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This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.

'Beauty is the first test: there is no permanent place in the world for ugly mathematics.'- G. H. Hardy Number theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science.'Mathematics is the queen of sciences - and number theory is the queen of mathematics,'according to Carl Friedrich Gauss, the lifelong Wunderkind, who himself enjoyed the epithet'Princeps Mathematicorum.'What could be more beautiful than a deep, satisfying relation between whole numbers. (One is almost tempted to call them wholesome numbers') In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the'untouched ones'. How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is taking on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.

This book comprises well over three-hundred exercises in matrix algebra and their solutions. The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to make them comprehensible independently of their source. To further insure that the restated exercises have this stand-alone property, I have included in the front matter a section on terminology and another on notation. These sections provide definitions, descriptions, comments, or explanatory material pertaining to certain terms and notational symbols and conventions from Matrix Algebra From a Statistician's Perspective that may be unfamiliar to a nonreader of that book or that may differ in generality or other respects from those to which he/she is accustomed. For example, the section on terminology includes an entry for scalar and one for matrix. These are standard terms, but their use herein (and in Matrix Algebra From a Statistician's Perspective) is restricted to real numbers and to rectangular arrays of real numbers, whereas in various other presentations, a scalar may be a complex number or more generally a member of a field, and a matrix may be a rectangular array of such entities.

Gaussian Integrals form an integral part of many subfields of applied mathematics and physics, especially in topics such as probability theory, statistics, statistical mechanics, quantum mechanics and so on. They are essential in computing quantities such as the statistical properties of normal random variables, solving partial differential equations involving diffusion processes, and gaining insight into the properties of particles. In Gaussian Integrals and their Applications, the author has condensed the material deemed essential for undergraduate and graduate students of physics and mathematics, such that for those who are very keen would know what to look for next if their appetite for knowledge remains unsatisfied by the time they finish reading this book. Features A concise and easily digestible treatment of the essentials of Gaussian Integrals Suitable for advanced undergraduates and graduate students in mathematics, physics, and statistics The only prerequisites are a strong understanding of multivariable calculus and linear algebra. Supplemented by numerous exercises (with fully worked solutions) at the end, which pertain to various levels of difficulty and are inspired by different fields in which Gaussian integrals are used.

Learn how to leverage the scientific computing and data analysis capabilities of Python, its standard library, and popular open-source numerical Python packages like NumPy, SymPy, SciPy, matplotlib, and more. This book demonstrates how to work with mathematical modeling and solve problems with numerical, symbolic, and visualization techniques. It explores applications in science, engineering, data analytics, and more. Numerical Python, Third Edition, presents many case study examples of applications in fundamental scientific computing disciplines, as well as in data science and statistics. This fully revised edition, updated for each library's latest version, demonstrates Python's power for rapid development and exploratory computing due to its simple and high-level syntax and many powerful libraries and tools for computation and data analysis. After reading this book, readers will be familiar with many computing techniques, including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling, and machine learning. What You'll Learn Work with vectors and matrices using NumPy Review Symbolic computing with SymPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Understand statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Who This Book Is For Developers who want to understand how to use Python and its ecosystem of libraries for scientific computing and data analysis.

This book explores the application of complex variables to econometric modeling. Providing a thorough introduction to the theory of complex numbers, it extends these concepts to develop complex-valued models that enhance the accuracy and depth of economic forecasting and data analysis. From simple to multiple complex linear regression, the monograph discusses model formulation, estimation techniques, and correlation analysis, supported by examples in R. This comprehensive guide is a useful resource for students, researchers, and practitioners aiming to apply advanced mathematical techniques to tackle complex real-life problems, making it a useful tool for enhancing predictive analytics in business, economics, and finance.

This book provides a self-contained account of continuous-parameter time series, starting with second-order models. Integration with respect to orthogonal increment processes, spectral theory and linear prediction are treated in detail. Lévy-driven models are incorporated, extending coverage to allow for infinite variance, a variety of marginal distributions and sample paths having jumps. The necessary theory of Lévy processes and integration of deterministic functions with respect to these processes is developed at length. Special emphasis is given to the analysis of continuous-time ARMA processes.

MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-2 weeks in duration. This book is a scientific record of the 24 programs held at MATRIX in 2021-2022, including tandem workshops with Mathematisches Forschungsinstitut Oberwolfach (MFO), with Research Institute for Mathematical Sciences Kyoto University (RIMS), and with Sydney Mathematical Research Institute (SMRI).

Available in English for the first time, this classic and influential book by the late Kohei Ohtsu presents real examples of ships in motion under irregular ocean waves, how to understand the characteristics of fluctuations of stochastic phenomena through spectral analysis methods and statistical modeling. It also explains how to realize prediction and optimal control based on time series models.In recent years, the need to improve safety and reduce environmental impact in ship operations has been increasing, and the statistical methods presented in this book will be increasingly needed in the future. In addition, the recent development of innovative AI technology and highspeed communications will make it possible to adapt this method not only to ship monitoring and control, but also to any field that involves irregular fluctuations, and it is expected to contribute to solving issues that have been difficult to solve in the past.Part 1 describes classical spectral method for the analysis of stochastic phenomena. In Part 2, this book explains methods to construct time series models using the information criterion, to capture the characteristics of ship and engine motions using the model, to design a model-based monitoring system that informs navigators operating the ship and managers ashore. Furthermore, it explains statistical control method to design an autopilot system and the governor of a marine engine, while showing actual examples. Part 3 presents the basic knowledge necessary for understanding these topics of the book, namely, the basic theory of ship motion, probability and statistics, Kalman filter and statistical optimal control theory.

This 13-volume set LNCS 14862-14874 constitutes - in conjunction with the 6-volume set LNAI 14875-14880 and the two-volume set LNBI 14881-14882 - the refereed proceedings of the 20th International Conference on Intelligent Computing, ICIC 2024, held in Tianjin, China, during August 5-8, 2024. The total of 863 regular papers were carefully reviewed and selected from 2189 submissions. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. Its aim was to unify the picture of contemporary intelligent computing techniques as an integral concept that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. Therefore, the theme for this conference was'Advanced Intelligent Computing Technology and Applications'. Papers that focused on this theme were solicited, addressing theories, methodologies, and applications in science and technology.

This book presents a groundbreaking new mathematical paradigm and system (including inventing a new number) that enables a new approach to advancing the foundations of science and technology. The new approach allows connecting subjective and objective points of view that do not rely solely on the classical deductive approach. There is no need to fear paradoxical situations, because it's precisely in them wherein lies the key to a new understanding that is more connected to life itself. This new model also serves to advance the theory of consciousness. Life is more colorful and diverse than just the binary colors of black and white. For this purpose, the authors propose a new type of number called Soft Number. The basic idea is to distinguish between the different multiples of the number zero. Soft Logic is a continuous extension of the idea of giving different meanings to the zero. The authors create a tangible model of an infinitely small world. This seemingly inconceivable world is important for understanding the essence of the connection between the external world of reality and the inner world of human beings and offers a new language to express it. This book systematically and axiomatically describes the mathematical development of Soft Logic and Soft Numbers and points to possible directions for scientific and technological applications. This book is a valuable resource for researchers working in mathematics, physics, biology, engineering, computer science and artificial intelligence as well as advanced-level students majoring in computer science, engineering and mathematics. Practitioners, Data Scientists, AI developers and readers interested in a scientific understanding of the concept of consciousness will also want to purchase this book.

This book does not focus solely on asymptotic extreme value distributions. In addition to the traditional asymptotic methods, it introduces a data-driven, computer-based method, which provides insights into the exact extreme value distribution inherent in the data, and which avoids asymptotics. It therefore differs from currently available texts on extreme value statistics in one very important aspect. The method described provides a unique tool for diagnostics, and for efficient and accurate extreme value prediction based on measured or simulated data. It also has straightforward extensions to multivariate extreme value distributions. The first half provides an introduction to extreme value statistics with an emphasis on applications. It includes chapters on classical asymptotic theories and threshold exceedance models, with many illustrative examples. The mathematical level is elementary and, to increase readability, detailed mathematical proofs have been avoided in favour of heuristic arguments. The second half presents in some detail specialized topics that illustrate the power and the limitations of the concepts discussed. With diverse applications to science, engineering and finance, the techniques described in this book will be useful to readers from many different backgrounds.

This book is for individuals with a scientific background who aspire to apply machine learning within various natural science disciplines—such as physics, chemistry, biology, medicine, psychology and many more. It elucidates core mathematical concepts in an accessible and straightforward manner, maintaining rigorous mathematical integrity. For readers more versed in mathematics, the book includes advanced sections that are not prerequisites for the initial reading. It ensures concepts are clearly defined and theorems are proven where it's pertinent. Machine learning transcends the mere implementation and training of algorithms; it encompasses the broader challenges of constructing robust datasets, model validation, addressing imbalanced datasets, and fine-tuning hyperparameters. These topics are thoroughly examined within the text, along with the theoretical foundations underlying these methods. Rather than concentrating on particular algorithms this book focuses on the comprehensive concepts and theories essential for their application. It stands as an indispensable resource for any scientist keen on integrating machine learning effectively into their research. Numerous texts delve into the technical execution of machine learning algorithms, often overlooking the foundational concepts vital for fully grasping these methods. This leads to a gap in using these algorithms effectively across diverse disciplines. For instance, a firm grasp of calculus is imperative to comprehend the training processes of algorithms and neural networks, while linear algebra is essential for the application and efficient training of various algorithms, including neural networks. Absent a solid mathematical base, machine learning applications may be, at best, cursory, or at worst, fundamentally flawed. This book lays the foundation for a comprehensive understanding of machine learning algorithms and approaches.

This book gathers outstanding papers presented at the International Conference on Data Science and Applications (ICDSA 2023), organized by Soft Computing Research Society (SCRS) and Malaviya National Institute of Technology Jaipur, India, from 14 to 15 July 2023. The book is divided into four volumes, and it covers theoretical and empirical developments in various areas of big data analytics, big data technologies, decision tree learning, wireless communication, wireless sensor networking, bioinformatics and systems, artificial neural networks, deep learning, genetic algorithms, data mining, fuzzy logic, optimization algorithms, image processing, computational intelligence in civil engineering, and creative computing.

This book constitutes the refereed proceedings of the 30th International Conference on MultiMedia Modeling, MMM 2024, held in Amsterdam, The Netherlands, during January 29–February 2, 2024.The 112 full papers included in this volume were carefully reviewed and selected from 297 submissions. The MMM conference were organized in topics related to multimedia modelling, particularly: audio, image, video processing, coding and compression; multimodal analysis for retrieval applications, and multimedia fusion methods.

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology.

The five-volume set LNCS 14961, 14962, 14963, 14964 and 14965 constitutes the refereed conference proceedings of the 8th International Joint Conference on Web and Big Data, APWeb-WAIM 2024, held in Jinhua, China, during August 30–September 1, 2024. The 171 full papers presented in these proceedings were carefully reviewed and selected from 558 submissions. The papers are organized in the following topical sections: Volume I: Natural language processing, Generative AI and LLM, Computer Vision and Recommender System. Volume II: Recommender System, Knowledge Graph and Spatial and Temporal Data. Volume III: Spatial and Temporal Data, Graph Neural Network, Graph Mining and Database System and Query Optimization. Volume IV: Database System and Query Optimization, Federated and Privacy-Preserving Learning, Network, Blockchain and Edge computing, Anomaly Detection and Security Volume V: Anomaly Detection and Security, Information Retrieval, Machine Learning, Demonstration Paper and Industry Paper.

This four-volume set constitutes the post-conference proceedings of the 7th EAI International Conference on Advanced Hybrid Information Processing, ADHIP 2023, held in Harbin, China, during September 22-24, 2023. The 108 full papers presented were selected from 270 submissions and focus on theory and application of hybrid information processing technology for smarter and more effective research and application. The theme of ADHIP 2022 was Hybrid Information Processing in Meta World. The papers are named in topical sections as follows: wireless communication for social information processing, artificial intelligence technology; Mobile education, mobile monitoring, behavior understanding and object tracking; wireless networks for social information processing, image information processing; mobile monitoring, civilian audio and acoustic signal processing.

This book offers accessible probabilistic modelling of relevant financial problems. It is divided into two parts. The first part (cookbook) is written by emphasizing the key definitions and theorems without wasting too much of the reader with unnecessary technical details. Here, the first kind of target audience is graduate students in Economics with no prior exposition to probability theory (except for undergraduate courses in Applied Statistics) which are provided by a self-contained account of probabilistic modelling mainly applied to finance. The fundamental concepts of random variable/vector and probability distributions are introduced beforehand with respect to the usual treatment of this subject in standard probability textbook, trying to strike a balance between precise mathematical definitions and their applied knowledge. All the analytic tools developed are illustrated through examples of probability distributions of future stock prices, returns and profit and loss, together with their main characteristics, such as moments, moment generating and characteristic functions, location-scale families, and quantiles. The extension to the multivariate case for fixed time horizons is presented, together with the fundamentals of stochastic processes both in discrete and continuous time as candidate models for asset prices and return dynamics. Convergence concepts are presented as applied to the problem of point estimation of means, variances, correlation coefficients and risk measures. Short sections on risk and copula functions, further illustrate the potential application of probability models to financial problems. The second part of the book can be accessed by those students with more mathematical preparation. All the relevant proofs of results which are only stated in the first part and some advanced exercises with complete solutions are presented.

This book constitutes the refereed proceedings of the 6th Conference on Research in Computer Science, CRI 2023, held in Yaounde, Cameroon, during December 12-13, 2023. The 16 full papers included in this book were carefully reviewed and selected from 72 submissions. The CRI 2023 proceedings focus on artificial intelligence, machine learning, natural language processing, computer vision, cryptography and distributed computing.

This book gathers the proceedings of the 8th International Conference on Advancements of Medicine and Health Care through Technology, MEDITECH 2022, held virtually on 20–22 October 2022, from Cluj-Napoca, Romania. It reports on both theoretical and practical developments in biomedical imaging and image processing, health technology, technologies for education, and biomedical signal processing and medical devices, measurements and instrumentation. Both the conference and the realization of this book were supported by the Romanian National Society for Medical Engineering and Biological Technology (SNIMTB).

This 6-volume set LNAI 14875-14880 constitutes - in conjunction with the 13-volume set LNCS 14862-14874 and the 2-volume set LNBI 14881-14882 - the refereed proceedings of the 20th International Conference on Intelligent Computing, ICIC 2024, held in Tianjin, China, during August 5-8, 2024. The total of 863 regular papers were carefully reviewed and selected from 2189 submissions. The intelligent computing annual conference primarily aims to promote research, development and application of advanced intelligent computing techniques by providing a vibrant and effective forum across a variety of disciplines. This conference has a further aim of increasing the awareness of industry of advanced intelligent computing techniques and the economic benefits that can be gained by implementing them. The intelligent computing technology includes a range of techniques such as Artificial Intelligence, Pattern Recognition, Evolutionary Computing, Informatics Theories and Applications, Computational Neuroscience & Bioscience, Soft Computing, Human Computer Interface Issues, etc.

This 13-volume set LNCS 14862-14874 constitutes - in conjunction with the 6-volume set LNAI 14875-14880 and the two-volume set LNBI 14881-14882 - the refereed proceedings of the 20th International Conference on Intelligent Computing, ICIC 2024, held in Tianjin, China, during August 5-8, 2024. The total of 863 regular papers were carefully reviewed and selected from 2189 submissions. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. Its aim was to unify the picture of contemporary intelligent computing techniques as an integral concept that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. Therefore, the theme for this conference was'Advanced Intelligent Computing Technology and Applications'. Papers that focused on this theme were solicited, addressing theories, methodologies, and applications in science and technology.

Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, and more. Compound Poisson Approximation synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems, and exercises, it will become the standard reference book on the topic. Features• Provides a comprehensive overview of this rapidly expanding field • Synthesizes the most important research results of recent years • Presents an array of special topics• Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics.

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation.Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations.This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:Markov chains, which are omnipresent and versatile models in applied probabilityPoisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networksBrownian motion, which models fluctuations in the stock market and the'white noise'of physicsWide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences.This book can be used as a text in various ways and at different levels of study. Essentially, it provides the material for a two-semester graduate course on probability and stochastic processes in a department of applied mathematics or for students in departments where stochastic models play an essential role. The progressive introduction of concepts and tools, along with the inclusion of numerous examples, also makes this book well-adapted for self-study.

This book is devoted to the fundamentals of order and rank statistics. Primarily focusing on theoretical properties, it also discusses practical aspects, including interesting applications of step and impulse functions for the distribution of random variables, magnitudes, and signs. New concepts are introduced, such as independent and semi-identically distributed random vectors and probability density-mass functions. This book also presents an investigation of relative magnitudes in order statistics, and of correlation coefficients among signs, ranks, and magnitudes. The basic concepts are described in clear terms, and step-by-step details are provided for most of the presented mathematical results. The exposition is accompanied by numerous examples and more than 100 exercises, for which a complete solution manual is available. Providing a useful reference, and requiring only a basic understanding of probability and random variables, the book will appeal to a wide readership.

This book presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and previous editions had essential updates and comprehensive coverage on critical topics in mathematics.This 3rd edition offers a self-contained description of relevant aspects of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices, in solutions of linear systems and in eigenanalysis. It also includes discussions of the R software package, with numerous examples and exercises.Matrix Algebra considers various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; as well as describing various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors. It covers numerical linear algebra—one of the most important subjects in the field of statistical computing. The content includes greater emphases on R, and extensive coverage of statistical linear models. Matrix Algebra is ideal for graduate and advanced undergraduate students, or as a supplementary text for courses in linear models or multivariate statistics. It's also ideal for use in a course in statistical computing, or as a supplementary text forvarious courses that emphasize computations.

This book constitutes the proceedings of the Third BenchCouncil International Symposium on Intelligent Computers, Algorithms, and Applications, IC 2023, which took place in Sanya, China, in December 2023. The 18 full papers and 8 short papers included in this book were carefully reviewed and selected from 50 submissions. They were organized in topical sections as follows: AI Algorithms and Systems; AI for Ocean science and engineering; AI in finance; AI for education; AI for materials science and engineering; AI for medicine; AI for civil aviation; AI for high energy physics; AI for law.

This textbook investigates in detail the methods for stochastic dynamic response and stability analyses of nonlinear systems (especially ships and ocean engineering systems), elucidating the advantages and disadvantages of each of the methods (the statistical linearization method, the perturbation method, the Monte Carlo Simulation method, the numerical path integration method, the global geometric method and the first passage theory). Studies on stochastic dynamic analysis of nonlinear systems have attracted engineers and scientists from various disciplines, such as aeronautical, civil, mechanical and ocean engineering. Pursuing a systematic approach, this book establishes a fundamental framework for this topic, while emphasizing the importance of accurate and efficient analysis as well as the significant influence of choosing a suitable method in the design and optimization of various nonlinear engineering systems (especially ships and ocean engineering systems).The textbook is intended for upper undergraduate and graduate students who are interested in advanced dynamic analysis technologies, researchers investigating nonlinear systems under stochastic dynamic excitations, and civil/mechanical/structural/ocean engineers working on designing and optimization of real-world nonlinear engineering systems. The basis of English translation of this book from its Chinese original manuscript was done with the help of artificial intelligence. A subsequent human revision of the content was done by the author.

This volume provides the reader with a comprehensive and up-to-date treatise positioned at the junction of the areas of Machine Learning (ML) and Granular Computing (GrC). ML offers a wealth of architectures and learning methods. Granular Computing addresses useful aspects of abstraction and knowledge representation that are of importance in the advanced design of ML architectures. In unison, ML and GrC support advances of the fundamental learning paradigm. As built upon synergy, this unified environment focuses on a spectrum of methodological and algorithmic issues, discusses implementations and elaborates on applications. The chapters bring forward recent developments showing ways of designing synergistic and coherently structured ML-GrC environment. The book will be of interest to a broad audience including researchers and practitioners active in the area of ML or GrC and interested in following its timely trends and new pursuits.

This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel (Wentzell) boundary condition, on the boundary of the domain. Most likely, a Markovian particle moves both by continuous paths and by jumps in the state space and obeys the Ventcel boundary condition, which consists of six terms corresponding to diffusion along the boundary, an absorption phenomenon, a reflection phenomenon, a sticking (or viscosity) phenomenon, and a jump phenomenon on the boundary and an inward jump phenomenon from the boundary. More precisely, we study a class of first-order Ventcel boundary value problems for second-order elliptic Waldenfels integro-differential operators. By using the Calderón–Zygmund theory of singular integrals, we prove the existence and uniqueness of theorems in the framework of the Sobolev and Besov spaces, which extend earlier theorems due to Bony–Courrège–Priouret to the vanishing mean oscillation (VMO) case. Our proof is based on various maximum principles for second-order elliptic differential operators with discontinuous coefficients in the framework of Sobolev spaces. My approach is distinguished by the extensive use of the ideas and techniques characteristic of recent developments in the theory of singular integral operators due to Calderón and Zygmund. Moreover, we make use of an Lp variant of an estimate for the Green operator of the Neumann problem introduced in the study of Feller semigroups by me. The present book is amply illustrated; 119 figures and 12 tables are provided in such a fashion that a broad spectrum of readers understand our problem and main results.

The book explores the convergence of healthcare and cutting-edge technology, making it a captivating subject for readers interested in future research. Smart healthcare with machine learning techniques offers a transformative paradigm that utilizes the power of new technology, data analytics, and interconnected devices to enhance the quality, efficiency, and accessibility of healthcare services. This involves leveraging Internet of Things (IoT) devices, wearable technology, and machine learning algorithms to monitor patient health, predict medical conditions, and offer personalized treatment recommendations. This innovative combination not only enhances diagnostics and treatment but also addresses the research challenges of healthcare access and delivery in an increasingly connected world. By exploring the synergy between smart healthcare and machine learning, the book helps to understand how these technologies can collaborate to revolutionize patient care and healthcare delivery. This book is an outcome with applications of future technologies to overcome the toughest humanitarian challenges from an engineering approach.

The main objective of this book is to introduce a student who is familiar with elementary math concepts to select topics in deep learning. It exploits strong connections between deep learning algorithms and the techniques of computational physics to achieve two important goals. First, it uses concepts from computational physics to develop an understanding of deep learning algorithms. Second, it describes several novel deep learning algorithms for solving challenging problems in computational physics, thereby offering someone who is interested in modeling physical phenomena with a complementary set of tools. It is intended for senior undergraduate and graduate students in science and engineering programs. It is used as a textbook for a course (or a course sequence) for senior-level undergraduate or graduate-level students.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

This book is the first to focus on the global flow of funds (GFF), providing an introduction to its fundamental concepts and establishing a theoretical framework for analysis. It connects the flow of funds within domestic economies to that of the rest of the world, offering a comprehensive analysis of GFF dynamics. This study enhances GFF statistics, enabling the assessment of global financial stability from both national and cross-border sectoral perspectives. The GFF data provide valuable insights into analyzing interconnectivity across borders and an understanding of global financial interdependencies. By examining the data sources and reconstructing the statistical framework to establish the GFF statistical matrix, this book conducts a case study to evaluate financial risks and influences in G20 countries. Subsequently, it connects the GFF matrix with sectoral account data and the flow of funds to establish the sectoral from-whom-to-whom financial stock matrix (SFSM). The SFSM aims to establish a new framework for conducting multi-country, multi-sector analysis within the G20, with a special emphasis on examining the national and cross-border exposures of sectors in China, Japan, and the USA. This involves constructing country-specific financial networks and connecting them based on cross-border exposures. The systematic analysis results effectively showcase the financial interconnections among G20 countries within the GFF and shed light on the attributes of external shocks and internal influences. The focus is particularly on the changes in risk exposure between China and the USA concerning their external assets and liabilities and the implications of economic decoupling of these dynamics.

Ecological dynamics are tremendously complicated and are studied at a variety of spatial and temporal scales. Ecologists often simplify analysis by describing changes in density of individuals across a landscape, and statistical methods are advancing rapidly for studying spatio-temporal dynamics. However, spatio-temporal statistics is often presented using a set of principles that may seem very distant from ecological theory or practice. This book seeks to introduce a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics. We provide a step-by-step illustration of techniques that combine core spatial-analysis packages in R with low-level computation using Template Model Builder. Techniques are showcased using real-world data from varied ecological systems, providing a toolset for hierarchical modelling of spatio-temporal processes. Spatio-Temporal Models for Ecologists is meant for graduate level students, alongside applied and academic ecologists.Key Features: Foundational ecological principles and analyses Thoughtful and thorough ecological examples Analyses conducted using a minimal toolbox and fast computation Code using R and TMB included in the book and available online

This book presents a new way of thinking about quantum mechanics and machine learning by merging the two. Quantum mechanics and machine learning may seem theoretically disparate, but their link becomes clear through the density matrix operator which can be readily approximated by neural network models, permitting a formulation of quantum physics in which physical observables can be computed via neural networks. As well as demonstrating the natural affinity of quantum physics and machine learning, this viewpoint opens rich possibilities in terms of computation, efficient hardware, and scalability. One can also obtain trainable models to optimize applications and fine-tune theories, such as approximation of the ground state in many body systems, and boosting quantum circuits'performance. The book begins with the introduction of programming tools and basic concepts of machine learning, with necessary background material from quantum mechanics and quantum information also provided. This enables the basic building blocks, neural network models for vacuum states, to be introduced. The highlights that follow include: non-classical state representations, with squeezers and beam splitters used to implement the primary layers for quantum computing; boson sampling with neural network models; an overview of available quantum computing platforms, their models, and their programming; and neural network models as a variational ansatz for many-body Hamiltonian ground states with applications to Ising machines and solitons. The book emphasizes coding, with many open source examples in Python and TensorFlow, while MATLAB and Mathematica routines clarify and validate proofs. This book is essential reading for graduate students and researchers who want to develop both the requisite physics and coding knowledge to understand the rich interplay of quantum mechanics and machine learning.

This book explores the complete system perspective, underlying theories, modeling, and applications of cyber-physical systems (CPS). Considering the interest of researchers and academicians, the editors present this book in a multidimensional perspective covering CPS at breadth. It covers topics ranging from discussion of rudiments of the system and efficient management to recent research challenges and issues. This book is divided into four sections discussing the fundamentals of CPS, engineering-based solutions, its applications, and advanced research challenges. The contents highlight the concept map of CPS including the latest technological interventions, issues, challenges, and the integration of CPS with IoT and big data analytics, modeling solutions, distributed management, efficient energy management, cyber-physical systems research, and education with applications in industrial, agriculture, and medical domains. This book is of immense interest to those in academia and industry.

Enhance your data science programming and analysis with the Wolfram programming language and Mathematica, an applied mathematical tools suite. This second edition introduces the latest LLM Wolfram capabilities, delves into the exploration of data types in Mathematica, covers key programming concepts, and includes code performance and debugging techniques for code optimization. You'll gain a deeper understanding of data science from a theoretical and practical perspective using Mathematica and the Wolfram Language. Learning this language makes your data science code better because it is very intuitive and comes with pre-existing functions that can provide a welcoming experience for those who use other programming languages. Existing topics have been reorganized for better context and to accommodate the introduction of Notebook styles. The book also incorporates new functionalities in code versions 13 and 14 for imported and exported data. You'll see how to use Mathematica, where data management and mathematical computations are needed. Along the way, you'll appreciate how Mathematica provides an entirely integrated platform: its symbolic and numerical calculation result in a mized syntax, allowing it to carry out various processes without superfluous lines of code. You'll learn to use its notebooks as a standard format, which also serves to create detailed reports of the processes carried out. What You Will Learn Create datasets, work with data frames, and create tables Import, export, analyze, and visualize data Work with the Wolfram data repository Build reports on the analysis Use Mathematica for machine learning, with different algorithms, including linear, multiple, and logistic regression; decision trees; and data clustering Who This Book Is For Data scientists who are new to using Wolfram and Mathematica as a programming language or tool. Programmers should have some prior programming experience, but can be new to the Wolfram language.

This book introduces Probability Theory with R software and explains abstract concepts in a simple and easy-to-understand way by combining theory and computation. It discusses conceptual and computational examples in detail, to provide a thorough understanding of basic techniques and develop an enjoyable read for students seeking suitable material for self-study. It illustrates fundamental concepts including fields, sigma-fields, random variables and their expectations, various modes of convergence of a sequence of random variables, laws of large numbers and the central limit theorem. Computational exercises based on R software are included in each Chapter Includes a brief introduction to the basic functions of R software for beginners in R and serves as a ready reference Includes Numerical computations, simulation studies, and visualizations using R software as easy tools to explain abstract concepts Provides multiple-choice questions for practice Incorporates self-explanatory R codes in every chapter This textbook is for advanced students, professionals, and academic researchers of Statistics, Biostatistics, Economics and Mathematics.

The six-volume set LNCS 14608, 14609, 14609, 14610, 14611, 14612 and 14613 constitutes the refereed proceedings of the 46th European Conference on IR Research, ECIR 2024, held in Glasgow, UK, during March 24–28, 2024.The 57 full papers, 18 finding papers, 36 short papers, 26 IR4Good papers, 18 demonstration papers, 9 reproducibility papers, 8 doctoral consortium papers, and 15 invited CLEF papers were carefully reviewed and selected from 578 submissions. The accepted papers cover the state of the art in information retrieval focusing on user aspects, system and foundational aspects, machine learning, applications, evaluation, new social and technical challenges, and other topics of direct or indirect relevance to search.

Adaptive filtering still receives attention in engineering as the use of the adaptive filter provides improved performance over the use of a fixed filter under the time-varying and unknown statistics environments. This application evolved communications, signal processing, seismology, mechanical design, and control engineering. The most popular optimization criterion in adaptive filtering is the well-known minimum mean square error (MMSE) criterion, which is, however, only optimal when the signals involved are Gaussian-distributed. Therefore, many'optimal solutions'under MMSE are not optimal. As an extension of the traditional MMSE, the minimum mean p-power error (MMPE) criterion has shown superior performance in many applications of adaptive filtering. This book aims to provide a comprehensive introduction of the MMPE and related adaptive filtering algorithms, which will become an important reference for researchers and practitioners in this application area. The book is geared to senior undergraduates with a basic understanding of linear algebra and statistics, graduate students, or practitioners with experience in adaptive signal processing.Key Features: Provides a systematic description of the MMPE criterion. Many adaptive filtering algorithms under MMPE, including linear and nonlinear filters, will be introduced. Extensive illustrative examples are included to demonstrate the results.

This book constitutes the post-conference proceedings of the First International Conference on Advanced Computational Applications of Geometric Algebra, ICACGA 2022, held in Denver, CO, USA, during October 2-5, 2022. The 18 full papers presented in this book together with 12 abstracts of invited talks were carefully reviewed and selected from 24 submissions. The papers are grouped in the following topical sections: geometric applications; computer science applications; technological applications; and applications to physics and mathematics.

The Instant New York Times Bestseller“Engaging and entertaining… a glimpse of the economy of the future.” —Tim Wu, New York Times Book ReviewFrom the New York Times bestselling author of The Signal and the Noise, the definitive guide to our era of risk—and the players raising the stakes In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates “the River,” the community of like-minded people whose mastery of risk allows them to shape—and dominate—so much of modern life. These professional risk-takers—poker players and hedge fund managers, crypto true believers and blue-chip art collectors—can teach us much about navigating the uncertainty of the twenty-first century. By immersing himself in the worlds of Doyle Brunson, Peter Thiel, Sam Bankman-Fried, Sam Altman, and many others, Silver offers insight into a range of issues that affect us all, from the frontiers of finance to the future of AI. Most of us don't have traits commonly found in the River: high tolerance for risk, appreciation of uncertainty, affinity for numbers—paired with an instinctive distrust of conventional wisdom and a competitive drive so intense it can border on irrational. For those in the River, complexity is baked in, and the work is how to navigate it. People in the River have increasing amounts of wealth and power in our society, and understanding their mindset—and the flaws in their thinking— is key to understanding what drives technology and the global economy today. Taking us behind the scenes from casinos to venture capital firms, and from the FTX inner sanctum to meetings of the effective altruism movement, On the Edge is a deeply reported, all-access journey into a hidden world of power bro­kers and risk-takers.

The book collects papers on several topics in probability and stochastic processes. These papers have been presented at a conference organised in honour of Professor Rajeeva L. Karandikar who turned 65 in 2021. He was a distinguished researcher and a teacher at the Indian Statistical Institute (ISI), Delhi Centre, for many years. He has been a multi-faceted academician, interacting with the Government of India and the industry. He has left an indelible mark in every endeavour of his and in his several different avatars—be it in the ISI, in the industry or as Director of Chennai Mathematical Institute. This book will be useful to senior undergraduate and graduate students, as well as researchers in probability, statistics and related fields.

This is an open access book. Big data is a large-scale and complex data set based on modern information technology. It has the characteristics of scale and diversity, and its information processing and storage capabilities have been significantly improved. The application of big data technology is to fully mine and analyze data, build cooperation and interaction between teachers and students, encourage students to communicate and interact with teachers, and give full play to the education and teaching effect of big data. In order to improve teaching quality and efficiency as much as possible, all kinds of teaching in the new era must have strong flexibility and foresight, so as to adapt to the development of modern society. So big data will give greater flexibility to educational activities. Therefore, big data will give greater flexibility to educational activities, and more and more scholars provide new ideas for the above research directions. To sum up, we will hold an international academic conference on big data and information education. The 2024 5th International Conference on Big Data and Informatization Education (ICBDIE2024) will be held on January 19–21, 2024 in Sanya, China. ICBDIE 2024 is to bring together innovative academics and industrial experts in the field of Big Data and Informatization Education to a common forum. The primary goal of the conference is to promote research and developmental activities in Big Data and Informatization Education and another goal is to promote scientific information interchange between researchers, developers, engineers, students, and practitioners working all around the world. The conference will be held every year to make it an ideal platform for people to share views and experiences in international conference on Big Data and Informatization Education and related areas.

Learn to write algorithms and program in the new field of quantum computing. This second edition is updated to equip you with the latest knowledge and tools needed to be a complex problem-solver in this ever-evolving landscape. The book has expanded its coverage of current and future advancements and investments by IT companies in this emerging technology. Most chapters are thoroughly revised to incorporate the latest updates to IBM Quantum's systems and offerings, such as improved algorithms, integrating hardware advancements, software enhancements, bug fixes, and more. You'll examine quantum computing in the cloud and run experiments there on a real quantum device. Along the way you'll cover game theory with the Magic Square, an example of quantum pseudo-telepathy. You'll also learn to write code using QISKit, Python SDK, and other APIs such as QASM and execute it against simulators (local or remote) or a real quantum computer. Then peek inside the inner workings of the Bell states for entanglement, Grover's algorithm for linear search, Shor's algorithm for integer factorization, and other algorithms in the fields of optimization, and more. Finally, you'll learn the current quantum algorithms for entanglement, random number generation, linear search, integer factorization, and others. By the end of this book, you'll understand how quantum computing provides massive parallelism and significant computational speedups over classical computersWhat You'll LearnWrite algorithms that provide superior performance over their classical counterpartsCreate a quantum number generator: the quintessential coin flip with a quantum twistExamine the quantum algorithms in use today for random number generation, linear search, and moreDiscover quantum teleportationHandle the counterfeit coin problem, a classic puzzle Put your knowledge to the testwith more than 150 practice exercises Who This Book Is ForDevelopers, programmers, computer science researchers, teachers, and students.

After developing fuzzy set theory, many contributors focused their research on the extension of fuzzy sets and their computational methodologies, strengthening modern science and technology. In some real-life phenomena, the conventional methods and traditional fuzzy sets cannot be explained, whereas the extension of fuzzy sets and effective new computing methods can explain it adequately. This edited book presents a new view of fuzzy set-measurement methods entitled'Fuzzy Optimization, Decision Making and Operations Research: Theory and Applications', which deals with different perspectives and areas of research. All chapters are divided into three parts: fuzzy optimization, fuzzy decision-making, and fuzzy operation research. The goal of this book is to provide a relevant methodological framework covering the core fields of fuzzy decision-making method, fuzzy optimization method, fuzzy graphics method, fuzzy operations research, fuzzy optimization using graph theory, fuzzy support systems and its real and industrial applications. For many people, fuzzy words'industrial engineering and scientific meanings are still an advanced system for improving modern science and technology. Although fuzzy logic can be applied to many different areas, people do not know how different fuzzy approaches can be applied to various products currently on the market. It is written for professionals who wish to share their expertise, improve their findings, and provide relevant information in the fields of fuzzy methods and their application in decision-making, optimization theory, graph theory and operations research. This book is aimed at experts and practitioners in the fields of fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

Spatio-Temporal Methods in Environmental Epidemiology with R, like its First Edition, explores the interface between environmental epidemiology and spatio-temporal modeling. It links recent developments in spatio-temporal theory with epidemiological applications. Drawing on real-life problems, it shows how recent advances in methodology can assess the health risks associated with environmental hazards. The book's clear guidelines enable the implementation of the methodology and estimation of risks in practice.New additions to the Second Edition include: a thorough exploration of the underlying concepts behind knowledge discovery through data; a new chapter on extracting information from data using R and the tidyverse; additional material on methods for Bayesian computation, including the use of NIMBLE and Stan; new methods for performing spatio-temporal analysis and an updated chapter containing further topics. Throughout the book there are new examples, and the presentation of R code for examples has been extended. Along with these additions, the book now has a GitHub site (https://spacetime-environ.github.io/stepi2) that contains data, code and further worked examples.Features:• Explores the interface between environmental epidemiology and spatio­-temporal modeling• Incorporates examples that show how spatio-temporal methodology can inform societal concerns about the effects of environmental hazards on health• Uses a Bayesian foundation on which to build an integrated approach to spatio-temporal modeling and environmental epidemiology• Discusses data analysis and topics such as data visualization, mapping, wrangling and analysis• Shows how to design networks for monitoring hazardous environmental processes and the ill effects of preferential sampling• Through the listing and application of code, shows the power of R, tidyverse, NIMBLE and Stan and other modern tools in performing complex data analysis and modelingRepresenting a continuing important direction in environmental epidemiology, this book – in full color throughout – underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Readers will learn how to identify and model patterns in spatio-temporal data and how to exploit dependencies over space and time to reduce bias and inefficiency when estimating risks to health.