Dynamics and Analysis of Alignment Models of Collective Behavior
This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
Systems Biology
This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction-diffusion equations based on different hypotheses concerning the process of morphogen gradient formation. The robustness of steady-state gradients is also covered through boundary value problems. The introduction gives an overview of the relevant biological concepts (cells, DNA, organism development) and provides the requisite mathematical preliminaries on continuous dynamics and stochastic modeling. A basic understanding of calculus is assumed. The techniques described in this book encompass a wide range of mechanisms, from molecular behavior to population dynamics, and the inclusion of recent developments in the literature together with first-hand results make it an ideal reference for both new students and experienced researchers in the field of systems biology and applied mathematics.
Triple Double
This book provides empirical evidence and statistical analyses to uncover answers to some of the most debated questions in the NBA. The sports world lives and breathes off of debates on who deserves an MVP award, and which athletes should be considered all-stars. This book provides some statistics-backed perspectives to some of these debates that are specific to the NBA. Was LeBron snubbed of an MVP in the 2010-2011 season? Why has the G.O.A.T. debate turned into LeBron vs. Jordan....Did Kobe get overlooked? How come Klay Thompson didn't get All-NBA honors in the 2018-2019 season? This book explores these questions and many more with empirical evidence. This book is invaluable for any undergraduate or masters level course in sport analytics, sports marketing, or sports management. It will also be incredibly useful for scouts, recruiters, and general managers in the NBA who would like to use analytics in their work.
Modelling of Complex Signals in Nerves
Introduction.- Part I Complexity and Waves.- Part II Dynamical Processes in Nerve Axons.- Part III Modelling of Dynamical Physiological Processes.- Appendix: The Numerical Scheme.- Index.
Mathematical Modeling
This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject.
Event History Analysis with R
This is the second edition of a practical book on using R for survival and event history analysis. There is an emphasis on applying the methods to problems from the social sciences through detailed real-world examples. The book has been updated with new chapters on reproducible research and register-based methods, and updates throughout.
Brouwer Degree
The Kronecker Index and the Brouwer Degree.- Continuation, Existence, and Bifurcation.- Infinite-Dimensional Problems.- Difference Equations.- Periodic Solutions of Differential Systems.- Two-Dimensional Problems.- The Degree of Some Classes of Mappings.- History of Brouwer Fixed Point Theorem.
Frontiers in Games and Dynamic Games
This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers with paths to further research, serving as a testimony to the vitality of the field. Experts cover a range of theory and applications related to games and dynamic games, with topics including: Dynamically stable cooperative provision of public goods under non-transferable utilityStrongly time-consistent solutions in cooperative dynamic gamesIncentive Stackelberg games for stochastic systemsStatic and inverse Stackelberg games in political economyCournot and Betrand competition on symmetric R&D networksNumerical Nash equilibria using curvilinear multistart algorithmMarkov chain approximation numerical scheme for infinite-horizon mean field gamesFrontiers in Games and Dynamic Games will appeal to an interdisciplinary audience of researchers, practitioners, and graduate students interested in games and dynamic games.
Methodologies in Biosimilar Product Development
Methodologies for Biosimilar Product Development covers the practical and challenging issues that are commonly encountered during the development, review, and approval of a proposed biosimilar product. These practical and challenging issues include, but are not limited to the mix-up use of interval hypotheses testing (i.e., the use of TOST) and confidence interval approach, a risk/benefit assessment for non-inferiority/similarity margin, PK/PD bridging studies with multiple references, the detection of possible reference product change over time, design and analysis of biosimilar switching studies, the assessment of sensitivity index for assessment of extrapolation across indications without collecting data from those indications not under study, and the feasibility and validation of non-medical switch post-approval. Key Features: Reviews withdrawn draft guidance on analytical similarity assessment. Evaluates various methods for analytical similarity evaluation based on FDA's current guidelines. Provides a general approach for the use of n-of-1 trial design for assessment of interchangeability. Discusses the feasibility and validity of the non-medical switch studies. Provides innovative thinking for detection of possible reference product change over time. This book embraces innovative thinking of design and analysis for biosimilar studies, which are required for review and approval of biosimilar regulatory submissions.
Statistik - Wie Und Warum Sie Funktioniert
Dieses Buch ist eine leicht verst瓣ndliche Einf羹hrung in die Statistik, die typische Schlussweisen der Mathematischen Statistik exemplarisch erl瓣utert: Warum kann aus den Ergebnissen einer Stichprobenuntersuchung auf die Gesamtheit geschlossen werden? Welche Ungenauigkeiten und Unsicherheiten sind dabei m繹glich? Wie und warum k繹nnen zufallsbedingte Abweichungen mit mathematischen Methoden analysiert werden?Aufgaben und Schaubilder verdeutlichen die m繹glichst weitgehend verbal beschriebenen Gedankeng瓣nge. Weitere didaktische Besonderheiten sind: Viele motivierende EinleitungenErl瓣uterungen der Resultate: was ist wichtig und warumDer mathematische Formalismus ist weitgehend in Ausblicke ausgelagertDie M繹glichkeit, nur Teile zu lesen (und trotzdem halbwegs zu verstehen)Der InhaltEinf羹hrung: Ein klassischer HypothesentestDie Mathematik des Zufalls: Ein ?berblick 羹ber die mathematische WahrscheinlichkeitsrechnungMethoden der Mathematischen StatistikEinf羹hrung in RF羹r die 2. Auflage wurde das Buch aktualisiert und um Musterl繹sungen bzw. L繹sungshinweise zu den meisten Aufgaben sowie um eine Einf羹hrung in das kostenlose Programm R erg瓣nzt, mit dem sich viele Berechnungen stark vereinfachen lassen.
Advances in Metric Fixed Point Theory and Applications
This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators.This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.
Bayesian Inverse Problems
This book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them.
Advanced Sampling Methods
This book discusses all major topics on survey sampling and estimation. It covers traditional as well as advanced sampling methods related to the spatial populations. The book presents real-world applications of major sampling methods and illustrates them with the R software. As a large sample size is not cost-efficient, this book introduces a new method by using the domain knowledge of the negative correlation between the variable of interest and the auxiliary variable in order to control the size of a sample. In addition, the book focuses on adaptive cluster sampling, rank-set sampling and their applications in real life. Advance methods discussed in the book have tremendous applications in ecology, environmental science, health science, forestry, bio-sciences, and humanities. This book is targeted as a text for undergraduate and graduate students of statistics, as well as researchers in various disciplines.
Theory of Information and Its Value
This English version of Ruslan L. Stratonovich's Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics.Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.
Pupil Reactions in Response to Human Mental Activity
This book focuses on a development for assessing mental changes using eye pupil reactions, namely extracting emotional change from the response to evaluate the viewer's interest in visual information. The pupil of the eye reacts to both brightness and emotional state, including interest, enjoyment, and mental workload. Because pupillary change is a biological signal, various artifacts influence measurements of eye images. Technical procedures are required to extract mental activities from pupillary changes, and they are summarized here step by step, although some procedures contain earlier techniques such as analog video processing. This study examines the possibility of estimating the viewer's interest and enjoyment of viewing movies by measuring the dynamic pupillary changes, blinking, and subjective interest responses. In evaluation of pupil size, there was a significant difference in pupil size between the higher and the lower shot for the degree of subject interest response in each kind of movies. The first part of the book shows a pupil reaction model for brightness changes to extract mental activities. Pupil reactions were observed for various visual stimuli in brightness changes. With regard to the characteristics of pupillary changes, a model with a three-layer neural network was developed and the performance was evaluated. Characteristics of pupil reactions during model development are summarized here. The second part examines the possibility of estimating the viewer's interest and enjoyment of television programs by measuring dynamic pupillary changes, blinking, and subjective interest responses. The final part describes a development of estimation model of pupil size for blink artifact. The model development was able to estimate pupillary changes and pupil size while the viewer was blinking and was applied to pupillary changes in viewing television programs.
Particle Emission Concept and Probabilistic Consideration of the Development of Infections in Systems
The book describes the possibility of making a probabilistic prognosis, which uses the mean n-day logarithm of case numbers in the past to determine an exponent for a probability density for a prognosis, as well as the particle emission concept, which is derived from contact and distribution rates that increase the exponent of the probable development to the extent that a group of people can be formed.
Current Trends in Dynamical Systems in Biology and Natural Sciences
This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop "Dynamical Systems Applied to Biology and Natural Sciences - DSABNS", held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.
Separable Optimization
In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.
Theory of Translation Closedness for Time Scales
Preface.- Preliminaries and Basic Knowledge on Time Scales.- A Classification of Closedness of Time Scales under Translations.- Almost Periodic Functions and Generalizations on Complete-Closed Time Scales.- Piecewise Almost Periodic Functions and Generalizations on Translation Time Scales.- Almost Automorphic Functions and Generalizations on Translation Time Scales.- Nonlinear Dynamic Equations on Translation Time Scales.- Impulsive Dynamic Equations on Translation Time Scales.- Almost Automorphic Dynamic Equations on Translation Time Scales.- Analysis of Dynamical System Models on Translation Time Scales.- Index.
Statistical Analysis of Empirical Data
Researchers and students who use empirical investigation in their work must go through the process of selecting statistical methods for analyses, and they are often challenged to justify these selections. This book is designed for readers with limited background in statistical methodology who seek guidance in defending their statistical decision-making in the worlds of research and practice. It is devoted to helping students and scholars find the information they need to select data analytic methods, and to speak knowledgeably about their statistical research processes. Each chapter opens with a conundrum relating to the selection of an analysis, or to explaining the nature of an analysis. Throughout the chapter, the analysis is described, along with some guidance in justifying the choices of that particular method.Designed to offer statistical knowledge to the non-specialist, this volume can be used in courses on research methods, or for courses on statistical applications to biological, medical, life, social, or physical sciences. It will also be useful to academic and industrial researchers in engineering and in the physical sciences who will benefit from a stronger understanding of how to analyze empirical data. The book is written for those with foundational education in calculus. However, a brief review of fundamental concepts of probability and statistics, together with a primer on some concepts in elementary calculus and matrix algebra, is included. R code and sample datasets are provided.
Pandemics: Insurance and Social Protection
This open access book collects expert contributions on actuarial modelling and related topics, from machine learning to legal aspects, and reflects on possible insurance designs during an epidemic/pandemic.Starting by considering the impulse given by COVID-19 to the insurance industry and to actuarial research, the text covers compartment models, mortality changes during a pandemic, risk-sharing in the presence of low probability events, group testing, compositional data analysis for detecting data inconsistencies, behaviouristic aspects in fighting a pandemic, and insurers' legal problems, amongst others.Concluding with an essay by a practicing actuary on the applicability of the methods proposed, this interdisciplinary book is aimed at actuaries as well as readers with a background in mathematics, economics, statistics, finance, epidemiology, or sociology.
Pandemics: Insurance and Social Protection
This open access book collects expert contributions on actuarial modelling and related topics, from machine learning to legal aspects, and reflects on possible insurance designs during an epidemic/pandemic.Starting by considering the impulse given by COVID-19 to the insurance industry and to actuarial research, the text covers compartment models, mortality changes during a pandemic, risk-sharing in the presence of low probability events, group testing, compositional data analysis for detecting data inconsistencies, behaviouristic aspects in fighting a pandemic, and insurers' legal problems, amongst others.Concluding with an essay by a practicing actuary on the applicability of the methods proposed, this interdisciplinary book is aimed at actuaries as well as readers with a background in mathematics, economics, statistics, finance, epidemiology, or sociology.
Scheduling and Control of Queueing Networks
Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin-Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.
Luck, Logic, and White Lies
This book considers a specific problem-generally a game or game fragment and introduces the mathematical methods. It contains a section on the historical development of the theories of games of chance, and combinatorial and strategic games.
Statistical Methods for Handling Incomplete Data
Due to recent theoretical findings and advances in statistical computing, there has been a rapid development of techniques and applications in the area of missing data analysis. This book covers the most up-to-date statistical theories and computational methods for analyzing incomplete data.
Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any It繫's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
A Complete Solution Guide to Real and Complex Analysis
This is a complete solution guide to all exercises from Chapters 1 to 20 in Rudin's Real and Complex Analysis. The features of this book are as follows: It covers all the 397 exercises from Chapters 1 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied. There are 40 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems. Sections in each chapter are added so as to increase the readability of the exercises. Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin. Many useful or relevant references are provided to some questions for your future research.
Differential Topology
This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem and the generalised Poincar矇 conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India.The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis and algebraic topology is recommended.
Studies in Evolution Equations and Related Topics
Introduction Chapter: Evolution Equations: present and future.- Invariant Stable Manifolds of epsilon-class for Partial Neutral Functional Differential Equations on a half-line (Thieu Huy).- Global Attractor in Alpha-norm for some Partial Functional Differential Equations of neutral and retarded type (Ezzinbi).- A study of an epidemic SIR model via Homotopy Analysis Method in the sense of Caputo-fractional system (Norouzi).- Structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin type boundary condition (Ouaro).- Optimal Control of averaged state of a population dynamic model (Kenne].- C0-semigroup and Stepanov-like almost automorphic functions in matched spaces of time scales (Wang).- A reaction diffusion model for salmonella transmission within an industrial hens house with distributed resistance to salmonella carrier-state (Zongo).- Impulsive Implicit Caputo Fractional q-Difference Equations in Finite and Infinite Dimensional Banach Spaces (Benchohrs).- Null Controllability of a cascade model in population dynamics (Maniar).
Modern Industrial Statistics
Modern Industrial Statistics The new edition of the prime reference on the tools of statistics used in industry and services, integrating theoretical, practical, and computer-based approachesModern Industrial Statistics is a leading reference and guide to the statistics tools widely used in industry and services. Designed to help professionals and students easily access relevant theoretical and practical information in a single volume, this standard resource employs a computer-intensive approach to industrial statistics and provides numerous examples and procedures in the popular R language and for MINITAB and JMP statistical analysis software. Divided into two parts, the text covers the principles of statistical thinking and analysis, bootstrapping, predictive analytics, Bayesian inference, time series analysis, acceptance sampling, statistical process control, design and analysis of experiments, simulation and computer experiments, and reliability and survival analysis. Part A, on computer age statistical analysis, can be used in general courses on analytics and statistics. Part B is focused on industrial statistics applications.The fully revised third edition covers the latest techniques in R, MINITAB and JMP, and features brand-new coverage of time series analysis, predictive analytics and Bayesian inference. New and expanded simulation activities, examples, and case studies--drawn from the electronics, metal work, pharmaceutical, and financial industries--are complemented by additional computer and modeling methods. Helping readers develop skills for modeling data and designing experiments, this comprehensive volume: Explains the use of computer-based methods such as bootstrapping and data visualizationCovers nonstandard techniques and applications of industrial statistical process control (SPC) chartsContains numerous problems, exercises, and data sets representing real-life case studies of statistical work in various business and industry settingsIncludes access to a companion website that contains an introduction to R, sample R code, csv files of all data sets, JMP add-ins, and downloadable appendicesProvides an author-created R package, mistat, that includes all data sets and statistical analysis applications used in the bookPart of the acclaimed Statistics in Practice series, Modern Industrial Statistics with Applications in R, MINITAB, and JMP, Third Edition, is the perfect textbook for advanced undergraduate and postgraduate courses in the areas of industrial statistics, quality and reliability engineering, and an important reference for industrial statisticians, researchers, and practitioners in related fields. The mistat R-package is available from the R CRAN repository.
The Python Book
The Python Book Discover the power of one of the fastest growing programming languages in the world with this insightful new resource The Python Book delivers an essential introductory guide to learning Python for anyone who works with data but does not have experience in programming. The author, an experienced data scientist and Python programmer, shows readers how to use Python for data analysis, exploration, cleaning, and wrangling. Readers will learn what in the Python language is important for data analysis, and why. The Python Book offers readers a thorough and comprehensive introduction to Python that is both simple enough to be ideal for a novice programmer, yet robust to be useful for those more experienced in the language. The book assists budding programmers to gradually increase their skills as they move through the book, always with an understanding of what they are covering and why it is useful. Used by major companies like Google, Facebook, Instagram, Spotify, and more, Python promises to remain central to the programming landscape for years to come. Containing a thorough discussion of Python programming topics like variables, equalities and comparisons, tuple and dictionary data types, while and for loops, and if statements, readers will also learn: How to use highly useful Python programming libraries, including Pandas and Matplotlib How to write Python functions and classes How to write and use Python scripts To deal with different data types within Python Perfect for statisticians, computer scientists, software programmers, and practitioners working in private industry and medicine, The Python Book will also be of interest to students in any of the aforementioned fields. As it assumes no programming experience or knowledge, the book is ideal for those who work with data and want to learn to use Python to enhance their work.
Material Geometry
This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
Mathematical Foundations of Infinite-Dimensional Statistical Models
In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Statistical Methods in Psychiatry Research and SPSS
This volume, Statistical Methods in Psychiatry Research and SPSS, now going into its second edition, has been helping psychiatrists expand their knowledge of statistical methods and fills the gaps in their applications as well as introduces data analysis software. It addresses the statistical needs of physicians and presents a simplified approach. The book emphasizes the classification of fundamental statistical methods in psychiatry research that are precise and simple. Professionals in the field of mental health and allied subjects without any mathematical background will easily understand all the relevant statistical methods and carry out the analysis and interpret the results in their respective field without consulting any statistician. This new volume has over 100 pages of new material, including several new appendixes.The sequence of the chapters, the sections within the chapters, the subsections within the sections, and the points within the subsections have all been arranged to help professionals in classification refine their knowledge in statistical methods and fills the gaps.
Meta-Analysis in Psychiatry Research
This book introduces the latest meta-analytical methods and discusses their applications in the field of psychiatry. A comprehensive list of methods used in meta-analysis has been described in simple language and demonstrated with real-time examples. This informative volume explains the importance of meta-analysis and describes how it differs from narrative and systematic reviews. It also relates the historical development of meta-analysis and explains methods used for locating and selecting the required studies in a given domain. Suitable software is examined in detail as well.
Time Series with Mixed Spectra
This book focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms. Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram.
Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains
Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more.This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.
Statistical Methods in Psychiatry Research and SPSS
This book has been prepared to help psychiatrists expand their knowledge of statistical methods and fills the gaps in their applications as well as introduces data analysis software. The book emphasizes the classification of fundamental statistical methods in psychiatry research that are precise and simple. Professionals in the field of mental health and allied subjects without any mathematical background can easily understand all the relevant statistical methods and carry out the analysis and interpret the results in their respective fields without consulting a statistician.The sequence of the chapters, the sections within the chapters, the subsections within the sections, and the points within the subsections have all been arranged to help professionals in classification refine their knowledge in statistical methods and fill the gaps, if any.Emphasizing simplicity, the fundamental statistical methods are demonstrated by means of arithmetical examples that may be reworked with pencil and paper in a matter of minutes. The results of the rework have to be checked by using SPSS, and in this way professionals are introduced to this psychiatrist-friendly data analysis software. Topics covered include: - An overview of psychiatry research - The organization and collection of data - Descriptive statistics - The basis of statistical inference- Tests of significance - Correlational data analysis - Multivariate data analysis - Meta-analysis - Reporting the results - Statistical software The language of the book is very simple and covers all aspects of statistical methods starting from organization and collection of data to descriptive statistics, statistical inference, multivariate analysis, and meta-analysis. Two chapters on computer applications deal with the most popular data analysis software: SPSS.The book will be very valuable to professionals and post-graduate students in psychiatry and allied fields, such as psychiatric social work, clinical psychology, psychiatric nursing, and mental health education and administration.
Bioinformatics
This title includes a number of Open Access chapters.The book introduces bioinformatic and statistical methodology and shows approaches to bias correction and error estimation. It also presents quantitative methods for genome and proteome analysis.
Biotechnology and Bioinformatics
Reflecting the interdisciplinary nature of biotechnology, this book covers the role of targeted delivery of polymeric nanodrugs to cancer cells, microbial detoxifying enzymes in bioremediation and bacterial plasmids in antimicrobial resistance. It addresses modern trends such as pharmacogenomics, evaluation of gene expression, recombinant proteins from methylotrophic yeast, identification of novel fermentation inhibitors of bioethanol production, and polyhydroxyalkanoate based biomaterials. The book highlights the practical utility of biotechnology and bioinformatics for bioenergy, production of high value biochemicals, modeling molecular interactions, drug discovery, and personalized medicine.
The Math of Life and Death
Brilliant and entertaining mathematician Kit Yates illuminates seven mathematical concepts that shape our daily lives. From birthdays to birth rates to how we perceive the passing of time, mathematical patterns shape our lives. But for those of us who left math behind in high school, the numbers and figures we encounter as we go about our days can leave us scratching our heads, feeling as if we're fumbling through a mathematical minefield. In this eye-opening and "welcome addition to the math-for-people-who-hate-math" (Kirkus Reviews), Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a "dizzying, dazzling" (Nature) tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, Ponzi schemes, viral marketing, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it's choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.
Stochastic Processes in Cell Biology
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process - Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. Thistext is primarily aimed at graduate students and researchers working in mathematical biology and applied mathematicians interested in stochastic modeling. Applied probabilists and theoretical physicists should also find it of interest. It assumes no prior background in statistical physics and introduces concepts in stochastic processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.
Applied Univariate, Bivariate, and Multivariate Statistics Using Python
Applied Univariate, Bivariate, and Multivariate Statistics Using Python A practical, "how-to" reference for anyone performing essential statistical analyses and data management tasks in PythonApplied Univariate, Bivariate, and Multivariate Statistics Using Python delivers a comprehensive introduction to a wide range of statistical methods performed using Python in a single, one-stop reference. The book contains user-friendly guidance and instructions on using Python to run a variety of statistical procedures without getting bogged down in unnecessary theory. Throughout, the author emphasizes a set of computational tools used in the discovery of empirical patterns, as well as several popular statistical analyses and data management tasks that can be immediately applied.Most of the datasets used in the book are small enough to be easily entered into Python manually, though they can also be downloaded for free from www.datapsyc.com. Only minimal knowledge of statistics is assumed, making the book perfect for those seeking an easily accessible toolkit for statistical analysis with Python. Applied Univariate, Bivariate, and Multivariate Statistics Using Python represents the fastest way to learn how to analyze data with Python.Readers will also benefit from the inclusion of: A review of essential statistical principles, including types of data, measurement, significance tests, significance levels, and type I and type II errorsAn introduction to Python, exploring how to communicate with PythonA treatment of exploratory data analysis, basic statistics and visual displays, including frequencies and descriptives, q-q plots, box-and-whisker plots, and data managementAn introduction to topics such as ANOVA, MANOVA and discriminant analysis, regression, principal components analysis, factor analysis, cluster analysis, among others, exploring the nature of what these techniques can vs. cannot do on a methodological levelPerfect for undergraduate and graduate students in the social, behavioral, and natural sciences, Applied Univariate, Bivariate, and Multivariate Statistics Using Python will also earn a place in the libraries of researchers and data analysts seeking a quick go-to resource for univariate, bivariate, and multivariate analysis in Python.
Risk and Insurance
This textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.
Fundamentals of Data Science Part I
In Part I of this series, we cover basic statistical inference and experimentation, focusing on: basic statistics;derivation and review of key distributions and their relations;hypothesis testing, including an in depth power analysis for the chi-squared statistic;experimentation, including A/B tests, stratification, one- and two-factor experiments, and an introduction to bandit algorithms; maximum likelihood;gradient descent;introduction to survival analysis and stochastic processes, including empirical estimation of online survival and event processes.The theory is illustrated with simulations in Python throughout the text.
Introduction to Complex Variables and Applications
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlev矇 equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
Introduction to Complex Variables and Applications
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlev矇 equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
Games and Dynamics in Economics
This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly--but not solely--based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact. Nonlinear dynamical systems, represented by difference and differential and functional equations, are extensively used to simulate the behavior of time-evolving economic systems, also in the presence of time lags, discontinuities, and hysteresis phenomena. In addition, some theoretical issues and particular applications are discussed, as well. The contributions gathered here offer an up-to-date review of the latest research in thisrapidly developing research area.
