Presents a novel covariance-driven approach to incorporate classical and modern techniques together
Encompasses cutting-edge skills like dimension reduction, banding, shrinking, penalizing, convolution, and transformer
Covers covariance regression model, network model, machine learning and covariance matrix, and tensor covariance model
This book demonstrates the application of covariance matrices through cutting-edge models and practical applications, as well as extensions induced by multivariate data and other related subjects. In data analysis, when studying the relationships among a set of variables, the covariance matrix plays an important role. It has been commonly and widely used across many fields, including agriculture, biology, business, communications, economics, engineering, finance, marketing, mathematics, medicine, data science, and social science, regardless of whether the data is dense or sparse, low-dimension or high-dimension, time series or non-time series, structured or unstructured, fixed or random, and training (learning) data or testing data. The covariance matrix is fundamental for extracting valuable information from multivariate data, such that this classical tool can be influential in modern data science and innovative statistical models.
Specifically, this book utilizes the covariance matrix to comprehensively unify classical multivariate methods (e.g., principal components and factor analysis) and innovative models and algorithms (e.g., spatial autoregressive and network autocorrelation models, matrix factor models, tensor covariance models, deep learning, and transfer learning). In so doing, it surveys statistical and data science techniques for estimation, selection, prediction, inference, and decision making. As a result, the book provides a unique approach for readers to understand how the traditional and modern techniques in data analysis, such as multivariate analysis and machine learning, can be unified with different features but the same foundation, which is the covariance matrix. This book is suitable for graduate students and researchers across various quantitative disciplines.
Includes the material from 4 intensive mini-courses on hot topics in discrete geometry
Provides the first systematic survey of the existential theory of reals
Illustrates the interplay between combinatorial, geometric, and topological methods
Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 31)
In the Fall of 2023, the Erdős Center (Budapest) hosted a special semester on ”Discrete Geometry and Convexity”, which brought together some of the strongest experts in the field and many outstanding young researchers. The program featured intensive one-week mini-courses during a Summer School, followed by conferences and workshops presenting cutting-edge research. Part I of the present volume includes the notes of three lecture series on (1) approximation in discrete geometry, (2) random polytopes, and (3) a structure theory for graphs embedded in the plane. Part II starts with a classic: Matoušek’s until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects. It is complemented by the first systematic and comprehensive survey of the corresponding complexity class: the existential theory of reals. This volume will be a valuable resource for graduate students, young researchers, and experts in related fields interested in discrete and computational geometry.
Honors the legacy of Professor M. V. Subbarao and the fields he contributed to fundamentally
Compiles research on modern contributions to number theory
Highlights modelling methods for pandemics with applications to COVID-19
Part of the book series: Fields Institute Communications (FIC, volume 90)
A symposium on number theory was organized at the Indian Institute of Science Education and Research Pune from July 12 - 16, 2021 in honour of Professor M. V. Subbarao (May 4, 1921 – February 15, 2006) on his birth centenary. Due to travel restrictions imposed by the COVID-19 pandemic, this symposium was conducted online and had participation from speakers all across the globe. The editors of this volume are glad to present the Proceedings of this symposium to readers.It contains twelve chapters contributed by symposium speakers, and a personal reminiscence of Professor Subbarao.These articles encompass a wide variety of topics, including those to which Prof. Subbarao has made fundamental contributions, such as partition theory, and the characterization of additive and multiplicative functions. Chapters touch upon wider themes in number theory, such as summation formulas arising from a boundary value problem in heat conduction, parity results for the generalized divisor function, probabilistic limit theorems for the zeta function, infinite-rank Euclidean lattices, the density of visible lattice points, and a question of Baker in transcendental number theory. Finally, in resonance with one of the most challenging problems that the world has faced (and continues to face) in recent times, this volume also contains an article on modelling pandemics with applications to COVID-19.
Presents results obtained in the second funding phase of the DFG Special Priority Program1962
Develops algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences
Considers a wide range of applications
Part of the book series: International Series of Numerical Mathematics (ISNM, volume 173)
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks.
Chapters are written by leading researchers and present results obtained in the second funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2019 to 2025.
This book highlights the statistical data analysis in Statistical Learning, Sustainability and Impact Evaluation
The book includes contributions from statistical scientific community which is interested in new advanced developments
This volume propose the application of new statistical methods in the sustainability and social fields
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 523)
This book contains a selection of the contributions presented at the conference of the Italian Statistical Society - SIS 2023 held in Ancona, 21-23 June 2023 with specific focus on “Statistical Learning, Sustainability and Impact Evaluation”.
Papers concern new challenges of digitalization, innovation and sustainability that are showing the crucial role of data-driven approaches in supporting decision-making processes. Methodologies resulting from the integration of different know-how provide reliable way to deal with the increasing need to measure the impact of the policies and to forecast scenarios. A non-exhaustive list of the topics include papers on: Data Analysis and Classification, Education and students’ assessment, Environmental and Sustainability assessment, Population and health dynamics, Machine and Statistical Learning, Spatial and Spatio-Temporal Modeling, Social and Statistical indicators.
This volume is addressed to researchers as well as to Ph.D. and MSc students interested in new trends and recent developments in the areas of Statistical Learning, Sustainability and Impact Evaluation.
Showcases cutting-edge applications of machine learning, deep learning and optimization in engineering and commerce
Covers real-world problems in facial expression recognition, blockchain security, smart energy and inventory management
Highlights advances in language technologies, recommendation systems, financial forecasting and environmental monitoring
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 526)
This book offers a comprehensive collection of 46 research contributions presented at the 13th International Conference on Soft Computing for Problem Solving (SocProS 2025): Artificial Intelligence for Viksit Bharat (that is, developed India), held at the Indian Institute of Technology Roorkee, Uttrakhand, India, from 24–26 February 2025. It discusses how machine learning, deep learning, optimization and intelligent systems are revolutionizing engineering and commercial practices through applications of mathematics. Covering diverse topics such as facial recognition security, cryptocurrency and blockchain technologies, automated trading, sustainable inventory management, personalized recommendation systems and IoT-driven smart solutions, the book highlights both theoretical advancements and practical implementations of mathematics across a wide range of disciplines.
This book also addresses emerging areas like green energy management, speech recognition, multilingual language technologies and climate analytics. With a strong emphasis on interdisciplinary research, the chapters integrate computational intelligence, engineering innovations and business applications, providing readers with a holistic view of current trends and future opportunities. This book serves as a valuable reference for researchers, practitioners, industry professionals and students aiming to leverage machine learning and optimization techniques for engineering and e-commerce challenges.
Lecture notes by world leading experts in mathematical analysis
Covers recent advancements in mathematical physics
Accessible to beginning researchers in the field
Part of the book series: Lecture Notes in Mathematics (LNM, volume 39)
This volume includes expanded lecture notes from the Mathemata Summer School and Festum Pi 2024 conference, held in Chania, Crete, in July 2024. The lectures focus on advanced analysis techniques for tackling problems in mathematical physics, covering recent advancements in the study of phase transitions, interacting particle systems, kinetic theory, qualitative properties of degenerate Vlasov equations, optimal transport methods for parabolic diffusion equations, and Ricci flow. This volume serves as a valuable resource for researchers exploring modern developments in mathematical analysis. Additionally, it includes two lectures on music theory, reflecting the spirit of Festum Pi 2024.
Highlights cutting-edge developments in change-point analysis, goodness-of-fit testing and nonparametric statistics
Presents invited contributions from renowned statisticians
Celebrates the distinguished career of Marie Hušková
This book on asymptotic and methodological statistics celebrates the distinguished career of Marie Hušková and her foundational work in modern mathematical statistics. It brings together original research contributions from renowned statisticians, focusing on asymptotic theory, methodological innovations, and applications in statistical inference. The volume highlights cutting-edge developments in change-point analysis, goodness-of-fit testing and nonparametric statistics, reflecting the extensive impact Marie Hušková has had in shaping the direction of contemporary statistical science. It serves both as a tribute to her career and as a valuable resource for researchers and PhD students.
Proceedings of the top conference in the field
Covers hot topics in the field
Top-level contributors
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 522)
This volume presents the refereed proceedings of the 16th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Waterloo, Ontario, Canada, and organized by the University of Waterloo in August 2024. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance, statistics, and computer graphics.
Comprehensive reference work important to researchers in industrial engineering, operations research, and mathematics
Revised and expanded third edition of successful reference work
Enhanced online content, up-to-date cross references, and entries keyed to MSC subject codes
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field.
In 2000, the first edition was widely acclaimed and received high praise. J.B. Rosen crowned it “an indispensable resource” and Dingzhu Du lauded it as “the standard most important reference in this very dynamic research field”. Top authors such as Herbert Hauptman (winner of the Nobel Prize) and Leonid Khachiyan (the Ellipsoid theorist) contributed and the second edition kept these seminal entries.
The second edition built upon the success of the first edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as “Algorithms for Genomics”, “Optimization and Radiotherapy Treatment Design”, and “Crew Scheduling”.
The broad field of optimization is dynamic and constantly changing with novel applications, models, and methodologies. The aim of the third edition is to keep this reference work as a defining and authoritative resource in the optimization field, and to reflect recent important advances and developments. In addition to updating a portion of the existing entries, the third edition will include about 200 new entries in several of the optimization areas that have burgeoned since publication of the second edition such as AI, Machine Learning, Robust Optimization, optimization of pharmaceutical manufacturing, and more.