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This unique volume is an introduction for computer scientists, including a formal study of theoretical algorithms for Big Data applications, which allows them to work on such algorithms in the future. It also serves as a useful reference guide for the general computer science population, providing a comprehensive overview of the fascinating world of such algorithms.
Calculus for the Life Sciences: A Modeling Approach by James L. Cornette; Ralph A. AckermanIn our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included.
Numerical Analysis : Theory and Experiments by Brian SuttonThis textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems--interpolation, integration, linear systems, zero finding, and differential equations--are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones, a dual emphasis on theory and experimentation, the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects, and many examples and exercises.
Model Identification and Data Analysis by Sergio BittantiThis book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control.
Written for graduate students, this textbook offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University.
Reversible Steganography and Authentication Via Transform Encoding by Jyotsna Kumar MandalThis book focuses on reversible steganography and authentication via transform encoding, fully discussing in detail the reversibility computation of six transformation techniques: DFT, DCT, wavelets, Z, binomial and grouplet, as well as chaos-based authentication. The book also describes algorithmic approaches based on all transformations along with implementation details and results. Further topics include embedding and extraction into the spatial domain, tuning using GA-based approaches and embedding into imaginary coefficients of the Z domain.
Riemann Problems and Jupyter Solutions by David I. Ketcheson; Randall J. LeVeque; Mauricio J. del RazoThis book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. The solution of the Riemann problem captures essential information about these models and is the key ingredient in modern numerical methods for their solution. This book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application.
An Introduction to Proofs with Set Theory by Daniel Ashlock; Colin LeeThis text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
Poisson Line Cox Process : Foundations and Applications to Vehicular Networks by Harpreet S. Dhillon; Vishnu Vardhan ChetlurThis book provides a comprehensive treatment of the Poisson line Cox process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a Poisson line process (PLP) as per an independent Poisson point process (PPP). For vehicular applications, one can imagine the layout of the road network as a PLP and the vehicles on the roads as the points of the PLCP. First, a brief historical account of the evolution of the theory of PLP is provided to familiarize readers with the seminal contributions in this area. In order to provide a self-contained treatment of this topic, the construction and key fundamental properties of both PLP and PLCP are discussed in detail. The rest of the book is devoted to the applications of these models to a variety of wireless networks, including vehicular communication networks and localization networks. Specifically, modeling the locations of vehicular nodes and roadside units (RSUs) using PLCP, the signal-to-interference-plus-noise ratio (SINR)-based coverage analysis is presented for both ad hoc and cellular network models. For a similar setting, the load on the cellular macro base stations (MBSs) and RSUs in a vehicular network is also characterized analytically. For the localization networks, PLP is used to model blockages, which is shown to facilitate the characterization of asymptotic blind spot probability in a localization application. Finally, the path distance characteristics for a special case of PLCP are analyzed, which can be leveraged to answer critical questions in the areas of transportation networks and urban planning. The book is concluded with concrete suggestions on future directions of research. Based largely on the original research of the authors, this is the first book that specifically focuses on the self-contained mathematical treatment of the PLCP. The ideal audience of this book is graduate students as well as researchers in academia and industry who are familiar with probability theory, have some exposure to point processes, and are interested in the field of stochastic geometry and vehicular networks. Given the diverse backgrounds of the potential readers, the focus has been on providing an accessible and pedagogical treatment of this topic by consciously avoiding the measure theoretic details without compromising mathematical rigor.
Statistical Analysis of Network Data with R by Eric D. Kolaczyk; Gábor CsárdiThe new edition of this book provides an easily accessible introduction to the statistical analysis of network data using R. It has been fully revised and can be used as a stand-alone resource in which multiple R packages are used to illustrate how to conduct a wide range of network analyses, from basic manipulation and visualization, to summary and characterization, to modeling of network data. The central package is igraph, which provides extensive capabilities for studying network graphs in R.
Lie Symmetry Analysis of Fractional Differential Equations by Mir Sajjad Hashemi; Dumitru BaleanuThe trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming by John T. BettsThis second edition of the popular text by John Betts incorporates lots of new material while maintaining the concise and focused presentation of the original edition. The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book. The relevant background in nonlinear programming methods that exploit sparse matrix technology is presented, along with description of discretization techniques for solving differential-algebraic equations.
Optimal Control in Bioprocesses : Pontryagin's Maximum Principle in Practice by Jérôme Harmand; Claude Lobry; Alain Rapaport; Tewfik SariOptimal control is a branch of applied mathematics that engineers need in order to optimize the operation of systems and production processes. Its application to concrete examples is often considered to be difficult because it requires a large investment to master its subtleties. The purpose of Optimal Control in Bioprocesses is to provide a pedagogical perspective on the foundations of the theory and to support the reader in its application, first by using academic examples and then by using concrete examples in biotechnology. The book is thus divided into two parts, the first of which outlines the essential definitions and concepts necessary for the understanding of Pontryagin's maximum principle - or PMP - while the second exposes applications specific to the world of bioprocesses. This book is unique in that it focuses on the arguments and geometric interpretations of the trajectories provided by the application of PMP.
Dutch Book Arguments by Richard Franklin PettigrewOur beliefs come in degrees. I'm 70 per cent confident it will rain tomorrow, and 0.001 per cent sure my lottery ticket will win. What's more, we think these degrees of belief should abide by certain principles if they are to be rational. For instance, you shouldn't believe that a person's taller than 6 ft more strongly than you believe that they're taller than 5 ft, since the former entails the latter. In Dutch Book arguments, we try to establish the principles of rationality for degrees of belief by appealing to their role in guiding decisions. In particular, we show that degrees of belief that don't satisfy the principles will always guide action in some way that is bad or undesirable.
Relations : Concrete, Abstract, and Applied : An Introduction by Herbert TothThis book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics). This book is a new - and the first of its kind - compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.
Statistics for HCI : Making Sense of Quantitative Data by Alan DixMany people find statistics confusing, and perhaps even more confusing given recent publicity about problems with traditional p-values and alternative statistical techniques including confidence intervals and Bayesian statistics. This book aims to help readers navigate this morass: to understand the debates, to be able to read and assess other people's statistical reports, and make appropriate choices when designing and analysing their own experiments, empirical studies, and other forms of quantitative data gathering.
p-adic Numbers : An Introduction by Fernando Q. GouvêaThere are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related to a chosen prime number p. They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students; this book provides an entryway to the subject for students with an undergraduate mathematics education.
The Bellman Function Technique in Harmonic Analysis by Vasily Vasyunin; Alexander VolbergThe Bellman function, a powerful tool originating in control theory, can be used successfully in a large class of difficult harmonic analysis problems and has produced some notable results over the last thirty years. This book by two leading experts is the first devoted to the Bellman function method and its applications to various topics in probability and harmonic analysis. Beginning with basic concepts, the theory is introduced step-by-step starting with many examples of gradually increasing sophistication, culminating with Calderón–Zygmund operators and end-point estimates.
An Introduction to Metric Spaces by Dhananjay Gopal; Aniruddha Deshmukh; Abhay S. Ranadive; Shubham YadavThis book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications. Some of the noteworthy features of this book include · Diagrammatic illustrations that encourage readers to think geometrically · Focus on systematic strategy to generate ideas for the proofs of theorems · A wealth of remarks, observations along with a variety of exercises · Historical notes and brief biographies appearing throughout the text
Geometric Algebra Applications, Vol. II : Robot Modelling and Control by Eduardo Bayro-CorrochanoThe goal of Geometric Algebra Applications, Vol. II is to present a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford, or geometric algebra. By treating a wide spectrum of problems in a common language, this volume offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with robotics.
Bandit Algorithms by Tor Lattimore; Csaba SzepesvariThis comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.
Partial Differential Equations : Classical Theory With a Modern Touch by A. K. NandakumaranSuitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics - Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.
An Introduction to Numerical Methods for the Physical Sciences by Colm T. WhelanThere is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.
Applied Structural Equation Modeling Using AMOS : Basic to Advanced Techniques by Joel E. CollierThis is an essential how-to guide on the application of structural equation modeling (SEM) techniques with the AMOS software, focusing on the practical applications of both simple and advanced topics. Written in an easy-to-understand conversational style, the book covers everything from data collection and screening to confirmatory factor analysis, structural model analysis, mediation, moderation, and more advanced topics such as mixture modeling, censored date, and non-recursive models. Through step-by-step instructions, screen shots, and suggested guidelines for reporting, Collier cuts through abstract definitional perspectives to give insight on how to actually run analysis. Unlike other SEM books, the examples used will often start in SPSS and then transition to AMOS so that the reader can have full confidence in running the analysis from beginning to end. Best practices are also included on topics like how to determine if your SEM model is formative or reflective, making it not just an explanation of SEM topics, but a guide for researchers on how to develop a strong methodology while studying their respective phenomenon of interest. With a focus on practical applications of both basic and advanced topics, and with detailed work-through examples throughout, this book is ideal for experienced researchers and beginners across the behavioral and social sciences.
Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman (Editor)The philosophy of mathematics can be traced back in time to the dawn of mathematics itself. The axiomatization of Euclid in "The Elements" did not hinder innovations in mathematical practice to develop outside the realm of the deductive method. In fact the history of mathematics shows a rich tapestry of practice that include visual, algorithmic, experimental, probabilistic and computational approaches. However the philosophy of mathematics as argued by Imre Lakatos suggests that the innovations and impasses in mathematical practice have remained more or less unacknowledged in philosophy.