In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how “free-Hilbert-space” Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how “inside” actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law.

Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its interdisciplinary applications. The design of dynamic systems of any type is an important issue as is the influence of uncertainty in model parameters and model sensitivity. The possibility of calculating the reachable sets may be a powerful additional tool in such tasks. This book can help graduate students, researchers, and engineers working in the field of computer simulation and model building, in the calculation of reachable sets of dynamic models.

The Boolean functions may be iterated either asynchronously, when their coordinates are computed independently of each other, or synchronously, when their coordinates are computed at the same time. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their use in modelling, author Serban E. Vlad presents a consistent and original mathematical theory of the discrete-time Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from the synchronous Boolean system theory and mostly from the synchronous real system theory, by analogy, and to indicate the way in which known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. The reader will be introduced to the dependence on the initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. A property of major importance is invariance, which is present in five versions. In relation to it, the reader will study the maximal invariant subsets, the minimal invariant supersets, the minimal invariant subsets, connectedness, separation, the basins of attraction, and attractors. The stability of the systems and their time-reversal symmetry end the topics that refer to the systems without input. The rest of the book is concerned with input systems. The most consistent chapters of this part of the book refer to the fundamental operating mode and to the combinational systems (systems without feedback). The chapter Wires, Gates, and Flip-Flops presents a variety of applications. The first appendix addresses the issue of continuous time, and the second one sketches the important theory of Daizhan Cheng, which is put in relation to asynchronicity. The third appendix is a bridge between asynchronicity and the symbolic dynamics of Douglas Lind and Brian Marcus.

Mathematics for Physical Chemistry, Fifth Edition includes exercises that enable readers to test their understanding and put theory into practice. Chapters are constructed around a sequence of mathematical topics, progressing gradually into more advanced material, before discussing key mathematical skills, including the analysis of experimental data and-new to this edition-complex variables. Includes additional new content on Mathematica and its advanced applications. Drawing on the experience of its expert authors, this book is the ideal supplementary text for practicing chemists and students wanting to sharpen their mathematics skills and understanding of key mathematical concepts for applications across physical chemistry.

Mathematical Modeling, Simulations, and Artificial Intelligence for Emergent Pandemic Diseases: Lessons Learned from COVID-19 includes new research, models and simulations developed during the COVID-19 pandemic into how mathematical methods and practice can impact future response. Chapters go beyond forecasting COVID-19, bringing different scale angles and mathematical techniques (e.g., ordinary differential and difference equations, agent-based models, artificial intelligence, and complex networks) which could have potential use in modeling other emergent pandemic diseases. A major part of the book focuses on preparing the scientific community for the next pandemic, particularly the application of mathematical modeling in ecology, economics and epidemiology. Readers will benefit from learning how to apply advanced mathematical modeling to a variety of topics of practical interest, including optimal allocations of masks and vaccines but also more theoretical problems such as the evolution of viral variants.

Deep Learning, Volume 48 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Generative Adversarial Networks for Biometric Synthesis, Data Science and Pattern Recognition, Facial Data Analysis, Deep Learning in Electronics, Pattern Recognition, Computer Vision and Image Processing, Mechanical Systems, Crop Technology and Weather, Manipulating Faces for Identity Theft via Morphing and Deepfake, Biomedical Engineering, and more.

Environmental Data Analysis with MATLAB, Third Edition, is a new edition that expands fundamentally on the original with an expanded tutorial approach, more clear organization, new crib sheets, and problem sets providing a clear learning path for students and researchers working to analyze real data sets in the environmental sciences. The work teaches the basics of the underlying theory of data analysis and then reinforces that knowledge with carefully chosen, realistic scenarios, including case studies in each chapter. The new edition is expanded to include applications to Python, an open source software environment. Significant content in Environmental Data Analysis with MATLAB, Third Edition is devoted to teaching how the programs can be effectively used in an environmental data analysis setting. This new edition offers chapters that can both be used as self-contained resources or as a step-by-step guide for students, and is supplemented with data and scripts to demonstrate relevant use cases.

Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes.

Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors.

Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find:* New ideas for dimension reduction.* Easy-to-implement algorithms.* Several examples of active subspaces in action.

The subject of information geometry blends several areas of statistics, computer science, physics, and mathematics. The subject evolved from the groundbreaking article published by legendary statistician C.R. Rao in 1945. His works led to the creation of Cramer-Rao bounds, Rao distance, and Rao-Blackawellization. Fisher-Rao metrics and Rao distances play a very important role in geodesics, econometric analysis to modern-day business analytics. The chapters of the book are written by experts in the field who have been promoting the field of information geometry and its applications.

Introduction to Chemical Engineering Analysis Using Mathematica, Second Edition reviews the processes and designs used to manufacture, use, and dispose of chemical products using Mathematica, one of the most powerful mathematical software tools available for symbolic, numerical, and graphical computing. Analysis and computation are explained simultaneously. The book covers the core concepts of chemical engineering, ranging from the conservation of mass and energy to chemical kinetics. The text also shows how to use the latest version of Mathematica, from the basics of writing a few lines of code through developing entire analysis programs. This second edition has been fully revised and updated, and includes analyses of the conservation of energy, whereas the first edition focused on the conservation of mass and ordinary differential equations.

New Optimization Algorithms and Applications: Atom-Based, Ecosystem-Based and Economics-Based presents the development of three new optimization algorithms - an Atom Search Optimization (ASO) algorithm, an Artificial Ecosystem-Based Optimization algorithm (AEO), a Supply Demand Based Optimization (SDO), and their applications within engineering. These algorithms are based on benchmark functions and typical engineering cases. The book describes the algorithms in detail and demonstrates how to use them in engineering. The title verifies the performance of the algorithms presented, simulation results are given, and MATLAB (R) codes are provided for the methods described. Over seven chapters, the book introduces ASO, AEO and SDO, and presents benchmark functions, engineering problems, and coding. This volume offers technicians and researchers engaged in computer and intelligent algorithm work and engineering with one source of information on novel optimization algorithms.

The Handbook of Reliability, Maintenance, and System Safety through Mathematical Modeling discusses the many factors affect reliability and performance, including engineering design, materials, manufacturing, operations, maintenance, and many more. Reliability is one of the fundamental criteria in engineering systems design, with maintenance serving as a way to support reliability throughout a system's life. Addressing these issues requires information, modeling, analysis and testing. Different techniques are proposed and implemented to help readers analyze various behavior measures (in terms of the functioning and performance) of systems.

New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications provides a detailed discussion on the underpinnings of the theory, methods and real-world applications of this numerical scheme. The book's authors explore how this efficient and accurate numerical scheme is useful for solving partial and ordinary differential equations, as well as systems of ordinary and partial differential equations with different types of integral operators. Content coverage includes the foundational layers of polynomial interpretation, Lagrange interpolation, and Newton interpolation, followed by new schemes for fractional calculus. Final sections include six chapters on the application of numerical scheme to a range of real-world applications. Over the last several decades, many techniques have been suggested to model real-world problems across science, technology and engineering. New analytical methods have been suggested in order to provide exact solutions to real-world problems. Many real-world problems, however, cannot be solved using analytical methods. To handle these problems, researchers need to rely on numerical methods, hence the release of this important resource on the topic at hand.

Data Science: Theory and Applications, Volume 44 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of interesting topics, including Modeling extreme climatic events using the generalized extreme value distribution, Bayesian Methods in Data Science, Mathematical Modeling in Health Economic Evaluations, Data Science in Cancer Genomics, Blockchain Technology: Theory and Practice, Statistical outline of animal home ranges, an application of set estimation, Application of Data Handling Techniques to Predict Pavement Performance, Analysis of individual treatment effects for enhanced inferences in medicine, and more. Additional sections cover Nonparametric Data Science: Testing Hypotheses in Large Complex Data, From Urban Mobility Problems to Data Science Solutions, and Data Structures and Artificial Intelligence Methods.

Reliability Analysis and Plans for Successive Testing: Start-up Demonstration Tests and Applications discusses all past and recent developments on start-up demonstration tests in the context of current numerical and illustrative examples to clarify available methods for distribution theorists and applied mathematicians dealing with control problems. Throughout the book, the authors focus on the panorama of open problems and issues of further interest. As contemporary manufacturers face tremendous commercial pressures to assemble works of high reliability, defined as 'the probability of the product performing its role under the stated conditions and over a specified period of time', this book helps address testing issues.

Advances in Mathematics for Industry 4.0 examines key tools, techniques, strategies, and methods in engineering applications. By covering the latest knowledge in technology for engineering design and manufacture, chapters provide systematic and comprehensive coverage of key drivers in rapid economic development. Written by leading industry experts, chapter authors explore managing big data in processing information and helping in decision-making, including mathematical and optimization techniques for dealing with large amounts of data in short periods.