Tropical Circuit Complexity
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Tropical Circuit Complexity
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Author : Stasys Jukna
language : en
Publisher: Springer Nature
Release Date : 2023-12-08
Tropical Circuit Complexity written by Stasys Jukna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-08 with Mathematics categories.
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems. In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min,+) or (max,+) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits. In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.
Tropical And Non Archimedean Geometry
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Author : Omid Amini
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-26
Tropical And Non Archimedean Geometry written by Omid Amini 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 2014-12-26 with Mathematics categories.
Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.
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 $texttt{polymake}$.
Randomization Relaxation And Complexity In Polynomial Equation Solving
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Author : Leonid Gurvits
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Randomization Relaxation And Complexity In Polynomial Equation Solving written by Leonid Gurvits 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 2011 with Mathematics categories.
This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28-March 5, 2010. It contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and examine core topics.
Integer Programming And Combinatorial Optimization
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Author : Alberto Del Pia
language : en
Publisher: Springer Nature
Release Date : 2023-05-21
Integer Programming And Combinatorial Optimization written by Alberto Del Pia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-21 with Computers categories.
This book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Topological And Statistical Methods For Complex Data
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Author : Janine Bennett
language : en
Publisher: Springer
Release Date : 2014-11-19
Topological And Statistical Methods For Complex Data written by Janine Bennett and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
Applied Cryptography And Network Security Workshops
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Author : Martin Andreoni
language : en
Publisher: Springer Nature
Release Date :
Applied Cryptography And Network Security Workshops written by Martin Andreoni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Voyager
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Author : Stephen J. Pyne
language : en
Publisher: Penguin
Release Date : 2010-07-22
Voyager written by Stephen J. Pyne and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-22 with Science categories.
A brilliant new account of the Voyager space program-its history, scientific impact, and cultural legacy Launched in 1977, the two unmanned Voyager spacecraft have completed their Grand Tour to the four outer planets, and they are now on course to become the first man-made objects to exit our solar system. To many, this remarkable achievement is the culmination of a golden age of American planetary exploration, begun in the wake of the 1957 Sputnik launch. More than this, Voyager may be one of the purest expressions of exploration in human history. For more than five hundred years the West has been powered by the impulse to explore, to push into a wider world. In this highly original book, Stephen Pyne recasts Voyager in the tradition of Magellan, Columbus, Cook, Lewis and Clark, and other landmark explorers. The Renaissance and Enlightenment-the First and Second Ages of Discovery- sent humans across continents and oceans to find new worlds. In the Third Age, expeditions have penetrated the Antarctic ice, reached the floors of the oceans, and traveled to the planets by new means, most spectacularly via semi-autonomous robot. Voyager probes how the themes of motive and reward are stunningly parallel through all three ages. Voyager, which gave us the first breathtaking images of Jupiter and Saturn, changed our sense of our own place in the universe.
Modeling And Simulation
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Author :
language : en
Publisher:
Release Date : 1980
Modeling And Simulation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Computer simulation categories.
Radar And Electronics
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Author :
language : en
Publisher:
Release Date : 1963
Radar And Electronics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Electronics categories.