Complex Symmetries
This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries).These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.
Bayes' Rule
What does a medical test tell us about the chances of having a particular disease? How can we tell if a spoken phrase is, 'four candles' or 'fork handles'? How do we a perceive a three-dimensional world from from the two-dimensional images on our retinas? The short answer is Bayes' rule, which transforms meaningless statistics and raw data into useful information. Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.
Evolutionary Equations
- Introduction.- Unbounded Operators.- The Time Derivative.- Ordinary Differential Equations.- The Fourier-Laplace Transformation and Material Law Operators.- Solution Theory for Evolutionary Equations.- Examples of Evolutionary Equations.- Causality and a Theorem of Paley and Wiener.- Initial Value Problems and Extrapolation Spaces.- Differential Algebraic Equations.- Exponential Stability of Evolutionary Equations.- Boundary Value Problems and Boundary Value Spaces.- Continuous Dependence on the Coefficients I.- Continuous Dependence on the Coefficients II.
Stochastic Processes with R
Stochastic Processes with R: An Introduction cuts through the heavy theory that is present in most courses on random processes and serves as practical guide to simulated trajectories and real-life applications for stochastic processes.
Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data
This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations.Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.
Evolutionary Equations
- Introduction.- Unbounded Operators.- The Time Derivative.- Ordinary Differential Equations.- The Fourier-Laplace Transformation and Material Law Operators.- Solution Theory for Evolutionary Equations.- Examples of Evolutionary Equations.- Causality and a Theorem of Paley and Wiener.- Initial Value Problems and Extrapolation Spaces.- Differential Algebraic Equations.- Exponential Stability of Evolutionary Equations.- Boundary Value Problems and Boundary Value Spaces.- Continuous Dependence on the Coefficients I.- Continuous Dependence on the Coefficients II.
Linear Regression With Python
Linear regression is the workhorse of data analysis. It is the first step, and often the only step, in fitting a simple model to data. This brief book explains the essential mathematics required to understand and apply regression analysis. The tutorial style of writing, accompanied by over 30 diagrams, offers a visually intuitive account of linear regression, including a brief overview of nonlinear and Bayesian regression. Hands-on experience is provided in the form of numerical examples, included as Python code at the end of each chapter, and implemented online as Python and Matlab code. Supported by a comprehensive glossary and tutorial appendices, this book provides an ideal introduction to regression analysis.
Linear Regression With Matlab
Linear regression is the workhorse of data analysis. It is the first step, and often the only step, in fitting a simple model to data. This brief book explains the essential mathematics required to understand and apply regression analysis. The tutorial style of writing, accompanied by over 30 diagrams, offers a visually intuitive account of linear regression, including a brief overview of nonlinear and Bayesian regression. Hands-on experience is provided in the form of numerical examples, included as Matlab code at the end of each chapter, and implemented online as Python and Matlab code. Supported by a comprehensive glossary and tutorial appendices, this book provides an ideal introduction to regression analysis.
Agent-based Models and Causal Inference
Agent-based Models and Causal Inference Scholars of causal inference have given little credence to the possibility that ABMs could be an important tool in warranting causal claims. Manzo's book makes a convincing case that this is a mistake. The book starts by describing the impressive progress that ABMs have made as a credible methodology in the last several decades. It then goes on to compare the inferential threats to ABMs versus the traditional methods of RCTs, regression, and instrumental variables showing that they have a common vulnerability of being based on untestable assumptions. The book concludes by looking at four examples where an analysis based on ABMs complements and augments the evidence for specific causal claims provided by other methods. Manzo has done a most convincing job of showing that ABMs can be an important resource in any researcher's tool kit.--Christopher Winship, Diker-Tishman Professor of Sociology, Harvard University, USA Agent-based Models and Causal Inference is a first-rate contribution to the debate on, and practice of, causal claims. With exemplary rigor, systematic precision and pedagogic clarity, this book contrasts the assumptions about causality that undergird agent-based models, experimental methods, and statistically based observational methods, discusses the challenges these methods face as far as inferences go, and, in light of this discussion, elaborates the case for combining these methods' respective strengths: a remarkable achievement.--Ivan Ermakoff, Professor of Sociology, University of Wisconsin-Madison, USA Agent-based models are a uniquely powerful tool for understanding how patterns in society may arise in often surprising and counter-intuitive ways. This book offers a strong and deeply reflected argument for how ABM's can do much more: add to actual empirical explanation. The work is of great value to all social scientists interested in learning how computational modelling can help unraveling the complexity of the real social world.--Andreas Flache, Professor of Sociology at the University of Groningen, Netherlands Agent-based Models and Causal Inference is an important and much-needed contribution to sociology and computational social science. The book provides a rigorous new contribution to current understandings of the foundation of causal inference and justification in the social sciences. It provides a powerful and cogent alternative to standard statistical causal-modeling approaches to causation. Especially valuable is Manzo's careful analysis of the conditions under which an agent-based simulation is relevant to causal inference. The book represents an exceptional contribution to sociology, the philosophy of social science, and the epistemology of simulations and models.--Daniel Little, Professor of philosophy, University of Michigan, USA Agent-based Models and Causal Inference delivers an insightful investigation into the conditions under which different quantitative methods can legitimately hold to be able to establish causal claims. The book compares agent-based computational methods with randomized experiments, instrumental variables, and various types of causal graphs. Organized in two parts, Agent-based Models and Causal Inference connects the literature from various fields, including causality, social mechanisms, statistical and experimental methods for causal inference, and agent-based computation models to help show that causality means different things within different methods for causal analysis, and that persuasive causal claims can only be built at the intersection of these various methods. Readers will also benefit from the inclusion of: A thorough comparison between agent-based computation models to randomized experiments, instrumental variables, and several types of causal graphs A compelling argument that observational and experimental methods are not qualitatively superior to simulatio
Emerging Problems in the Homogenization of Partial Differential Equations
Nika, G. and Vernescu, B., Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids.- Jerez-Hanckes, C. et al., Multiscale analysis of myelinated axons.- P矇rez-Mart穩nez, M., Homogenization for alternating boundary conditions with large reaction terms concentrated in small regions.- G. Fulgencio, R. and Guib矇, O., Quasilinear Elliptic Problems in a Two-Component Domain with L^1 data.- Donato, P. et al., Homogenization of an eigenvalue problem in a two-component domain with interfacial jump.
Statistical Models in Toxicology
This book is intended to present an up-to-date and comprehensive account of mathematical statistics problems that occur in toxicology. The aim is to introduce a wide variety of statistical models that are currently utilized for dose-response modeling and risk analysis.
Game Theory for Cyber Deception
This book introduces game theory as a means to conceptualize, model, and analyze cyber deception. Drawing upon a collection of deception research from the past 10 years, the authors develop a taxonomy of six species of defensive cyber deception. Three of these six species are highlighted in the context of emerging problems such as privacy against ubiquitous tracking in the Internet of things (IoT), dynamic honeynets for the observation of advanced persistent threats (APTs), and active defense against physical denial-of-service (PDoS) attacks. Because of its uniquely thorough treatment of cyber deception, this book will serve as a timely contribution and valuable resource in this active field. The opening chapters introduce both cybersecurity in a manner suitable for game theorists and game theory as appropriate for cybersecurity professionals. Chapter Four then guides readers through the specific field of defensive cyber deception. A key feature of the remaining chapters is the development of a signaling game model for the species of leaky deception featured in honeypots and honeyfiles. This model is expanded to study interactions between multiple agents with varying abilities to detect deception. Game Theory for Cyber Deception will appeal to advanced undergraduates, graduate students, and researchers interested in applying game theory to cybersecurity. It will also be of value to researchers and professionals working on cybersecurity who seek an introduction to game theory.
Non-Gaussian Autoregressive-Type Time Series
1. Basics of Time Series.- 2. Statistical Inference for Stationary Time Series.- 3. AR Models with Stationary Non-Gaussian Positive Marginals.- 4. AR Models with Stationary Non-Gaussian Real-Valued Marginals.- 5. Some Nonlinear AR-type Models for Non-Gaussian Time series.- 6. Linear Time Series Models with Non-Gaussian Innovations.- 7. Autoregressive-type Time Series of Counts.
Diophantine Approximation and Dirichlet Series
1. A Review of Commutative Harmonic Analysis.- 2. Ergodic Theory and Kronecker's Theorems.- 3. Diophantine Approximation.- 4. General Properties of Dirichlet Series.- 5. Probabilistic Methods for Dirichlet Series.- 6. Hardy Spaces of Dirichlet Series.- 7. Voronin Type theorems.- 8. Composition Operators on the Space H2 of Dirichlet Series.
Forecasting with Maximum Entropy
A unifying framework, based on Information Entropy and its maximization, to connect the phenomenology of evolutionary biology, community ecology, financial economics, and statistical physics, plus a forecasting method for important practical problems in these disciplines,
Linear Regression
Linear regression is the workhorse of data analysis. It is the first step, and often the only step, in fitting a simple model to data. This brief book explains the essential mathematics required to understand and apply regression analysis. The tutorial style of writing, accompanied by over 30 diagrams, offers a visually intuitive account of linear regression, including a brief overview of nonlinear and Bayesian regression. Hands-on experience is provided in the form of numerical examples, implemented online with Python and Matlab code. Supported by a comprehensive glossary and tutorial appendices, this book is an ideal introduction to regression analysis.
Topology and Approximate Fixed Points
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory.This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces-and fundamental properties of their topologies-are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fr矇chet-Urysohn property.The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies.By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Calculus of One Variable
This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.
Modeling Biomaterials
Farago, O., A Beginner's Short Guide to Membrane Biophysics.- Misailidis, G., Ferenc, J., Tsiairis, C., Self-Organization of Tissues through Biochemical and Mechanical Signals.- Righi, M., Balbi, V., Foundations of Viscoelasticity and Application to Soft Tissue Mechanics.- Klika, V., Modeling of Biomaterials as an Application of the Theory of Mixtures.- Miller, R., et al., Modeling Biomechanics in the Healthy and Diseased Heart.- Chabiniok, R., et al., Translational Cardiovascular Modeling: Tetralogy of Fallot and Modeling of Diseases.
Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment.
Analysis of Longitudinal Data with Examples
Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas. Key Features: -Includes the most up-to-date methods -Use simple examples to demonstrate complex methods -Uses real data from a number of areas -Examples utilize R code
Operators Between Sequence Spaces and Applications
1. Introduction.- 2. Matrix Domains.- 3. Operators between Matrix Domains.- 4. Statistical Convergence.- 5. Inclusion Equations.- 6. Sequence Space Equations.- 7. Solvability.
Statistical Methods for Mediation, Confounding and Moderation Analysis Using R and SAS
This book introduces general definitions of third-variable effects that are adaptable to all different types of response (categorical or continuous), exposure, or third-variables. Readers of all disciplines familiar with introductory statistics will find this a valuable resource for analysis.
Real Analysis and Infinity
Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions. Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge. Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.
Infectious Diseases and Our Planet
This book features recent research in mathematical modeling of indirectly and directly transmitted infectious diseases in humans, animals, and plants. It compiles nine not previously published studies that illustrate the dynamic spread of infectious diseases, offering a broad range of models to enrich understanding. It demonstrates the capability of mathematical modeling to capture disease spread and interaction dynamics as well as the complicating factors of various evolutionary processes. In addition, it presents applications to real-world disease control by commenting on key parameters and dominant pathways related to transmission. While aimed at early-graduate level students, the book can also provide insights to established researchers in that it presents a survey of current topics and methodologies in a constantly evolving field.
Operator Theory and Differential Equations
This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book provides a state-of-the-art account of various fascinating areas of operator theory, ranging from various classes of operators (positive operators, convolution operators, backward shift operators, singular and fractional integral operators, partial differential operators) to important applications in differential equations, inverse problems, approximation theory, metric theory of surfaces, the Hubbard model, social stratification models, and viscid incompressible fluids.
Statistics
Data are everywhere. This book introduces, in a conversational style, the foundational techniques and concepts necessary to permit the data to tell their story. You'll learn not only about the mechanics of basic data analyses but also about when to use the methods and about the statistical concepts relevant to the meaning of the results. Several key statistical concepts are introduced early and reinforced often: the importance of randomization in collecting data, statistical inference and three distinct types (statements about cause/effect, making predictions and forecasts, and generalizing from samples to populations), interpreting the results of an analysis, and common misconceptions. Designed to be used in a one-semester course in introductory statistics, the text comes complete with problem sets for each section. Contents: Chapter 1: An Introduction to Data Chapter 2: Summarizing Data Chapter 3: Producing Data Chapter 4: Probability Chapter 5: Probability Distributions for Random Sampling Chapter 6: Hypothesis Testing Chapter 7: Confidence Intervals Chapter 8: Inference About Two Groups
An Introduction to Infinite Products
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
Modal View of Atmospheric Variability
This book reviews the theory and applications of the normal-mode functions in numerical weather prediction and weather and climate dynamics. The normal-mode functions, the eigensolutions of the linearized primitive equations describing the evolution of atmospheric winds and mass variables, have been used for a long time. They have played an important role in the development of data assimilation schemes and the initialization of numerical weather prediction models. Chapters also present how the normal modes can be applied to many theoretical and numerical problems in the atmospheric sciences, such as equatorial wave dynamics, baroclinic instability, energy transfers, and predictability across scales.
Game Theory
This book is based on the concept of game theory with real-life examples and non-mathematical analysis. It examines individual as well as social decision-making scenarios via a variety of GAEORY techniques. Game theory is a vast and unique field, a very promising and interesting field of study. As a game theorist, my cognitive analysis decodes that, ""GAEORY"" will be a universal subject, theory of generation and disciple of next century, the main research analysis of this book to establish game theory as a subject. Research scholar S. J. Tripathi give it to name that is GAEORY. This book, the first time briefly discussed GAEORY (Game theory as a separate subject), propounded by the author.
On the disposition of the prime numbers
Academic Paper from the year 2021 in the subject Mathematics - Analysis, grade: 2.00, language: English, abstract: In this paper, a mathematical structure is formed which consists of a matrix of all of the odd numbers. It then follows that the matrix contains all of the prime numbers with the exception of 2. In conjunction with a prime number counting function denoted by pi(x) we can determine the number of primes in any row of the matrix and their location using the prime number search method developed, which uses the prime number counting function data compiled from various sources by A V Kulsha. The columns of the matrix are of infinite extent and in some there are either one or no prime numbers. In a column where there is a single prime number, this without exception appears in the first row. The matrix shows that there are prime numbers which can never be twinned and that it is not possible, with the exception of 3,5,7 that three consecutive odd numbers can be prime. Further it is demonstrated, in some of the rows, even although the distribution of the primes is random, that it is possible to predict the next prime, and in some instances the prime following it, thus predicting a set of twins. Moreover in many cases the gap between consecutive primes can be predicted. The work, in particular the Discussion contains numerous examples . Any odd number can, in principle be located precisely within the matrix. In the Appendix it is shown how, using only the prime number counting function data, to determine the primality (or otherwise) of any odd number without examining forensically the number itself. It is noted that, in contradistinction to formulae which predict particular prime numbers, such as those of Mersenne and Sophie Germain, the analysis presented here makes no distinction between any of the 'types' of primes.
Examples and Problems in Advanced Calculus
This book includes over 500 most challenging exercises and problems in calculus. Topical problems and exercises are discussed on set theory, numbers, functions, limits and continuity, derivative, integral calculus, Rolle's theorem, mean value theorem, optimization problems, sequences and series. All the seven chapters recall important definitions, theorems and concepts, making this book immensely valuable to undergraduate students of engineering, mathematics, statistics, computer science and basic sciences.
Research in Mathematics and Public Policy
This volume features a variety of research projects at the intersection of mathematics and public policy. The topics included here fall in the areas of cybersecurity and climate change, two broad and impactful issues that benefit greatly from mathematical techniques. Each chapter in the book is a mathematical look into a specific research question related to one of these issues, an approach that offers the reader insight into the application of mathematics to important public policy questions. The articles in this volume are papers inspired by a Workshop for Women in Mathematics and Public Policy, held January 22-25, 2019 at the Institute for Pure and Applied Mathematics and the Luskin Center at the University of California, Los Angeles. The workshop was created to promote and develop women at all levels of their careers as researchers in mathematics and public policy. The idea was modeled after other successful Research Collaboration Conferences for Women, where junior and senior women come together at week-long conferences held at mathematics institutes to work on pre-defined research projects. The workshop focused on how mathematics can be used in public policy research and was designed to foster collaborative networks for women to help address the gender gap in mathematics and science.
Nonlinear Dynamics, Chaos, and Complexity
Chapter 1. Professor Valentin Afraimovich by Alexandra Afraimovich Chapter 2.The need for more integration between machine learning and neuroscience by Adrian Hernandez, Jose M. Amigo Chapter 3.Quasiperiodic Route to Transient Chaos in Vibroimpact System by Victor Bazhenov, Olga Pogorelova, Tatiana Postnikova Chapter 4. Modeling Ensembles of Nonlinear Dynamic Systems in Ultrawideb and Active Wireless Direct Chaotic Networks by A.S. Dmitriev, R.Yu. Yemelyanov, M.Yu. Gerasimov, Yu.V. Andreyev Chapter 5.Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species by Messoud Efendiev, Vitali Vougalter Chapter6.Chaos-based communication using isochronal synchronization: considerations about the synchronization manifold byJ.M.V. Grzybowski, E.E.N. Macau, T. Yoneyama Chapter 7.A sequential order of periodic motions in a 1-dimensional, time-delay, dynamical system by Siyuan Xing and Albert C. J. Luo Chapter 8.On the Geometric Approach to Transformations of the Coordinates of Inertial Frames of Reference by A.A. Talyshev Chapter 9.Corpuscular models of information transfer in a random environment by V.V. Uchaikin Chapter 10. Kinetic equation for systems with resonant captures and scatterings by A.V. Artemyev, A.I. Neishtadt, A.A. Vasiliev Chapter 11. Solvability In The Sense Of Sequences For Some Non-Fredholm Operators In Higher Dimensions by Vitali Vougalter, Vitaly Volpert
Mathematics (Education) in the Information Age
This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique--an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.
Stability Analysis of Neural Networks
1. Introduction.- 2. LMI-Based Stability Criteria for BAM Neural Networks.- 3. Exponential Stability Criteria for Uncertain Inertial BAM Neural Networks.- 4. Exponential Stability of Impulsive Cohen-Grossberg BAM Neural Networks.- 5. Exponential Stability of Recurrent Neural Networks with Impulsive and Stochastic Effects.- 6. Stability of Markovian Jumping Stochastic Impulsive Uncertain BAM Neural Networks.- 7. Global Robust Exponential Stability of Stochastic Neutral-Type Neural Networks.- 8. Exponential Stability of Discrete-Time Cellular Uncertain BAM Neural Networks.- 9. Exponential Stability of Discrete-Time Stochastic Impulsive BAM Neural Networks.- 10. Stability of Discrete-Time Stochastic Quaternion-Valued Neural Networks.- 11. Robust Finite-Time Passivity of Markovian Jump Discrete-Time BAM Neural Networks.- 12 Robust Stability of Discrete-Time Stochastic Genetic Regulatory Networks.
Time Series for Data Science
Practical Time Series Analysis for Data Science is an accessible guide that doesn't require a background in calculus to be engaging but does not shy away from deeper explanations of the techniques discussed.
Advanced Statistics in Regulatory Critical Clinical Initiatives
This book is focused on the critical clinical initiatives introduced by the 21st Century Cure Act passed by the United States Congress in December 2016. The book covers everything from the outline of the initiatives to analysis on the effect on biopharmaceutical research and development.
Geometry of Deep Learning
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Hardy Operators on Euclidean Spaces and Related Topics
In many branches of mathematical analysis and mathematical physics, the Hardy operator and Hardy inequality are fundamentally important and have been intensively studied ever since the pioneer researches. This volume presents new properties of higher-dimensional Hardy operators obtained by the authors and their collaborators over the last decade. Its prime focus is on higher-dimensional Hardy operators that are based on the spherical average form.The key motivation for this monograph is based on the fact that the Hardy operator is generally smaller than the Hardy-Littlewood maximal operator, which leads to, on the one hand, the operator norm of the Hardy operator itself being smaller than the latter. On the other hand, the former characterizing the weight function class or function spaces is greater than the latter.
Classical Lie Algebras at Infinity
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension.The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Hypergroup Theory
The book presents an updated study of hypergroups, being structured on 12 chapters in starting with the presentation of the basic notions in the domain: semihypergroups, hypergroups, classes of subhypergroups, types of homomorphisms, but also key notions: canonical hypergroups, join spaces and complete hypergroups. A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.A special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. The bibliography presented is an updated one in the field, followed by an index of the notions presented in the book, useful in its study.
Lectures in Nonlinear Functional Analysis
This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.
Turnpike Theory for the Robinson-Solow-Srinivasan Model
This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson-Solow-Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.
Polarized Light and the Mueller Matrix Approach
This revised compendium integrates basic concepts of polarization phenomena from the dual viewpoints of polarization of electromagnetic waves and transformations by the action of material media. Through selected examples, it illustrates actual and potential applications in materials science, biology, and optics technology.
