Tropical Circuit Complexity

Author : Stasys Jukna
Publisher : Springer Nature
Page : 138 pages
File Size : 48,9 Mb
Release : 2023-12-08
Category : Mathematics
ISBN : 9783031423543

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Tropical Circuit Complexity by Stasys Jukna Pdf

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.

Author : Omid Amini,Matthew Baker,Xander Faber
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 42,8 Mb
Release : 2014-12-26
Category : Mathematics
ISBN : 9781470410216

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Tropical and Non-Archimedean Geometry by Omid Amini,Matthew Baker,Xander Faber Pdf

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.

Author : Michael Joswig
Publisher : American Mathematical Society
Page : 398 pages
File Size : 43,6 Mb
Release : 2021-12-08
Category : Mathematics
ISBN : 9781470467418

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Essentials of Tropical Combinatorics by Michael Joswig Pdf

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 $texttt{polymake}$.

Author : Leonid Gurvits
Publisher : American Mathematical Soc.
Page : 230 pages
File Size : 40,7 Mb
Release : 2011
Category : Algorithms
ISBN : 9780821852286

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Randomization, Relaxation, and Complexity in Polynomial Equation Solving by Leonid Gurvits Pdf

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.

Author : Alberto Del Pia,Volker Kaibel
Publisher : Springer Nature
Page : 494 pages
File Size : 45,6 Mb
Release : 2023-05-21
Category : Computers
ISBN : 9783031327261

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Integer Programming and Combinatorial Optimization by Alberto Del Pia,Volker Kaibel Pdf

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.

Author : Wesley Dáttilo,Victor Rico-Gray
Publisher : Springer
Page : 202 pages
File Size : 44,9 Mb
Release : 2018-02-08
Category : Science
ISBN : 9783319682280

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Ecological Networks in the Tropics by Wesley Dáttilo,Victor Rico-Gray Pdf

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.

Author : Janine Bennett,Fabien Vivodtzev,Valerio Pascucci
Publisher : Springer
Page : 297 pages
File Size : 42,8 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9783662449004

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Topological and Statistical Methods for Complex Data by Janine Bennett,Fabien Vivodtzev,Valerio Pascucci Pdf

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.

Author : James S. Duncan
Publisher : Routledge
Page : 228 pages
File Size : 55,9 Mb
Release : 2016-05-23
Category : Science
ISBN : 9781317117735

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In the Shadows of the Tropics by James S. Duncan Pdf

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.

Author : M. Bonell,L. A. Bruijnzeel
Publisher : Cambridge University Press
Page : 960 pages
File Size : 54,9 Mb
Release : 2004
Category : Nature
ISBN : 0521829534

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Forests, Water and People in the Humid Tropics by M. Bonell,L. A. Bruijnzeel Pdf

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.

Author : Stephen J. Pyne
Publisher : Penguin
Page : 423 pages
File Size : 51,7 Mb
Release : 2010-07-22
Category : Science
ISBN : 9781101190296

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Voyager by Stephen J. Pyne Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 536 pages
File Size : 51,5 Mb
Release : 1999
Category : Forest conservation
ISBN : STANFORD:36105121708502

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Tropical Forest Update by Anonim Pdf

Author : Eileen Crist,H. Bruce Rinker
Publisher : MIT Press
Page : 782 pages
File Size : 44,9 Mb
Release : 2010
Category : Nature
ISBN : 9780262033756

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Gaia in Turmoil by Eileen Crist,H. Bruce Rinker Pdf

Essays link Gaian science to such global environmental quandaries as climate change and biodiversity destruction, providing perspectives from science, philosophy, politics, and technology.

Author : Eugene A. Sharkov
Publisher : Unknown
Page : 344 pages
File Size : 53,9 Mb
Release : 1998-10-27
Category : Science
ISBN : MINN:31951D01780775Z

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Remote Sensing of Tropical Regions by Eugene A. Sharkov Pdf

The tropical regions of the Earth play a crucial role in the evolution of the global thermodynamic surface-atmosphere system, and in the socio-ecological processes on our planet. The well known clichés describing the tropics as "the firebox of the atmosphere" and "the lungs of the planet" are not exaggerations. The principle purposes of this book are to demonstrate the unique capabilities of modern remote sensing techniques for the observation and monitoring of tropical ecosystems, and to substantiate the scientific rationale for studies of the Earth?s tropical regions. In the first part of this book, the author places particular emphasis on specific features of low-latitude conditions, such as tropical cyclones, mesoscale tropical systems, dynamical features in tropical oceans, and the temperature and humidity structure of the tropical atmosphere. Remote sensing of the tropics in the visual and infrared bands is severely limited by cloud cover, and for this reason microwave remote sensing is of great importance for observations of tropical systems. In the second part of this book, the author considers the basic principles of microwave sounding, and the role of both passive and active remote sensing methods for tropical ecosystem monitoring. He presents examples of applications in areas such as rainforest monitoring, crop mapping, population distribution, hydrology studies and the monitoring of biomass burning and active geodetic zones. The book concludes with a synopsis of the current status of operational satellite systems and future plans for tropical studies using remote sensing. Readership: Undergraduate and postgraduate students of geography, meteorology, climatology, atmospheric physics, geophysics, oceanography, tropical agriculture and environmental science. Professional scientists, environmentalists and engineers concerned with tropical ecosystems, and government agencies and industries involved with management, planning and hazard assessment in tropical regions.

Author : Ilia Itenberg,Grigory Mikhalkin,Eugenii I. Shustin
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 41,6 Mb
Release : 2009-05-30
Category : Mathematics
ISBN : 9783034600484

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Tropical Algebraic Geometry by Ilia Itenberg,Grigory Mikhalkin,Eugenii I. Shustin Pdf

These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Author : J. Davidson,John Michael Davidson,Tho Yow Pong,Maarten Bijleveld
Publisher : Unknown
Page : 132 pages
File Size : 46,9 Mb
Release : 1985
Category : Forest conservation
ISBN : IND:39000009174645

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The Future of Tropical Rain Forests in South East Asia by J. Davidson,John Michael Davidson,Tho Yow Pong,Maarten Bijleveld Pdf