Fuzzy Mathematics, Graphs, and Similarity Measures
Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change. Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor's manual supports teaching across a range of course contexts.
Modeling Spatio-Temporal Data
Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Aims to fill some of this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets.
Quadrature Formulae
No detailed description available for "Quadrature Formulae".
The Statistical Analysis of Small Data Sets
We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses. The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.
Introduction to Transfer Learning
Transfer learning is one of the most important technologies in the era of artificial intelligence and deep learning. It seeks to leverage existing knowledge by transferring it to another, new domain. Over the years, a number of relevant topics have attracted the interest of the research and application community: transfer learning, pre-training and fine-tuning, domain adaptation, domain generalization, and meta-learning. This book offers a comprehensive tutorial on an overview of transfer learning, introducing new researchers in this area to both classic and more recent algorithms. Most importantly, it takes a "student's" perspective to introduce all the concepts, theories, algorithms, and applications, allowing readers to quickly and easily enter this area. Accompanying the book, detailed code implementations are provided to better illustrate the core ideas of several important algorithms, presenting good examples for practice.
Advanced Techniques in Control Charting
The book Advanced Techniques in Control Charting for Process Monitoring offers a timely and insightful look into the contemporary uses of control charts. It delivers a comprehensive analysis of advanced methods, focusing on their impact in optimizing process control, improving quality, and increasing efficiency across multiple industries. Covering topics such as the integration of machine learning algorithms and multivariate control charts, this book presents a diverse range of innovative techniques that are revolutionizing how processes are monitored and managed in modern industrial settings.
The Statistical Analysis of Small Data Sets
We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses. The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.
Dynamics of Circle Mappings
This book explores recent developments in the dynamics of invertible circle maps, a rich and captivating topic in one-dimensional dynamics. It focuses on two main classes of invertible dynamical systems on the circle: global diffeomorphisms and smooth homeomorphisms with critical points. The latter is the book's core, reflecting the authors' recent research interests.Organized into four parts and 14 chapters, the content covers rigid rotations, circle homeomorphisms, and the concept of rotation number in the first part. The second part delves into circle diffeomorphisms, presenting classical results. The third part introduces multicritical circle maps--smooth homeomorphisms of the circle with a finite number of critical points. The fourth and final part centers on renormalization theory, analyzing the fine geometric structure of orbits of multicritical circle maps. Complete proofs for several fundamental results in circle dynamics are provided throughout. The book concludes with a list of open questions.Primarily intended for graduate students and young researchers in dynamical systems, this book is also suitable for mathematicians from other fields with an interest in the subject. Prerequisites include familiarity with the content of a standard graduate course in real analysis, along with some understanding of ergodic theory and dynamical systems. Basic knowledge of complex analysis is needed for specific chapters.
Probabilistic Spiking Neuronal Nets
This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection.The book's focus on mathematically tractable objects distinguishes it from other texts on theoretical neuroscience. The biological complexity of neurons is not ignored, but reduced to some of its main features, such as the intrinsic randomness of neuronal dynamics. This reduction in complexity aims at explaining and reproducing statistical regularities and collective phenomena that are observed in experimental data, an approach that leads to mathematically rigorous results. With an emphasis on a constructive and algorithmic point of view, this book is directed towards mathematicians interested in learning about stochastic network models and their neurobiological underpinning, and neuroscientists interested in learning how to build and prove results with mathematical models that relate to actual experimental settings.
Foundation Engineering Mathematics
This new textbook will prepare readers to continue to develop analytical and numerical skills, through the study of a variety of mathematical techniques. The statistical element of this textbook enhances the readers' ability to organize and interpret data.
Foundations of Quantitative Finance, Book VI
Every finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the competitive edge these books offer the astute reader.
Understanding Elections through Statistics
Regarding elections and polls, it explores this random phenomenon from three primary points of view: predicting election outcome using opinion polls, testing outcome using government-reported data, and exploring election data to better understand the people.
Bayesian Adaptive Methods for Clinical Trials
Written by leading pioneers of Bayesian clinical trial designs, this book explores the growing role of Bayesian thinking in clinical trial analysis. Covering Phase I, II, and III clinical trials, it establishes the basic principles before extending them to specific phases and endpoints. The authors also discuss special topics that span different
Foundation Mathematics for Engineers and Scientists with Worked Examples
This straightforward and step-by-step presentation of mathematics for engineers and scientists is written primarily for students at levels 3 and 4, typically in the early stages of a degree in engineering or a related discipline, or on foundation or certificate, HNC, International Foundation Year, and International Year One courses.
Introduction to Mathematical Logic
This bestselling, classic textbook continues to provide a complete one-semester introduction to mathematical logic. The sixth edition incorporates recent work on G繹del's second incompleteness theorem as well as an appendix on consistency proofs for first-order arithmetic. It also offers historical perspectives and many new exercises of varying d
Introduction to General and Generalized Linear Models
Providing a flexible framework for data analysis and model building, this text focuses on the statistical methods and models that can help predict the expected value of an outcome, dependent, or response variable. It offers a sound introduction to general and generalized linear models using the popular and powerful likelihood techniques. The aut
Measure and Integral
This classic text provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then introducing a more general treatment based on abstract notions characterized by axioms and with less geometric content. Packed with new exercises and material, the long-awaited s
Statistical Methods in Biology
Written in simple language with relevant examples, this illustrative introductory book presents best practices in experimental design and simple data analysis. Taking a practical and intuitive approach, it only uses mathematical formulae to formalize the methods where necessary and appropriate. The text features extended discussions of examples
Integral Transforms and Their Applications
Through numerous examples and end-of-chapter exercises, this book develops readers' analytical and computational skills in the theory and applications of transform methods. It covers advanced mathematical methods for many applications in science and engineering. The book presents a systematic development of the underlying theory as well as a mod
Foundation Mathematics for Engineers and Scientists with Worked Examples
This straightforward and step-by-step presentation of mathematics for engineers and scientists is written primarily for students at levels 3 and 4, typically in the early stages of a degree in engineering or a related discipline, or on foundation or certificate, HNC, International Foundation Year, and International Year One courses.
A Stitch in Line
This book provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way.
Invertibility and Asymptotics of Toeplitz Matrices
No detailed description available for "Invertibility and Asymptotics of Toeplitz Matrices".
Theory of Nonlinear Operators
No detailed description available for "Theory of Nonlinear Operators".
The (wrong) paths of tourism
This study deals with the socio-environmental issues related to the implementation and paving of the GO-239 road, called Estrada-parque Prefeito Divaldo Rinco, which links Alto Para穩so de Goi獺s to Colinas do Sul, in the Chapada dos Veadeiros, in Goi獺s. The road borders and also leads to the Chapada dos Veadeiros National Park (PNCV) and its route presents a scenic beauty typical of the region, showing the high-altitude Cerrado all around. The objectives are to describe the condition of the road and to show what people think about it. This is a qualitative, exploratory study that used direct observation of the road and interviews with residents and institutional agents (PNCV, Municipal Tourism Office) to capture their perceptions of the road's importance and issues surrounding its construction. It was concluded that the road still lacks the conditions that characterise it as a parkway, such as a management plan, but that it has great tourist potential due to the landscape that surrounds it.
Statistical Machine Learning for Engineering with Applications
Mathematical Modelling
This book investigates human-machine systems through the use of case studies such as crankshaft maintenance, liner piston maintenance, and biodiesel blend performance.
A Stitch in Line
This book provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way.
Everything Is Predictable
A "fascinating, witty, and perspective-shifting" (Oliver Burkeman, New York Times bestselling author) tour of Bayes's theorem and its global impact on modern life from the acclaimed science writer and author of The Rationalist's Guide to the Galaxy.At its simplest, Bayes's theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes's theorem is a description of almost everything. But who was the man who lent his name to this theorem? How did an 18th-century Presbyterian minister and amateur mathematician uncover a theorem that would affect fields as diverse as medicine, law, and artificial intelligence? "Witty, lively, and best of all, extremely nerdy" (Tim Harford, author of The Undercover Economist), Everything Is Predictable is an entertaining and accessible illustration of how a single compelling idea can have far reaching consequences.
General Mathematical Theory Dynamic Global Politic Eco
William Jevons (1866 and 1871) established a ground-breaking milestone with 'A General Mathematical Theory of Political Economy' for economic analysis. Jevons' work was praised as the start of the mathematical method in the discipline of economics, which is inherently a subject involved with mathematics and quantities. This book focuses on the most fast-evolving and encompassing area in political economy -- the dynamic global political economy. Under the high level of globalization currently, intertemporal and cross-boundary interactive elements are present in political-economic encounters. Indeed, almost all studies in the political economy may fall into the study of dynamic global political economy. Since the world has changed significantly, new mathematics developed by the authors of this book is used to formulate a general mathematical theory for the dynamic global political economy nowadays. A distinctive feature of the current book is that it combines advanced mathematics, game-theoretic concepts, and economics to develop a general mathematical theory supporting the study of the dynamic global political economy.The book covers mathematical theory for different areas of the dynamic global political economy. In addition, it explicates the application of the mathematical theory in real-world scenarios, including (i) environmental degradation under an uncoordinated interaction scenario, (ii) global climate accords with collaboration and cooperation, (iii) trade network involving the Belt-Road Initiative (BRI) and Build Back Better World (B3W) Initiative, and (iv) random termination of international joint ventures.
Distribution Dependent Stochastic Differential Equations
Corresponding to the link of It繫's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.
46 Ways to Play Math
Math Games Enhance LearningMath games build mental flexibility and strategic reasoning in players of all ages. And even people who hated math in school can enjoy the friendly challenge of a game.These are NOT the typical memory-and-speed-based math games you've probably seen online, but true battles of wit and skill (plus a bit of luck). Even the preschool games can be fun for adults, too.Most of the games take only seconds to learn and less than 15 minutes to play, making them perfect ice-breakers for family gatherings, classroom warmups, or for launching a group game night.You'll love these strategic challenges for preschoolers to adult gamers. Easy to learn, quick to play! Who knew math could be so much fun?Includes six skill-level game chapters: Early Counting Games: 7 Ways to Play Math with Young LearnersCounting Games with Bigger Numbers: 7 Ways to Play Math with Primary StudentsEarly Mental Math: 6 Ways to Play Math with Primary StudentsIntermediate Mental Math: 6 Ways to Play Math in the Middle GradesAdvanced Mental Math: 6 Ways to Play Math with Older StudentsGraphing Games: 6 Ways to Play Math with Older StudentsPlus four bonus chapters for all ages: The Best Math Game Ever: Creative Math for All AgesCreative Nim: Make Your Own Math & Logic GamesThe Function Machine: A Card Game of Algebraic ThinkingNumber Neighborhoods: Two Math Games of Logical Deduction46 Ways To Play Math features instructions and math game pages in full-color, tips for the teacher, and plenty of room to record your game modification or house rules.Grab a deck of cards, a few dice, or markers and graph paper, and let's play some math!
The Non-Uniform Riemann Approach to Stochastic Integration
This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.
Optimal Transport on Quantum Structures
The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flowsdynamics and quantum optimal transportquantum couplings and many-body problemsquantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erd繹s Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.
Flows in Networks
A landmark work that belongs on the bookshelf of every researcher working with networks In this classic book, first published in 1962, L. R. Ford, Jr., and D. R. Fulkerson set the foundation for the study of network flow problems. The models and algorithms introduced in Flows in Networks are used widely today in the fields of transportation systems, manufacturing, inventory planning, image processing, and Internet traffic. The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction. With an incisive foreword by Robert Bland and James Orlin, Flows in Networks is rich with insights that remain relevant to current research in engineering, management, and other sciences.
Fluid Waves
The book covers mathematical basis for fluid waves in science and engineering illustrating basis to undertake pertinent calculations in varied areas. It covers fundamentals of fluid dynamics including chapters explaining specialized applications. All concepts are supported by narrative examples, illustrations, and case studies.
Advanced Probability and Statistics
The chapters in this book deal with: Basic formulation of waveguide cavity resonator equations The reviews of basic statistical signal processing The Hartree-Fock equations
Multivariate Statistical Methods
For those looking to become proficient in multivariate statistical methods, but who might not be deeply versed in the language of mathematics, provides conceptual intros to methods, practical suggestions, new references, and a more extensive collection of R functions and code that will deepen toolkit of multivariate statistical methods.
Stochastic Models in Reliability Engineering
This book is a collective work by many leading scientists, analysts, mathematicians, and engineers who have been working on the front end of reliability science and engineering. The book covers conventional and contemporary topics in reliability science, which have seen extended research activates in the recent years.
Selected Topics in Statistical Inference
This book focuses exclusively on the domain of parametric inference and that, too, from a reader's perspective, i.e., covering only point estimation of parameter(s). It covers those topics in parametric inference which need clarity of exposure to students, researchers, and teachers alike; mere statements of theorems and proofs may not always reveal the inner beauty and significance of some aspects of inference. To ensure clarity, the book discusses the following topics at an advanced level-(1) sequential (unbiased) point estimation of 'p' and its functions; generalization to trinomial and tetranomial populations; (2) some aspects of the use of additional resources in finite population inference; (3) the concept of sufficiency vis-?-vis the notion of sufficient experiments and comparison of experiments; (4) estimation of the size of a finite population with special features; and (5) unbiased estimation of reliability in exponential samples and other settings. This book provides a platform for thought-provoking, creative, and challenging discussions on a variety of topics in statistical estimation theory, it is also ideal for research methodology course for statistics research scholars, and for clarification of basic ideas in topics discussed at basic/advanced levels.
Frontiers of Fractal Analysis
This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.
Multivariate Statistical Modeling in Engineering and Management
The book focuses on problem solving for practitioners and model building for academicians under multivariate situations. This book helps readers in understanding the issues, such as knowing variability, extracting patterns, building relationships, and making objective decisions.
Multi-Fractal Traffic and Anomaly Detection in Computer Communications
This book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks.
Compressible Flow with Applications to Engines, Shocks and Nozzles
This book is part of the series "Mathematics and Physics Applied to Science and Technology." The book presents the mathematical theory of partial differential equations. It includes applications to acoustic, elastic, water, electromagnetic and other waves, to the diffusion of heat, mass and electricity, and to their interactions.
Analysis of Fork-Join Systems
With the boom of big data and machine learning and the subsequent need for parallel processing technologies, fork-join queues are more relevant now than ever before. In this book, new estimates of the average response time in fork-join queues are proposed, which form the basis for new research opportunities.
