Optimization, Discrete Mathematics and Applications to Data Sciences

This book delves into the dynamic intersection of optimization and discrete mathematics, offering a comprehensive exploration of their applications in data sciences. Through a collection of high-quality papers, readers will gain insights into cutting-edge research and methodologies that address complex problems across a wide array of topics.

The chapters cover an impressive range of subjects, including advances in the study of polynomials, combinatorial identities, and global optimization algorithms. Readers will encounter innovative approaches to predictive models for non-performing loans, rainbow greedy matching algorithms, and the cost of detection in interaction testing. The book also examines critical issues such as demand aggregation, mid-term energy planning, and minimum-cost energy flow. Contributions from expert authors provide a deep dive into multilevel low-rank matrices, the protection of medical image authenticity, and the mathematical intricacies of the Braess paradox. This volume invites readers to explore diverse perspectives and theoretical insights that are both practical and forward-thinking.

This publication is an invaluable resource for graduate students and advanced researchers in the fields of optimization and discrete mathematics. It is particularly beneficial for those interested in their applications within data sciences. Academics across these disciplines will find the book's content relevant to their work, while practitioners seeking to apply these concepts in industry will appreciate its practical case studies. Whether you are a scholar or a professional, this book offers a wealth of knowledge that bridges theory with real-world applications.

The volume appeals to a wide readership The chapters present the state-of-the art knowledge on the problems studied The readers are introduced to problems of vibrant activity

Auteur

Ashkan Nikeghbali holds the Chair in Financial Mathematics at the University of Zürich. His fields of research span through a broad spectrum of areas, including finance mathematics, number theory, random matrices, and stochastic processes. Since 2016 Professor Nikeghbali has been a member of the Scientific Advisory Board of swissQuant and a member of the Advisory Board of EVMTech. He is also a strategy advisor for data analysis and modeling of stochastic processes at Roche Holding in Basel, Switzerland. Professor Nikeghbali has authored/edited several books. In 2019, he was awarded with an Honorary Doctorate from the "1 Decembrie 1918" University of Alba Iulia.

Panos Pardalos is a Distinguished Emeritus Professor in the Department of Industrial and Systems Engineering at the University of Florida, and an affiliated faculty of Biomedical Engineering and Computer Science & Information & Engineering departments. He is a world-renowned leader in Global Optimization, Mathematical Modeling, Energy Systems, Financial applications, and Data Sciences. He is a Fellow of AAAS, AAIA, AIMBE, EUROPT, and INFORMS and was awarded the 2013 Constantin Caratheodory Prize of the International Society of Global Optimization. In addition, Panos Pardalos has been awarded the 2013 EURO Gold Medal prize bestowed by the Association for European Operational Research Societies. This medal is the preeminent European award given to Operations Research (OR) professionals for "scientific contributions that stand the test of time." He has also been awarded the prestigious Humboldt Research Award (2018-2019). The Humboldt Research Award is granted in recognition of a researcher's entire achievements to date - fundamental discoveries, new theories, insights that have had significant impact on their discipline.

Michael Th. Rassias is an Associate Professor at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F Nash, Jr. (Nobel Prize, 1994 and Abel Prize, 2015) the volume Open Problems in Mathematics, Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books, including the edited volume Analysis at Large jointly with A. Avila (Fields Medal, 2014) and Y. Sinai (Abel Prize, 2014). His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach's conjecture, the distribution of prime numbers, approximation theory, functional equations, analytic inequalities and Cryptography.

Contenu

On the morphism 1 121, 2 12221.- Polynomials and combinatorial identities.- Rainbow Greedy Matching Algorithms.- Predictive models of Non-Performing Loans: the case of Greece.- The Cost of Detection in Interaction Testing.- On the study of cycle chains representing non-reversible Markov chains associated with random walks with jumps in fixed environments.- Applying Distance Measures for Discrete Data.- Demand aggregation and mid-term energy planning problem on the business layer.- Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices.- A Code-based Watermarking Scheme for the Protection of Authenticity of Medical Images.- The minimum cost energy flow problem under demand uncertainty Effect on optimal solution, variability, worst and best case scenarios.- A mathematical study of the Braess's Paradox within a network comprising four nodes, five edges, and linear time functions.- On similiarities between two global optimization algorithms based on different (Bayesian and Lipschitzian) approaches.