Format: Hardback,
296 pages, height x width: 235x155 mm,
149 Illustrations, color; 8 Illustrations, black and white; IV, 296 p. 157 illus., 149 illus. in color.
Series: Unsupervised and Semi-Supervised Learning
Pub. Date: 24-Jun-2022
ISBN-13: 9783030991418
This book focuses on recent advances, approaches, theories, and applications related Hidden Markov Models (HMMs). In particular, the book presents recent inference frameworks and applications that consider HMMs. The authors discuss challenging problems that exist when considering HMMs for a specific task or application, such as estimation or selection, etc. The goal of this volume is to summarize the recent advances and modern approaches related to these problems. The book also reports advances on classic but difficult problems in HMMs such as inference and feature selection and describes real-world applications of HMMs from several domains. The book pertains to researchers and graduate students, who will gain a clear view of recent developments related to HMMs and their applications.
Chapter1. A Roadmap to Hidden Markov Models and A Review of its Application in Occupancy Estimation.
Chapter2. Bounded asymmetric Gaussian mixture-based hidden Markov models.
Chapter3. Using HMM to model neural dynamics and decode useful signals for neuroprosthetic control.
Chapter4. Fire Detection in Images with Discrete Hidden Markov Models.
Chapter5. Hidden Markov Models: Discrete Feature Selection in Activity Recognition.-
Chapter6. Bayesian Inference of Hidden Markov Models using Dirichlet Mixtures.
Chapter7. Online learning of Inverted Beta-Liouville HMMs for Anomaly Detection in Crowd Scenes.
Chapter8. A Novel Continuous Hidden Markov Model for Modeling Positive Sequential Data.
Chapter9. Multivariate Beta-based Hidden Markov Models Applied to Human Activity Recognition.-
Chapter10. Multivariate Beta-based Hierarchical Dirichlet Process Hidden Markov Models in Medical Applications.
Chapter11. Shifted-Scaled Dirichlet Based Hierarchical Dirichlet Process Hidden Markov Models with Variational Inference Learning.
Format: Hardback,
360 pages, height x width: 235x155 mm,
29 Illustrations, black and white; XV, 360 p. 29 illus
Series: Undergraduate Texts in Mathematics
Pub. Date: 28-Jun-2022
ISBN-13: 9783030989309
This innovative undergraduate textbook approaches number theory through
the lens of abstract algebra. Written in an engaging and whimsical style,
this text will introduce students to rings, groups, fields, and other algebraic
structures as they discover the key concepts of elementary number theory.
Inquiry-based learning (IBL) appears throughout the chapters, allowing
students to develop insights for upcoming sections while simultaneously
strengthening their understanding of previously covered topics.
The text is organized around three core themes: the notion of what a “number”
is, and the premise that it takes familiarity with a large variety of number
systems to fully explore number theory; the use of Diophantine equations
as catalysts for introducing and developing structural ideas; and the role
of abstract algebra in number theory, in particular the extent to which
it provides the Fundamental Theorem of Arithmetic for various new number
systems. Other aspects of modern number theory ? including the study of
elliptic curves, the analogs between integer and polynomial arithmetic,
p-adic arithmetic, and relationships between the spectra of primes in various
rings ? are included in smaller but persistent threads woven through chapters
and exercise sets.
Each chapter concludes with exercises organized in four categories: Calculations
and Informal Proofs, Formal Proofs, Computation and Experimentation, and
General Number Theory Awareness. IBL “Exploration” worksheets appear in
many sections, some of which involve numerical investigations. To assist
students who may not have experience with programming languages, Python
worksheets are available on the book’s website. The final chapter provides
five additional IBL explorations that reinforce and expand what students
have learned, and can be used as starting points for independent projects.
The topics covered in these explorations are public key cryptography, Lagrange’s
four-square theorem, units and Pell’s Equation, various cases of the solution
to Fermat’s Last Theorem, and a peek into other deeper mysteries of algebraic
number theory.
Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the “numberverse.”
Preface.- What is a Number?- A Quick Survey of the Last Two Millenia.-
Number Theory in mathcal{Z} Beginning.- Number Theory in the Mod-n Era.-
Gaussian Number Theory: mathcal{Z}[ i] of the Storm.- Number Theory: From
Where We mathcal{R} to across the mathcal{C}.- Cyclotomic Number Theory:
Roots and Reciprocity. Number Theory Unleashed: Release mathcal{Z}_p!-
The Adventure Continues.- Appendix: Number Systems.
Format: Hardback,
210 pages, height x width: 235x155 mm,
45 Illustrations, color; 28 Illustrations, black and white; X, 210 p. 73 illus., 45 illus. in color.
Series: Lecture Notes in Morphogenesis
Pub. Date: 25-May-2022
ISBN-13: 9783030977962
This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point. The construction of differential assemblages will be introduced in the present study from the mathematical point of view, outlining the heterogeneity of the differential constraints and of the associated phase spaces, that are continously changing in space and time. If homogeneous constraints well describe a form of swarm intelligence or crowd behaviour, it reduces dynamics to automatisms, by excluding any form of imaginative and creative aspect. With this study we aim to problematize the procedure of homogeneization that is dominant in life and social science and to outline the dynamical heterogeneity of life and its affective, semiotic, social, historical aspects. Particularly, the use of sub-Riemannian geometry instead of Riemannian one allows to introduce disjointed and autonomous areas in the virtual plane. Our purpose is to free up the dynamic becoming from any form of unitary and totalizing symmetry and to develop forms, action, thought by means of proliferation, juxtaposition, and disjunction devices.
After stating the concept of differential heterogenesis with the language of contemporary mathematics, we will face the problem of the emergence of the semiotic function, recalling the limitation of classical approaches (Hjelmslev, Saussure, Husserl) and proposing a possible genesis of it from the heterogenetic flow previously defined. We consider the conditions under which this process can be polarized to constitute different planes of Content (C) and Expression (E), each one equipped with its own formed substances. A possible (but not unique) process of polarization is constructed by means of spectral analysis, that is introduced to individuate E/C planes and their evolution. The heterogenetic flow, solution of differential assemblages, gives rise to forms that are projected onto the planes, offering a first referring system for the flow, that constitutes a first degree of semiosis.
Introduction.- Elements of morphodynamics.- Multiplicity and Assemblages.- Differential heterogenesis.- Differential cognitive neuroscience.- Expression and semiogenesis.- Chiusa: Morphodynamic poetry.- Plates
Format: Hardback,
740 pages, height x width: 235x155 mm,
143 Illustrations, black and white; XX, 740 p. 143 illus
Series: Springer Monographs in Mathematics
Pub. Date: 17-Jun-2022
ISBN-13: 9789811910982
This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems.
The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability.
The scope of the author’s work has been and continues to be powerful methods
of functional analysis for future research of elliptic boundary value problems
and Markov processes via semigroups. A broad spectrum of readers can appreciate
easily and effectively the stochastic intuition that this book conveys.
Furthermore, the book will serve as a sound basis both for researchers
and for graduate students in pure and applied mathematics who are interested
in a modern version of the classical potential theory and Markov processes.
For advanced undergraduates working in functional analysis, partial differential
equations, and probability, it provides an effective opening to these three
interrelated fields of analysis. Beginning graduate students and mathematicians
in the field looking for a coherent overview will find the book to be a
helpful beginning.
This work will be a major influence in a very broad field of study for a long time.
1. Introduction and Summary.- Part I Foundations of Modern Analysis.-
2. Sets, Topology and Measures.-
3. A Short Course in Probability Theory.-
4. Manifolds, Tensors and Densities.-
5. A Short Course in Functional Analysis.-
6. A Short Course in Semigroup Theory.- Part II Elements of Partial Differential Equations.
7. Distributions, Operators and Kernels.-
8. L2 Theory of Sobolev Spaces.-
9. L2 Theory of Pseudo-Differential Operators.- Part III Maximum Principles and Elliptic Boundary Value Problems.-
10. Maximum Principles for Degenerate Elliptic Operators.- Part IV L2 Theory of Elliptic Boundary Value Problems.-
11. Elliptic Boundary Value Problems.- Part V Markov Processes, Feller Semigroups and Boundary Value Problems.-
12. Markov Processes, Transition Functions and Feller Semigroups.-
13. L2 Approach to the Construction of Feller Semigroups.-
14. Concluding Remarks.- Part VI Appendix.- A A Brief Introduction to the Potential Theoretic Approach.- References.- Index.
Format: Hardback,
186 pages, height x width: 235x155 mm, 87 Tables, color;
69 Illustrations, color; 20 Illustrations, black and white; VI, 186 p. 89 illus., 69 illus. in color.
Series: Trends in Mathematics
Pub. Date: 03-Jul-2022
ISBN-13: 9783030991159
This volume collects papers based on talks given at the conference “Geometrias'19: Polyhedra and Beyond”, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference’s theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.
Synthetic Methods for Constructing Polyhedra.- Sources and Features of the Small Stellated Dodecahedrons Painted in Genoa.- Polyhedral Transformation Based on Confocal Quadratic Surface Properties. Graphical Speculations.- Concave Deltahedral Rings based on the Geometry of the Concave Antiprisms of the Second Sort.- Filling Space with Gyroid Symmetry.- Odd Or Even, Jitterbug Versus Grunbaum's Double Polyhedra.- From Geometry to Reality: Designing Geodesic Structures.- Vittorio Giorgini's Architectural Experimentations at the Dawn of Parametric Modelling.- Architectural Inversions: The Intangible Aspect as a Form-Finding Factor in the Combined Work of Antoni Gaudi and John Pickering.- An Introduction to Solid Tessellations with Students of Architecture.
Format: Hardback,
height x width: 235x155 mm,
24 Illustrations, black and white; Approx. 105 p. 24 illus.
Series: CIMAT Lectures in Mathematical Sciences
Pub. Date: 24-Aug-2022
ISBN-13: 9783030992972
This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen's part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-Garci a's minicourse was completed in collaboration with Jesu s Nun ez-Zimbro n. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesu s Nun ez-Zimbro n's contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.
Rigidity of Alexandrov spaces.-
2. Three-dimensional Alexandrov spaces: a survey.-
3. Topological and geometric rigidity for spaces with curvature bounded below.
Format: Hardback,
490 pages, height x width: 235x155 mm,
53 Illustrations, color; 30 Illustrations, black and white; X, 490 p. 83 illus., 53 illus. in color
Pub. Date: 04-Jul-2022
ISBN-13: 9783030975593
Description
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Mobius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
1 Ken'ichi Ohshika and Athanase Papadopoulos, Introduction.- 2 Michael Kapovich, A survey of complex hyperbolic Kleinian groups.- 3 Graham Smith, Moebius structures, hyperbolic ends and K-surfaces in hyperbolic space.- 4 Joan Porti, Cone 3-manifods.- 5 Takahiro Kitayama, A survey of the Thurston norm.- 6 Georgios Kydonakis, From hyperbolic Dehn filling to surgeries in representation varieties.- 7 Sang-Hyun Kim, Acute geodesic triangulations of manifolds.- 8 Ismail Saglam, Signature calculation of the area Hermitian form on some spaces of polygons.- 9 Mikhail Chernaviskikh, Altan Erdnigor, Nikita Kalinin, and Alexandr Zakharov, Equilateral convex triangulations of RP2 with three conical points of equal defect.- 10 Mahan Mj and Sabyasachi Mukherjee, Combination theorems in groups, geometry and dynamics.- 11 Kevin Pilgrim, On the pullback relation on curves induced by a Thurston map.- 12 William Floyd, The pullback map on Teichmuller space induced from a Thurston map.- 13 Russell Lodge, Yauhen Mikulich and Dierk Schleicher, A classification of postcritically finite Newton maps.- 14 Sarah Rees, The development of the theory of automatic groups.- 15 Thomas Koberda, Geometry and combinatorics via right-angled Artin groups.