Tropical Circuit Complexity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Tropical Circuit Complexity PDF full book. Access full book title Tropical Circuit Complexity by Stasys Jukna. Download full books in PDF and EPUB format.
Author: Stasys Jukna
Publisher: Springer Nature
ISBN: 3031423542
Category : Mathematics
Languages : en
Pages : 138
Get Book Here
Book Description
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: Stasys Jukna
Publisher: Springer Nature
ISBN: 3031423542
Category : Mathematics
Languages : en
Pages : 138
Get Book Here
Book Description
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
Publisher: American Mathematical Soc.
ISBN: 1470410214
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
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
ISBN: 1470467410
Category : Mathematics
Languages : en
Pages : 398
Get Book Here
Book Description
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.
ISBN: 0821852280
Category : Mathematics
Languages : en
Pages : 230
Get Book Here
Book Description
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
Publisher: Springer Nature
ISBN: 3031327268
Category : Computers
Languages : en
Pages : 494
Get Book Here
Book Description
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: Janine Bennett
Publisher: Springer
ISBN: 3662449005
Category : Mathematics
Languages : en
Pages : 297
Get Book Here
Book Description
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: Wesley Dáttilo
Publisher: Springer
ISBN: 3319682288
Category : Science
Languages : en
Pages : 207
Get Book Here
Book Description
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: James S. Duncan
Publisher: Routledge
ISBN: 1317117735
Category : Science
Languages : en
Pages : 229
Get Book Here
Book Description
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: J. Davidson
Publisher:
ISBN:
Category : Forest conservation
Languages : en
Pages : 132
Get Book Here
Book Description
Author: M. Bonell
Publisher: Cambridge University Press
ISBN: 9780521829533
Category : Nature
Languages : en
Pages : 960
Get Book Here
Book Description
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.
