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An Invitation to Statistics in Wasserstein Space
This book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation.
An Invitation to Abstract Mathematics
this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.
An Introduction to Quantum and Vassiliev Knot Invariants
Provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.
An Introduction to Kolmogorov Complexity and Its Applications
Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications.
Algorithms on Trees and Graphs : With Python Code
Introduces graph algorithms on an intuitive basis followed by a detailed exposition using structured pseudocode, with correctness proofs as well as worst-case analyses. Centered around the fundamental issue of graph isomorphism, the content goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. Numerous illustrations, examples, problems, exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference. Furthermore, Python code for all algorithms presented is given in an appendix. Topics and features: Algorithms are first presented on an intuitive basis, followed by a detailed exposition using structured pseudocode / Correctness proofs are given, together with a worst-case analysis of the algorithms / Full implementation of all the algorithms in Python / An extensive chapter is devoted to the algorithmic techniques used in the book / Solutions to all the problems
Algorithms in Invariant Theory
The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions.
Algorithms in Bioinformatics ; Vol. 3692 ; 5th international workshop, WABI 2005, Mallorca, Spain, October 3-6, 2005, Proceedings
this book present the proceedings of the 5th Workshop on Algorithmsin Bioinformatics (WABI 2005) which took place in Spain, 2005. The Workshop on Algorithms in Bioinformatics highlights research workspecifically developed to address algorithmic problems in biosequence analysis. The emphasis is therefore on statistical and probabilistic algorithms that addressimportant problems in the field of molecular and structural biology. the workshop aims to present recent research results, includingsignificant work in progress, and to identify and explore directions of futureresearch.Original research papers (including significant work in progress) or state-of-the-art surveys were solicited on all aspects of algorithms in bioinformatics,including, but not limited to: exact and approximate algorithms for genomics,genetics, sequence analysis, gene and signal recognition, alignment, molecularevolution, phylogenetics, structure determination or prediction, gene expressionand gene networks, proteomics, functional genomics, and drug design.
Algorithms in Bioinformatics ; 8th International Workshop, WABI 2008, Karlsruhe, Germany, September 15-19, 2008. Proceedings
This book constitutes the refereed proceedings of the 8th International Workshop on Algorithms in Bioinformatics, WABI 2008, held in Karlsruhe, Germany, in September 2008 as part of the ALGO 2008 meeting.
Algorithms for Decision Making
A broad introduction to algorithms for decision making under uncertainty, introducing the underlying mathematical problem formulations and the algorithms for solving them. Automated decision-making systems or decision-support systems—used in applications that range from aircraft collision avoidance to breast cancer screening—must be designed to account for various sources of uncertainty while carefully balancing multiple objectives. This textbook provides a broad introduction to algorithms for decision making under uncertainty, covering the underlying mathematical problem formulations and the algorithms for solving them.
Algorithms for a New World : When Big Data and Mathematical Models Meet
Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.
Algorithms and Programming : Problems and Solutions
This book containing classical and well-known problems supplemented by clear and in-depth explanations. The material covered includes such topics as combinatorics, sorting, searching, queues, grammar and parsing, selected well-known algorithms and much more.
Algorithms and data structures ; 9th international workshop, WADS 2005, Waterloo, Canada, August 15-17, 2005, Proceedings
The papers in this volume were presented at the 9th Workshop on Algorithmsand Data Structures (WADS 2005). at the University of Waterloo, Waterloo, Canada. The workshopalternates with the Scandinavian Workshop on Algorithm Theory (SWAT), con-tinuing the tradition of SWAT and WADS starting with SWAT 1988 and WADS1989. From 90 submissions, the Program Committee selected 37 papers for pre-sentation at the workshop. includ Algorithm Analysis and Problem Complexity Data Structures Discrete Mathematics in Computer Science Computer Graphics Numeric Computing
Algorithms and computation ; 19th International symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings
This book constitutes the refereed proceedings of the 19th International Symposium on Algorithms and Computation, ISAAC 2008, held in Gold Coast, Australia in December 2008.
Algorithms and computation ; 15th international symposium, ISAAC 2004, Hong Kong, China, December 20-22, 2004, Proceedings
This volume contains the proceedings of the 15th Annual International Sym- sium on Algorithms and Computation (ISAAC 2004), held in Hong Kong, 2004. ISAAC is an annual international symposium that covers a wide range of topics,namelyalgorithmsandcomputation. aftar review process the committee selected 76 papers, the decisions being based on originality and relevance to the ?eld of algorithms and computation.
Algorithms - ESA 2008 ; 16th Annual European Symposium, Karlsruhe, Germany, September 15-17, 2008. Proceedings
This book constitutes the refereed proceedings of the 16th Annual European Symposium on Algorithms, ESA 2008, held in Karlsruhe, Germany, in September 2008 in the context of the combined conference ALGO 2008.
Algorithms – ESA 2007 ; 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007, Proceedings
This book presented submissions in the engineering and applications track. The papers address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applicat.
Algorithms - ESA 2006 ; 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006, Proceedings
This book constitutes the refereed proceedings of the 14th Annual European Symposium on Algorithms, ESA 2006, held in Zurich, Switzerland, in the context of the combined conference ALGO 2006. The book presents 70 revised full papers together with abstracts of 3 invited lectures. The papers address all current subjects in algorithmics, reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.
Algorithms – ESA 2005 ; 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005, Proceedings
This volume contains the 75 contributed papers and the abstracts of the threeinvited lectures presented at the 13th Annual European Symposium on Algo-rithms (ESA 2005), held in Spain, 2005. respectively.Papers were solicited in all areas of algorithmic research, including but notlimited to algorithmic aspects of networks, approximation and on-line algo-rithms, computational biology, computational geometry, computational financeand algorithmic game theory, data structures, database and information re-trieval, external memory algorithms, graph algorithms, graph drawing, machinelearning, mobile computing, pattern matching and data compression, quantumcomputing, and randomized algorithms. The algorithms could be sequential,distributed, or parallel. Submissions were especially encouraged in the area ofmathematical programming and operations research, including combinatorialoptimization, integer programming, polyhedral combinatorics, and semidefiniteprogramming.Each extended abstract was submitted to one of the two tracks.
Algorithmic number theory ; 8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings
This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008.
Algorithmic Game Theory ; 1st International Symposium, SAGT 2008, Paderborn, Germany, April 30-May 2, 2008. Proceedings
This book constitutes the refereed proceedings of the First International Symposium on Algorithmic Game Theory, SAGT 2008, held in Paderborn, Germany, in April/May 2008.
