Qplex: A Computational Modeling and Analysis Methodology for Stochastic Systems
Linear Algebra
This is an introductory text on linear algebra and its contemporary applications to data science, artificial intelligence, and more.
Applied Satisfiability
Apply satisfiability to a range of difficult problems The Boolean Satisfiability Problem (SAT) is one of the most famous and widely-studied problems in Boolean logic. Optimization versions of this problem include the Maximum Satisfiability Problem (MaxSAT) and its extensions, such as partial MaxSAT and weighted MaxSAT, which concern not merely whether but to what extent a solution satisfies a given set of problems. Numerous applications of SAT and MaxSAT have emerged in fields related to logic and computing technology. Applied Satisfiability: Cryptography, Scheduling and Coalitional Games outlines some of these applications in three specific fields. It offers a huge range of SAT applications and their possible impacts, allowing readers to tackle previously challenging optimization problems with a new selection of tools. Professionals and researchers in this field will find the scope of their computational solutions to otherwise intractable problems vastly increased. Applied Satisfiability readers will also find: Coding and problem-solving skills applicable to a variety of fields Chapters covering topics including cryptographic key recovery, various forms of scheduling, coalition structure generation, and many more Specific experiments and case studies that demonstrate the effectiveness of satisfiability-aided methods Applied Satisfiability is ideal for researchers, graduate students, and practitioners in these fields looking to bring a new skillset to bear in their studies and careers.
Measuring and Modeling by Examples
This book starts with an anthology of mathematical functions that can be useful to describe phenomena that occur in the world we see, and how their features can be adjusted by changing their parameters. Then we have a look at the art of measuring and quantifying the world, and how to do this most efficiently and precisely.The most important part is about finding the "pattern" in the measurements: a mathematical function that "fits" with the data. This can be chosen according to several criteria, and using different algorithms, for example the new "multidirectional least squares regression". The last part shows many real life examples in various fields of science: experiments and their analyses.
Functional Analysis for the Applied Mathematician
This self-contained volume provides a rigorous introduction to functional analysis and its applications. It is accessible to graduate and advanced undergraduate students with a solid background in undergraduate mathematics and an appreciation of mathematical rigor.
Complex Analysis
The book comprises six chapters, each meticulously structured to build a comprehensive understanding of complex analysis. Chapter 1 covers the most fundamental concepts, providing the essential groundwork that permeates the entire text. Chapter 2 delves into normal families, the Riemann mapping theorem, and conformal mapping. Chapter 3 focuses on the zeros of analytic functions, while Chapter 4 explores the essential properties of harmonic and subharmonic functions. Chapter 5 introduces H^p spaces and the Fourier transform, highlighting their interconnections. The final chapter discusses uniform approximation by rational functions.Emphasizing foundational theories, modern methods, and key ideas in complex analysis, this book also presents some cutting-edge research problems and recent advancements. The topics are thoughtfully selected, and the exposition is clear and rigorous. This book is an excellent resource for graduate students and independent learners alike. It features many new and concise proofs of classical theorems, and offers numerous challenging exercises to deepen understanding.
Power and Sample Size in R
Power and Sample Size in R guides the reader through power and sample size calculations for a wide variety of study outcomes and designs and illustrates their implementation in R software. It is designed to be used as a learning tool for students as well as a resource for experienced statisticians and investigators. The book begins by explaining the process of power calculation step by step at an introductory level and then builds to increasingly complex and varied topics. For each type of study design, the information needed to perform a calculation and the factors that affect power are explained. Concepts are explained with statistical rigor but made accessible through intuition and examples. Practical advice for performing sample size and power calculations for real studies is given throughout.The book demonstrates calculations in R. It is integrated with the companion R package powertools and also draws on and summarizes the capabilities of other R packages. Only a basic proficiency in R is assumed.Topics include comparison of group means and proportions; ANOVA, including multiple comparisons; power for confidence intervals; multistage designs; linear, logistic and Poisson regression; crossover studies; multicenter, cluster randomized and stepped wedge designs; and time to event outcomes. Chapters are also devoted to designing noninferiority, superiority by a margin and equivalence studies and handling multiple primary endpoints.By emphasizing statistical thinking about the factors that influence power for different study designs and outcomes as well as providing R code, this book equips the reader with the knowledge and tools to perform their own calculations with confidence. Supplemental material available at: https: //powerandsamplesize.org/.Key Features: Explains power and sample size calculation for a wide variety of study designs and outcomes Suitable for both students and experienced researchers Highlights key factors influencing power and provides practical tips for designing real studies Includes extensive examples with R code
Mathematical Analysis
This book provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics in Mathematical Analysis. Each chapter highlights new research directions, making this book suitable for graduate students, faculty, and researchers.
Na簿ve Set Theory
This book aims to provide a complete and unitary presentation of naive set theory as the foundation of the whole mathematics. Suitable for undergraduate students, this book focuses on the main foundational issues.
Mathematical Optimization Theory and Operations Research: Recent Trends
This book constitutes the revised selected papers from the 23rd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2024, held in Omsk, Russia from June 30 to July 06, 2024. The 26 full papers included in this book were carefully reviewed and selected from 79 submissions. These papers have been organized in the following topical sections: Mathematical programming; Combinatorial optimization; Operations research; and Machine learning and optimization.
Complex Analysis and Special Functions
The first two parts of this book focus on developing standard analysis concepts in the extended complex plane. We cover differentiation and integration of functions of one complex variable. Famous Cauchy formulas are established and applied in the frame of residue theory. Taylor series is used to investigate analytic functions, and they are connected to harmonic functions. Laurent series theory is developed. The third part of the book finds applications of the earlier chapter in conformal mappings and the Laplace transform. Special functions solving ordinary differential equations are studied extensively, along with their asymptotic behavior. A highlight of the book is the elliptic function of Weierstrass and Jacobi. Finally, we present Laplace's method, which is applied to find large arguments asymptotic of some special functions. The book is filled with examples, exercises, and problems of varying degrees of difficulty. This makes it useful to all students in mathematics, physics, and related fields.
Summary Statistics
Statistics is used to conduct research, evaluate outcomes, develop critical thinking and make informed decisions about a set of data. The main purpose of statistics seeks to provide an analysis of quantitative data. The principles of statistics also provide guidelines for conducting surveys. Statisticians know how to gather information while avoiding bias and using a random sample. There are a variety of benefits of studying statistics. It improves ability to identify and communicate patterns and outcomes. Learning statistics also incorporates the use of probability. Businesses and individuals can use statistics to calculate the probability of their desired outcome and evaluate whether the probable benefits outweigh the cost. This cost-benefit analysis can improve decision-making and reduce losses. Statistical inference is a calculation that uses data analysis to infer the root causes, effects and properties of a correlation or statistical trend. Statistical models can offer more accurate projections of sales, results and returns. Statistics focuses on a cause-and-effect relationship between variables.
Exploring Stochastic Approaches to Epidemic Modeling
Stochastic calculus has become an essential mathematical tool for modeling complex biological systems characterized by randomness and uncertainty. Unlike deterministic models, which may overlook the variability inherent in biological processes, stochastic calculus allows for explicitly incorporating noise and random fluctuations into the governing equations. This approach has proven particularly effective in fields such as population dynamics, gene regulation, neural activity, and the transmission of infectious diseases, where systems are influenced by random factors at both micro and macro scales. Researchers can use stochastic differential equations (SDEs) and It繫 calculus to model biological systems' temporal evolution, accounting for deterministic components and stochastic disturbances. Applying stochastic calculus in biological modeling improves the precision of predictions and deepens our understanding of the mechanisms driving biological variability. As the discipline progresses, stochastic calculus is expected to play a growing role in enhancing our comprehension of complex biological phenomena and optimizing interventions in medicine, ecology, and biotechnology.
Quantitative Data Analysis
This handbook is designed to provide students and others with an introduction to the fundamental concepts of quantitative data analysis. Aimed primarily at students who will be carrying out field surveys and collecting data, it is also an introductory guide to sampling methods, without requiring advanced prior knowledge of statistics or mathematics. The manual is designed to be accessible and educational, with practical illustrations to help students understand and assimilate the concepts.
Manual of analysis methods and techniques
This book is the synthesis of years of teaching analytical methods and techniques, aimed at second-year Master's students in animal production and nutrition in the Department of Agronomic Sciences and Biotechnology. It aims to support the learning of various biological, biochemical and enzyme-linked immunosorbent analysis techniques and methods. The aim is to introduce students to laboratory work, particularly in the context of their final dissertation.The manuscript is divided into four main chapters, arranged chronologically by analytical method, as follows: 1- Spectral methods. 2- Fractionation methods. 3- Labeling methods.4- Electron microscopy.Like any work, it may contain errors and gaps. So it's always encouraging and motivating to receive corrections, advice and recommendations from fellow teachers and researchers working in the field.
The Dynamics of Front Propagation in Nonlocal Reaction-Diffusion Equations
Lectures on Advanced Topics in Categorical Data Analysis
This book continues the mission of the previous text by the author, Lectures on Categorical Data Analysis, by expanding on the introductory concepts from that volume and providing a mathematically rigorous presentation of advanced topics and current research in statistical techniques which can be applied in the social, political, behavioral, and life sciences. It presents an intuitive and unified discussion of an array of themes in categorical data analysis, and the emphasis on structure over stochastics renders many of the methods applicable in machine learning environments and for the analysis of big data. The book focuses on graphical models, their application in causal analysis, the analytical properties of parameterizations of multivariate discrete distributions, marginal models, and coordinate-free relational models. To guide the readers in future research, the volume provides references to original papers and also offers detailed proofs of most of the significant results. Like the previous volume, it features exercises and research questions, making it appropriate for graduate students, as well as for active researchers.
Engineering Data Analysis with MATLAB(R)
This uses MATLAB(R) for data analysis and statistics, offering a broad review of computational data analysis, in particular algebra, trigonometry, regression modeling, correlation, and graphical representation of results, covering both basic and more complex material, with a large number of worked examples and practice exercises.
Multiaxial Notch Fracture and Fatigue
This book presents unified fatigue life prediction equations for a low/medium/high cycle fatigue of metallic materials, relevant to plain materials and notched components.
Computational Methods for Transition States and Pathways in Rare Events
Based on the calculation of transition states and the identification of transition paths, the book aims to provide a comprehensive guide to understanding and simulating rare events.
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.
Useful Game Theory
Useful Game Theory offers a refreshing perspective on modern wisdom, empowering readers to master strategic decision-making with the tools they already possess. Every decision you make involves an element of game theory, often without you even realizing it. In this insightful book, economist Jay Prag and marketing strategist Amanda Ishak Prag delve into the essence of human nature, transforming the mathematical principles of game theory into practical, everyday strategies. Through familiar proverbs and timeless wisdom, readers will explore how elements like reputation, biases, cooperation, and family dynamics influence our strategic interactions. From navigating a four-way stop and choosing take-out dinners to understanding the complexities of nuclear disarmament, Useful Game Theory demonstrates how recognizing the structure of games--players, choices, and outcomes--can enhance decision-making in all aspects of life.
Mathematics for Engineers (V2)
This second volume in our series is intended primarily as a companion text for the second semester mathematics preliminaries for students and lecturers of electrical engineering and other engineering disciplines.In a clear and concise manner, and without too much abstraction, it introduces students to the topics covered in the basic mathematics lectures. Volume 2 also provides students at universities and applied universities with a largely accurate, but always illustrative, presentation as a practical aid to entry into higher mathematics.Mathematical concepts are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely avoided. Instead, many applications not only support the application of mathematics, but also contribute to a better understanding of mathematics.
Mathematics for Engineers (V2)
This second volume in our series is intended primarily as a companion text for the second semester mathematics preliminaries for students and lecturers of electrical engineering and other engineering disciplines.In a clear and concise manner, and without too much abstraction, it introduces students to the topics covered in the basic mathematics lectures. Volume 2 also provides students at universities and applied universities with a largely accurate, but always illustrative, presentation as a practical aid to entry into higher mathematics.Mathematical concepts are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely avoided. Instead, many applications not only support the application of mathematics, but also contribute to a better understanding of mathematics.
Survival Analysis
This textbook provides a unified account of estimating the survival function, hazard rate, cumulative hazard, density, regression, conditional distributions, and linear functionals for the current status censored and right-censored data. The book contains the theory and methodology of efficient estimation, adaptation, dimension reduction, and confidence bands as well as the universal E-estimator for small samples. Exercises and a large number of simulated and real-life examples that can be repeated and modified using the complementary R package are also included. This coverage, together with the intuitive style of presentation, is ideal for people entering this field. The context is suitable for self-study or a one-semester course for graduate students with majors ranging from biostatistics and data analytics to econometrics and actuarial science.
Women in Mathart
This volume contains the proceedings from the first Women in MathArt Research Collaboration Conference for Women, showcasing women mathematicians researching and curating creative pedagogies at the intersection of mathematics and the arts. This volume contains contributions to mathart projects from student-mentor teams and researchers in all stages of their careers. The volume also contains survey articles on new mathart intersections such as neuroaesthetics, generative design, generative adversarial networks, and Langlands Program. New results of particular interest are: diamond Langlands; generative design in the geometrization of the local Langlands Program; investigations of the grammatology and visual epistemology of perfectoid diamonds in mathematics as grammatological metaphor; infinity-category constructions of pro-Generative Adversarial Networks; infinity-stackification of mathematical exigency; condensing temporal logic with entropic categorizations; perfectoid diamond holography; neuroaesthetics in immunology. Also included is the result to foster a more inclusive work community of mathematicians using the arts as a tool to bring more vulnerability and integrity to each individual's research life. Readers are herein provided a rigorous overview of current mathart developments and future mathart projects.
An Introduction to Na簿ve Set Theory and Its Applications
Primarily designed for graduate students of mathematics, this textbook delves into Na簿ve set theory, offering valuable insights for senior undergraduate students and researchers specializing in set theory. Commencing with a comprehensive exploration of functions and relations, the book extends its coverage to various applications of Na簿ve set theory across multiple mathematical branches, including real analysis, linear and abstract algebra, general topology, and introductory aspects of complex analysis and measure theory. The text meticulously introduces cardinal and ordinal numbers, along with transfinite induction, following the natural progression discovered by Cantor during his examination of trigonometric series. While this book provides a solid foundation, students intrigued by set theory for its intrinsic value should recognize that the subject extends far beyond the scope of this text.
Designing Experiments and Analyzing Data
The pedagogical approach used throughout the book enables readers to gain an overview of experimental design, from conceptualization of the research question to analysis of the data. Ideal for students and researchers.
Measure and Integral
This accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them.
Analysis of Toeplitz Operators
No detailed description available for "Analysis of Toeplitz Operators".
Spatial Statistics
Geospatial information modeling and mapping has become an important tool for the investigation and management of natural resources at the landscape scale. Spatial Statistics: GeoSpatial Information Modeling and Thematic Mapping reviews the types and applications of geospatial information data, such as remote sensing, geographic information systems (GIS), and GPS as well as their integration into landscape-scale geospatial statistical models and maps. The book explores how to extract information from remotely sensed imagery, GIS, and GPS, and how to combine this with field data--vegetation, soil, and environmental--to produce a spatial model that can be reconstructed and displayed using GIS software. Readers learn the requirements and limitations of each geospatial modeling and mapping tool. Case studies with real-life examples illustrate important applications of the models.Topics covered in this book include: An overview of the geospatial information sciences and technology and spatial statistics Sampling methods and applications, including probability sampling and nonrandom sampling, and issues to consider in sampling and plot design Fine and coarse scale variability Spatial sampling schemes and spatial pattern Linear and spatial correlation statistics, including Moran's I, Geary's C, cross-correlation statistics, and inverse distance weighting Geospatial statistics analysis using stepwise regression, ordinary least squares (OLS), variogram, kriging, spatial auto-regression, binary classification trees, cokriging, and geospatial models for presence and absence data How to use R statistical software to work on statistical analyses and case studies, and to develop a geospatial statistical model
Analysis of Internal Control Procedures
Internal Control plays a vital role in all types of organization, helping to improve the efficiency and economy of certain decision-making processes, minimize and anticipate risks, ensure the reliability of economic and financial data, and guarantee compliance and the application of procedures. In the wake of financial scandals in major multinational corporations, numerous measures have been taken in advanced countries, requiring these companies to set up an Internal Control system and regularly assess its effectiveness against the Internal Control model recognized and recommended by the relevant standards.The case study focused on the analysis of the Internal Control system of the Soci矇t矇 Malienne de gestion de l'Eau Potable "SOMAGEP-SA", where an attempt was made to analyze the effectiveness of the Internal Control system in place, and to highlight the main risks, by proceeding in stages, starting with the study of existing documentation, to participate in Internal Control missions to practice the control activity.
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
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.
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.
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.
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.
