The Magic Theorem
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things. Begun as a standard second edition by the original author team, it changed in scope following the passing of John Conway. This version of the book fulfills the original vision for the project: an elementary introduction to the orbifold signature notation and the theory behind it.The Magic Theorem features all the material contained in Part I of The Symmetries of Things, now redesigned and even more lavishly illustrated, along with new and engaging material suitable for a novice audience. This new book includes hands-on symmetry activities for the home or classroom and an online repository of teaching materials avaialble at themagictheorem.com
Mean Field Guided Machine Learning
This book explores the integration of Mean Field Game (MFG) theory with machine learning (ML), presenting both theoretical foundations and practical applications. Drawing from extensive research, it provides insights into how MFG can improve various ML techniques, including supervised learning, reinforcement learning, and federated learning. MFG theory and ML are converging to address critical challenges in high-dimensional spaces and multi-agent systems. While ML has transformed industries by leveraging vast data and computational power, scalability and robustness remain key concerns. MFG theory, which models large populations of interacting agents, offers a mathematical framework to simplify and optimize complex systems, enhancing ML's efficiency and applicability. By bridging these two fields, this book aims to drive innovation in scalable and robust machine learning. The integration of MFG with ML not only expands research possibilities but also paves the way for more adaptive and intelligent systems. Through this work, the authors hope to inspire further exploration and development in this promising interdisciplinary domain. With case studies and real-world examples, this book serves as a guide for researchers and students in communications and networks seeking to harness MFG's potential in advancing ML. Industry managers, practitioners and government research workers in the fields of communications and networks will find this book a valuable resource as well.
Connection Matrices in Combinatorial Topological Dynamics
This book provides an introduction to the theory of connection matrices in the context of combinatorial multivector fields. The theory of connection matrices was proposed by Conley and Franzosa for classical continuous-time dynamical systems as a tool for studying connecting orbits between isolated invariant sets. It generalizes the Morse complex in Morse theory, and has found numerous applications in dynamics. Connection matrices have been and still are a challenging topic to study, as there are no complete introductory texts, and both their intricate definition and properties are scattered over numerous research papers. In recent years, dynamical concepts have found their way into a combinatorial context. Starting with combinatorial vector fields, introduced by Forman to generalize classical Morse theory, it has been realized that this transfer of ideas can lead to important applications. Similarly, Conley's theory of isolated invariant sets has been transferred to the combinatorial setting. This, when combined with the concept of multivector fields, opens the door to a complete combinatorial dynamical theory. In this book, we take Conley's theory one step further, by presenting a complete discussion of connection matrices for combinatorial multivector fields. While some of the results in this book are based on known approaches, we show in a detailed way how they can be carried over to the case of multivector fields on general Lefschetz complexes. Along the way, we introduce notions which are new even in the classical setting, such as a formal approach to addressing the nonuniqueness of connection matrices, as well as mechanisms for comparing connection matrices even under poset changes. Finally, we show that specifically for the case of Forman's gradient combinatorial vector fields connection matrices are necessarily unique, and can be determined explicitly in a straightforward way. Focusing on the combinatorial theory of connection matrices has a number of advantages. On the one hand, many of the technical difficulties of the classical continuous-time dynamics situation are not present in the discrete combinatorial context. This allows us to provide a complete and informal introduction to the theory in the second section of the book. This in turn will enable the readers to construct and analyze their own examples easily. On the other hand, the complete theory, including the existence of connecting orbits in the combinatorial setting can be presented in detail, based on an explicit distinction between the algebraic and topological parts of the theory. In this way, it is our hope that this book will be an impetus for further knowledge transfer between dynamics and combinatorics, and even topological data analysis. This text is aimed at researchers in the fields of dynamics and topological data analysis, and it is suitable for advanced graduate students interested in applying connection matrix methods to their own studies.
Continuous Optimization for Data Science
The text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods.The second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems.The third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. Throughout, the text provides numerous applications to data science, such as linear regression, maximum likelihood estimation, expectation-maximization algorithms, support vector machines, and linear neural networks.
Continuous Optimization for Data Science
The text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods.The second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems.The third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. Throughout, the text provides numerous applications to data science, such as linear regression, maximum likelihood estimation, expectation-maximization algorithms, support vector machines, and linear neural networks.
Quantum Unmanned Aerial Vehicle
This book is intended for a technical audience with advanced learning and in-depth analysis of the latest real-world developments in the field of quantum computing. The book is focused on modeling emerging drone-based applications. The methods of developing faster drive with the new trending technology of quantum genetic heuristics, artificial intelligence, and machine-based applications are discussed. Researchers will find novel ways to secure the data and Quantum drone networks. The book examines the most promising exploratory quantum-computed drone that optimizes, secures, and dynamically analyses various sectors, including healthcare, the educational industry, finance, transportation, and manufacturing.
Advanced Statistical Methods in Life Science
This book introduces the principles and foundations of advanced statistical methods for designing experiments and testing hypotheses in Life sciences. Advanced statistical methods like testing of hypotheses, etc. as demonstrated by real data, and their integration into life sciences are included in the book.
The Language of Machines
Introduction to LLMs offers a clear and comprehensive overview of Large Language Models, capturing their historical development, technological foundations, and transformative impact across various sectors such as healthcare, education, software development, and creative industries. This book is tailored to both newcomers and experienced professionals, guiding readers through the evolution, architecture, applications, and ethical dimensions of LLMs.Structured to progressively build understanding, the chapters explore key aspects-from the origins of language modeling and recent breakthroughs to the societal challenges and responsibilities tied to AI use. By combining theoretical depth with practical insights and real-world case studies, the book strikes a balance between accessibility and rigor.Whether used as a foundational text or a reference for advanced exploration, Introduction to LLMs equips readers with the knowledge and critical perspective needed to engage with one of the most transformative technologies of our time.
Mastering Data Science with R and SAS
The second edition of Mastering Data Science with R and SAS: From Foundations to Advanced Statistical Modeling offers an expanded and updated roadmap for mastering modern data analysis using R and SAS. Building on the solid foundation of the first edition, this version dives deeper into advanced statistical modeling techniques, including multivariate regression, generalized linear models (GLMs), longitudinal data analysis, principal component analysis (PCA), and factor analysis.Enhanced chapters on R provide improved guidance on the RStudio environment, programming workflows, debugging, and troubleshooting, enabling readers to write more efficient and reliable code. The coverage of SAS software has been significantly broadened to include advanced data manipulation, statistical inference, error handling, and practical lab exercises designed to develop real-world problem-solving skills.Rich with practical examples, hands-on exercises, and comprehensive explanations, this edition is designed to meet the evolving needs of students, researchers, and data professionals. Whether you are new to data science or looking to deepen your expertise, this book equips you with the essential tools.
Mathematical Optimization Theory and Operations Research
This book LNCS 15681 constitutes the refereed proceedings of the 24th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2025, held in Novosibirsk, Russia, during July 7-11, 2025. The 27 full papers were carefully reviewed and selected from 72 submissions. The proceeding focus on Mathematical Programming; Optimal Control; Game Theory; Operations Research and Applications; Machine Learning and Optimization.
Lean Management In Aircraft Industry
In the recent years practitioners and researchers have paid lot of attention towards lean manufacturing. Lean manufacturing practices, principles, tools and benefits to service as well as manufacturing organizations are well documented in the extant literature. Although numerous articles dealing with the concept and implication of lean manufacturing has been published inleading journals all over the world but the fact is that only few organizations have been successful in implementing lean manufacturing in totality to reduce the expected total cost and carried out a significant improvement in the their performance similar to that of Toyota Motor Corporation (TMC). Maximum of the success stories of lean implementation belongs to developed countries and lean implementation in totality is hardly evidenced in Indian Aircraft industry but Indian industries have a lot of scope for lean implementation. In this research an attempt has been made to explore cost benefits with supply chain. Also lean implementation, supplier's issues, lean tools, various waste identified, performance parameters and investment priorities for lean implementation in Indian scenario have been studied.
Derivative-Free Optimization
This book offers a pioneering exploration of classification-based derivative-free optimization (DFO), providing researchers and professionals in artificial intelligence, machine learning, AutoML, and optimization with a robust framework for addressing complex, large-scale problems where gradients are unavailable. By bridging theoretical foundations with practical implementations, it fills critical gaps in the field, making it an indispensable resource for both academic and industrial audiences. The book introduces innovative frameworks such as sampling-and-classification (SAC) and sampling-and-learning (SAL), which underpin cutting-edge algorithms like Racos and SRacos. These methods are designed to excel in challenging optimization scenarios, including high-dimensional search spaces, noisy environments, and parallel computing. A dedicated section on the ZOOpt toolbox provides practical tools for implementing these algorithms effectively. The book's structure moves from foundational principles and algorithmic development to advanced topics and real-world applications, such as hyperparameter tuning, neural architecture search, and algorithm selection in AutoML. Readers will benefit from a comprehensive yet concise presentation of modern DFO methods, gaining theoretical insights and practical tools to enhance their research and problem-solving capabilities. A foundational understanding of machine learning, probability theory, and algorithms is recommended for readers to fully engage with the material.
AI for Research and Scalable, Efficient Systems
This book constitutes the proceedings of the Second International Workshop, AI4Research 2025, and First International Workshop, SEAS 2025, which were held in conjunction with AAAI 2025, Philadelphia, PA, USA, during February 25-March 4, 2025. AI4Research 2025 presented 8 full papers from 35 submissions. The papers covered diverse areas such as agent debate evaluation, taxonomy expansion, hypothesis generation, AI4Research benchmarks, caption generation, drug discovery, and financial auditing. SEAS 2025 accepted 7 full papers from 17 submissions. These papers explore the efficiency and scalability of AI models.
Solved problems on Markov chains
Markov chains have many applications, ranging from modeling communication networks to analyzing stock prices, Markov chains can be used in market research studies, they can model the probabilities of claims for insurance, they are used in the fields of public health and medicine, also they are used in ranking of websites in web searches. In general, Markov chains are particularly useful in modeling systems that have a finite number of states and transitions between those states and can be used to analyze and predict the long-term behavior of such systems.Most books on Markov chains are dedicated to reviewing theoretical concepts. The objective of this work is to make available to students and teachers a collection of solved problems on discrete-time Markov chains. In this sense, the work consists of solving 74 problems of different types. In them are obtained the transition probabilities and the transition matrix, the state spaces and the classes of those states, the n-step transition probabilities, the recurrence and transience, the invariant distributions, the mean return time and the convergence to equilibrium.
Supervised Machine Learning for Science
Machine learning has revolutionized science, from folding proteins and predicting tornadoes to studying human nature. While science has always had an intimate relationship with prediction, machine learning amplified this focus. But can this hyper-focus on prediction models be justified? Can a machine learning model be part of a scientific model? Or are we on the wrong track?In this book, we explore and justify supervised machine learning in science. However, a naive application of supervised learning won't get you far because machine learning in raw form is unsuitable for science. After all, it lacks interpretability, uncertainty quantification, causality, and many more desirable attributes. Yet, we already have all the puzzle pieces needed to improve machine learning, from incorporating domain knowledge and ensuring the representativeness of the training data to creating robust, interpretable, and causal models. The problem is that the solutions are scattered everywhere.In this book, we bring together the philosophical justification and the solutions that make supervised machine learning a powerful tool for science.After the introduction, the book consists of two parts: Part 1 justifies the use of machine learning in science.Part 2 discusses how to integrate machine learning into science.
Time Series Forecasting of Meteorological Parameters
This book focuses on the time series forecasting of critical meteorological parameters including temperature, rainfall, humidity, and wind. It explores classical statistical models such as ARIMA, Holt-Winters, and Exponential Smoothing, along with a novel enhancement-the Modified Sliding Window Algorithm. The objective is to improve prediction accuracy in meteorological datasets by applying adaptive techniques. Real-time weather data has been analyzed using these models, and a comparative study highlights the performance of each. This work is beneficial for researchers, meteorologists, and data scientists working in climate modeling and weather prediction.
Performance Enhancement in Multiprocessing Systems
Parallel processing is an efficient form of information processing that emphasizes the concurrent manipulation of data elements belonging to one or more processes solving a single problem. It makes a tremendous impact on many areas of computer applications like computational simulations for scientific and engineering applications, commercial applications in data mining, transaction processing etc. It is one of the approaches known today, to make computation feasible. Heterogeneous systems create unlimited opportunities and challenges in the fields of parallel processing, design of algorithms, and partitioning and mapping of parallel tasks. In mapping of parallel tasks, scheduling plays an important role. In this book, three algorithms Task oriented Dynamic Scheduling Algorithm (TDSA), Dynamic Task Duplication based Scheduling Algorithm (DyDupSA) and Dynamic Ant Colony Optimization (DyACO) are proposed. TDSA algorithm use the concept of migration, DyDupSA applies duplication and migration and DyACO meta heuristic to minimize the makespan and to maximize the processor utilization. Among the proposed algorithms, DyACO algorithm outperforms the other algorithms.
Statistical Computing With Machine Learning
Statistical Computing with Machine Learning explores the powerful synergy between statistical analysis and machine learning techniques in addressing real-world medical challenges. With a strong focus on disease prediction and diagnosis, this book bridges foundational theory with cutting-edge applications, offering researchers, practitioners, and students a comprehensive guide to modern healthcare analytics.
Functional Phase Space Methods
This book focuses on functional phase space methods in quantum optics and provides a comprehensive introduction to the Wigner functional formalism. The book shows how this formalism can be used for analyzing and designing practical photonic quantum information systems. It also explains in detail the application of the Wigner functional formalism to parametric down-conversion, an important process in quantum optics.
Applied Cluster Analysis - Part I
This book is Part 1 of a series on cluster analysis, developed through a search to define its boundaries. While many existing sources mention topics covered here, this book offers new reflections, developments, and example applications that provide fresh insights into cluster analysis. Its primary goal is to introduce new perspectives while exploring various ideas and approaches. Topics include the goals and assumptions of cluster analysis, its importance and applications, and an overview of common clustering models along with their use, distance measures, and selection criteria. The book also covers popular methods for evaluating clustering quality and validating clusters, supported by multiple example applications.Additionally, it addresses common challenges in determining the number of clusters, with attention to both hierarchical and non-hierarchical methods. The book concludes with a discussion on typical cluster types found in datasets and offers guidance on how to classify them accurately.
Sampling Techniques
"Sampling Techniques: From Fundamentals to Advanced Applications" is a comprehensive guide that covers both classical and modern approaches to sampling. Aimed at master's level students and professionals, the book blends theory, real-world applications, and computational tools.It begins with core sampling concepts and classical methods like SRS, stratified, and cluster sampling, then advances to specialized topics including adaptive sampling, Bayesian methods, and model-assisted techniques. Each chapter includes theorems, proofs, examples, illustrations, exercises with solutions, and coding practices in R and Python.This book equips readers with the knowledge to design efficient surveys and analyze data in fields such as public health, business, environment, and policy research.
Determinants of Project Success in Emergency Projects
This book investigates the critical success factors (CSFs) for Emergency Humanitarians projects in the Tigray region of Ethiopia for the period of the concurrent post conflict situation. A total of 46 respondents selected from various humanitarian non-governmental organizations participated in the study, yielding a response rate of 92%. The research employed a binary regression model to identify the significant determinants of project success. The findings reveal that project team experience and commitment, stakeholder management, proposal designing, monitoring and evaluation, implementation management, and communication management significantly influence project success, with p-values less than 0.05. These factors collectively account for an 89.1% project success ratio. Interestingly, project risk management, often considered a key aspect of project success, was not found to be a significant determinant in this context (p>0.05). The study underscores the meaningful achievements made by emergency humanitarian projects across all technical components and households exposed to more project activities. It concludes that effective management involvement, communication, team commitment.
Practice Exercises in Probability Distributions
This book presents a comprehensive collection of solved exercises in probability theory, intended for students, educators, and practitioners in the fields of mathematics, statistics, and related disciplines. The work covers both discrete and continuous probability distributions, exploring fundamental concepts such as random variables, expectation, variance, probability laws, conditional probability, independence, and the central limit theorem. Through a series of carefully structured problems accompanied by rigorous solutions, readers are introduced to classical distributions including binomial, geometric, Poisson, uniform, exponential, and normal distributions. Each chapter is designed to strengthen conceptual understanding and to develop analytical proficiency through application-driven scenarios such as quality control, random sampling, reliability modeling, and statistical inference. In addition to core topics, the book integrates advanced problem-solving strategies, approximation techniques (e.g., normal approximation to the binomial distribution), and real-world applications that bridge theoretical concepts with practical relevance.
The Football
An illustration-packed dive into the geometry, engineering, and physics of soccer balls The Football takes readers on an entertaining and fact-filled exploration of the mathematical secrets of the most popular spherical object on the planet. The football is familiar to billions of fans across the globe, but how many really look at it? Do footballs all have the same shape? Spoiler: not exactly. How does their shape affect how they play? With ?tienne Ghys as our guide, we discover why ballistics, friction, and air flow are key to scoring goals--and why the football is a mathematical problem that engineers are still trying to solve. Ghys begins with the classic Telstar ball used in the 1970 World Cup in Mexico. Its twelve black pentagons and twenty white hexagons are what most of us picture when we think of the sport. Following the story through successive World Cups, he shows how engineers constantly challenge themselves to reinvent the ball, aiming for a perfect sphere while accounting for manufacturing requirements and aerodynamics. Along the way, Ghys introduces us to the mathematics of Platonic solids, symmetries, polyhedra, turbulence, roughness, drag, and spin. He paints engaging portraits of the engineers and sports insiders who study and apply these phenomena and explains how the skills of players factor into how the ball behaves, whether the game is being played in stadiums, schoolyards, or backyards. Featuring a wealth of color illustrations, The Football blends a lively narrative with insights from a world-renowned geometer to tell a mathematical story unlike any other.
Modern Statistical Computing and Data Analysis with RStudio and SAS
Modern Statistical Computing and Data Analysis with RStudio and SAS offers a practical, hands-on introduction to the essential tools and techniques used in modern data science. Blending statistical theory with real-world applications, this book guides readers through data manipulation, visualization, modeling, and interpretation using two of the most powerful platforms in the field RStudio and SAS. Ideal for students, researchers, and professionals, it emphasizes clarity, reproducibility, and the integration of computational thinking in statistical analysis.
Nonlinear Analysis and Computational Techniques
The book focuses on the theory of fixed points, which is a foundation for many branches of pure and applied mathematics. Fixed point theorems have been studied in various function spaces. The book contains modern results on these theorems, investigated in generalized spaces such as S-metric spaces, convex metric spaces, and bipolar metric spaces, with applications in medical imaging. The nonlinear analysis presented in the book is valuable for modeling and solving real-world problems. It includes work on specific nonlinear operators and nonlinear fractional integral equations in Banach spaces. Relevant studies are also included on statistical convergence, inventory model modeling, computational techniques for Sentiment Analysis on Twitter Data, and Blood Management applications. The book is intended for young researchers interested in nonlinear analysis, fixed-point theory, and computational techniques.
Applied Analysis (3rd Ed)
This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.
Select Methods in Quantitative Analysis
"Select Methods in Quantitative Analysis" presents a comprehensive overview of essential techniques for analyzing numerical data. Written by Byron William Cheever and Frank Clemes Smith, this book is designed to equip researchers, students, and professionals with the skills necessary to conduct rigorous quantitative research. It covers a range of topics, from basic statistical methods to more advanced analytical procedures, providing a solid foundation for understanding and interpreting complex datasets.With clear explanations and practical examples, this book serves as an invaluable resource for anyone seeking to enhance their analytical capabilities and gain deeper insights from quantitative information. This work is an enduring guide to effectively employing quantitative methods in diverse fields.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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
Select Methods in Quantitative Analysis
"Select Methods in Quantitative Analysis" presents a comprehensive overview of essential techniques for analyzing numerical data. Written by Byron William Cheever and Frank Clemes Smith, this book is designed to equip researchers, students, and professionals with the skills necessary to conduct rigorous quantitative research. It covers a range of topics, from basic statistical methods to more advanced analytical procedures, providing a solid foundation for understanding and interpreting complex datasets.With clear explanations and practical examples, this book serves as an invaluable resource for anyone seeking to enhance their analytical capabilities and gain deeper insights from quantitative information. This work is an enduring guide to effectively employing quantitative methods in diverse fields.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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Conway-Maxwell-Poisson Distribution
While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.
Statistical Learning in Genetics
This book provides an introduction to computer-based methods for the analysis of genomic data. Breakthroughs in molecular and computational biology have contributed to the emergence of vast data sets, where millions of genetic markers for each individual are coupled with medical records, generating an unparalleled resource for linking human genetic variation to human biology and disease. Similar developments have taken place in animal and plant breeding, where genetic marker information is combined with production traits. An important task for the statistical geneticist is to adapt, construct and implement models that can extract information from these large-scale data. An initial step is to understand the methodology that underlies the probability models and to learn the modern computer-intensive methods required for fitting these models. The objective of this book, suitable for readers who wish to develop analytic skills to perform genomic research, is to provide guidance to take this first step. This book is addressed to numerate biologists who may lack the formal mathematical background of the professional statistician. For this reason, considerably more detailed explanations and derivations are offered. Examples are used profusely and a large proportion involves programming with the open-source package R. The code needed to solve the exercises is provided and it can be downloaded, allowing students to experiment by running the programs on their own computer. Part I presents methods of inference and computation that are appropriate for likelihood and Bayesian models. Part II discusses prediction for continuous and binary data using both frequentist and Bayesian approaches. Some of the models used for prediction are also used for gene discovery. The challenge is to find promising genes without incurring a large proportion of false positive results. Therefore, Part II includes a detour on the False Discovery Rate, assuming frequentist and Bayesian perspectives. The last chapter of Part II provides an overview of a selected number of non-parametric methods. Part III consists of exercises and their solutions. This second edition has benefited from many clarifications and extensions of themes discussed in the first edition. Daniel Sorensen holds PhD and DSc degrees from the University of Edinburgh and is an elected Fellow of the American Statistical Association. He was professor of Statistical Genetics at Aarhus University where, at present, he is professor emeritus.
Change Point Analysis
A crucial statistical technique for detecting structural breaks within datasets, applicable in diverse fields such as finance and weather forecasting.
Complex Analytic Cycles II
This book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are: - Fundamental class of a cycle and relative fundamental class of an analytic family of cycles - Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces - Holomorphic currents on reduced complex spaces - Chow varieties and cycle spaces of quasi-projective complex spaces - Natural morphism from the Douady space to the cycle space - Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles - Strong K瓣hlerianity of cycle spaces of K瓣hler manifolds - Numerous important applications of cycle space theory Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Sp矇cialis矇s and during the translation process the authors have in many ways improved the original version.
Practical Healthcare Statistics with Examples in Python and R
This book provides a clear and straightforward introduction to statistical methods in healthcare. Designed for recent graduates, new analysts, and professionals transitioning into healthcare analytics, it offers practical guidance on tackling real-world problems using statistical concepts and programming.
Practical Healthcare Statistics with Examples in Python and R
Practical Healthcare Statistics with Examples in Python and R provides a clear and straightforward introduction to statistical methods in healthcare. Designed for recent graduates, new analysts, and professionals transitioning into healthcare analytics, it offers practical guidance on tackling real-world problems using statistical concepts and programming. The book is divided into three primary sections. The first section provides an introduction to healthcare data and measures. In these chapters, readers will learn about the nuances of administrative claims and electronic health records, as well as common industry measures related to quality and efficiency of care. The second section will cover foundational techniques, such as hypothesis testing and regression analysis, as well as more advanced approaches, like generalized additive models and hierarchical models. In the last section, readers will be introduced to epidemiological techniques such as direct and indirect standardization, measures of disease frequency and association, and time-to-event analysis.The book emphasizes interpretable methods that are both effective and easy to communicate to clinical and non-technical stakeholders. Each technique presented in the book is accompanied by statistical notation described in plain English, as well as a self-contained example implemented in both Python and R. These examples help readers connect statistical methods to real healthcare scenarios without requiring extensive programming experience. By working through these examples, readers will build technical skills and a practical understanding of how to analyze healthcare data.These methods are not only central to improving patient care but are also adaptable to other areas within and beyond healthcare. This book is a practical resource for analysts, data scientists, health researchers, and others looking to make informed, data-driven decisions in healthcare.
Probability and Statistics for Data Science
This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book include random variables, nonparametric and parametric models, correlation, estimation of population parameters, hypothesis testing, principal component analysis, and both linear and nonlinear methods for regression and classification. Examples throughout the book draw from real-world datasets to demonstrate concepts in practice and confront readers with fundamental challenges in data science, such as overfitting, the curse of dimensionality, and causal inference. Code in Python reproducing these examples is available on the book's website, along with videos, slides, and solutions to exercises. This accessible book is ideal for undergraduate and graduate students, data science practitioners, and others interested in the theoretical concepts underlying data science methods.
Deep Learning for Computational Imaging
Computational techniques for image reconstruction problems enable imaging technologies including high-resolution microscopy, astronomy and seismology, computed tomography, and magnetic resonance imaging. Until recently, methods for solving such inverse problems were derived by experts without any learning. Now, the best performing image reconstruction methods are based on deep learning. This textbook gives the first comprehensive introduction to deep learning based image reconstruction methods. This book first introduces important inverse problems in imaging, including denoising and reconstructing an image from few and noisy measurements, and explains what makes those problems hard and interesting. Then, the book briefly discusses traditional optimization and sparsity based reconstruction methods, as well as optimization techniques as a basis for training and deriving deep neural networks for image reconstruction. The main part of the book is about how to solve image reconstruction problems with deep learning techniques: The book first disuses supervised deep learning approaches that map a measurement to an image as well as network architectures for imaging including convolutional neural networks and transformers. Then, reconstruction approaches based on generative models such as variational autoencoders and diffusion models are discussed, and how un-trained neural networks and implicit neural representations enable signal and image reconstruction. The book ends with a discussion on the robustness of deep learning based reconstruction as well as a discussion on the important topic of evaluating models and datasets, which are a critical ingredient of deep learning based imaging.
Robust Small Area Estimation
In recent years there has been substantial and growing interest in small area estimation (SAE) that is largely driven by practical demands. Here, the term "small area" typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain.Keywords in SAE are "borrowing strength". Because there are insufficient samples from the small areas to produce reliable direct estimates, statistical methods are sought to utilize other sources of information to do better than the direct estimates. A typical way of borrowing strength is via statistical modelling. On the other hand, there is no "free lunch". Yes, one can do better by borrowing strength, but there is a cost. This is the main topic discussed in this text.Features A comprehensive account of methods, applications, as well as some open problems related to robust SAE Methods illustrated by worked examples and case studies using real data Discusses some advanced topics including benchmarking, Bayesian approaches, machine learning methods, missing data, and classified mixed model prediction Supplemented with code and data via a website Robust Small Area Estimation: Methods, Applications, and Open Problems is primarily aimed at researchers and graduate students of statistics and data science and would also be suitable for geography and survey methodology researchers. The practical approach should help persuade practitioners, such as those in government agencies, to more readily adopt robust SAE methods. It could be used to teach a graduate-level course to students with a background in mathematical statistics.
Mathematics of Networks
Mathematics of Networks: Modulus Theory and Convex Optimization is a book that seeks to answer the question: "What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?"
Deep Learning for Computational Imaging
Computational techniques for image reconstruction problems enable imaging technologies including high-resolution microscopy, astronomy and seismology, computed tomography, and magnetic resonance imaging. Until recently, methods for solving such inverse problems were derived by experts without any learning. Now, the best performing image reconstruction methods are based on deep learning. This textbook gives the first comprehensive introduction to deep learning based image reconstruction methods. This book first introduces important inverse problems in imaging, including denoising and reconstructing an image from few and noisy measurements, and explains what makes those problems hard and interesting. Then, the book briefly discusses traditional optimization and sparsity based reconstruction methods, as well as optimization techniques as a basis for training and deriving deep neural networks for image reconstruction. The main part of the book is about how to solve image reconstruction problems with deep learning techniques: The book first disuses supervised deep learning approaches that map a measurement to an image as well as network architectures for imaging including convolutional neural networks and transformers. Then, reconstruction approaches based on generative models such as variational autoencoders and diffusion models are discussed, and how un-trained neural networks and implicit neural representations enable signal and image reconstruction. The book ends with a discussion on the robustness of deep learning based reconstruction as well as a discussion on the important topic of evaluating models and datasets, which are a critical ingredient of deep learning based imaging.
On the Solution of Numerical Functional Equations; Illustrated by an Account of a Popular Puzzle and of its Solution
"On the Solution of Numerical Functional Equations" by Eric Harold Neville explores the methods for solving numerical functional equations, using a popular puzzle as a central example. This work offers a detailed account of the puzzle's solution, illustrating key mathematical principles and techniques applicable to a broader range of problems. Neville's exposition provides valuable insights for students and researchers interested in numerical analysis and problem-solving strategies.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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
Variational Methods in Nonlinear Analysis
The second edition covers the fundamentals of nonlinear analysis, variational methods and their applications. Also it covers Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems. The new edition includes new topics on nonlinear operators, evolution and multivalued problems.
Chart to Facilitate the Calculation of Partial Coefficients of Correlation and Regression Equations
"Chart to Facilitate the Calculation of Partial Coefficients of Correlation and Regression Equations" by Truman Lee Kelley, originally published in 1921, offers a method for simplifying complex statistical calculations. This work provides a visual aid designed to assist researchers and statisticians in determining partial coefficients of correlation and developing regression equations more efficiently. The chart serves as a tool to navigate the intricate processes involved in statistical analysis, making it an invaluable resource for those engaged in quantitative research. Though first published nearly a century ago, the underlying mathematical principles remain relevant, offering both a historical perspective on statistical techniques and a potentially useful resource for modern researchers and students.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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
On the Solution of Numerical Functional Equations; Illustrated by an Account of a Popular Puzzle and of its Solution
"On the Solution of Numerical Functional Equations" by Eric Harold Neville explores the methods for solving numerical functional equations, using a popular puzzle as a central example. This work offers a detailed account of the puzzle's solution, illustrating key mathematical principles and techniques applicable to a broader range of problems. Neville's exposition provides valuable insights for students and researchers interested in numerical analysis and problem-solving strategies.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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
