From Counting to Continuum
Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.
From Counting to Continuum
Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.
Coin-Turning, Random Walks and Inhomogeneous Markov Chains
This research monograph explores new frontiers in Markov chains. Although time-homogeneous Markov chains are well understood, this is not at all the case with time-inhomogeneous ones. The book, after a review on the classical theory of homogeneous chains, including the electrical network approach, introduces several new models which involve inhomogeneous chains as well as related new types of random walks (for example, "coin turning", "conservative" and "Rademacher" walk). Scaling limits, the breakdown of the classical limit theorems as well as recurrence and transience are investigated. The relationship with urn models is the subject of two chapters, providing additional connections to other parts of probability theory.Random walks on random graphs are discussed as well, as an area where the method of electric networks is especially useful. This is illustrated by presenting random walks in random environments and random labyrinths.The monograph puts emphasis on showing examples and open problems besides providing rigorous analysis of the models.Several figures illustrate the main ideas, and a large number of exercises challenge the interested reader.
Mathematical and Statistical Applications in Food Engineering
Written by experts from all over the world, the book comprises the latest applications of mathematical and models in food engineering and fermentation. It provides the fundamentals on statistical methods to solve standard problems associated with food engineering and fermentation technology.
Introduction to Probability and Statistics for Data Science
Introduction to Probability and Statistics for Data Science provides a solid course in the fundamental concepts, methods and theory of statistics for students in statistics, data science, biostatistics, engineering, and physical science programs. It teaches students to understand, use, and build on modern statistical techniques for complex problems. The authors develop the methods from both an intuitive and mathematical angle, illustrating with simple examples how and why the methods work. More complicated examples, many of which incorporate data and code in R, show how the method is used in practice. Through this guidance, students get the big picture about how statistics works and can be applied. This text covers more modern topics such as regression trees, large scale hypothesis testing, bootstrapping, MCMC, time series, and fewer theoretical topics like the Cramer-Rao lower bound and the Rao-Blackwell theorem. It features more than 250 high-quality figures, 180 of which involve actual data. Data and R are code available on our website so that students can reproduce the examples and do hands-on exercises.
Geometric and Analytic Aspects of Functional Variational Principles
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.
Algorithmic Aspects of Discrete Choice in Convex Optimization
This book develops a framework to analyze algorithmic aspects of discrete choice models in convex optimization. The central aspect is to derive new prox-functions from discrete choice surplus functions, which are then incorporated into convex optimization schemes. The book provides further economic applications of discrete choice prox-functions within the context of convex optimization such as network manipulation based on alternating minimization and dynamic pricing for online marketplaces.
The History of Correlation
History of the word "correlation" and various meanings it was given in publications by scientists during the past two centuries, but also a history of how the correlation coefficient has been interpreted during that time and of how the explanation of its meaning evolved in textbooks and journal articles.
Multiple Stopping Problems
This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models.
Biostatistics for Bioassay
In recent decades, there has been enormous growth in biologics research and development, with the accompanying development of biological assays for emerging products. In parallel, there have been substantial advances in statistical methodology, as well as technological advances in computer power, enabling new techniques to be implemented via statistical software. Biostatistics for Bioassay presents an overview of the statistical analysis techniques that are needed in order to report the results of biological assays. These assays are needed for testing all biological medicines, such as vaccines and cell therapies, to allow them to be released for use. Beginning with consideration of the performance characteristics required of a bioassay, including accuracy, precision, and combinations of these two attributes, the book builds a framework for statistical bioassay design.Features: Explains the statistical methods needed at each stage of the lifecycle of a bioassay Describes the demonstration of the bioassay's performance, known as validation Covers the statistical techniques for monitoring the bioassay's performance over time Details how to transfer the bioassay to another laboratory or replace critical reagents Provides examples at every stage, to allow the reader to work through the techniques and consolidate their understanding The book provides a resource for interested bioassay analysts, and statisticians working with bioassays. In bringing together best practices in statistics across the bioassay lifecycle into a single volume, it aims to provide a comprehensive and useful textbook for statistical analysis in bioassay.
The History of Correlation
History of the word "correlation" and various meanings it was given in publications by scientists during the past two centuries, but also a history of how the correlation coefficient has been interpreted during that time and of how the explanation of its meaning evolved in textbooks and journal articles.
Adv Math & Comp Tool Metrol XIII
This volume contains original, refereed contributions by researchers from national metrology institutes, universities and laboratories across the world involved in metrology and testing. The volume has been produced by the International Measurement Confederation (IMEKO) Technical Committee 21, Mathematical Tools for Measurements, in association with IMEKO Technical Committee 6, Digitalisation, and the European Network for Mathematics and Statistics for Metrology, following presentations made at the Advanced Mathematical and Computational Tools in Metrology online conference, hosted by the Institute of Metrology of Bosnia and Herzegovina, Sarajevo, in September 2023. The volume covers the application of novel mathematical and statistical modelling techniques and data analysis and machine learning approaches to metrology and measurement science, uncertainty quantification, and knowledge representation and reasoning to enable the digitalization of metrological services.This volume is of interest to all researchers, data scientists, engineers and practitioners who need to characterize the capabilities of measurement systems, evaluate measurement data, quantify uncertainties and make inferences and decisions based on models and data. It will also be of interest to those working in the quality infrastructure concerned with the reliability, transparency, trustworthiness and reproducibility of data, data analytics, machine learning and AI, in engineering, physical, environmental and the life sciences.
Multiple Stopping Problems
This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models.
Exploring Complex Survey Data Analysis Using R
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. Additionally, this book teaches readers how to interpret and communicate results of survey data effectively.
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
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
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.
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.
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.
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.
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.
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.
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
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.
