Mathematical Modeling in Biology
The aim of this textbook, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods.
Integer Sequences
This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.
An Introduction to Continuous-Time Stochastic Processes
This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields.Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the It繫 Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations.An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.
Handbook of Graphs and Networks in People Analytics
Starting with an overview of the origins of graph theory and its current applications in the social sciences, the book proceeds to give in-depth technical instruction on how to construct and store graphs from data, how to visualize those graphs compellingly and how to convert common data structures into graph-friendly form.
Important Applications of the Behrens-Fisher Statistic and the False Discovery Rate
This book discusses important applications of the Behrens-Fisher statistic and the False Discovery Rate (FDR). Covered applications include ANOVA and MANOVA under potentially non-normal errors and heteroscedasticity; and an intuitive method of analyzing s x r contingency tables when the column variable is ordinal. This book also explores the novel possibility that these applications may be deemed nonparametric.
Linear Mixed Models
The third edition provides a comprehensive update of the available tools for fitting linear mixed-effects models in the newest versions of SAS, SPSS, R, Stata, and HLM. There is a focus on new tools for visualization of results and interpretation. New conceptual and theoretical developments in mixed-effects modeling have been included
Statistical Approaches in Oncology Clinical Development
Oncology is a rapidly developing area in medical science. A significant investment in terms of costs, resources and time is required for oncology drug development. Understanding of the challenges at all stages is vital for a successful drug launching. The purpose of this book is to provide an overview and practical solutions to some of these cha
Leibniz Algebras
Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations.
Population Genomics with R
This book provides a reference on modern statistical and data exploration methods for the population genomics. It covers a wide range of methods within the R computing environment. The readers will be assumed to have basic knowledge in population genetics, computational methods, and statistics, although some basic principles will be explained.
Statistical Learning Using Neural Networks
Statistical Learning using Neural Networks: A Guide for Statisticians and Data Scientists with Python introduces artificial neural networks starting from the basics and increasingly demanding more effort from readers, who can learn the theory and its applications in statistical methods with concrete Python code examples. It presents a wide range of widely used statistical methodologies, applied in several research areas with Python code examples, which are available online. It is suitable for scientists and developers as well as graduate students.Key Features: Discusses applications in several research areas Covers a wide range of widely used statistical methodologies Includes Python code examples Gives numerous neural network models This book covers fundamental concepts on Neural Networks including Multivariate Statistics Neural Networks, Regression Neural Network Models, Survival Analysis Networks, Time Series Forecasting Networks, Control Chart Networks, and Statistical Inference Results. This book is suitable for both teaching and research. It introduces neural networks and is a guide for outsiders of academia working in data mining and artificial intelligence (AI). This book brings together data analysis from statistics to computer science using neural networks.
Classical Vector Algebra
Vector algebra discussed in this book addresses primarily the vectors in 3-dimensional Euclidian space, and more specifically in Cartesian R^3 space.The book is intended to be a comprehensive introduction to vector algebra in 3-dimensional Euclidean space, and its application to analytic geometry.
Applied Calculus of Variations for Engineers, Third Edition
This third edition extends the focus of the book to academia to also support variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.
Introductory Mathematical Analysis for Quantitative Finance
This textbook is designed to enable students with little knowledge of mathematical analysis to engage with modern quantitative finance. The exposition of the topics is concise as chapters are intended to represent a preliminary contact with the mathematical concepts used in QF.
Non-Algorithmic Encryption
This report describe encryp-tion in a wider class of computation, as compared to ordinary clas-sic encryption algorithms. The security of the pro-posed systems are investig-ated, and it is shown, that the non-al-gorithmic ciphers have many advant-ageous properties. The theoretical foundation is presented with many con-venient refer-ences. The report also contain a discussion of the relev-ance, of the theory, in the real world. Practical issues, of cipher design, are discussed, and the Reader should easily be able to design a secure cipher; adopted to any local requirements or restrictions.
Differential Equations and Their Applications
This textbook is a unique blend of the theory of differential equations and their exciting application to --real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting '-real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equations are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting --Disciples at Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modern forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we try to determine whether tightly sealed drums filled with concentrated waste material will crack upon impact with the ocean floor. In this section we also describe several tricks for obtaining informa- tion about solutions of a differential equation that cannot be solved explicitly.
Modelling with Ordinary Differential Equations
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available
Essentials of Statistics for Scientists and Technologists
Statistics is of ever-increasing importance in Science and Technology and this book presents the essentials of the subject in a form suitable either as the basis of a course of lectures or to be read and/or used on its own. It assumes very little in the way of mathematical knowledge-just the ability to substitute numerically in a few simple formulae. However, some mathematical proofs are outlined or given in full to illustrate the derivation of the subject; these can be omitted without loss of understanding. The book does aim at making clear the scope and nature of those essential tests and methods that a scientist or technologist is likely to need; to this end each chapter has been divided into sections with their own subheadings and some effort has been made to make the text unambiguous (if any reader finds a misleading point anywhere I hope he will write to me about it). Also with this aim in view, the equality of probability to proportion of population is stated early, then the normal distribution and the taking of samples is discussed. This occupies the first five chapters. With the principles of these chapters understood, the student can immediately learn the significance tests of Chapter 6 and, if he needs it, the analysis of variance of Chapter 7. For some scientists this will be most of what they need. However, they will be in a position to read and/or use the remaining chapters without undue difficulty.
Geometric Properties for Parabolic and Elliptic Pde's
This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.
Probability Theory
Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub- ject, generally attributed to investigations by the renowned french mathe- matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure- theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefi- nite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome.
Waves in Flows
This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school "Waves in Flows", held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave-current interactionsWater-wave problemsGravity wave propagationFlow-acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Generalized B*-Algebras and Applications
1. Introduction.- 2. A Spectral Theory for Locally Convex Algebras.- 3. Generalized B*-Algebras: Functional Representation Theory.- 4. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.- 5. Extended C*-Algebras and Extended W*-Algebras.- 6. Generalized B*-Algebras: Unbounded *-Representation Theory.- 7. Applications I: Miscellanea.- 8. Applications II: Tensor Products.
Structures of Domination in Graphs
This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms.The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.
The Secret Lives of Numbers
We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning, usage, and connotation in the larger world. The Secret Lives of Numbers takes readers on a journey through integers, considering their numerological assignments as well as their significance beyond mathematics and in the realm of popular culture. Of course we all know that the number 13 carries a certain value of unluckiness with it. The phobia of the number is called Triskaidekaphobia; Franklin Delano Roosevelt was known to invite and disinvite guests to parties to avoid having 13 people in attendance; high-rise buildings often skip the 13th floor out of superstition. There are many explanations as to how the number 13 received this negative honor, but from a mathematical point of view, the number 13 is also the smallest prime number that when its digits are reversed is also a prime number. It is honored with a place among the Fibonacci numbers and integral Pythagorean triples, as well as many other interesting and lesser-known occurrences. In The Secret Lives of Numbers, popular mathematician Alfred S. Posamentier provides short and engaging mini-biographies of more than 100 numbers, starting with 1 and featuring some especially interesting numbers -like 6,174, a number with most unusual properties -to provide readers with a more comprehensive picture of the lives of numbers both mathematically and socially. ,
Topics in Global Real Analytic Geometry
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert's problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert's problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer. In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. Duringthe redaction some proofs have been simplified with respect to the original ones.
The Number-System of Algebra
I THEORETICAL1. THE POSITIVE INTEGER, AND THE LAWS WHICH REGULATE THE ADDITION AND MULTIPLICATION OF POSITIVE INTEGERS.2. SUBTRACTION AND THE NEGATIVE INTEGER.3. DIVISION AND THE FRACTION.4. THE IRRATIONAL5. THE IMAGINARY COMPLEX NUMBERS.6. GRAPHICAL REPRESENTATION OF NUMBERS. THE VARIABLE.7. THE FUNDAMENTAL THEOREM OF ALGEBRA.8. INFINITE SERIES.9. THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS UNDETERMINED COEFFICIENTS INVOLUTION AND EVOLUTION. THE BINOMIAL THEOREM HISTORICAL 10. PRIMITIVE NUMERALS.11. HISTORIC SYSTEMS OF NOTATION.12. THE FRACTION.13. ORIGIN OF THE IRRATIONAL14. ORIGIN OF THE NEGATIVE AND THE IMAGINARY THE EQUATION.15. ACCEPTANCE OF THE NEGATIVE, THE GENERAL IRRATIONAL, AND THE IMAGINARY AS NUMBERS.16. RECOGNITION OF THE PURELY SYMBOLIC CHARACTER OF ALGEBRA. QUATERNIONS. AUSDEHNUNGSLEHRE.
On The Study and Difficulties of Mathematics
I. Introductory Remarks on the Nature and Objects of MathematicsII. On Arithmetical NotationIII. Elementary Rules of ArithmeticIV. Arithmetical FractionsV. Decimal FractionsVI. Algebraical Notation and PrinciplesVII. Elementary Rules of AlgebraVIII. Equations of the First DegreeIX. On the Negative Sign, etcX. Equations of the Second DegreeXI. On Roots in General, and LogarithmsXII. On the Study of AlgebraXIII. On the Definitions of GeometryXIV. On Geometrical ReasoningXV. On AxiomsXVI. On ProportionXVII. Application of Algebra to the Measurement of Lines, Angles, Proportion of Figures, and Surfaces
Predicting Pandemics in a Globally Connected World, Volume 1
This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system. Chapters in this volume address these items, as well as offer perspectives for the future.
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero.The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space.We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve inducesthe same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists.In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the 矇tale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Principles of Biostatistics
Principles of Biostatistics, Third Edition is a concepts-based introduction to statistical procedures that prepares public health, medical, and life sciences students to conduct and evaluate research. With an engaging writing style and helpful graphics, the emphasis is on concepts over formulas or rote memorization. Throughout the book, the authors use practical, interesting examples with real data to bring the material to life. Thoroughly revised and updated, this third edition includes a new chapter introducing the basic principles of Study Design, as well as new sections on sample size calculations for two-sample tests on means and proportions, the Kruskal-Wallis test, and the Cox proportional hazards model.Key Features: Includes a new chapter on the basic principles of study design Additional review exercises have been added to each chapter Datasets and Stata and R code are available on the book's website The book is divided into three parts. The first five chapters deal with collections of numbers and ways in which to summarize, explore, and explain them. The next two chapters focus on probability and introduce the tools needed for the subsequent investigation of uncertainty. It is only in the eighth chapter and thereafter that the authors distinguish between populations and samples and begin to investigate the inherent variability introduced by sampling, thus progressing to inference. Postponing the slightly more difficult concepts until a solid foundation has been established makes it easier for the reader to comprehend them.
An Elementary Treatise on Fourier Series
CHAPTER I. IntroductionCHAPTER II. Development in Trigonometric SeriesCHAPTER III. Convergence of Fourier's SeriesCHAPTER IV. Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's SeriesCHAPTER V. Zonal HarmonicsCHAPTER VI. Spherical HarmonicsCHAPTER VII. Cylindrical Harmonics (Bessel's Functions)CHAPTER VIII. Laplace's Equation in Curvilinear Co]ordinates. Ellipsoidal HarmonicCHAPTER IX. Historical Summary
A Mathematician's Apology
A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content and gives the layman an insight into the mind of a working mathematician. It is an attempt to justify and explain, pure mathematics. One of the main themes of the book is the beauty that mathematics possesses, which Hardy compares to painting and poetry.G. H. Hardy (7 Feb 1877 - 1 Dec 1947) was an eccentric British mathematician who worked extensively in mathematical analysis and analytical number theory alongside J.E Littlewood. He is perhaps even better known for his adoption and mentoring of the self-taught Indian mathematical genius, Srinivasa Ramanujan. Hardy wanted his work to be referred to as pure mathematics rather than applied mathematics. In his view, mathematics was not something to be used in social destruction and to fulfill political purposes.
Cherlin's Conjecture for Finite Primitive Binary Permutation Groups
This book gives a proof of Cherlin's conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan's theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin's conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest toa wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers
Ramified Surfaces
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon's program of braid monodromy factorization.By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.
Engineering Statistics
This book presents a concise and focused introduction to engineering statistics, emphasizing topics and concepts that a practicing engineer is mostly likely to use: the display of data, confidence intervals, hypothesis testing, fitting straight lines to data, and designing experiments to find the impact of process changes on a system or its output. It introduces the language of statistics, derives equations with sufficient detail so that there is no mystery as to how they came about, makes extensive use of tables to collect and summarize important formulas and concepts, and utilizes enhanced graphics that are packed with visual information to illustrate the meaning of the equations and their usage. The book can be used as an introduction to the subject, to refresh one's knowledge of engineering statistics, to complement course materials, as a study guide, and to provide a resource in laboratories where data acquisition and analysis are performed.Created specifically forthe book are 16 interactive graphics (IGs) that can be used to replicate all numerical calculations appearing in the book and many of its figures, numerically evaluate all formulas appearing in tables, solve all exercises, and determine probabilities and critical values for commonly used probability distributions. After downloading a free program, the IGs are ready to use and are self-explanatory in the context of the material.
Predictive Analytics in System Reliability
This book provides engineers and researchers knowledge to help them in system reliability analysis using machine learning, artificial intelligence, big data, genetic algorithm, information theory, multi-criteria decision making, and other techniques. It will also be useful to students learning reliability engineering.The book brings readers up to date with how system reliability relates to the latest techniques of AI, big data, genetic algorithm, information theory, and multi-criteria decision making and points toward future developments in the subject.
Elements and Relations
This book develops the core proposition that systems theory is an attempt to construct an "exact and scientific metaphysics," a system of general ideas central to science that can be expressed mathematically. Collectively, these ideas would constitute a nonreductionist "theory of everything" unlike what is being sought in physics. Inherently transdisciplinary, systems theory offers ideas and methods that are relevant to all of the sciences and also to professional fields such as systems engineering, public policy, business, and social work. To demonstrate the generality and importance of the systems project, the book structures its content in three parts: Essay, Notes, and Commentary. The Essay section is a short distillation of systems ideas that illuminate the problems that many types of systems face. Commentary explains systems thinking, its value, and its relation to mainstream scientific knowledge. It shows how systems ideas revise our understanding of science and how they impact our views on religion, politics, and history. Finally, Notes contains all the mathematics in the book, as well as scientific, philosophical, and poetic content that is accessible to readers without a strong mathematical background. Elements and Relations is intended for researchers and students in the systems (complexity) field as well as related fields of social science modeling, systems biology and ecology, and cognitive science. It can be used as a textbook in systems courses at the undergraduate or graduate level and for STEM education. As much of the book does not require a background in mathematics, it is also suitable for general readers in the natural and social sciences as well as in the humanities, especially philosophy.
Geometry and Its Applications
This unique textbook combines traditional geometry with current ideas to present a contemporary approach that is grounded in real-world applications. It balances introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes.
A Topology of Mind
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: -The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes. - Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. - Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
Comparative Genomics
This book constitutes the refereed proceedings of the 19th Annual RECOMB Satellite Workshop on Comparative Genomics, RECOMB-CG which took place in La Jolla, USA, during May 20-21, 2022. The 18 full papers included in this book were carefully reviewed and selected from 28 submissions. The papers were organized in topical sections on evolution; phylogenetics; homology and reconciliation; genome rearrangements; metagenomics; and genomic sequencing.
Markov Renewal and Piecewise Deterministic Processes
This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous: insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.
Characterizing Groupoid C*-Algebras of Non-Hausdorff ?tale Groupoids
This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian-Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian-Renault theory toa much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
Analysis at Large
On the joint spectral radius (E. Breuillard).- The failure of the fractal uncertainty principle for the Walsh-Fourier transform (C. Demeter).- The continuous formulation of shallow neural networks as Wasserstein-type gradient flows (X. Fern獺ndez-Real).- On the Origins, Nature and Impact of Bourgain's Discretized Sum-Product Theorem (A. Gamburd).- Cartan Covers and Doubling Bernstein Type Inequalities on Analytic Subsets of C2 (M. Goldstein).- A Weighted Prekopa-Leindler inequality and sumsets with quasicubes (B. Green).- Equidistribution of affine random walks on some nilmanifolds (E. Lindenstrauss).- Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrodinger operators with smooth potentials (S. Jitomirskaya).- The slicing problem by Bourgain (B. Klartag).- On the work of Jean Bourgain in nonlinear dispersive equations (E. Kenig).- On Trace sets of restricted continued fraction semigroups (A. Kontorovich).- Polynomial Equations in Subgroups and Applications (V. Konyagin).- Exponential sums, twisted multiplicativity and moments (E. Kowalski).- The ternary Goldbach problem with a missing digit and other primes of special types (Th. Rassias).- A note on harmonious sets (Y. Franc cois Meyer).- On the multiplicative group generated by two primes in Z/QZ (P. Varju).
