Non-K瓣hler Complex Surfaces and Strongly Pseudoconcave Surfaces
Mathematics in Architecture, Art, Nature, and Beyond
There is little opportunity in classrooms today for teachers to explore the amazing applications of mathematics outside the curriculum. This book is intended to show how mathematics manifests itself in areas that most people are unaware of. One can even revel in the history of how our number system evolved and how that has enabled us to define the beauty in mathematics as well as in art, architecture, nature, and beyond.The first two chapters of this book introduce the Fibonacci numbers and investigate their amazing relationships and applications in our general environment. The following four chapters focus on the Golden Ratio and the Golden Rectangle, exploring how they manifest all around us, often hiding in plain sight: in everything from architectural wonders such as the Taj Mahal to coin design, and from Greek vases to petal formation. We conclude our enjoyable journey through these mathematical wonders by considering conic sections and how they explain many aspects of everyday life, such as radar dishes, headlight reflectors, and whispering halls. This exposure to aspects of mathematics that are usually bypassed in the school curriculum will provide high school students, teachers, and general readers with an opportunity to truly appreciate the power and beauty of mathematics.
Minimum Gamma-Divergence for Regression and Classification Problems
This book introduces the gamma-divergence, a measure of distance between probability distributions that was proposed by Fujisawa and Eguchi in 2008. The gamma-divergence has been extensively explored to provide robust estimation when the power index γ is positive. The gamma-divergence can be defined even when the power index γ is negative, as long as the condition of integrability is satisfied. Thus, the authors consider the gamma-divergence defined on a set of discrete distributions. The arithmetic, geometric, and harmonic means for the distribution ratios are closely connected with the gamma-divergence with a negative γ. In particular, the authors call the geometric-mean (GM) divergence the gamma-divergence when γ is equal to -1. The book begins by providing an overview of the gamma-divergence and its properties. It then goes on to discuss the applications of the gamma-divergence in various areas, including machine learning, statistics, and ecology. Bernoulli, categorical, Poisson, negative binomial, and Boltzmann distributions are discussed as typical examples. Furthermore, regression analysis models that explicitly or implicitly assume these distributions as the dependent variable in generalized linear models are discussed to apply the minimum gamma-divergence method. In ensemble learning, AdaBoost is derived by the exponential loss function in the weighted majority vote manner. It is pointed out that the exponential loss function is deeply connected to the GM divergence. In the Boltzmann machine, the maximum likelihood has to use approximation methods such as mean field approximation because of the intractable computation of the partition function. However, by considering the GM divergence and the exponential loss, it is shown that the calculation of the partition function is not necessary, and it can be executed without variational inference.
Dependence Models Via Hierarchical Structures
Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific dependence models, including exchangeable, Markov, moving average and, in general, spatio-temporal models. All constructions maintain a desired property of pre-specifying the marginal distribution and keeping it invariant. They do not separate the dependence from the marginals and the mechanisms followed to induce dependence are so general that they can be applied to a very large class of parametric distributions. All the constructions are based on appropriate definitions of three building blocks: prior distribution, likelihood function and posterior distribution, in a Bayesian analysis context. All results are illustrated with examples and graphical representations. Applications with data and code are interspersed throughout the book, covering fields including insurance and epidemiology.
Approximation Theory and Applications
Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.
Convex Functions and Their Applications
This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems. To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics. Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.
Measure Theory for Analysis and Probability
This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon-Nikodym and Jordan-Hahn theorems, providing a detailed account of ���� spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions. The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea's theorem and Kolmogorov's consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.
Approximation & Regular Methods Operator-Function Equations
This book presents an overview of the most recent research and results in the field of approximation and regularisation methods for operator-functional equations, and explores their applications in electrical and power engineering. It presents the state of the art in building operator theory, regularised numerical methods, and in the verification of mathematical models for dynamical models based on integral and differential equations. Special attention is paid to Volterra models, a powerful tool for modelling hereditary dynamics.This book begins by exploring the solvability of singular integral equations, and moves on to study approximation methods for linear operator equations and nonlinear integral equations. Following this, it examines loaded equations and bifurcation analysis, before concluding with an investigation of the applications of the contents of the book in electrical engineering and automation. Each chapter provides an overview and analysis of the relevant problem statements, outlines current methods within the field, and identifies future directions for research.With an interdisciplinary approach, this book is essential reading for anyone interested in operator-functional equations. Graduate students and professors in the fields of applied mathematics, physics, material science, and numerical analysis will find this work insightful and valuable, as will industry professionals in related fields.
Applied Nonparametric Statistical Methods
A comprehensive course text in nonparametric techniques suitable for undergraduate mathematics students. Assumes only basic experience of statistics with algebra kept to a minimum. Ideal for quantitative methods modules delivered to undergraduate or postgrad students in science, business, and health service training.
Random Number Generators for Computer Simulation and Cyber Security
This book discusses the theory and practice of random number generators that are useful for computer simulation and computer security applications. Random numbers are ubiquitous in computation. They are used in randomized algorithms to perform sampling or choose randomly initialized parameters or perform Markov Chain Monte Carlo (MCMC). They are also used in computer security applications for various purposes such as cryptographic nuances or in authenticators. In practice, the random numbers used by any of these applications are from a pseudo-random sequence. These pseudo-random sequences are generated by RNGs (random number generators). This book discusses the theory underlying such RNGs, which are used by all programmers. However, few try to understand the theory behind them. This topic is an active area of research, particularly when the generators are used for cryptographic applications. The authors introduce readers to RNGs, how they are judged for quality, the mathematical and statistical theory behind them, as well as provide details on how these can be implemented in any programming language. The book discusses non-linear transformations that use classical linear generators for cryptographic applications and how to optimize to make such generators more efficient. In addition, the book provides up-to-date research on RNGs including a modern class of efficient RNGs and shows how to search for new RNGs with good quality and how to parallelize these RNGs.
Derivatives Pricing
This is a masters-level overview of the mathematical concepts needed to fully grasp the art of derivatives pricing, and a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, this textbook allows students with limited technical background to build a solid knowledge of the most important principles. It offers a unique compromise between intuition and mathematics, even when discussing abstract ideas such as change of measure. Mathematical concepts are introduced initially using toy examples, before moving on to examples of finance cases, both in discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students' understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code and an interactive app.
Intelligent Systems and Pattern Recognition
This Three-volume set CCIS 2303-2305 constitutes the proceedings of the 4th International Conference on Intelligent Systems and Pattern Recognition, ISPR 2024, held in Istanbul, Turkey, in June 26-28, 2024. The 77 full papers presented were thoroughly reviewed and selected from the 210 submissions. The conference provided an interdisciplinary forum for the exchange of innovative advancements in the fields of artificial intelligence and pattern recognition.
Intelligent Systems and Pattern Recognition
This Three-volume set CCIS 2303-2305 constitutes the proceedings of the 4th International Conference on Intelligent Systems and Pattern Recognition, ISPR 2024, held in Istanbul, Turkey, in June 26-28, 2024. The 77 full papers presented were thoroughly reviewed and selected from the 210 submissions. The conference provided an interdisciplinary forum for the exchange of innovative advancements in the fields of artificial intelligence and pattern recognition.
The Siml Filtering Method for Noisy Non-Stationary Economic Time Series
Exercises in Statistical Reasoning
Exercises designed to strengthen creative problem-solving skills, designed to encourage readers to understand the key points of a problem while seeking knowledge, rather than separating out these two activities. To complete the exercises, readers may need to reference the literature, which is how research-based knowledge is often acquired.
Bayesian Statistics
Bayesian Statistics: The Basics provides a comprehensive yet accessible introduction to Bayesian statistics, specifically tailored for any researcher with an interest in statistical methods. It covers the theoretical foundations of Bayesian inference, contrasting it with classical statistical methods like null hypothesis significance testing. The book emphasizes key concepts such as prior and posterior distributions, Bayes' theorem, and the Bayes factor, making them understandable even for readers with minimal mathematical backgrounds.Methodologically, the book offers practical, step-by-step guides on how to conduct Bayesian analyses using the free software package JASP. Each chapter focuses on applying Bayesian methods to common research designs with real-world data. Readers will benefit from the clear examples, visualizations, and JASP screenshots that ensure the learning experience is interactive and easy to follow.Full of practical content, the book emphasizes the advantages of Bayesian model comparison over traditional approaches, especially in quantifying evidence for competing hypotheses. Readers will also learn how to perform sensitivity analyses to assess the impact of different prior assumptions on their results.By the end of the book, readers will get both the theoretical understanding and practical skills to implement Bayesian methods in their own research, making it an invaluable resource for both novice and experienced researchers studying Bayesian Statistics.
Intelligent Systems and Pattern Recognition
This Three-volume set CCIS 2303-2305 constitutes the proceedings of the 4th International Conference on Intelligent Systems and Pattern Recognition, ISPR 2024, held in Istanbul, Turkey, in June 26-28, 2024. The 77 full papers presented were thoroughly reviewed and selected from the 210 submissions. The conference provided an interdisciplinary forum for the exchange of innovative advancements in the fields of artificial intelligence and pattern recognition.
Game Theory Explained
This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash's proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a 'bonus' appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author's particular area of study.
Higher Recursion Theory and Set Theory
This volume celebrates the research contributions of Professors Theodore A Slaman and W Hugh Woodin, marking their distinguished careers in higher recursion theory and set theory as they approached the milestone of their 65th birthdays in 2019. It originates from the Institute for Mathematical Sciences program, Higher Recursion Theory and Set Theory, held at the National University of Singapore (May 20-June 14, 2019).The program explored cutting-edge developments in higher recursion theory, set theory, and their intricate interconnections. Topics discussed during the workshop included Martin's conjecture, higher randomness, the HOD conjecture, descriptive inner model theory, and the Ultimate-L program.This volume presents 15 peer-reviewed contributions by leading experts in the field, offering a comprehensive overview of recent advances in higher recursion theory and set theory, with a focus on their dynamic interactions.
Mathematical Theory of Compressible Fluids on Moving Domains
The Art of Uncertainty
How dangerous is our diet? How much of sports falls into the realm of luck? When authorities categorize a given event as "highly likely"--how likely is that, really? Whether we're trying to decide if the benefits of a new medication are worth the chance of side effects or if artificial intelligence truly threatens humanity, our lives are riddled with uncertainties both everyday and existential--yet it can be difficult to know how to properly weigh all those unknowns. Luckily for us, renowned statistician David Spiegelhalter has spent his career dissecting data to resolve the apparently random and decode the many decisions we face with imperfect information. In The Art of Uncertainty, he shows how we can become better at dealing with what we don't know to make smarter choices in a world so full of puzzling variablesIn lucid, lively prose, Spiegelhalter guides us through the principles of probability, illustrating how they can help us think more analytically about everything from medical advice to sports to climate change forecasts. He demonstrates how taking a mathematical approach to phenomena we might otherwise attribute to fate or luck can help us sort hidden patterns from mere coincidences, better evaluate cause and effect, and predict what's likely to happen in the future. Along the way, we learn how a misinterpretation of a probability contributed to the infamous Bay of Pigs fiasco, why a ship twice the size of the Titanic sank without a trace, and why we can be so confident that no two properly shuffled decks of cards have ever been in the same orderSparkling with wit and fascinating real-world examples, this is an essential guide to navigating uncertainty while also retaining the humility to admit what we don't, or simply cannot, know.
Fuzzy Mathematics
This book aims to introduce readers without a strong mathematical background to the basic ideas of fuzzy set theory and logic. Fuzzy mathematics is the mathematics of vagueness, a universal property of this world. There are many objects that are called vague because they cannot be precisely defined. Since vagueness is so common, a tool is needed to describe it and to effectively deal with it. Fuzzy mathematics is such a tool, and it is used by most researchers and scholars. As such, this book provides a short overview of the field written for non-specialists. This book allows readers to delve into the theory of fuzzy sets and introduces core mathematical ideas without using the usual formalities of books in mathematics, i.e. theorems, proofs, etc.
Deep Learning in Time Series Analysis
The concept of deep machine learning is easier to understand by paying attention to the cyclic stochastic time series and a time series whose content is non-stationary not only within the cycles, but also over the cycles as the cycle-to-cycle variations.
State-of-the-Art of Mathematical Modeling, Dynamics, and Control of Wind Turbines Engineering
Hands-On Mathematical Optimization with Python
This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.
Leningrad Mathematical Olympiads (1961-1991)
This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period -- on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.
Theory of Stochastic Integrals
Theory of Stochastic Integrals aims to provide an answer to the problem of phenomena that cannot be analyzed through the classical It繫 theory by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales.
Leningrad Mathematical Olympiads (1961-1991)
This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period -- on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.
Random Patterns and Structures in Spatial Data
The book presents a general mathematical framework able to detect and to characterize, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tool employed is a Gibbs point process with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples.Features: Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions Proposes a general methodology for morphological and statistical characterisation of patterns based on three branches, probabilistic modeling, stochastic simulation, and statistical inference Includes application examples from cosmology, environmental sciences, geology, and social networks Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used Provides access to C]+ and R code to encourage the reader to experiment and to develop new ideas Includes references and pointers to mathematical and applied literature to encourage further study The book is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students, so could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?
Database Systems for Advanced Applications
The seven-volume set LNCS 14850-14856 constitutes the proceedings of the 29th International Conference on Database Systems for Advanced Applications, DASFAA 2024, held in Gifu, Japan, in July 2024. The total of 147 full papers, along with 85 short papers, presented together in this seven-volume set was carefully reviewed and selected from 722 submissions. Additionally, 14 industrial papers, 18 demo papers and 6 tutorials are included. The conference presents papers on subjects such as: Part I: Spatial and temporal data; database core technology; federated learning. Part II: Machine learning; text processing. Part III: Recommendation; multi-media. Part IV: Privacy and security; knowledge base and graphs. Part V: Natural language processing; large language model; time series and stream data. Part VI: Graph and network; hardware acceleration. Part VII: Emerging application; industry papers; demo papers.
Approximation and Online Algorithms
This book constitutes the refereed proceedings of the 22nd International Workshop on Approximation and Online Algorithms, WAOA 2024, held in Egham, UK, during September 5-6, 2024. The 15 full papers included in this book were carefully reviewed and selected from 47 submissions. They were organized in topical sections as follows: 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 designing and analyzing approximation and online algorithms, resource augmentation, and scheduling problems.
Very First Steps in Random Walks
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Seminal Ideas and Controversies in Statistics
Statistics has developed as a field through seminal ideas and fascinating controversies. This book concerns a wide-ranging set of 13 important statistical topics, grouped into three general areas.
