Basic Concepts of Global Optimization
This textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field. With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization problems under application-relevant conditions sets a new accent that enriches the stock of previous textbooks on optimization. Using the theory and algorithms of smooth convex optimization, the book illustrates that the global solution of a class of optimization problems frequently encountered in practice is efficiently possible, while for the more difficult-to-handle non-convex problems itdevelops in detail the ideas of branch-and-bound methods. This book is the English translation of the 2nd edition of "Grundz羹ge der Globalen Optimierung" (Springer, 2021) written in German. The translation was done with the help of artificial intelligence. A subsequent revision was performed by the author to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness. It may, however, read stylistically different from a conventional translation.
Exploring Complex Survey Data Analysis Using R
Surveys are powerful tools for gathering information, uncovering insights, and facilitating decision-making. However, to ensure the accurate interpretation of results, they require specific analysis methods. In this book, readers embark on an in-depth journey into conducting complex survey analysis with the {srvyr} package and tidyverse family of functions from the R programming language. Intended for intermediate R users familiar with the basics of the tidyverse, this book gives readers a deeper understanding of applying appropriate survey analysis techniques using {srvyr}, {survey}, and other related packages. With practical walkthroughs featuring real-world datasets, such as the American National Election Studies and Residential Energy Consumption Survey, readers will develop the skills necessary to perform impactful survey analysis on survey data collected through a randomized sample design. Additionally, this book teaches readers how to interpret and communicate results of survey data effectively.Key Features: Uses the {srvyr} package and tidyverse family of packages. Grants a conceptual understanding of the statistical methods that the functions apply to. Includes practical walkthroughs using publicly available survey data. Provides the reader with the tools for interpreting, visualizing, and presenting results.
Nonstandard Analysis
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view. Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject.
Decision Superhero Book 1
Decision Superhero is a modern practical guide to making better decisions using probability. Understand essential psychological and mathematical models for effective decision-making, implement decision science models in Excel, and build an organization that tests assumptions, discerns variables, and predicts outcomes using decision models.Eric Torkia and Bill Klimack have masterfully distilled decades of experience into a guide that is both accessible and profoundly insightful. This book is not just a manu-al for analysts but a blueprint for anyone looking to navigate the complex landscape of modern decision-making.In a world where data is king, "Decision Superhero" empowers its readers to become the architects of their own destiny, leveraging the principles of decision science to drive impactful outcomes. Whether you're a seasoned professional or just starting your journey, this book will equip you with the tools and mindset needed to make better, faster, and more informed decisions.With its blend of theory, practical application, and real-world examples, "Decision Superhero" stands out as an essential read for anyone looking to elevate their deci-sion-making prowess. Eric and Bill have created a resource that is sure to become a staple on the bookshelf of every data-driven leader. This is the book that will turn good analysts into great decision-makers.Jordan Goldmeier, Author of Becoming a Data Head and Data SmartDecision Superhero is a compelling guide to mastering decision science, crafted with clarity and depth. This book invites readers to explore the art and science of making better choices, blending real-world exam-ples, historical anecdotes, and practical insights to create a rich learning experience. From operations research during WWII to contemporary decision analysis, the authors present a cohesive narrative that demonstrates the evolution of this criti-cal field. The early chapters offer fascinating stories of decision-making challenges, such as Abraham Wald's work on survivorship bias, grounding readers in the time-less relevance of decision science.Douglas W. Hubbard, Author of How to Measure Anything: Finding the Value of Intangibles in Business and The Failure of Risk Management: Why It's Broken and How to Fix ItUnafraid to blend insights from famous statisticians and Arnold Schwarzenegger in the same breath, Tork-ia and Klimack provide spirited advocacy for the notion that our mental models should often be replaced or augmented by more explicit, conscious modeling and careful analysis; that this can lead to surprising results and drive organizational val-ue; and that it can often be accomplished with fewer prerequisites than we might be inclined to assume.Peter Cotton, Author of Microprediction: Buildiung an Open AI Network and, Co-Founder and Chief Scientific Officer at Crunch LabsDecision Superhero by Eric Torkia and Bill Klimack is a standout guide in the field of decision science, penned by a pioneer whose expertise illuminates every chapter. They masterfully bridge the gap between complex theoretical concepts and practical business applications, making decision science accessible to data professionals of varying technical skill levels. Through historical anecdotes and real-world exam-ples, they illustrate the impactful role of decision science across various industries and its pairing with data science to optimize business strategies.George Mount, Author of Advancing into Analytics and Modern Data Analytics in Excel
Decision Superhero Book 1
Decision Superhero is a modern practical guide to making better decisions using probability. Understand essential psychological and mathematical models for effective decision-making, implement decision science models in Excel, and build an organization that tests assumptions, discerns variables, and predicts outcomes using decision models.Eric Torkia and Bill Klimack have masterfully distilled decades of experience into a guide that is both accessible and profoundly insightful. This book is not just a manu-al for analysts but a blueprint for anyone looking to navigate the complex landscape of modern decision-making.In a world where data is king, "Decision Superhero" empowers its readers to become the architects of their own destiny, leveraging the principles of decision science to drive impactful outcomes. Whether you're a seasoned professional or just starting your journey, this book will equip you with the tools and mindset needed to make better, faster, and more informed decisions.With its blend of theory, practical application, and real-world examples, "Decision Superhero" stands out as an essential read for anyone looking to elevate their deci-sion-making prowess. Eric and Bill have created a resource that is sure to become a staple on the bookshelf of every data-driven leader. This is the book that will turn good analysts into great decision-makers. Jordan Goldmeier, Author of Becoming a Data Head and Data SmartDecision Superhero is a compelling guide to mastering decision science, crafted with clarity and depth. This book invites readers to explore the art and science of making better choices, blending real-world exam-ples, historical anecdotes, and practical insights to create a rich learning experience. From operations research during WWII to contemporary decision analysis, the authors present a cohesive narrative that demonstrates the evolution of this criti-cal field. The early chapters offer fascinating stories of decision-making challenges, such as Abraham Wald's work on survivorship bias, grounding readers in the time-less relevance of decision science.Douglas W. Hubbard, Author of How to Measure Anything: Finding the Value of Intangibles in Business and The Failure of Risk Management: Why It's Broken and How to Fix ItUnafraid to blend insights from famous statisticians and Arnold Schwarzenegger in the same breath, Tork-ia and Klimack provide spirited advocacy for the notion that our mental models should often be replaced or augmented by more explicit, conscious modeling and careful analysis; that this can lead to surprising results and drive organizational val-ue; and that it can often be accomplished with fewer prerequisites than we might be inclined to assume.Peter Cotton, Author of Microprediction: Buildiung an Open AI Network and, Co-Founder and Chief Scientific Officer at Crunch LabsDecision Superhero by Eric Torkia and Bill Klimack is a standout guide in the field of decision science, penned by a pioneer whose expertise illuminates every chapter. They masterfully bridge the gap between complex theoretical concepts and practical business applications, making decision science accessible to data professionals of varying technical skill levels. Through historical anecdotes and real-world exam-ples, they illustrate the impactful role of decision science across various industries and its pairing with data science to optimize business strategies.George Mount, Author of Advancing into Analytics and Modern Data Analytics in Excel
Model & Computat Approach Multi-Scale Phenom Cancer Research
Cancer development and progression is the result of biological phenomena that occur across multiple temporal and spatial scales. Recent years have seen a flurry of multi-scale mathematical models developed to generate and test new biological hypotheses related to cancer development, progression, and various treatment approaches. This has led to the development of new computational and analytical approaches aimed at investigating these multi-scale models.This review volume summarises the state of the art related to the modelling, experimental investigation, and data assimilation of multi-scale phenomena during cancer development, evolution, and treatment, as well as the computational and analytical investigation of the multi-scale models developed to reproduce the biological phenomena. The book also identifies the experimental and theoretical open problems that will have to be addressed in the near future in order to advance this field. Modelling and Computational Approaches for Multi-Scale Phenomena in Cancer Research is an excellent resource for both early career and advanced researchers.
Plausibility and the Solution to the Behrens-Fisher Problem
'Plausibility and the Solution to the Behrens-Fisher Problem' is a detective story that reveals the solution to a mathematical conundrum that has kept statisticians perplexed for over a century.The problem concerns what we can say about the difference between the true mean values of two normal distributions from the information available in small samples.Despite years of attempts by academia to find the answer, usually involving either Fisher's notion of 'fiducial probability' or Bayes' Rule and a 'prior' distribution, until now, a precise solution has not been found.The book shows that the Behrens-Fisher problem concerns what is plausible and that, while they are connected, what is plausible is not the same as what is probable. Moreover, plausibility cannot be defined; it must be discovered.In the first part of the book, we follow a familiar trail that leads to Behrens' and Fishers' solution, but then by correctly interpreting an observation by Bartlett (who questioned Fisher's approach), we are shown that this solution cannot be true because it does not utilise all the available information.The second part shows how to find the plausibility of the features of any probability distribution and proceeds to obtain the plausibility densities of all the parameters controlling the Normal distribution. But all this is cast into doubt when a well-known result obtained by Neyman (who was a fierce critic of Fisher) is shown to be false.This surprising twist leads to the conclusion that some entrenched assumptions must be abandoned and shows why all previous attempts to find a solution have failed.We are also forced to acknowledge that none of the results obtained so far reveal how to combine one plausibility with another, a Combinatorial Rule which is essential for the solution to the problem.In part three, we find the answer to all these issues and, with the resolution of another troubling problem in statistics, the only possible correct solution to the Behrens-fisher problem is revealed.This book brings a fresh perspective to one of the most daunting challenges in the field and is a must-read not only for statisticians, but anyone fascinated by the power of logical reasoning and the thrill of cracking what was once considered an unsolvable problem.While pitched at the mathematically sophisticated reader, it provides useful insights for anyone interested in assessments and deductions from statistical data.
Plausibility and the Solution to the Behrens-Fisher Problem
'Plausibility and the Solution to the Behrens-Fisher Problem' is a detective story that reveals the solution to a mathematical conundrum that has kept statisticians perplexed for over a century.The problem concerns what we can say about the difference between the true mean values of two normal distributions from the information available in small samples.Despite years of attempts by academia to find the answer, usually involving either Fisher's notion of 'fiducial probability' or Bayes' Rule and a 'prior' distribution, until now, a precise solution has not been found.The book shows that the Behrens-Fisher problem concerns what is plausible and that, while they are connected, what is plausible is not the same as what is probable. Moreover, plausibility cannot be defined; it must be discovered.In the first part of the book, we follow a familiar trail that leads to Behrens' and Fishers' solution, but then by correctly interpreting an observation by Bartlett (who questioned Fisher's approach), we are shown that this solution cannot be true because it does not utilise all the available information.The second part shows how to find the plausibility of the features of any probability distribution and proceeds to obtain the plausibility densities of all the parameters controlling the Normal distribution. But all this is cast into doubt when a well-known result obtained by Neyman (who was a fierce critic of Fisher) is shown to be false.This surprising twist leads to the conclusion that some entrenched assumptions must be abandoned and shows why all previous attempts to find a solution have failed.We are also forced to acknowledge that none of the results obtained so far reveal how to combine one plausibility with another, a Combinatorial Rule which is essential for the solution to the problem.In part three, we find the answer to all these issues and, with the resolution of another troubling problem in statistics, the only possible correct solution to the Behrens-fisher problem is revealed.This book brings a fresh perspective to one of the most daunting challenges in the field and is a must-read not only for statisticians, but anyone fascinated by the power of logical reasoning and the thrill of cracking what was once considered an unsolvable problem.While pitched at the mathematically sophisticated reader, it provides useful insights for anyone interested in assessments and deductions from statistical data.
Stochastic Lagrangian Adaptation
This book introduces a cutting-edge continuous time stochastic linear quadratic (LQ) adaptive control algorithm for fully observed linear stochastic systems with unknown parameters. The adaptive estimation algorithm is engineered to drive the maximum likelihood estimate into the set of parameters representing the true closed-loop dynamics. By incorporating a performance monitoring feature, this approach ensures that the estimate converges to the true system parameters. Concurrently, it delivers optimal long-term LQ closed-loop performance. This groundbreaking work offers a significant advancement in the field of stochastic control systems.
Data Science and Artificial Intelligence
This book constitutes the proceedings of the Second refereed proceedings of the Second International Conference on Data Science and Artificial Intelligence, DSAI 2024, held in Medan, Indonesia, during November 13-15, 2024. The 18 full papers, 2 short papers and 3 invited talks were included in this book were carefully reviewed and selected from 69 submissions. They are organized in the following topical sections: Keynote Presentations; Natural and Sign Language Processing; Applications of Data Science and Artificial Intelligence; Affective Computing and AI Games; Embedded AI and Applications; Data Science; AI and Healthcare.
Buckling of Beams, Plates and Shells
This book contains an introduction to the fundamental principles of the theory of stability of elastic bodies and structures. Beginning with very basic explanations of stability problems, this book starts with the treatment of systems of rigid beams, before beams under normal force and bending as well as the classical field of beam buckling are treated. For the case of beam buckling, an energetic consideration then follows, which forms the basis for a series of approximation methods. In addition to beam buckling, the stability cases of lateral-torsional buckling and lateral buckling are also of fundamental importance, to each of which a separate chapter is dedicated. This is followed by a discussion of plate buckling, and the book concludes with an introduction to shell buckling. This book is aimed at students at technical colleges and universities, as well as engineers in practice and researchers in the engineering sciences.
Decision Analysis Through Modeling and Game Theory
This unique book presents decision analysis in the context of mathematical modeling and game theory. The author emphasizes and focuses on the model formulation and modeling building skills required for decision analysis, as well as the technology to support the analysis.
Mindmatics
Mindmatics invites readers into a captivating exploration where the boundaries between mind and mathematics dissolve. Professor Neuman delves into the profound connections between cognitive processes and mathematical expression in this groundbreaking work. From how children grasp abstract concepts to symmetry's role in art and mathematics, this book uncovers the hidden structures that shape our understanding of the world. With insightful discussions on the relationship between poetry and mathematics and the essential role of the unconscious in fostering mathematical imagination, Mindmatics offers a unique perspective on the interplay of thought, creativity, and logic. This book is a must-read for anyone curious about the deeper links between the human mind and the mathematical universe.
Probability Analysis of Selected Population Models
This book explores the dynamics of some population models under stochastic perturbations and regime switching across different environmental patches. By integrating Markovian switching processes, we investigate the stability and ergodicity characteristics of the model, providing insights into how random fluctuations and discrete regime shifts impact population persistence and extinction probabilities. The research initially focuses on the stability and ergodicity of some stochastic models under regime switching, highlighting how environmental variability across patches influences the long-term behavior of the population. Mathematical analysis and numerical simulations demonstrate that the model exhibits varying degrees of stability depending on the stochastic parameters and the switching mechanisms involved. Further, the analysis extends to the impact of Markovian switching on the population model, elucidating how changes in environmental states governed by a Markov process affect population dynamics. This study examines the conditions under which the population persists or faces extinction, considering both slow and fast switching regimes.
Brownian Motion and Potential Theory, Modern and Classical
In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
Foundation of Probability Theory
This textbook presents measure theory in a concise yet clear manner, providing readers with a solid foundation in the mathematical axiomatic system of probability theory. Unlike elementary probability theory, which deals with random events through specific examples of random trials, Foundations of Probability Theory offers a comprehensive mathematical framework for rigorous descriptions of these events.As a result, this course embodies all the characteristics of mathematical theories: abstract content, extensive applications, complete structures, and clear conclusions. Due to the abstract nature of the material, learners may encounter various challenges. To overcome these difficulties, it is essential to keep concrete examples in mind when trying to understand abstract concepts and to compare the abstract theory with related courses previously studied, particularly the Lebesgue measure theory.To enhance the readability of the book, each section begins with a brief introduction outlining the main objectives based on the preceding content, highlighting the primary structure, and explaining the key ideas of the study. This approach ensures that readers can follow the material more easily and grasp the essential concepts effectively.
Brownian Motion and Potential Theory, Modern and Classical
In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
Scientific Data Analysis with R
This book is intended for students, researchers, and professionals eager to harness the combined power of biostatistics, data science, and the R programming language while gathering vital statistical knowledge needed for cutting-edge scientists in all fields.
Text Book of Practical Analytical Chemistry
Experimental Book of Pharmaceutical Analysis enables students to gain fundamental knowledge of the vital concepts, techniques, and applications of the chemical analysis of pharmaceutical ingredients, final pharmaceutical products, and drug substances in biological fluids. A unique emphasis on pharmaceutical laboratory practices, such as sample preparation and separation techniques, provides an efficient and practical educational framework for undergraduate studies in areas such as pharmaceutical sciences, analytical chemistry, and forensic analysis. Suitable for foundational courses, this essential undergraduate text introduces the common analytical methods used in quantitative and qualitative chemical analysis of pharmaceuticals.
Stochastic Analysis For Some Non-Linear Epidemic Models
Stochastic calculus has emerged as a robust mathematical framework for modeling complex biological systems characterized by inherent randomness and uncertainty. Unlike traditional deterministic models, which often fail to capture the variability observed in biological processes, stochastic calculus allows for directly incorporating noise and random fluctuations into the modeling equations. This approach is efficient in areas such as population dynamics, gene expression, neural activity, and the spread of infectious diseases, where biological systems are influenced by numerous random factors at both the microscopic and macroscopic levels. By utilizing tools such as stochastic differential equations (SDEs) and the It繫 calculus, researchers can describe the temporal evolution of biological systems in a manner that accounts for both the deterministic trends and stochastic perturbations.
Intermediate Poker Mathematics
This book provides a fascinating collection of mathematical questions set in the diverse world of poker. This book is not intended primarily as a players' strategy manual, but rather as a means of building up readers understanding of the mathematical concepts at play in the complex world of poker.
Random Number Generators on Computers
This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1, z1) and (d2, z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2, z) with high probability by Sunzi's theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2, z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi's theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.
Probability Theory, an Analytic View
The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies. The main changes are the inclusion of the Gaussian isoperimetric inequality plus many improvements and clarifications throughout the text. With more than 750 exercises, it is ideal for first-year graduate students with a good grasp of undergraduate probability theory and analysis. Starting with results about independent random variables, the author introduces weak convergence of measures and its application to the central limit theorem, and infinitely divisible laws and their associated stochastic processes. Conditional expectation and martingales follow before the context shifts to infinite dimensions, where Gaussian measures and weak convergence of measures are studied. The remainder is devoted to the mutually beneficial connection between probability theory and partial differential equations, culminating in an explanation of the relationship of Brownian motion to classical potential theory.
Reviewing Knowledge
The book is a collection of critical reviews that are essential for teacher training. The texts in this collection deal with themes that are important to the academic world. They are dialogues with theories and knowledge constructed by different authors with a view to contributing to the training of teachers in this century and to innovating their pedagogical praxis. In this work, we bring to the focus of the dialogue texts such as: 'Beyond Abyssal Thinking: From Global Lines to an Ecology of Knowledges' by Professor Boaventura de Souza; notes on 'Conscientisation: Theory and Practice of Liberation: An Introduction to the Thought of Paulo Freire; Edgar Morin's 'Seven Knowledges Necessary for the Education of the Future' and finally a contextualisation of teacher training: 'Teacher Training in the Context of the Pedagogical Proposals of Rudolf Steiner (Waldorf Pedagogy), Maria Montessori and the Escola da Ponte Experience' by Evelaine C. dos Santos.
Database Systems for Advanced Applications
The seven-volume set LNCS 14850-14856 constitutes the proceedings of the 29th International Conference on Database Systems for Advanced Applications, DASFAA 2024, held in Gifu, Japan, in July 2024. The total of 147 full papers, along with 85 short papers, presented together in this seven-volume set was carefully reviewed and selected from 722 submissions. Additionally, 14 industrial papers, 18 demo papers and 6 tutorials are included. The conference presents papers on subjects such as: Part I: Spatial and temporal data; database core technology; federated learning. Part II: Machine learning; text processing. Part III: Recommendation; multi-media. Part IV: Privacy and security; knowledge base and graphs. Part V: Natural language processing; large language model; time series and stream data. Part VI: Graph and network; hardware acceleration. Part VII: Emerging application; industry papers; demo papers.
Transactions on Large-Scale Data- And Knowledge-Centered Systems LVII
The LNCS journal Transactions on Large-scale Data and Knowledge-centered Systems focuses on data management, knowledge discovery, and knowledge processing, which are core and hot topics in computer science. Since the 1990s, the Internet has become the main driving force behind application development in all domains. An increase in the demand for resource sharing (e.g., computing resources, services, metadata, data sources) across different sites connected through networks has led to an evolution of data- and knowledge-management systems from centralized systems to decentralized systems enabling large-scale distributed applications providing high scalability. This, the 57th issue of Transactions on Large-Scale Data and Knowledge-Centered Systems, contains five fully revised selected regular papers. Topics covered include leveraging machine learning for effective data management, access control models, reciprocal authorizations, Internet of Things, digital forensics, code similarity search, volunteered geographic information, and spatial data quality.
Topics in Infinite Group Theory
This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems. New edition now includes the topics on universal free groups, quasiconvex subgroups and hyperbolic groups, and also Stallings foldings and subgroups of free groups. New results on groups of F-types are added.
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.
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.
Quadrature Formulae
No detailed description available for "Quadrature Formulae".
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.
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.
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.
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.
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.
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.
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
