Tropical Circuit Complexity

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Tropical Circuit Complexity

Author : Stasys Jukna
Publisher : Springer Nature
ISBN 13 : 3031423542
Total Pages : 138 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Tropical Circuit Complexity by : Stasys Jukna

Download or read book Tropical Circuit Complexity written by Stasys Jukna and published by Springer Nature. This book was released on 2023-12-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Omid Amini
Publisher : American Mathematical Soc.
ISBN 13 : 1470410214
Total Pages : 274 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tropical and Non-Archimedean Geometry by : Omid Amini

Download or read book Tropical and Non-Archimedean Geometry written by Omid Amini and published by American Mathematical Soc.. This book was released on 2014-12-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Michael Joswig
Publisher : American Mathematical Society
ISBN 13 : 1470467410
Total Pages : 398 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Essentials of Tropical Combinatorics by : Michael Joswig

Download or read book Essentials of Tropical Combinatorics written by Michael Joswig and published by American Mathematical Society. This book was released on 2021-12-08 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Leonid Gurvits
Publisher : American Mathematical Soc.
ISBN 13 : 0821852280
Total Pages : 230 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Randomization, Relaxation, and Complexity in Polynomial Equation Solving by : Leonid Gurvits

Download or read book Randomization, Relaxation, and Complexity in Polynomial Equation Solving written by Leonid Gurvits and published by American Mathematical Soc.. This book was released on 2011 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Alberto Del Pia
Publisher : Springer Nature
ISBN 13 : 3031327268
Total Pages : 494 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Integer Programming and Combinatorial Optimization by : Alberto Del Pia

Download or read book Integer Programming and Combinatorial Optimization written by Alberto Del Pia and published by Springer Nature. This book was released on 2023-05-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Janine Bennett
Publisher : Springer
ISBN 13 : 3662449005
Total Pages : 297 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Topological and Statistical Methods for Complex Data by : Janine Bennett

Download or read book Topological and Statistical Methods for Complex Data written by Janine Bennett and published by Springer. This book was released on 2014-11-19 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ecological Networks in the Tropics

Author : Wesley Dáttilo
Publisher : Springer
ISBN 13 : 3319682288
Total Pages : 207 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Ecological Networks in the Tropics by : Wesley Dáttilo

Download or read book Ecological Networks in the Tropics written by Wesley Dáttilo and published by Springer. This book was released on 2018-02-08 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on graph theory studies this book seeks to understand how tropical species interact with each other and how these interactions are affected by perturbations in some of the most species-rich habitats on earth. Due to the great diversity of species and interactions in the tropics, this book addresses a wide range of current and future issues with empirical examples and complete revisions on different types of ecological networks: from mutualisms to antagonisms. The goal of this publication is not to be only for researchers but also for undergraduates in different areas of knowledge, and also to serve as a reference text for graduate-level courses mainly in the life sciences.

Extremal Combinatorics

Author : Stasys Jukna
Publisher : Springer Science & Business Media
ISBN 13 : 3662046504
Total Pages : 389 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Extremal Combinatorics by : Stasys Jukna

Download or read book Extremal Combinatorics written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.

In the Shadows of the Tropics

Author : James S. Duncan
Publisher : Routledge
ISBN 13 : 1317117735
Total Pages : 229 pages
Book Rating : 4.3/5 (171 download)

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Book Synopsis In the Shadows of the Tropics by : James S. Duncan

Download or read book In the Shadows of the Tropics written by James S. Duncan and published by Routledge. This book was released on 2016-05-23 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this original work James Duncan explores the transformation of Ceylon during the mid-nineteenth century into one of the most important coffee growing regions of the world and investigates the consequent ecological disaster which erased coffee from the island. Using this fascinating case study by way of illustration, In the Shadows of the Tropics reveals the spatial unevenness and fragmentation of modernity through a focus on modern governmentality and biopower. It argues that the practices of colonial power, and the differences that race and tropical climates were thought to make, were central to the working out of modern governmental rationalities. In this context, the usefulness of Foucault's notions of biopower, discipline and governmentality are examined. The work contributes an important rural focus to current work on studies of governmentality in geography and offers a welcome non-state dimension by considering the role of the plantation economy and individual capitalists in the lives and deaths of labourers, the destabilization of subsistence farming and the aggressive re-territorialization of populations from India to Ceylon.

The Future of Tropical Rain Forests in South East Asia

Author : J. Davidson
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis The Future of Tropical Rain Forests in South East Asia by : J. Davidson

Download or read book The Future of Tropical Rain Forests in South East Asia written by J. Davidson and published by . This book was released on 1985 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Forests, Water and People in the Humid Tropics

Author : M. Bonell
Publisher : Cambridge University Press
ISBN 13 : 9780521829533
Total Pages : 960 pages
Book Rating : 4.8/5 (295 download)

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Book Synopsis Forests, Water and People in the Humid Tropics by : M. Bonell

Download or read book Forests, Water and People in the Humid Tropics written by M. Bonell and published by Cambridge University Press. This book was released on 2004 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forests, Water and People in the Humid Tropics is the most comprehensive review available of the hydrological and physiological functioning of tropical rain forests, the environmental impacts of their disturbance and conversion to other land uses, and optimum strategies for managing them. The book brings together leading specialists in such diverse fields as tropical anthropology and human geography, environmental economics, climatology and meteorology, hydrology, geomorphology, plant and aquatic ecology, forestry and conservation agronomy. The editors have supplemented the individual contributions with invaluable overviews of the main sections and provide key pointers for future research. Specialists will find authenticated detail in chapters written by experts on a whole range of people-water-land use issues, managers and practitioners will learn more about the implications of ongoing and planned forest conversion, while scientists and students will appreciate a unique review of the literature.

Boolean Function Complexity

Author : Stasys Jukna
Publisher : Springer Science & Business Media
ISBN 13 : 3642245080
Total Pages : 618 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Boolean Function Complexity by : Stasys Jukna

Download or read book Boolean Function Complexity written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.

Introduction to Tropical Geometry

Author : Diane Maclagan
Publisher : American Mathematical Society
ISBN 13 : 1470468565
Total Pages : 363 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Tropical Geometry by : Diane Maclagan

Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

Complexity

Author : M. Mitchell Waldrop
Publisher : Open Road Media
ISBN 13 : 150405914X
Total Pages : 492 pages
Book Rating : 4.5/5 (4 download)

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Book Synopsis Complexity by : M. Mitchell Waldrop

Download or read book Complexity written by M. Mitchell Waldrop and published by Open Road Media. This book was released on 2019-10-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: “If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly

Tropical Trees and Forests

Author : F. Halle
Publisher : Springer Science & Business Media
ISBN 13 : 3642811906
Total Pages : 457 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Tropical Trees and Forests by : F. Halle

Download or read book Tropical Trees and Forests written by F. Halle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Cryptography and Network Security Workshops

Author : Martin Andreoni
Publisher : Springer Nature
ISBN 13 : 3031614895
Total Pages : 253 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Applied Cryptography and Network Security Workshops by : Martin Andreoni

Download or read book Applied Cryptography and Network Security Workshops written by Martin Andreoni and published by Springer Nature. This book was released on with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Voyager

Author : Stephen J. Pyne
Publisher : Penguin
ISBN 13 : 1101190299
Total Pages : 431 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Voyager by : Stephen J. Pyne

Download or read book Voyager written by Stephen J. Pyne and published by Penguin. This book was released on 2010-07-22 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.