject areas as follows: plenary lectures; number theory and related areas; novel formalisations of mathematics in lean; software for the applications of group theory to combinatorics; classical algebraic geometry & modern computer algebra: innovative software design and its applications; advancing computer algebra with massively parallel methods; computer algebra applications in the life sciences; machine learning within computer algebra systems; numerical software for special functions; mathematical research data; symbolic-numeric methods in algebraic geometry; Polyhedral geometry and combinatorics; general session.
Topological And Ergodic Theory Of Symbolic Dynamics
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Author : Henk Bruin
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-20
Topological And Ergodic Theory Of Symbolic Dynamics written by Henk Bruin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Intelligent Systems And Applications
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Author : Kohei Arai
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Intelligent Systems And Applications written by Kohei Arai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Technology & Engineering categories.
This book presents Proceedings of the 2021 Intelligent Systems Conference which is a remarkable collection of chapters covering a wider range of topics in areas of intelligent systems and artificial intelligence and their applications to the real world. The conference attracted a total of 496 submissions from many academic pioneering researchers, scientists, industrial engineers, and students from all around the world. These submissions underwent a double-blind peer-review process. Of the total submissions, 180 submissions have been selected to be included in these proceedings. As we witness exponential growth of computational intelligence in several directions and use of intelligent systems in everyday applications, this book is an ideal resource for reporting latest innovations and future of AI. The chapters include theory and application on all aspects of artificial intelligence, from classical to intelligent scope. We hope that readers find the book interesting and valuable; it provides the state-of-the-art intelligent methods and techniques for solving real-world problems along with a vision of the future research.
Invitation To Nonlinear Algebra
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Author : Mateusz Michałek
language : en
Publisher: American Mathematical Society
Release Date : 2021-03-05
Invitation To Nonlinear Algebra written by Mateusz Michałek and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-05 with Mathematics categories.
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
Existence Of Unimodular Triangulations Positive Results
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Author : Christian Haase
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Existence Of Unimodular Triangulations Positive Results written by Christian Haase and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
The Computer Algebra System Oscar
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Author : Wolfram Decker
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
The Computer Algebra System Oscar written by Wolfram Decker and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.
This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.