Sampling In Combinatorial And Geometric Set Systems

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Sampling in Combinatorial and Geometric Set Systems

Nabil H. Mustafa
Sampling in Combinatorial and Geometric Set Systems Book PDF

Author : Nabil H. Mustafa
Publisher : American Mathematical Society
Page : 251 pages
File Size : 54,6 Mb
Release : 2022-01-14
Category : Mathematics
ISBN : 9781470461560

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Sampling in Combinatorial and Geometric Set Systems by Nabil H. Mustafa Pdf

Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems having been resolved during this time. These include optimal lower bounds for epsilon-nets for many geometric set systems, the use of shallow-cell complexity to unify proofs, simpler and more efficient algorithms, and the use of epsilon-approximations for construction of coresets, to name a few. This book presents a thorough treatment of these probabilistic, combinatorial, and geometric methods, as well as their combinatorial and algorithmic applications. It also revisits classical results, but with new and more elegant proofs. While mathematical maturity will certainly help in appreciating the ideas presented here, only a basic familiarity with discrete mathematics, probability, and combinatorics is required to understand the material.

Recovery Methodologies: Regularization and Sampling

Willi Freeden,M. Zuhair Nashed
Recovery Methodologies Regularization and Sampling Book PDF

Author : Willi Freeden,M. Zuhair Nashed
Publisher : American Mathematical Society
Page : 505 pages
File Size : 50,6 Mb
Release : 2023-08-21
Category : Mathematics
ISBN : 9781470473457

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Recovery Methodologies: Regularization and Sampling by Willi Freeden,M. Zuhair Nashed Pdf

The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.

Self-similar and Self-affine Sets and Measures

Balázs Bárány,Károly Simon,Boris Solomyak
Self similar and Self affine Sets and Measures Book PDF

Author : Balázs Bárány,Károly Simon,Boris Solomyak
Publisher : American Mathematical Society
Page : 466 pages
File Size : 40,6 Mb
Release : 2023-11-16
Category : Mathematics
ISBN : 9781470470463

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Self-similar and Self-affine Sets and Measures by Balázs Bárány,Károly Simon,Boris Solomyak Pdf

Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.

Approximation and Online Algorithms

Jarosław Byrka,Andreas Wiese
Approximation and Online Algorithms Book PDF

Author : Jarosław Byrka,Andreas Wiese
Publisher : Springer Nature
Page : 246 pages
File Size : 43,8 Mb
Release : 2023-12-21
Category : Mathematics
ISBN : 9783031498152

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Approximation and Online Algorithms by Jarosław Byrka,Andreas Wiese Pdf

This book constitutes the refereed proceedings of the 21st International Workshop on Approximation and Online Algorithms, WAOA 2023, held in Amsterdam, The Netherlands, during September 7–8, 2023 The 16 full papers included in this book are carefully reviewed and selected from 43 submissions. The topics of WAOA 2023 were algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT-approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, resource augmentation, and scheduling problems

Multidimensional Residue Theory and Applications

Alekos Vidras,Alain Yger
Multidimensional Residue Theory and Applications Book PDF

Author : Alekos Vidras,Alain Yger
Publisher : American Mathematical Society
Page : 556 pages
File Size : 51,5 Mb
Release : 2023-10-18
Category : Mathematics
ISBN : 9781470471125

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Multidimensional Residue Theory and Applications by Alekos Vidras,Alain Yger Pdf

Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.

Algebras, Lattices, Varieties

Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor
Algebras Lattices Varieties Book PDF

Author : Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor
Publisher : American Mathematical Society
Page : 496 pages
File Size : 48,6 Mb
Release : 2022-10-28
Category : Mathematics
ISBN : 9781470467975

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Algebras, Lattices, Varieties by Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor Pdf

This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Amenability of Discrete Groups by Examples

Kate Juschenko
Amenability of Discrete Groups by Examples Book PDF

Author : Kate Juschenko
Publisher : American Mathematical Society
Page : 180 pages
File Size : 46,6 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781470470326

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Amenability of Discrete Groups by Examples by Kate Juschenko Pdf

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

Completion Problems on Operator Matrices

Dragana S. Cvetković Ilić
Completion Problems on Operator Matrices Book PDF

Author : Dragana S. Cvetković Ilić
Publisher : American Mathematical Society
Page : 170 pages
File Size : 51,7 Mb
Release : 2022-06-07
Category : Mathematics
ISBN : 9781470469870

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Completion Problems on Operator Matrices by Dragana S. Cvetković Ilić Pdf

Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.

Iwasawa Theory and Its Perspective, Volume 2

Tadashi Ochiai
Iwasawa Theory and Its Perspective Volume 2 Book PDF

Author : Tadashi Ochiai
Publisher : American Mathematical Society
Page : 228 pages
File Size : 41,7 Mb
Release : 2024-04-25
Category : Mathematics
ISBN : 9781470456733

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Iwasawa Theory and Its Perspective, Volume 2 by Tadashi Ochiai Pdf

Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.

Inverse Problems and Zero Forcing for Graphs

Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader
Inverse Problems and Zero Forcing for Graphs Book PDF

Author : Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader
Publisher : American Mathematical Society
Page : 302 pages
File Size : 45,6 Mb
Release : 2022-07-21
Category : Mathematics
ISBN : 9781470466558

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Inverse Problems and Zero Forcing for Graphs by Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader Pdf

This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.

Characterization of Probability Distributions on Locally Compact Abelian Groups

Gennadiy Feldman
Characterization of Probability Distributions on Locally Compact Abelian Groups Book PDF

Author : Gennadiy Feldman
Publisher : American Mathematical Society
Page : 253 pages
File Size : 49,9 Mb
Release : 2023-04-07
Category : Mathematics
ISBN : 9781470472955

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Characterization of Probability Distributions on Locally Compact Abelian Groups by Gennadiy Feldman Pdf

It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.

Automorphic Forms Beyond $mathrm {GL}_2$

Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun
Automorphic Forms Beyond mathrm GL 2 Book PDF

Author : Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun
Publisher : American Mathematical Society
Page : 199 pages
File Size : 42,8 Mb
Release : 2024-03-26
Category : Mathematics
ISBN : 9781470474928

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Automorphic Forms Beyond $mathrm {GL}_2$ by Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun Pdf

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Residuated Structures in Algebra and Logic

George Metcalfe,Francesco Paoli,Constantine Tsinakis
Residuated Structures in Algebra and Logic Book PDF

Author : George Metcalfe,Francesco Paoli,Constantine Tsinakis
Publisher : American Mathematical Society
Page : 282 pages
File Size : 48,7 Mb
Release : 2023-11-06
Category : Mathematics
ISBN : 9781470469856

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Residuated Structures in Algebra and Logic by George Metcalfe,Francesco Paoli,Constantine Tsinakis Pdf

This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators

Horst R. Thieme
Discrete Time Dynamics of Structured Populations and Homogeneous Order Preserving Operators Book PDF

Author : Horst R. Thieme
Publisher : American Mathematical Society
Page : 357 pages
File Size : 47,7 Mb
Release : 2024-05-07
Category : Mathematics
ISBN : 9781470474652

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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators by Horst R. Thieme Pdf

A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

The Classification of the Finite Simple Groups, Number 10

Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
The Classification of the Finite Simple Groups Number 10 Book PDF

Author : Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
Publisher : American Mathematical Society
Page : 587 pages
File Size : 53,6 Mb
Release : 2023-10-23
Category : Mathematics
ISBN : 9781470475536

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The Classification of the Finite Simple Groups, Number 10 by Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon Pdf

This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.