On the Modified Caputo’s Derivative Operator
Doctoral Thesis / Dissertation from the year 2022 in the subject Mathematics - Analysis, grade: 4.00, language: English, abstract: The main subject of this study coincides with the recently adapted methodology in the theory of univalent functions via applications of fractional calculus. The Caputo's definition of fractional derivative of order has not been obviously applied in the field. However, it plays a vital role in other areas like physics and engineering due to its simple restrictions compared to Liouville's integral operator. By modifying the Caputo's derivative operator, a new modified Caputo's operator is defined in this book. Consequently, new subclasses of analytic functions are introduced, and basic properties, such as distortion theorems, extremal functions, coefficient bounds, the integral transform, superordination and subordination results are discussed. The radii of basic well known properties (Univalency, Starlikeness, Convexity) are also obtained for the new subclasses. Moreover, some results of the modified Hadamard product (convolution) are provided by applying the famous Cauchy-Schwartz inequality. In order to expand the application of the modified Caputo's operator, two new subclasses of analytic p-valent functions are introduced and investigated through the concepts of neighbourhood and inclusion relations. Further, the definition of Univalency with respect to 1 together with subordination are used to solve a sharp functional of Fekete-Szeg繹 problem. Moreover, some interesting results related to Hankel determinant are obtained.
Statistical Methods Applied to Education
In this book, Harold Ordway Rugg explores the use of statistical methods in education. His clear and concise explanations make it an accessible resource for educators and researchers who want to improve their understanding of the subject.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.
A Course in Mathematical Analysis, Volume 2, part 2
This advanced mathematics textbook covers a range of topics including complex analysis, Fourier analysis, and partial differential equations. It is ideal for graduate students, researchers, and professionals in the field.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.
High-Dimensional Optimization and Probability
This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces.The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas.Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Bulletins of the Zoological Society of San Diego; no.21 (1945)
This collection of scientific papers covers a wide variety of topics in zoology, from the behavior of reptiles to the classification of birds. With contributions from esteemed researchers and comprehensive studies, it is an important resource for zoologists and biology enthusiasts.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.
Introduction to Chaos, Fractals and Dynamical Systems
This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems particularly focuses on natural and human phenomenon that can be modeled as fractals, using simple examples to explain the theory of chaos and how it affects all of us. Then, using straightforward mathematic and intuitive descriptions, computer generated graphics and photographs of natural scenes are used to illustrate the beauty of fractals and their importance in our world. Finally, the concept of Dynamical Systems, that is, time-dependent systems, the foundation of Chaos and Fractal, is introduced. Everyday examples are again used to illustrate concepts, and the importance of understanding how these vital systems affect our lives. Throughout the fascinating history of the evolution of chaos theory, fractals and dynamical systems is presented, along with brief introductions to the scientists, mathematicians and engineers who created this knowledge.Introduction to Chaos, Fractals and Dynamical Systems contains ample mathematical definitions, representations, discussions and exercises, so that this book can be used as primary or secondary source in home schooling environments.The book is suitable for homeschooling as a focused course on the subject matter or as a classroom supplement for a variety of courses at the late junior high or early high-school level. For example, in addition to a standalone course on Chaos, Fractals and Dynamical Systems (or similar title), this book could be used with the following courses: PrecalculusGeometryComputer programming (e.g. Rust, C, C++, Python, Java, Pascal)Computer graphicsThe text can also be used in conjunction with mathematics courses for undergraduates for non-science majors. The book can also be used for informal and lively family study and discussion.For each chapter, exercises and things to do are included. These activities range from simple computational tasks to more elaborate computer projects, related activities, biographical research and writing assignments.
Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups
This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are L矇vy processes on some simply connected nilpotent Lie groups. Both the limit L矇vy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit L矇vy processes in the context of (non-commutative) nilpotent groups.
Spatial Statistics for Data Science
Spatial data is crucial to improve decision-making in a wide range of fields including environment, health, ecology, urban planning, economy, and society. This book describes statistical methods, modeling approaches, and visualization techniques to analyze spatial data using R.
Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure
In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions.
Analysis and Quantum Groups
This volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of 'Haar integrals' on locally compact quantum groups, and is thus treated quite extensively The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.
Applied Machine Learning Using Mlr3 in R
mlr3 is an award-winning ecosystem of R packages that have been developed to enable state-of-the-art machine learning capabilities in R. This book gives an overview of flexible and robust machine learning methods, with an emphasis on how to implement them using mlr3 in R.
Evaluating What Works
Objective intervention research is vital to improve outcomes, but this is a complex area, where it is all too easy to misinterpret evidence. This book uses practical examples to increase awareness of the numerous sources of bias that can lead to mistaken conclusions when evaluating interventions.
Starting Out With Python
This book covers the main models within the GLM (i.e., logistic, Poisson, negative binomial, ordinal, and multinomial). For each model, estimations, interpretations, model fit, diagnostics, and how to convey results graphically are provided. There is a focus on graphic displays of results as these are a core strength of using R for statistical analysis. Many in the social sciences are transitioning away from using Stata, SPSS and SAS, to using R, and this book uses statistical models which are relevant to the social sciences. Social Science Applications of Regression for Categorical Outcomes Using R will be useful for graduate students in the social sciences who are looking to expand their statistical knowledge, and for Quantitative social scientists due to it's ability to act as a practitioners guide. Key Features: Applied- in the sense that we will provide code that others can easily adapt Flexible- R is basically just a fancy calculator. Our programs will enable users to derive quantities that they can use in their work Timely- many in the social sciences are currently transitioning to R or are learning it now. Our book will be a useful resource Versatile- we will write functions into an R package that can be applied to all of the regression models we will cover in the book Aesthetically pleasing- one advantage of R relative to other software packages is that graphs are fully customizable. We will leverage this feature to yield high-end graphical displays of results Affordability- R is free. R packages are free. There is no need to purchase site licenses or updates.
An Advanced Course in Probability and Stochastic Processes
An Advanced Course in Probability and Stochastic Processes provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Fundamental stochastic processes are explored in considerable depth
Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
This is the first comprehensive book on Trotter-Kato approximations of stochastic differential equations (SDEs) in infinite dimensions and applications. This research monograph brings together the varied literature on this topic since 1985 when such a study was initiated. The author provides a clear and systematic introduction to the theory of Trotter-Kato approximations of SDEs and also presents its applications to practical topics such as stochastic stability and stochastic optimal control. The theory assimilated here is developed slowly and methodically in digestive pieces.The book begins with a motivational chapter introducing several different models that highlight the importance of the theory on abstract SDEs that will be considered in the subsequent chapters. The author next introduces the necessary mathematical background and then leads the reader into the main discussion of the monograph, namely, the Trotter-Kato approximations of many classes of SDEs in Hilbert spaces, Trotter-Kato approximations of SDEs in UMD Banach spaces and some of their applications. Most of the results presented in the main chapters appear for the first time in a book form. The monograph also contains many illustrative examples on stochastic partial differential equations and one in finance as an application of the Trotter-Kato formula. The key steps are included in all proofs which will help the reader to get a real insight into the theory of Trotter-Kato approximations and its use. This book is intended for researchers and graduate students in mathematics specializing in probability theory. It will also be useful to numerical analysts, engineers, physicists and practitioners who are interested in applying the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is accessible to a wider audience including non-specialists in stochastic processes.
Fairy Tales and the Art of Subversion
Methodologies and recipes to regularize any machine learning and deep learning model using cutting-edge technologies such as stable diffusion, Dall-E and GPT-3Purchase of the print or Kindle book includes a free PDF eBookKey Features: Learn to diagnose the need for regularization in any machine learning modelRegularize different ML models using a variety of techniques and methodsEnhance the functionality of your models using state of the art computer vision and NLP techniquesBook Description: Regularization is an infallible way to produce accurate results with unseen data, however, applying regularization is challenging as it is available in multiple forms and applying the appropriate technique to every model is a must. The Regularization Cookbook provides you with the appropriate tools and methods to handle any case, with ready-to-use working codes as well as theoretical explanations.After an introduction to regularization and methods to diagnose when to use it, you'll start implementing regularization techniques on linear models, such as linear and logistic regression, and tree-based models, such as random forest and gradient boosting. You'll then be introduced to specific regularization methods based on data, high cardinality features, and imbalanced datasets. In the last five chapters, you'll discover regularization for deep learning models. After reviewing general methods that apply to any type of neural network, you'll dive into more NLP-specific methods for RNNs and transformers, as well as using BERT or GPT-3. By the end, you'll explore regularization for computer vision, covering CNN specifics, along with the use of generative models such as stable diffusion and Dall-E.By the end of this book, you'll be armed with different regularization techniques to apply to your ML and DL models.What You Will Learn: Diagnose overfitting and the need for regularizationRegularize common linear models such as logistic regressionUnderstand regularizing tree-based models such as XGBoosUncover the secrets of structured data to regularize ML modelsExplore general techniques to regularize deep learning modelsDiscover specific regularization techniques for NLP problems using transformersUnderstand the regularization in computer vision models and CNN architecturesApply cutting-edge computer vision regularization with generative modelsWho this book is for: This book is for data scientists, machine learning engineers, and machine learning enthusiasts, looking to get hands-on knowledge to improve the performances of their models. Basic knowledge of Python is a prerequisite.
Topics in Complex Analysis
This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 -- a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
Nikola Tesla
Nikola Tesla is one of the most fascinating figures in modern history. His groundbreaking work in the field of electrical engineering, coupled with his innovative ideas and visionary outlook, has made him an icon of innovation and creativity.In this book, readers will embark on a journey through the life and work of Nikola Tesla, exploring his early years and education, his contributions to science and technology, his personal life and relationships, and his legacy and influence on modern society. Some of the topics covered in this book include: ChildhoodEducation and Early CareerPatents and PoliticsThe Eccentric GeniusTesla's Coil and the Niagara ContractInfluential Friends and the Lure of Flight1914 and BeyondAnd much more!The book is designed for children aged 8-12 years old and is written in an easy-to-understand language that makes the stories accessible to children of all reading levels. It is illustrated with colorful, engaging illustrations that help bring the story to life.
Mathematical Analysis: A Very Short Introduction
Very Short Introductions: Brilliant, sharp, inspiring The 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians--especially Bolzano, Cauchy, and Weierstrass--began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis. This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Anova with Dependent Errors
This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in several scientific fields. A test for the existence of interactions is also proposed. The book deals with asymptotics when the number of groups is fixed and sample size diverges. This framework distinguishes the approach of the book from panel data and longitudinal analyses, which mostly deal with cases in which the number of groups is large. The usefulness of the theory in this book is illustratedby numerical simulation and real data analysis. This book is suitable for theoretical statisticians and economists as well as psychologists and data analysts.
Monogenic Functions in Spaces with Commutative Multiplication and Applications
This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.
Flows on Compact Surfaces
This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e.g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.
Value of Information for Healthcare Decision-Making
For health economic modellers and researchers, in industry, government, or academia, who wish to perform VOI analysis in health economic evaluations. For postgraduate researchers and students in health economics or medical statistics who are required to learn the principles of VOI or undertake VOI analyses in their projects.
Trends and Challenges in Cognitive Modeling
This book presents interdisciplinary research in the science of Human Cognition through mathematical and computational modeling and simulation. Featuring new approaches developed by leading experts in the field of cognitive science, it highlights the relevance and depth of this important area of social sciences and its expanding reach into the biological, physical, computational and mathematical sciences. This contributed volume compiles the most recent advancements and cutting-edge applications of cognitive modeling, employing a genuinely multidisciplinary approach to simulate thinking, memory, and decision-making. The topics covered encompass a wide range of subjects, such as Agent-based Modeling in psychological research, the Nyayasutra proof pattern, the utilization of the Pheromone Trail Algorithm for modeling Analog Memory, the theory and practical applications of Social Laser Theory, addressing the challenges of probabilistic learning in brain and behavior models, adopting a Physicalistic perspective to understand the emergence of cognition and computation, an in-depth analysis of the conjunction fallacy as a factual occurrence, exploring quantum modeling and causality in physics and its extensions, examining compositional vector semantics within spiking neural networks, delving into the realms of Optimality, Prototypes, and Bilingualism, and finally, investigating the intricate dimensionality of color perception. Given its scope and approach, the book will benefit researchers and students of computational social sciences, mathematics and its applications, quantum physics.
Extended Abstracts 2021/2022
This book offers an overview of the research results presented by group members and guests of the Ghent Analysis & PDE Center during the weekly seminar that took place from 2021 to 2022. It is an informal event of the Analysis & PDE Center and associated researchers, where everyone can present their work or relevant literature for about 20-30 minutes. The seminar aims to exchange ideas and foster effective learning and collaboration.In this book, group members and guests summarise their results presented during the seminar and provide outlooks for future work. In this way, the book also provides an overview of the recent developments in the Ghent Analysis & PDE Center. The main topics are functional analysis, Fourier analysis, noncommutative analysis, geometric analysis, partial differential equations of different types, harmonic analysis, functional inequalities, pseudo-differential operators, fractional derivatives, special functions, microlocal analysis, inverseproblems and imaging. The target audience of this book is any researcher working in the above fields.
A Guide to Robust Statistical Methods
Robust statistical methods are now being used in a wide range of disciplines. The appeal of these methods is that they are designed to perform about as well as classic techniques when standard assumptions are true--but they continue to perform well in situations where classic methods perform poorly. This book provides a relatively non-technical guide to modern methods. The focus is on applying modern methods using R, understanding when and why classic methods can be unsatisfactory, and fostering a conceptual understanding of the relative merits of different techniques. A recurring theme is that no single method reveals everything one would like to know about the population under study. An appeal of robust methods is that under general conditions they provide much higher power than conventional techniques. Perhaps more importantly, they help provide a deeper and more nuanced understanding of data. The book is for readers who had at least one semester of statistics, aimed at non-statisticians.
Multilevel and Longitudinal Modeling Using Stata, Volume II
Multilevel and Longitudinal Modeling Using Stata, Fourth Edition, is a complete resource for learning to model data in which observations are grouped. With comprehensive coverage, researchers who need to apply multilevel models will find this book to be the perfect companion. It is also the ideal text for courses in multilevel modeling because it provides examples from a variety of disciplines as well as end-of-chapter exercises that allow students to practice newly learned material. The book comprises two volumes. Volume II focuses on generalized linear models for binary, ordinal, count, and other types of outcomes.
Mathematical Conundrums
Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers).
Building Your Career as a Statistician
This book is intended for anyone who is considering a career in statistics or a related field, or those at any point in their career with sufficient work time remaining such that investing in additional learning could be beneficial. As such, the book would be suitable for anyone pursing an MS or PhD in statistics or those already working in statistics. The book focuses on the non-statistical aspects of being a statistician that are crucial for success. These factors include 1) productivity and prioritization, 2) innovation and creativity, 3) communication, 4) critical thinking and decisions under uncertainty, 5) influence and leadership, 6) working relationships, and 7) career planning and continued learning. Each of these chapters includes sections on foundational principles and a section on putting those principles into practice. Connections between these individual skills are emphasized such that the reader can appreciate how the skills build upon each other leading to a whole that is greater than the sum of its parts. By including the individual perspectives from other experts on the fundamental principles and their application, readers will have a well-rounded view on how to build upon and fully leverage their technical skills in statistics. The primary audience for the book is large and diverse. It will be useful for self-study by virtually any statistician, but could also be used as a text in a graduate program that includes a course on careers and career development. Key Features: Takes principles proven to be useful in other settings and applies them to statisticians and statistical settings. Focused Concise Accessible to all levels, from grad students to mid-later career statisticians.
Mathematical Conundrums
Want to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included. Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge. But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisite Variety of algebraic, route-drawing, and geometrical conundrums Hints section for the lateral puzzles Warm-up excercises to sharpen the wits Full solutions to every problem Barry R. Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Reader's Digest, The Sunday Telegraph, and Prospect magazine. His book Challenging Logic Puzzles Mensa has sold over 100,000 copies. As well as a PhD in Shakespeare Studies, Barry has a master's degree and academic publications in quantum physics. He is now working on a revised theory of the hydrogen atom. Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist! For more information please visit http: //barryispuzzled.com. 　 　
Building Your Career as a Statistician
This book is intended for anyone who is considering a career in statistics or a related field, or those at any point in their career with sufficient work time remaining such that investing in additional learning could be beneficial. As such, the book would be suitable for anyone pursing an MS or PhD in statistics or those already working in statistics. The book focuses on the non-statistical aspects of being a statistician that are crucial for success. These factors include 1) productivity and prioritization, 2) innovation and creativity, 3) communication, 4) critical thinking and decisions under uncertainty, 5) influence and leadership, 6) working relationships, and 7) career planning and continued learning. Each of these chapters includes sections on foundational principles and a section on putting those principles into practice. Connections between these individual skills are emphasized such that the reader can appreciate how the skills build upon each other leading to a whole that is greater than the sum of its parts. By including the individual perspectives from other experts on the fundamental principles and their application, readers will have a well-rounded view on how to build upon and fully leverage their technical skills in statistics. The primary audience for the book is large and diverse. It will be useful for self-study by virtually any statistician, but could also be used as a text in a graduate program that includes a course on careers and career development. Key Features: Takes principles proven to be useful in other settings and applies them to statisticians and statistical settings. Focused Concise Accessible to all levels, from grad students to mid-later career statisticians.
Introduction to Probability Models
*Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner, 2024* A trusted market leader for four decades, Sheldon Ross's Introduction to Probability Models offers a comprehensive foundation of this key subject with applications across engineering, computer science, management science, the physical and social sciences and operations research. Through its hallmark exercises and real examples, this valuable course text Introduction to Probability Models provides the reader with a comprehensive course in the subject, from foundations to advanced topics.
Sparse Graphical Modeling for High Dimensional Data
This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines. Key Features: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference
Machine Learning for Factor Investing
Machine learning (ML) is progressively reshaping the fields of quantitative finance and algorithmic trading. ML tools are increasingly adopted by hedge funds and asset managers, notably for alpha signal generation and stocks selection. The technicality of the subject can make it hard for non-specialists to join the bandwagon, as the jargon and coding requirements may seem out-of-reach. Machine learning for factor investing: Python version bridges this gap. It provides a comprehensive tour of modern ML-based investment strategies that rely on firm characteristics. The book covers a wide array of subjects which range from economic rationales to rigorous portfolio back-testing and encompass both data processing and model interpretability. Common supervised learning algorithms such as tree models and neural networks are explained in the context of style investing and the reader can also dig into more complex techniques like autoencoder asset returns, Bayesian additive trees and causal models. All topics are illustrated with self-contained Python code samples and snippets that are applied to a large public dataset that contains over 90 predictors. The material, along with the content of the book, is available online so that readers can reproduce and enhance the examples at their convenience. If you have even a basic knowledge of quantitative finance, this combination of theoretical concepts and practical illustrations will help you learn quickly and deepen your financial and technical expertise.
Attractors, Shadowing, and Approximation of Abstract Semilinear Differential Equations
The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
Comparative Genomics
This book constitutes the refereed proceedings of the 20th Annual RECOMB Satellite Workshop on Comparative Genomics, RECOMB-CG 2023 which took place in Istanbul, Turkey, in April 2023. The 15 full papers included in this book were carefully reviewed and selected from 25 submissions. The papers present cutting edge research in comparative genomics, with an emphasis on computational approaches and novel experimental results.Chapters "Inferring Clusters of Orthologous and Paralogous Transcripts" and "Gene Order Phylogeny via Ancestral Genome Reconstruction under Dollo" are published Open Access under Creative Commons Attribution license (CC BY 4.0).
Elliptic Integrals and Elliptic Functions
This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader's convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book.For each notion a clear motivation is given for its study, answering the question 'Why do we consider such objects?', and the theory is developed in a natural way that mirrors its historical development (e.g., 'If there is such and such an object, then you would surely expect this one'). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.
Model Risk Management
This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.
Well-Posed Nonlinear Problems
This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.
A Friendly Approach to Complex Analysis
The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
A Friendly Approach to Complex Analysis
The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
The Fundamentals of People Analytics
This open access book prepares current and aspiring analytics professionals to effectively address this need by curating key concepts spanning the entire analytics lifecycle, along with step-by-step instructions for their applications to real-world problems, using ubiquitous and freely available open-source software. This book does not assume prior knowledge of statistics, how to query databases, or how to write performant code; early chapters include an introduction to R and SQL as well as an overview of statistical foundations. Human capital is an organization's most important asset. Without the knowledge and skills of people, an organization can accomplish nothing. The acquisition, development, and retention of critical talent has become increasingly more complex and challenging, and organizations are making significant investments to gain a deeper, data-informed understanding of organizational phenomena impacting the bottom line. By the end of this book, readers will be able to: - Design and conduct empirical research - Query and wrangle data using SQL - Profile, clean, and analyze data using R - Apply appropriate statistical and ML models to a range of people analytics use cases - Package and present analyses to communicate impactful insights to stakeholders
The Fundamentals of People Analytics
This open access book prepares current and aspiring analytics professionals to effectively address this need by curating key concepts spanning the entire analytics lifecycle, along with step-by-step instructions for their applications to real-world problems, using ubiquitous and freely available open-source software. This book does not assume prior knowledge of statistics, how to query databases, or how to write performant code; early chapters include an introduction to R and SQL as well as an overview of statistical foundations. Human capital is an organization's most important asset. Without the knowledge and skills of people, an organization can accomplish nothing. The acquisition, development, and retention of critical talent has become increasingly more complex and challenging, and organizations are making significant investments to gain a deeper, data-informed understanding of organizational phenomena impacting the bottom line. By the end of this book, readers will be able to: - Design and conduct empirical research - Query and wrangle data using SQL - Profile, clean, and analyze data using R - Apply appropriate statistical and ML models to a range of people analytics use cases - Package and present analyses to communicate impactful insights to stakeholders
A Course on Holomorphic Discs
This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov's nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology.This text can be used as the basis for a graduate course, and it is also immensely suitable for independentstudy. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed.This book is also part of the Virtual Series on Symplectic Geometry.
Knowledge Structures: Recent Developments in Theory and Application
Founded in 1985 by Jean-Claude Falmagne and Jean-Paul Doignon, Knowledge Structure Theory (KST) constitutes a rigorous and current mathematical theory for the representation and the assessment of human knowledge. The seminal work of these authors initiated a highly active research strand with an ever-growing literature, mostly scattered across various technical journals.Starting from a concise but comprehensive introduction to its foundations, this volume provides a state-of-the-art review of KST. For the first time the volume brings together the most important theoretical developments and extensions of the last decade and presents new areas of application beyond education, with contributions by key researchers in the field.Among the important advances covered by this book are (1) a comprehensive treatment of probabilistic models in KST; (2) polytomous extensions of the theory; (3) KST-based psychological diagnostics and neuropsychological assessment; (4) the representation and assessment of cognitive skills in problem solving, as well as procedural skills. In addition, this book also includes an overview of available software for the application of KST.
