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检索条件"丛书名=Proceedings in Applied Mathematics"

共 197 条记录，以下是1-10 订阅

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An Excursion Through Discrete Differential Geometry

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丛书名： proceedings of Symposia in applied mathematics

2020年

作者： Keenan Crane

ISBN: (数字)9781470460037

ISBN: (纸本)9781470446628

Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course “Discrete Differential Geometry,” held January 8–9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.

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Sum of Squares: Theory and Applications

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丛书名： proceedings of Symposia in applied mathematics

2020年

作者： Pablo A. Parrilo Rekha R. Thomas

ISBN: (数字)9781470460402

ISBN: (纸本)9781470450250

This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.

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Rigorous Numerics in Dynamics

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丛书名： proceedings of Symposia in applied mathematics

2018年

作者： Jan Bouwe van den Berg Jean-Philippe Lessard

ISBN: (数字)9781470447298

ISBN: (纸本)9781470428143

This volume is based on lectures delivered at the 2016 AMS Short Course “Rigorous Numerics in Dynamics”, held January 4–5, 2016, in Seattle, Washington. Nonlinear dynamics shapes the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell. Mathematically these phenomena are modeled by nonlinear dynamical systems, in the form of ODEs, PDEs and delay equations. The presence of nonlinearities complicates the analysis, and the difficulties are even greater for PDEs and delay equations, which are naturally defined on infinite dimensional function spaces. With the availability of powerful computers and sophisticated software, numerical simulations have quickly become the primary tool to study the models. However, while the pace of progress increases, one may ask: just how reliable are our computations? Even for finite dimensional ODEs, this question naturally arises if the system under study is chaotic, as small differences in initial conditions (such as those due to rounding errors in numerical computations) yield wildly diverging outcomes. These issues have motivated the development of the field of rigorous numerics in dynamics, which draws inspiration from ideas in scientific computing, numerical analysis and approximation theory. The articles included in this volume present novel techniques for the rigorous study of the dynamics of maps via the Conley-index theory; periodic orbits of delay differential equations via continuation methods; invariant manifolds and connecting orbits; the dynamics of models with unknown nonlinearities; and bifurcations diagrams.

关键词：数学

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Random Growth Models

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丛书名： proceedings of Symposia in applied mathematics

2018年

作者： Michael Damron Firas Rassoul-Agha Timo Seppäläinen

ISBN: (数字)9781470449070

ISBN: (纸本)9781470435530

The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.

关键词：数学

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Finite Frame Theory

引用

丛书名： proceedings of Symposia in applied mathematics

2016年

作者： Kasso A. Okoudjou

ISBN: (数字)9781470432126

ISBN: (纸本)9781470420192

Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics. This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX. Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.

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Modern aspects of random matrix theory : AMS Short Course, Random Matrices, January 6-7, 2013, Sa...

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2014年

作者： AMS Short Course Random Matrices

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M-band Wavelet Based Pseudo Quantum Watermarking

M-band Wavelet Based Pseudo Quantum Watermarking

引用

International Conference on applied, Numerical and Computational mathematics

作者： TONG LIU XUAN XU XIAODI WANG Department of Math Tsinghua University Department of Chemistry Hong Kong University of Science and Technology Department of Math Western Connecticut State University

ISBN: (纸本)9781618043283

Computational methods derived from digital signal processing are playing a significant role in the security and copyrights of audio, video, and visual arts. In light of the quantum computing, the corresponding algorithms are becoming a new research direction in today's high-technology world. The nature of quantum computer guarantees the security of quantum data, so a safe and effective quantum watermarking algorithm is in demand. Quantum watermarking is the technique that embeds the invisible quantum signal into quantum multimedia data for copyright protection. Different from most traditional algorithms, we propose new algorithms which apply a quantum or a pseudo quantum watermarking in M-band wavelet domain. Assured by the Heisenberg uncertainty principle and quantum no-cloning theorem, the security of quantum watermark can reach a very high-level standard. In other words, these watermarking algorithms can defeat nearly all attackers, no matter using classical computer or quantum computer.

关键词： Discrete M-band wavelet transforms (DMWT) Quantum and pseudo watermarks Quantum computing Quantum and pseudo Images quantum computing quanta Watermarking Quantum computers M-line Visual arts copyrights audio video Uncertainty principle Security Digital signal processing computational methods algorithms Pseudo

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Applications of Knot Theory (proceedings of Symposia in applied mathematics)

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丛书名： proceedings of Symposia in applied mathematics 066

2009年

作者： Dorothy Buck and Erica Flapan

ISBN: (纸本)9780821844663

Over the past 20–30 years, knot theory has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions of the entanglements and properties of natural phenomena—from strings to organic compounds to DNA. This volume is based on the 2008 AMS Short Course, Applications of Knot Theory. The aim of the Short Course and this volume, while not covering all aspects of applied knot theory, is to provide the reader with a mathematical appetizer, in order to stimulate the mathematical appetite for further study of this exciting field. No prior knowledge of topology, biology, chemistry, or physics is assumed. In particular, the first three chapters of this volume introduce the reader to knot theory (by Colin Adams), topological chirality and molecular symmetry (by Erica Flapan), and DNA topology (by Dorothy Buck). The second half of this volume is focused on three particular applications of knot theory. Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology.

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Robotics 1

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丛书名： proceedings of Symposia in applied mathematics

2012年

作者： Roger Brockett

ISBN: (数字)9780821892565

ISBN: (纸本)9780821801635

The central problem of robotics is the analysis and replication of patterns of movement required to accomplish useful tasks. Physicists have found that deeper examination of the physical world often reveals inadequacies in the vocabulary and mathematics used to describe it; in much the same way, roboticists have found it quite awkward to give precise, succinct descriptions of effective movements using the syntax and semantics in common use. What is needed to produce general purpose robots is a more expressive means for discussing movement. This volume focuses on some of the ways that mathematics can be used to address problems in this area. Focusing on some of the important mathematical questions arising in the field of robotics, this book conveys a sense for the effectiveness of mathematics in capturing the essence of robotics problems. In addition, the book will make readers aware of the way in which computer control interacts with geometry. The first four papers deal with kinematics and control, relying on realistic models for kinematic processes. The last two papers have more of the flavor of computer science and are concerned with the symbolic descriptions of motion, including the treatment of uncertainty. The book is directed toward mathematically literate readers interested in finding out about the questions that arise in robotics and how mathematics can help answer them. A mathematical background at the level of an undergraduate degree in mathematics and some knowledge of basic mechanics is assumed.

关键词： Applications

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Advances in applied and Computational Topology 1

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丛书名： proceedings of symposia in applied mathematics

2012年

作者： Afra Zomorodian Afra Zomorodian

ISBN: (数字)9780821889978

ISBN: (纸本)9780821853276

What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.

关键词： symposia appli proceedings topology applied computational advances

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