Boundary Elements and other Mesh Reduction Methods XLV
Advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences are reported in the papers that form this volume.As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process.The maturity of BEM since 1978 has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general.The included papers originate from the 45th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) and describe theoretical developments and new formulations, helping to expand the range of applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments.
Discrete Time Analysis of Multi-Server Queueing Systems in Material Handling and Service
In this doctoral thesis, performance parameters of multi-server queueing systems are estimated under general stochastic assumptions. We present an exact calculation method for the discrete time distribution of the number of customers in the queueing system at the arrival moment of an arbitrary customer. The waiting time distribution and the sojourn time distribution are estimated exactly, as well. For the calculation of the inter departure time distribution, we present an approximation method.
Seduced by Mathematics: The Enduring Fascination of Mathematics
Seduction is not just an end result, but a process - and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people - not just those for whom math plays a key role in their day-to-day lives - have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," - because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.This book contains material capable of being appreciated by students in elementary school - as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.
Seduced by Mathematics: The Enduring Fascination of Mathematics
Seduction is not just an end result, but a process - and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people - not just those for whom math plays a key role in their day-to-day lives - have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," - because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.This book contains material capable of being appreciated by students in elementary school - as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.
Backseat Driver
Buying the safest car for your family shouldn't be up for debate. Yet for decades, car safety advocates, manufacturers, and lawmakers in the United States have clashed over whether to make automobiles safer. All sides armed themselves with data in the hopes of winning the great car safety debates. In this way, crash statistics and the analysts who studied them made history. But data were always in the backseat, merely supporting different points of view. That is, until now. With car safety, it's the value we place on every human life that counts. Automobile safety expert Dr. Norma Faris Hubele delivers a lively discussion of the role data play in protecting you and your family on the road. You'll gain a greater appreciation for how: A World War I pilot's near-death experience birthed the U.S. car safety movement Data from real car crashes helped create the first vehicle safety standards A shift toward fuel-efficient cars affected fatality risk in the 1970s-1980s versus now Vehicle size has changed, and the problems that creates for you and others sharing the road Car safety rating systems, even when limited, empower consumers and motivate manufacturers Federal regulators decide whether to issue a safety recall on your vehicle Data's role is evolving with the advent of driver-assist and self-driving technologies Further information can be found on the book's website: www.TheAutoProfessor.com/book [US only].
Fractional Differential Equations
This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.
Smooth Functions and Maps
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor's formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor's formula in a nonconvex area (Chapter I, 禮8), Whitney's extension theorem for smooth function (Chapter I, 禮11) and some of its corollaries, global diffeomorphism theorem (Chapter II, 禮5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
Applied Mathematical Problems in Geophysics
This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes.This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.
Approximation Theory and Analytic Inequalities
This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss-Jacobi and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam's stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Detection and characterization of inclusions in impedance tomography
The topic of this work are two further developments of the Factorization method for electrical impedance tomography.We present a modification of this method that is capable of detecting mixed inclusions, i.e. both inclusions with a higher as well as inclusions with a lower conductivity than the background medium. In addition, we derive a new method to compute the conductivity inside inclusions after they have been localized.
Time Series for Data Science
Practical Time Series Analysis for Data Science is an accessible guide that doesn't require a background in calculus to be engaging but does not shy away from deeper explanations of the techniques discussed.
Solving Physics Problems
This book provides a complete, consistent, and open system for studying physics problems, which not only provides high-quality teaching materials for the field of physics education (especially for Physics Olympiad training) but also points out a new direction for physics education. In this book, a form of methodology, which can comprehensively present cogitation discipline, is built up for analyzing and solving complex physics problems. The text analyzes plenty of physics problems (classical mechanics) from both theoretical and philosophical points of view to reveal the way of exerting this form. As a set of methodology reflecting the cogitation discipline, the thinking paradigm proposed in this book (called the MLQ-(ST)C paradigm) is a theoretical tool to develop people's acquisition of this ability. The paradigm successfully deconstructs the elements and the structure in physical thinking and then eliminates the obstacles of people's underlying thinking, so that all the thinking built on it can be clear and ordered. The physics problems included in this book are significantly more difficult than similar books within the same theoretical domains involved, leading to better teaching and learning value.
Palm theory, mass transports and ergodic theory for group-stationary processes
This work is about random measures stationary with respect to a possibly non-transitive group action. It contains chapters on Palm Theory, the Mass-Transport Principle and Ergodic Theory for such random measures. The thesis ends with discussions of several new models in Stochastic Geometry (Cox Delauney mosaics, isometry stationary random partitions on Riemannian manifolds). These make crucial use of the previously developed techniques and objects.
Analytic Continuation and Q-Convexity
1. Analytic Continuation and Pseudoconvexity.- 2. q-Plurisubharmonicity.- 3. q-Pseudoconvexity.- 4. q-Convexity and q-Completeness.- References.- Index.
Mathematics for Biomedical Applications
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.
Water in the Making of a Socio-Natural Landscape
Water in the Making of a Socio-Natural Landscape explores the transition from early modern to modern water management in late nineteenth-century Rome.
Mathematics for Biomedical Applications
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.
Differentiability in Banach Spaces, Differential Forms and Applications
This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fr矇chet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the finalchapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales
The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance.
Engineering Mathematics and Computing
This book contains select papers presented at the 3rd International Conference on Engineering Mathematics and Computing (ICEMC 2020), held at the Haldia Institute of Technology, Purba Midnapur, West Bengal, India, from 5-7 February 2020. The book discusses new developments and advances in the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, hybrid intelligent systems, etc. The book, containing 19 chapters, is useful to the researchers, scholars, and practising engineers as well as graduate students of engineering and applied sciences.
Cluster Randomised Trials
Cluster Randomised Trials, Second Edition explores the advantages of cluster randomisation, with special attention given to evaluating the effects of interventions against infectious diseases. Avoiding unnecessary mathematical detail, it covers basic concepts underlying the use of cluster randomisation.
Rational Sphere Maps
This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing research from the last forty years, the author aims for accessibility by balancing abstract concepts with concrete examples. Numerous computations are worked out in detail, and more than 100 optional exercises are provided throughout for readers wishing to better understand challenging material.The text begins by presenting core concepts in complex analysis and a wide variety of results about rational sphere maps. The subsequent chapters discuss combinatorial and optimization results about monomial sphere maps, groups associated with rational sphere maps, relevant complex and CR geometry, and some geometric properties of rational sphere maps. Fifteen open problems appear in the final chapter, with references provided to appropriate parts of the text. These problemswill encourage readers to apply the material to future research.Rational Sphere Maps will be of interest to researchers and graduate students studying several complex variables and CR geometry. Mathematicians from other areas, such as number theory, optimization, and combinatorics, will also find the material appealing.See the author's research web page for a list of typos, clarifications, etc.: https: //faculty.math.illinois.edu/ jpda/research.html
Ranking of Multivariate Populations
This book presents a novel permutation-based nonparametric approach for ranking several multivariate populations. Using data collected from both experimental and observation studies, it covers some of the most useful designs widely applied in research and industry investigations. The book introduces the main theoretical ideas of ranking multivar
Algorithms for a New World
Covid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios. Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.
Data Science
Data Science: A First Introduction focuses on using the R programming language in Jupyter notebooks to perform data manipulation and cleaning, create effective visualizations, and extract insights from data using classification, regression, clustering, and inference. The text emphasizes workflows that are clear, reproducible, and shareable, and includes coverage of the basics of version control. All source code is available online, demonstrating the use of good reproducible project workflows. Based on educational research and active learning principles, the book uses a modern approach to R and includes accompanying autograded Jupyter worksheets for interactive, self-directed learning. The book will leave readers well-prepared for data science projects. The book is designed for learners from all disciplines with minimal prior knowledge of mathematics and programming. The authors have honed the material through years of experience teaching thousands of undergraduates in the University of British Columbia's DSCI100: Introduction to Data Science course.
Regression Analysis in R
This book covers the basic applications of multiple linear regression all the way through to more complex regression applications and extensions. Written for graduate level students of social science disciplines this book walks readers through bivariate correlation.
Advances in Matrix Inequalities
This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.
Statistical Hypothesis Testing in Context
Fay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with Wilcoxon-Mann-Whitney tests and Kaplan-Meier estimates. Examples, exercises, and the R package asht support practical use.
Game-Theoretical Models in Biology
Covering the major topics of evolutionary game theory, this book presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. The text is also useful to biologists.
A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
Control Systems and Reinforcement Learning
A high school student can create deep Q-learning code to control her robot, without any understanding of the meaning of 'deep' or 'Q', or why the code sometimes fails. This book is designed to explain the science behind reinforcement learning and optimal control in a way that is accessible to students with a background in calculus and matrix algebra. A unique focus is algorithm design to obtain the fastest possible speed of convergence for learning algorithms, along with insight into why reinforcement learning sometimes fails. Advanced stochastic process theory is avoided at the start by substituting random exploration with more intuitive deterministic probing for learning. Once these ideas are understood, it is not difficult to master techniques rooted in stochastic control. These topics are covered in the second part of the book, starting with Markov chain theory and ending with a fresh look at actor-critic methods for reinforcement learning.
Arc-Search Techniques for Interior-Point Methods
This book discusses one of the most recent developments in interior-point methods, the arc-search techniques. Introducing these techniques result in an efficient interior-point algorithm with the lowest polynomial bound, which solves a long-standing issue of the interior-point methods in linear programming.
Asymptotic Statistical Inference
The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators andcarrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.
Introduction to Multiscale Mathematical Modeling
This book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research.The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method.The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine.
Stationary Stochastic Models: An Introduction
This volume provides a unified mathematical introduction to stationary time series models and to continuous time stationary stochastic processes. The analysis of these stationary models is carried out in time domain and in frequency domain. It begins with a practical discussion on stationarity, by which practical methods for obtaining stationary data are described. The presented topics are illustrated by numerous examples. Readers will find the following covered in a comprehensive manner: At the end, some selected topics such as stationary random fields, simulation of Gaussian stationary processes, time series for planar directions, large deviations approximations and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.
The History of the International Biometric Society
The History of the International Biometric Society presents a deep dive into the voluminous archival records, with primary focus on IBS's first fifty years. It contains numerous photos and extracts from the archival materials, and features many photos of important leaders who served IBS across the decades.
Probability, Statistics, and Stochastic Processes for Engineers and Scientists
Featuring recent advances in probability, statistics, and stochastic processes, this new textbook presents Probability and Statistics, and an introduction to Stochastic Processes.
Multiplicative Differential Calculus
This book is devoted to the multiplicative differential calculus. It summarizes the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses.
Fundamentals of Statistical Thinking
Written for students with basic experience in college algebra and applied calculus, Fundamentals of Statistical Thinking: Tools and Applications familiarizes readers with fundamental concepts in statistical thinking in order to prepare them for specialized management courses such as econometrics and quantitative analysis. The book is organized into four sections, each of which focuses on a common tool used in application. Chapters 1 through 4 discuss data analysis and summaries, with an emphasis on descriptive statistics and visualization. In Chapters 5 through 8 students learn about probability models and sampling distributions. Chapters 9 and 10 deal with statistical inferences, while Chapters 11 and 12 provide further applications for categorical data and simple linear regression models. Graphical illustrations support the written text and each chapter concludes with a visual summary. Rooted in over ten years of classroom experience at both the undergraduate and graduate levels, Fundamentals of Statistical Thinking helps readers understand the importance of the main technical tools of statistical decision making, and explains when they can most appropriately be used for applied studies.
Rigid Body Dynamics
This monograph provides a complete and up-to-date examination of rigid body dynamics using a Lagrangian approach. All known integrable cases, which were previously scattered throughout the literature, are collected here for convenient reference. Also contained are particular solutions to diverse problems treated within rigid body dynamics. The first seven chapters introduce the elementary dynamics of the rigid body and its main problems. A full historical account of the discovery and development of each of the integrable cases is included as well. Instructors will find this portion of the book well-suited for an undergraduate course, having been formulated by the author in the classroom over many years. The second part includes more advanced topics and some of the author's original research, highlighting several unique methods he developed that have led to significant results. Some of the specific topics covered include the twelve known solutions of the equations of motion in the classical problem, which has not previously appeared in English before; a collection of completely new integrable cases; and the motion of a rigid body around a fixed point under the action of an asymmetric combination of potential and gyroscopic forces. Rigid Body Dynamics will appeal to researchers in the area as well as those studying dynamical and integrable systems theory.
Functional Distribution of Anomalous and Nonergodic Diffusion: From Stochastic Processes to Pdes
This volume presents a pedagogical review of the functional distribution of anomalous and nonergodic diffusion and its numerical simulations, starting from the studied stochastic processes to the deterministic partial differential equations governing the probability density function of the functionals. Since the remarkable theory of Brownian motion was proposed by Einstein in 1905, it had a sustained and broad impact on diverse fields, such as physics, chemistry, biology, economics, and mathematics. The functionals of Brownian motion are later widely attractive for their extensive applications. It was Kac, who firstly realized the statistical properties of these functionals can be studied by using Feynman's path integrals.In recent decades, anomalous and nonergodic diffusions which are non-Brownian become topical issues, such as fractional Brownian motion, L矇vy process, L矇vy walk, among others. This volume examines the statistical properties of the non-Brownian functionals, derives the governing equations of their distributions, and shows some algorithms for solving these equations numerically.
Black Box Optimization, Machine Learning, and No-Free Lunch Theorems
This edited volume illustrates the connections between machine learning techniques, black box optimization, and no-free lunch theorems. Each of the thirteen contributions focuses on the commonality and interdisciplinary concepts as well as the fundamentals needed to fully comprehend the impact of individual applications and problems. Current theoretical, algorithmic, and practical methods used are provided to stimulate a new effort towards innovative and efficient solutions. The book is intended for beginners who wish to achieve a broad overview of optimization methods and also for more experienced researchers as well as researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, who will benefit from access to a quick reference to key topics and methods. The coverage ranges from mathematically rigorous methods to heuristic and evolutionary approaches in an attempt to equip the reader with different viewpoints of the same problem.
An Intuitive Exploration of Artificial Intelligence
This book develops a conceptual understanding of Artificial Intelligence (AI), Deep Learning and Machine Learning in the truest sense of the word. It is an earnest endeavor to unravel what is happening at the algorithmic level, to grasp how applications are being built and to show the long adventurous road in the future.An Intuitive Exploration of Artificial Intelligence offers insightful details on how AI works and solves problems in computer vision, natural language understanding, speech understanding, reinforcement learning and synthesis of new content. From the classic problem of recognizing cats and dogs, to building autonomous vehicles, to translating text into another language, to automatically converting speech into text and back to speech, to generating neural art, to playing games, and the author's own experience in building solutions in industry, this book is about explaining how exactly the myriad applications of AI flow out of its immense potential.The book is intended to serve as a textbook for graduate and senior-level undergraduate courses in AI. Moreover, since the book provides a strong geometrical intuition about advanced mathematical foundations of AI, practitioners and researchers will equally benefit from the book.
Medical Statistics for Cancer Studies
Cancer is a dreaded disease. One in two people will be diagnosed with cancer within their lifetime. Medical Statistics for Cancer Studies shows how cancer data can be analysed in a variety of ways, covering cancer clinical trial data, epidemiological data, biological data, and genetic data. It gives some background in cancer biology and genetics, followed by detailed overviews of survival analysis, clinical trials, regression analysis, epidemiology, meta-analysis, biomarkers, and cancer informatics. It includes lots of examples using real data from the author's many years of experience working in a cancer clinical trials unit. Features: A broad and accessible overview of statistical methods in cancer research Necessary background in cancer biology and genetics Details of statistical methodology with minimal algebra Many examples using real data from cancer clinical trials Appendix giving statistics revision.
Data Science Techniques for Cryptocurrency Blockchains
This book brings together two major trends: data science and blockchains. It is one of the first books to systematically cover the analytics aspects of blockchains, with the goal of linking traditional data mining research communities with novel data sources. Data science and big data technologies can be considered cornerstones of the data-driven digital transformation of organizations and society. The concept of blockchain is predicted to enable and spark transformation on par with that associated with the invention of the Internet. Cryptocurrencies are the first successful use case of highly distributed blockchains, like the world wide web was to the Internet. The book takes the reader through basic data exploration topics, proceeding systematically, method by method, through supervised and unsupervised learning approaches and information visualization techniques, all the way to understanding the blockchain data from the network science perspective. Chapters introduce the cryptocurrency blockchain data model and methods to explore it using structured query language, association rules, clustering, classification, visualization, and network science. Each chapter introduces basic concepts, presents examples with real cryptocurrency blockchain data and offers exercises and questions for further discussion. Such an approach intends to serve as a good starting point for undergraduate and graduate students to learn data science topics using cryptocurrency blockchain examples. It is also aimed at researchers and analysts who already possess good analytical and data skills, but who do not yet have the specific knowledge to tackle analytic questions about blockchain transactions. The readers improve their knowledge about the essential data science techniques in order to turn mere transactional information into social, economic, and business insights.
Tree-Based Methods for Statistical Learning in R
This book provides a thorough introduction to both individual decision tree algorithms (Part I) and ensembles thereof (Part II). Part I of the book brings several different tree algorithms into focus, both conventional and contemporary.
