Census Of The Philippine Islands, Taken Under The Direction Of The Philippine Commission In The Year 1903, In Four Volumes ... Comp. And Pub. By The United States Bureau Of The Census; Volume 2
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Statistical Abstract of the World
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements of the Differential Calculus
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures On the Theory of Elliptic Functions; Volume 1
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Baseball Mysteries
The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles. To jump in, all you need is logic and a casual fan's knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts.The logic in the puzzles is like legal reasoning. A solution must argue from evidence (the facts) and law (the rules). Unlike legal arguments, however, a solution must reach an unassailable conclusion.There are many puzzle books. But there's nothing remotely like this book. The puzzles here, while rigorously deductive, are firmly attached to actual events, to struggles that are reported in the papers every day.The puzzles offer a unique and scintillating connection between abstract logic and gritty reality.Actually, this book offers the reader an unlimited number of puzzles. Once you've solved a few of the challenges here, every boxscore you see in the papers or online is a new puzzle! It can be anywhere from simple, to complex, to impossible. For anyone who enjoys logical puzzles For anyone interested in legal reasoning For anyone who loves the game of baseball. Jerry Butters has a BA in mathematics from Oberlin College, and an MS in mathematics and a PhD in economics from the University of Chicago. He taught mathematics for two years at Mindanao State University in the Philippines as a Peace Corps volunteer. He taught economics for five years at Princeton University. For most of his career, he worked on consumer protection cases and policy issues at the Federal Trade Commission. In his retirement, he has become a piano teacher and performer. He enjoys hobbies ranging from reading Chinese to practicing Taiji. This book is an outgrowth of another of his hobbies - his love of designing and solving puzzles of all sorts.Jim Henle has a BA in mathematics from Dartmouth College and a PhD from M.I.T. He taught for two years at U. P. Baguio in the Philippines as a Peace Corps volunteer, two years at a middle school as alternative service, and 42 years at Smith College. His research is primarily in logic and set theory, with additional papers in geometry, graph theory, number theory, games, economics, and music. He edited columns for The Mathematical Intelligencer. He authored or co-authored five books. His most recent book, The Proof and the Pudding, compares mathematics and gastronomy. He has collaborated with Jerry on puzzle papers and chamber music concerts.
The Baseball Mysteries
This book contains numerous logical baseball puzzles. To jump in, all you need is logic and a casual fan's knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts. The puzzles offer a unique and scintillating connection between abstract logic and gritty reality.
How Data Quality Affects Our Understanding of the Earnings Distribution
This open access book demonstrates how data quality issues affect all surveys and proposes methods that can be utilised to deal with the observable components of survey error in a statistically sound manner. This book begins by profiling the post-Apartheid period in South Africa's history when the sampling frame and survey methodology for household surveys was undergoing periodic changes due to the changing geopolitical landscape in the country. This book profiles how different components of error had disproportionate magnitudes in different survey years, including coverage error, sampling error, nonresponse error, measurement error, processing error and adjustment error. The parameters of interest concern the earnings distribution, but despite this outcome of interest, the discussion is generalizable to any question in a random sample survey of households or firms. This book then investigates questionnaire design and item nonresponse by building a response propensity modelfor the employee income question in two South African labour market surveys: the October Household Survey (OHS, 1997-1999) and the Labour Force Survey (LFS, 2000-2003). This time period isolates a period of changing questionnaire design for the income question. Finally, this book is concerned with how to employee income data with a mixture of continuous data, bounded response data and nonresponse. A variable with this mixture of data types is called coarse data. Because the income question consists of two parts -- an initial, exact income question and a bounded income follow-up question -- the resulting statistical distribution of employee income is both continuous and discrete. The book shows researchers how to appropriately deal with coarse income data using multiple imputation. The take-home message from this book is that researchers have a responsibility to treat data quality concerns in a statistically sound manner, rather than making adjustments to public-use data in arbitrary ways, often underpinned by undefensible assumptions about an implicit unobservable loss function in the data. The demonstration of how this can be done provides a replicable concept map with applicable methods that can be utilised in any sample survey.
Celebrating J.D. Murray's Contributions to Mathematical Biology
The Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including: Original research articles focused on new biological insights gained with the help of tools from the mathematical sciences or new mathematical tools and methods with demonstrated applicability to biological investigationsResearch in mathematical biology educationReviewsCommentariesPerspectives, and contributions that discuss issues important to the professionAll contributions are peer-reviewed.
How Data Quality Affects Our Understanding of the Earnings Distribution
This open access book demonstrates how data quality issues affect all surveys and proposes methods that can be utilised to deal with the observable components of survey error in a statistically sound manner. This book begins by profiling the post-Apartheid period in South Africa's history when the sampling frame and survey methodology for household surveys was undergoing periodic changes due to the changing geopolitical landscape in the country. This book profiles how different components of error had disproportionate magnitudes in different survey years, including coverage error, sampling error, nonresponse error, measurement error, processing error and adjustment error. The parameters of interest concern the earnings distribution, but despite this outcome of interest, the discussion is generalizable to any question in a random sample survey of households or firms. This book then investigates questionnaire design and item nonresponse by building a response propensity modelfor the employee income question in two South African labour market surveys: the October Household Survey (OHS, 1997-1999) and the Labour Force Survey (LFS, 2000-2003). This time period isolates a period of changing questionnaire design for the income question. Finally, this book is concerned with how to employee income data with a mixture of continuous data, bounded response data and nonresponse. A variable with this mixture of data types is called coarse data. Because the income question consists of two parts -- an initial, exact income question and a bounded income follow-up question -- the resulting statistical distribution of employee income is both continuous and discrete. The book shows researchers how to appropriately deal with coarse income data using multiple imputation. The take-home message from this book is that researchers have a responsibility to treat data quality concerns in a statistically sound manner, rather than making adjustments to public-use data in arbitrary ways, often underpinned by undefensible assumptions about an implicit unobservable loss function in the data. The demonstration of how this can be done provides a replicable concept map with applicable methods that can be utilised in any sample survey.
Advances in Optimization and Applications
This book constitutes the refereed proceedings of the 13th International Conference on Advances in Optimization and Applications, OPTIMA 2022, held in Petrovac, Montenegro, during September 26-30, 2022. The 13 full papers included in this book were carefully reviewed and selected from 26 submissions. They were organized in topical sections as follows: ​mathematical programming; global optimization; discrete and combinatorial optimization; optimization and data analysis; game theory and mathematical economics; and applications.
Collected Papers in Honor of Yoshihiro Shibata
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here -- on the occasion of his 70th birthday -- are written by world-renowned researchers and celebrate his decades of outstanding achievements.
Schr繹dinger Operators: Eigenvalues and Lieb-Thirring Inequalities
Motion Control: Multi-Faceted Movement in Space, Time and Neurological Impairment
This book addresses the mathematical and the practical aspects of motion implied by advanced control theory. The richness and power of the theory are demonstrated by separate analyses of single-model and multi-modal repertoires, consisting of verities of estimation and control facets. Starting with purely mathematical concepts, specifically, abstract probability and information theories, model control theory is gradually revealed as a rather amazing domain. The mathematical equations, taking essentially simple forms, are exposed as powerful generators of motion. Moreover, seemingly obvious applications of the theory, such as high-performance aircraft control make room for unexpected virtual reality feedback in control of motion for the neurologically impaired.Following the presentation of some historical milestones and mathematical preliminaries, the book is divided into four parts. The first deals with minimal-order models of state estimation and control. The second addresses multi-modal estimation and control, which facilitates the operation of high-performance aircraft in large flight envelopes. The third presents the transition from naturally nonlinear control of movement in obstacle avoidance and object targeting to virtually linear control of movement in the neurologically impaired. The fourth and final part of the book addresses the application of virtual sensory feedback in walking with specific neurological impairment. While the clinical studies reported were all based on a single-model paradigm, a later reflection reveals that, given the variety of neurological symptoms associated with the relevant disorders, a multi-modal approach, as that addressed in the control of high-performance aircraft in a large flight envelope, would be similarly applicable in the treatment of neurological disorders.
Deterministic, Stochastic and Thermodynamic Modelling of Some Interacting Species
This book presents the understanding of how the different forms of regulatory mechanisms, like birth and death, competition, consumption and the like, result in changes in the stability and dynamics of ecological systems. It deals with a profound and unique insight into the mathematical richness of basic ecological models. Organised into eight chapters, the book discusses the models of mathematical ecology, the dynamical models of single-species system in a polluted environment, the dynamical behaviour of different nonautonomous two species systems in a polluted environment, the influence of environmental noise in Gompertzian and logistic growth models, stability behaviour in randomly fluctuating versus deterministic environments of two interacting species, stochastic analysis of a demographic model of urbanization and stability behaviour of a social group by means of loop analysis, thermodynamic criteria of stability and stochastic criteria of stability. The book will be useful tothe researchers and graduate students who wish to pursue research in mathematical ecology.
Index Theory Beyond the Fredholm Case
This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case'.Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.
Bayes Factors for Forensic Decision Analyses with R
Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability--keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics: Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information--scientific evidence--ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.This book would be relevant to students, practitioners, and applied statisticiansinterested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.This book is Open Access.
Classical Numerical Analysis
Numerical Analysis is a broad field, and coming to grips with all of it may seem like a daunting task. This text provides a thorough and comprehensive exposition of all the topics contained in a classical graduate sequence in numerical analysis. With an emphasis on theory and connections with linear algebra and analysis, the book shows all the rigor of numerical analysis. Its high level and exhaustive coverage will prepare students for research in the field and become a valuable reference as they continue their career. Students will appreciate the simple notation, clear assumptions and arguments, as well as the many examples and classroom-tested exercises ranging from simple verification to qualifying exam-level problems. In addition to the many examples with hand calculations, readers will also be able to translate theory into practical computational codes by running sample MATLAB codes as they try out new concepts.
Optimization and Applications
This book constitutes the refereed proceedings of the 13th International Conference on Optimization and Applications, OPTIMA 2022, held in Petrovac, Montenegro, during September 26-30, 2022.The 17 full papers and presented were carefully reviewed and selected from 43 submissions. They were organized into the following as follows: mathematical programming; global optimization; discrete and combinatorial optimization; optimal control; optimization and data analysis; and game theory and mathematical economics.
P-Adic Banach Space Representations
This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces.This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
Quantum Machine Learning and Optimisation in Finance
Learn the principles of quantum machine learning and how to apply themWhile focus is on financial use cases, all the methods and techniques are transferable to other fieldsPurchase of Print or Kindle includes a free eBook in PDFKey Features: - Discover how to solve optimisation problems on quantum computers that can provide a speedup edge over classical methods- Use methods of analogue and digital quantum computing to build powerful generative models- Create the latest algorithms that work on Noisy Intermediate-Scale Quantum (NISQ) computersBook Description: With recent advances in quantum computing technology, we finally reached the era of Noisy Intermediate-Scale Quantum (NISQ) computing. NISQ-era quantum computers are powerful enough to test quantum computing algorithms and solve hard real-world problems faster than classical hardware.Speedup is so important in financial applications, ranging from analysing huge amounts of customer data to high frequency trading. This is where quantum computing can give you the edge. Quantum Machine Learning and Optimisation in Finance shows you how to create hybrid quantum-classical machine learning and optimisation models that can harness the power of NISQ hardware.This book will take you through the real-world productive applications of quantum computing. The book explores the main quantum computing algorithms implementable on existing NISQ devices and highlights a range of financial applications that can benefit from this new quantum computing paradigm.This book will help you be one of the first in the finance industry to use quantum machine learning models to solve classically hard real-world problems. We may have moved past the point of quantum computing supremacy, but our quest for establishing quantum computing advantage has just begun!What You Will Learn: - Train parameterised quantum circuits as generative models that excel on NISQ hardware- Solve hard optimisation problems- Apply quantum boosting to financial applications- Learn how the variational quantum eigensolver and the quantum approximate optimisation algorithms work- Analyse the latest algorithms from quantum kernels to quantum semidefinite programming- Apply quantum neural networks to credit approvalsWho this book is for: This book is for Quants and developers, data scientists, researchers, and students in quantitative finance. Although the focus is on financial use cases, all the methods and techniques are transferable to other areas.Table of Contents- The Principles of Quantum Mechanics- Adiabatic Quantum Computing- Quadratic Unconstrained Binary Optimisation- Quantum Boosting- Quantum Boltzmann Machine- Qubits and Quantum Logic Gates- Parameterised Quantum Circuits and Data Encoding- Quantum Neural Network- Quantum Circuit Born Machine- Variational Quantum Eigensolver- Quantum Approximate Optimisation Algorithm- The Power of Parameterised Quantum Circuits- Looking Ahead- Bibliography
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.
Maximum-Entropy Sampling
Overview.- Notation.- The problem and basic properties.- Branch-and-bound.- Upper bounds.- Environmental monitoring.- Opportunities.- Basic formulae and inequalities.- References.- Index.
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).
Multivariate Statistical Methods
This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.
Sharpening Mathematical Analysis Skills
This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research.The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren't commonly seen in regular textbooks.
Special Functions of Fractional Calculus: Applications to Diffusion and Random Search Processes
This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Stochastic Partial Differential Equations with Additive Gaussian Noise - Analysis and Inference
The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.
Partial Differential Inequalities with Nonlinear Convolution Terms
This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting.This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the presentwork appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.
Statistics All-In-One for Dummies
The odds-on best way to master stats. Statistics All-in-One For Dummies is packed with lessons, examples, and practice problems to help you slay your stats course. Develop confidence and understanding in statistics with easy-to-understand (even fun) explanations of key concepts. Plus, you'll get access to online chapter quizzes and other resources that will turn you into a stats master. This book teaches you how to interpret graphs, determine probability, critique data, and so much more. Written by an expert author and serious statistics nerd, Statistics AIO For Dummies explains everything in terms anyone can understand. Get a grasp of basic statistics concepts required in every statistics course Clear up the process of interpreting graphs, understanding polls, and analyzing data Master correlation, regression, and other data analysis tools Score higher on stats tests and get a better grade in your high school or college classStatistics All-in-One For Dummies follows the curriculum of intro college statistics courses (including AP Stats!) so you can learn everything you need to know to get the grade you need--the Dummies way.
Combinatorial, Linear, Integer and Nonlinear Optimization Apps
This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and relatedmathematics.
Statistical and Multivariate Analysis in Material Science
The present work is an introductory text in statistics, addressed to researchers and students in the field of material science. It aims to give the readers basic knowledge on how statistical reasoning is exploitable in this field, improving their knowledge of statistical tools.
An Introduction to Bayesian Inference, Methods and Computation
These lecture notes provide a rapid, accessible introduction to Bayesian statistical methods. The course covers the fundamental philosophy and principles of Bayesian inference, including the reasoning behind the prior/likelihood model construction synonymous with Bayesian methods, through to advanced topics such as nonparametrics, Gaussian processes and latent factor models. These advanced modelling techniques can easily be applied using computer code samples written in Python and Stan which are integrated into the main text. Importantly, the reader will learn methods for assessing model fit, and to choose between rival modelling approaches.
Applied Statistics in Social Sciences
A comprehensive account of different univariate and multivariate discrete and continuous distributions, the work comprises applications in economics and different financial problems and other scenarios in which these recently developed statistical models have been applied.
Robust Latent Feature Learning for Incomplete Big Data
Incomplete big data are frequently encountered in many industrial applications, such as recommender systems, the Internet of Things, intelligent transportation, cloud computing, and so on. It is of great significance to analyze them for mining rich and valuable knowledge and patterns. Latent feature analysis (LFA) is one of the most popular representation learning methods tailored for incomplete big data due to its high accuracy, computational efficiency, and ease of scalability. The crux of analyzing incomplete big data lies in addressing the uncertainty problem caused by their incomplete characteristics. However, existing LFA methods do not fully consider such uncertainty. In this book, the author introduces several robust latent feature learning methods to address such uncertainty for effectively and efficiently analyzing incomplete big data, including robust latent feature learning based on smooth L1-norm, improving robustness of latent feature learning using L1-norm, improving robustness of latent feature learning using double-space, data-characteristic-aware latent feature learning, posterior-neighborhood-regularized latent feature learning, and generalized deep latent feature learning. Readers can obtain an overview of the challenges of analyzing incomplete big data and how to employ latent feature learning to build a robust model to analyze incomplete big data. In addition, this book provides several algorithms and real application cases, which can help students, researchers, and professionals easily build their models to analyze incomplete big data.
Continuous Distributions in Engineering and the Applied Sciences -- Part I
Continuous Distributions in Engineering and the Applied Sciences -- Part II
This is the second part of our book on continuous statistical distributions. It covers inverse-Gaussian, Birnbaum-Saunders, Pareto, Laplace, central ����簡, ����, ����, Weibull, Rayleigh, Maxwell, and extreme value distributions. Important properties of these distribution are documented, and most common practical applications are discussed. This book can be used as a reference material for graduate courses in engineering statistics, mathematical statistics, and econometrics. Professionals and practitioners working in various fields will also find some of the chapters to be useful.Although an extensive literature exists on each of these distributions, we were forced to limit the size of each chapter and the number of references given at the end due to the publishing plan of this book that limits its size. Nevertheless, we gratefully acknowledge the contribution of all those authors whose names have been left out.Some knowledge in introductoryalgebra and college calculus is assumed throughout the book. Integration is extensively used in several chapters, and many results discussed in Part I (Chapters 1 to 9) of our book are used in this volume.Chapter 10 is on Inverse Gaussian distribution and its extensions. The Birnbaum-Saunders distribution and its extensions along with applications in actuarial sciences is discussed in Chapter 11. Chapter 12 discusses Pareto distribution and its extensions. The Laplace distribution and its applications in navigational errors is discussed in the next chapter. This is followed by central chi-squared distribution and its applications in statistical inference, bioinformatics and genomics. Chapter 15 discusses Student's ���� distribution, its extensions and applications in statistical inference. The ���� distribution and its applications in statistical inference appears next. Chapter 17 is on Weibull distribution and its applications in geology and reliability engineering. Next two chapters are on Rayleigh and Maxwell distributions and its applications in communications, wind energy modeling, kinetic gas theory, nuclear and thermal engineering, and physical chemistry. The last chapter is on Gumbel distribution, its applications in the law of rare exceedances.Suggestions for improvement are welcome. Please send them to rajan.chattamvelli@vit.ac.in.
Functional Analysis Tools for Practical Use in Sciences and Engineering
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don't have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, whichintroduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don't need to delve deep into the underlying theory.
The Significance Test Controversy Revisited
This book explains the misuses and abuses of Null Hypothesis Significance Tests, which are reconsidered in light of Jeffreys' Bayesian concept of the role of statistical inference, in experimental investigations. Minimizing the technical aspects, the studies focuses mainly on methodological contributions. The first part of the book gives an overview of the major approaches to statistical testing and an enlightening discussion of the philosophies of Fisher, Neyman-Pearson and Jeffrey. The conceptual and methodological implications of current practices of reporting effect sizes and confidence intervals are also examined and challenged. This sheds new light on the "significance testing controversy" and provides an appropriate Bayesian framework for a comprehensive approach to the analysis and interpretation of experimental data. The second part of the book provides concrete Bayesian routine procedures that bypass common misuses of significance testing and arereadily applicable in a wide range of real applications. This approach addresses the need for objective reporting of experimental data, that is acceptable to the scientific community. This is emphasized by the name fiducial (from the Latin fiducia = confidence). The fiducial Bayesian procedures provide the reader with a real opportunity to think sensibly about problems of statistical inference. This book prepares students and researchers to critically read statistical analyses reported in the literature and equips them with an appropriate alternative to the use of significance testing.
Applied Categorical and Count Data Analysis
This second edition explains how to perform the statistical analysis of discrete data, including categorical and count outcomes. It covers classic concepts and popular topics, such as logistic regression models, along with modern areas including models for zero-modified count outcomes.
Large Deviations for Markov Chains
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Mathematical Problem Factories
A problem factory consists of a traditional mathematical analysis of a type of problem that describes many, ideally all, ways that the problems of that type can be cast in a fashion that allows teachers or parents to generate problems for enrichment exercises, tests, and classwork. Some problem factories are easier than others for a teacher or parent to apply, so we also include banks of example problems for users. This text goes through the definition of a problem factory in detail and works through many examples of problem factories. It gives banks of questions generated using each of the examples of problem factories, both the easy ones and the hard ones. This text looks at sequence extension problems (what number comes next?), basic analytic geometry, problems on whole numbers, diagrammatic representations of systems of equations, domino tiling puzzles, and puzzles based on combinatorial graphs. The final chapter previews other possible problem factories.
Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak-Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.
Markov Chains on Metric Spaces
This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes. The book can serve as the core for a semester- or year-long graduate course in probability theory withan emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.
Fractional Sobolev Spaces and Inequalities
The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.
Mathematical Theory of Uniformity and Its Applications in Ecology and Chaos
This book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory performs better than other indices such as entropy and Lyapunov exponent in chaos measurement by numerous examples. This book develops a new mathematical tool for studying chaos so it will be appealing to students and researchers interested in theory of chaos. It also has potential applications in various fields such as Engineering, Forestry and Ecology.
Introducing Financial Mathematics
This book seeks to replace existing books with a more rigorous stand-alone text that covers fewer examples but with more proofs, and also provides example computer programs, mainly in Octave/MATLAB but also as spreadsheets and Macsyma scripts, with which students may experiment on real data.
Stochastic Modelling of Big Data in Finance
This book provides a rigorous overview and exploration of stochastic modelling of big data in finance (BDF). The book describes various stochastic models, including multivariate models, to deal with big data in finance. This includes data in high-frequency and algorithmic trading, specifically in limit order books (LOB).
Synthetic Aperture Radar (Sar) Data Applications
This carefully curated volume presents an in-depth, state-of-the-art discussion on many applications of Synthetic Aperture Radar (SAR). Integrating interdisciplinary sciences, the book features novel ideas, quantitative methods, and research results, promising to advance computational practices and technologies within the academic and industrial communities. SAR applications employ diverse and often complex computational methods rooted in machine learning, estimation, statistical learning, inversion models, and empirical models. Current and emerging applications of SAR data for earth observation, object detection and recognition, change detection, navigation, and interference mitigation are highlighted. Cutting edge methods, with particular emphasis on machine learning, are included. Contemporary deep learning models in object detection and recognition in SAR imagery with corresponding feature extraction and training schemes are considered. State-of-the-art neural network architectures in SAR-aided navigation are compared and discussed further. Advanced empirical and machine learning models in retrieving land and ocean information -- wind, wave, soil conditions, among others, are also included.
