Format: Hardback, 508 pages, height x width: 235x155 mm, 50 Illustrations, color;
15 Illustrations, black and white; X, 508 p. 65 illus., 50 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 476
Pub. Date: 20-Feb-2025
ISBN-13: 9789819789061
This volume includes chapters on topics presented at the conference on Recent Trends in Convex Optimization: Theory, Algorithms and Applications (RTCOTAA-2020), held at the Department of Mathematics, Indian Institute of Technology Patna, Bihar, India, from 29?31 October 2020. It discusses a comprehensive exploration of the realm of optimization, encompassing both the theoretical underpinnings and the multifaceted real-life implementations of the optimization theory. It meticulously features essential optimization concepts, such as convex analysis, generalized convexity, monotonicity, etc., elucidating their theoretical advancements and significance in the optimization sphere. Multiobjective optimization is a pivotal topic which addresses the inherent difficulties faced in conflicting objectives. The book delves into various theoretical concepts and covers some practical algorithmic approaches to solve multiobjective optimization, such as the line search and the enhanced non-monotone quasi-Newton algorithms. It also deliberates on several other significant topics in optimization, such as the perturbation approach for vector optimization, and solution methods for set-valued optimization. Nonsmooth optimization is extensively covered, with in-depth discussions on various well-known tools of nonsmooth analysis, such as convexificators, limiting subdifferentials, tangential subdifferentials, quasi-differentials, etc.
Notable optimization algorithms, such as the interior point algorithm and Lemkefs algorithm, are dissected in detail, offering insights into their applicability and effectiveness. The book explores modern applications of optimization theory, for instance, optimized image encryption, resource allocation, target tracking problems, deep learning, entropy optimization, etc. Ranging from gradient-based optimization algorithms to metaheuristic approaches such as particle swarm optimization, the book navigates through the intersection of optimization theory and deep learning, thereby unravelling new research perspectives in artificial intelligence, machine learning and other fields of modern science. Designed primarily for graduate students and researchers across a variety of disciplines such as mathematics, operations research, electrical and electronics engineering, computer science, robotics, deep learning, image processing and artificial intelligence, this book serves as a comprehensive resource for someone interested in exploring the multifaceted domain of mathematical optimization and its myriad applications.
P. Marechal, Elements of Convex Analysis.- T. Antczak, Solution Concepts
in Vector Optimization an Overview.- J.-P. Crouzeix, Generalized Convexity
and Generalized Monotonicity.- N. Dinh, D. H. Long, A Perturbation Approach
to Vector Optimization Problems.- K. Som, V. Vetrivel, Results on Existence
of l-Minimal and u-Minimal Solutions in Set-Valued Optimization: a Brief
Survey.- Q. H. Ansari, N. Hussain, Pradeep Kumar Sharma, Scalarization for
Set Optimization in Vector Spaces.- A. K. Das, A. Dutta, R. Jana,
Complementarity Problems and Its Relation with Optimization Theory.- B.
Kohli, Convexificators and Their Role in Nonsmooth Optimization.- S. Treanta,
N. Abdulaleem, On Variational Derivative and Controlled Variational
Inequalities.- L. T. Tung, Tangential Subdifferential and Its Role in
Optimization.- K. Som, J. Dutta, Limiting subdifferential and its role in
optimization.- V. Laha, H. N. Singh, S. K. Mishra, On Quasidifferentiable
Mathematical Programs with Vanishing Constraints.- N. Kanzi, A. Kabgani, G.
Caristi, D. Barilla, On Nonsmooth Semi-Infinite Programming Problems.- P.
Marechal, Entropy Optimization.- S. K. Neogy, G. Singh, Lemkes Algorithm and
a Class of Convex Optimization Problem.- S. K. Neogy, R. Chakravorty, S.
Ghosh, Interior Point Methods for Some Special Classes of Optimization
Problems.- G. Panda, M. A. T. Ansary, Review on Line Search Techniques for
Nonlinear Multi-objective Optimization Problems.- K. Kumar, A. Singh, A.
Upadhayay, D. Ghosh, An Improved Nonmonotone Quasi-Newton Method for
Multiobjective Optimization Problems.- A. K. Agrawal, S. Yadav, A. Chouksey,
A. Ray, Particle Swarm Optimization and Its role in Solving Unconstrained and
Constrained Optimization Problems.- E. Pauwels, Introduction to Optimization
for Deep Learning.- G. Shukla, N. D. Chaturvedi, Optimization in Resource
Allocation Network.- M. Kumar, B. Mishra, N. Deep, A Survey on Optimized
Based Image Encryption Techniques.- U. Asfia and R. Radhakrishnan,
Parametrised Maximum Correntropy Estimation for 2D and 3D Angles-Only Target
Tracking Problem.
Format: Hardback, 404 pages, height x width: 235x155 mm, 4 Illustrations, black and white; VI, 404 p. 4 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 477
Pub. Date: 15-Feb-2025
ISBN-13: 9783031753251
This proceedings volume gathers a selection of cutting-edge research in both commutative and non-commutative ring theory and factorization theory. The papers were presented at the Conference on Rings and Factorization held at the University of Graz, Austria, July 1014, 2023. The volume covers a wide range of topics including multiplicative ideal theory, Dedekind, Prufer, Krull, and Mori rings, non-commutative rings and algebras, rings of integer-valued polynomials, topological aspects in ring theory, factorization theory in rings and semigroups, and direct-sum decomposition of modules. The conference also featured two special sessions dedicated to Matej Brear and Sophie Frisch on the occasion of their 60th birthdays.
This volume is aimed at graduate students and researchers in these areas as well as related fields and provides new insights into both classical and contemporary research in ring and factorization theory.
The directed Cayley diameter and the Davenport constant.- Heaps and
trusses.- Prufer v-multiplication domains, a survey.- Some applications of a
new approach to factorization.- Atomicity in integral domains.- Norms,
normsets, and factorization.-On the Ratliff-Rush closure of an ideal of a
one-dimensional ring.- Graded identities of infinite-dimensional Lie
algebras.-On a class of quotients of Rees algebras: a survey.- P-adic
approximation of algebraic integers and residue class rings of integer-valued
polynomials.- On matrix superalgebras with pseudoautomorphism.- Krull Rings,
Semistar Operations, and Bases of Regularity.- Descriptions of radicals in
polynomial ring extensions.- Boolean inverse semigroups and their type
monoids.-Generalized derivations characterized by their action on Jordan
products.- Open problems on relations of numerical semigroups.- Irreducible
integer-valued polynomials with prescribed minimal power that factors
non-uniquely.- The role of divisors in non-commutative ideal theory.-
Essential-like properties for integer-valued polynomial rings: a survey with
a note on valuation domains.- On the isomorphism problem for power
semigroups.- Dimension-free matricial Nullstellensatze for noncommutative
polynomials.
Pages: 400
ISBN: 978-981-12-9676-5 (hardcover)
This book starts with an anthology of mathematical functions that can be useful to describe phenomena that occur in the world we see, and how their features can be adjusted by changing their parameters. Then we have a look at the art of measuring and quantifying the world, and how to do this most efficiently and precisely.
The most important part is about finding the "pattern" in the measurements: a mathematical function that "fits" with the data. This can be chosen according to several criteria, and using different algorithms, for example the new "multidirectional least squares regression". The last part shows many real life examples in various fields of science: experiments and their analyses.
Introduction
Some Useful Functions to Describe the World:
Functions and their Linear Transformations
Polynomials
Power Functions
Homographic Functions
Other Rational Functions
Exponential Functions
Logarithmic Functions
Sigmoid-Like Functions
Peak Shaped Functions
Periodic and Semiperiodic Functions
Miscellaneous Functions
Harvesting Data:
Measurement Uncertainties
Resolution Versus Accuracy
"Difficult" Quantities
Disturbance by Measurements
Error Propagation
Minimizing Errors
Finding the Pattern:
Some Rudimentary Tools
Regression Analysis ? What Is It?
Going Toward the Best Fit
Regression Analysis ? Use It Wisely
Judging the Model
Case Studies:
Physics, Chemistry, Engineering
Geography, Climate etc.
Life Sciences
Psychology etc.
Economy etc.
High school and college students who has the basics of calculus and statistics. Teachers and researchers who need inspiration and a new view on some old problems. Engineers and anyone who needs models for prediction, calibration and hypothesis testing.
Pages: 500
ISBN: 978-981-12-9832-5 (hardcover)
After a construction of the complete ultrametric fields K, the book presents most of properties of analytic and meromorphic functions in K: algebras of analytic elements, power series in a disk, order, type and cotype of growth of entire functions, clean functions, question on a relation true for clean functions, and a counter-example on a non-clean function. Transcendence order and transcendence type are examined with specific properties of certain p-adic numbers.
The Kakutani problem for the "corona problem" is recalled and multiplicative semi-norms are described. Problems on exponential polynomials, meromorphic functions are introduced and the Nevanlinna Theory is explained with its applications, particularly to problems of uniqueness. Injective analytic elements and meromorphic functions are examined and characterized through a relation.
The Nevanlinna Theory out of a hole is described. Many results on zeros of a meromorphic function and its derivative are examined, particularly the solution of the Hayman conjecture in a P-adic field is given. Moreover, if a meromorphic functions in all the field, admitting primitives, admit a Picard value, then it must have enormously many poles. Branched values are examined, with links to growth order of the denominator.
The Nevanlinna theory on small functions is explained with applications to uniqueness for a pair of meromorphic functions sharing a few small functions.
A short presentation in characteristic p is given with applications on Yoshida equation.
Monotonous and Circular Filters
Hensel Lemma
Extensions of Ultrametric Fields: The Field Cp
Spherically Complete Extensions
Transcendence Order and Transcendence Type
Analytic Elements
Power and Laurent Series
Mittag-Leffler Theorem and Dual of H(D)
Vanishing Along a Monotonous Filter
Zeros of Power Series
Image of a Disk
Logarithm and Exponential in a p-adic field
Problems on p-adic exponentials
Michel Lazard's Problem
Motzkin Factorization, Roots of Analytic Functions
Order of Growth for Entire Functions
Type of Growth for Entire Functions
The Corona Problem
Meromorphic Functions in K
Bezout Algebras of Analytic Functions
Meromorphic Functions Out of a Hole
Injective Analytic Elements
A Non-Clean Entire Function
Nevanlinna Theory in K and Inside a Disk
Exceptional Values of Functions and Derivatives
Small Functions
Meromorphic Functions Sharing Some Small Ones
The p-adic Hayman conjecture
Urscm and Ursim
Nevanlinna Theory in Characteristic p0
Strong Uniqueness and Urscm in Characteristic p
Yoshida's Equation in the Field K
Undergraduate researchers in ultrametric analysis and all researchers in ultrametric analysis. The book may be used in a course of Master or preparation of a. Doctorate. Researchers in number theory, researchers in physics using p-adic numbers.
ISBN: 978-1-80061-642-4 (hardcover)
Calabi?Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kahler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi?Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.
The first edition of Calabi?Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi?Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.
Preface
Preface, 2024 Edition
Spiritus Movens
Constructions:
Complex Kindergarten
Complete Intersections in Products of Projective Spaces
Some More General Embeddings
Group Actions, Quotients and Singularities
Embeddings in Weighted Projective Spaces
Fibered Products
Cohomology:
(Co)homology Basics
Topological Triple Couplings
(Co)homological Algebra
Tangent Bundle Valued Cohomology
Other Tangent Bundle Related Cohomology
The (2, 1) Triple Couplings and Generalization
Changelings:
Parameter Spaces: From Afar
Parameter Spaces: A Closer Look
Concordance:
A Prelude to Quantum Geometry
Lexicon
Afterword
Bibliography
Index
This book is suitable for physics and mathematics graduate and advanced undergraduate students, postdocs and faculty, as well as active researchers in the fields of string theory and algebraic geometry.
Peking University Series in Mathematics: Volume 8
Pages: 400
Principles of classical Hamiltonian mechanics say that the evolution of a dynamical system is determined by the Poisson bracket of observable functions with the given Hamiltonian function of the system. In Quantum Mechanics, these principles are modified so that the algebra of observable functions should be replaced by a noncommutative algebra of operators and the Poisson bracket by their commutator so that the canonical commutation relations hold. Thus, working with quantum systems, we must determine the "quantization" of our observables, i.e. to choose a noncommutative algebra whose elements would play the role of the observables. With some modifications, this question is the main content of the Deformation Quantization problem formulated in 1978 by Flato and others.
This book is based on the course that the author taught in the Fall semester of 2019 at Peking University. The main purpose of that course and of this book is to acquaint the reader with the vast scope of ideas related to the Deformation Quantization of Poisson manifolds. The book begins with Quantum Mechanics and Moyal product formula and covers the three main constructions that solve the Deformation Quantization problem: Lecomte and de Wilde deformation of symplectic manifolds, Fedosov's quantization theory and Kontsevich's formality theorem. In the appendices, the Tamarkin's proof of formality theorem is outlined.
The book is written in a reader-friendly manner and is as self-contained as possible. It includes several sets of problems and exercises that will help the reader to master the material.
General Quantization Principles
Poisson Structures, Quantization and Cohomology
Hochschild Homology and Cohomology
Obstructions and Deformation Quantization of Symplectic Manifolds
Fedosov Quantization
Higher Homotopy Algebras, Kontsevich's Theorem
Kontsevich's Quantization: Properties and Applications
The Appendices Contain a Short Introduction into Operads Theory Necessary to Give Tamarkin's Proof of Kontsevich's Theorem, as well as the Proof Itself
Postgraduate and advanced undergraduate students of Mathematics and Physics, researchers and scholars in the fields of Quantum Physics and Mathematics, aiming at learning the basics of deformation quantization theory, or to teach a course on this subject. Researchers in the fields of Applied Physics and Mathematics.
Pages: 250
Inferring latent structure and causality is crucial for understanding underlying patterns and relationships hidden in the data. This book covers selected models for latent structures and causal networks and inference methods for these models.
After an introduction to the EM algorithm on incomplete data, the book provides a detailed coverage of a few widely used latent structure models, including mixture models, hidden Markov models, and stochastic block models. EM and variation EM algorithms are developed for parameter estimation under these models, with comparison to their Bayesian inference counterparts. We make further extensions of these models to related problems, such as clustering, motif discovery, Kalman filtering, and exchangeable random graphs. Conditional independence structures are utilized to infer the latent structures in the above models, which can be represented graphically. This notion generalizes naturally to the second part on graphical models that use graph separation to encode conditional independence. We cover a variety of graphical models, including undirected graphs, directed acyclic graphs (DAGs), chain graphs, and acyclic directed mixed graphs (ADMGs), and various Markov properties for these models. Recent methods that learn the structure of a graphical model from data are reviewed and discussed. In particular, DAGs and Bayesian networks are an important class of mathematical models for causality. After an introduction to causal inference with DAGs and structural equation models, we provide a detailed review of recent research on causal discovery via structure learning of graphs. Finally, we briefly introduce the causal bandit problem with sequential intervention.
Introduction and Review
Latent Structure Models:
Incomplete Data and the EM Algorithm
Mixture Modeling
Hidden Markov Models
Random Graphs for Modeling Network Data
Causal Graphical Models:
Undirected Graphical Models
Directed Acyclic Graphs
DAG-Based Causal Inference
Structure Learning of DAGs
Learning Generalized DAG Models
Directed Mixed Graphs for Latent Variables
Partitioned, Federated, and Active Learning
This book is suitable for graduate students in statistics, data science, computer science and other quantitative and computational sciences. The book can be used as a textbook for courses on statistical modeling, causal inference, graphical models, and machine learning. It is also suitable for researchers interested in causal inference, causal discovery, graphical models, Bayesian networks, structure learning, latent structure models, and related areas.