Advanced Mathematical Applications in Data Science comprehensively explores the crucial role mathematics plays in the field of data science. Each chapter is contributed by scientists, researchers, and academicians. The 13 chapters cover a range of mathematical concepts utilized in data science, enabling readers to understand the intricate connection between mathematics and data analysis. The book covers diverse topics, including, machine learning models, the Kalman filter, data modeling, artificial neural networks, clustering techniques, and more, showcasing the application of advanced mathematical tools for effective data processing and analysis. With a strong emphasis on real-world applications, the book offers a deeper understanding of the foundational principles behind data analysis and its numerous interdisciplinary applications. This reference is an invaluable resource for graduate students, researchers, academicians, and learners pursuing a research career in mathematical computing or completing advanced data science courses. Key Features: Comprehensive coverage of advanced mathematical concepts and techniques in data science Contributions from established scientists, researchers, and academicians Real-world case studies and practical applications of mathematical methods Focus on diverse areas, such as image classification, carbon emission assessment, customer churn prediction, and healthcare data analysis In-depth exploration of data science's connection with mathematics, computer science, and artificial intelligence Scholarly references for each chapter Suitable for readers with high school-level mathematical knowledge, making it accessible to a broad audience in academia and industry.

Ongoing advancements in modern technology have led to significant developments in intelligent systems. With the numerous applications available, it becomes imperative to conduct research and make further progress in this field. Intelligent Systems: Concepts, Methodologies, Tools, and Applications contains a compendium of the latest academic material on the latest breakthroughs and recent progress in intelligent systems. Including innovative studies on information retrieval, artificial intelligence, and software engineering, this multi-volume book is an ideal source for researchers, professionals, academics, upper-level students, and practitioners interested in emerging perspectives in the field of intelligent systems.

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

This book comprehensively discusses the modeling of real-world industrial problems and innovative optimization techniques such as heuristics, finite methods, operation research techniques, intelligent algorithms, and agent- based methods. Discusses advanced techniques such as key cell, Mobius inversion, and zero suffix techniques to find initial feasible solutions to optimization problems. Provides a useful guide toward the development of a sustainable model for disaster management. Presents optimized hybrid block method techniques to solve mathematical problems existing in the industries. Covers mathematical techniques such as Laplace transformation, stochastic process, and differential techniques related to reliability theory. Highlights application on smart agriculture, smart healthcare, techniques for disaster management, and smart manufacturing. Advanced Mathematical Techniques in Computational and Intelligent Systems is primarily written for graduate and senior undergraduate students, as well as academic researchers in electrical engineering, electronics and communications engineering, computer engineering, and mathematics.

The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.

It is with great pleasure to present the proceedings of the International Conference on Computational Intelligence and Mathematical Applications (ICCIMA 2023), held on 21-22 December 2023, at Panipat Institute of Engineering and Technology, Panipat. This conference brought scholars, researchers, professionals, and intellectuals together from diverse fields to exchange ideas, share insights, and foster collaborations in Optimization, Computational Intelligence and Mathematical Applications. The ICCIMA 2023 served as a platform for contributors to demonstrate their latest findings, discuss emerging trends, and explore innovations to the problems that different disciplines are currently experiencing. The conference’s scope and depth of themes reflect our community’s rich diversity of interests and levels of competence.

This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.

This volume contains original, refereed contributions by researchers from national metrology institutes, universities and laboratories across the world involved in metrology and testing. The volume has been produced by the International Measurement Confederation Technical Committee 21, Mathematical Tools for Measurements and is the twelfth in the series. The papers cover topics in numerical analysis and computational tools, statistical inference, regression, calibration and metrological traceability, computer science and data provenance, and describe applications in a wide range of application domains. This volume is useful to all researchers, engineers and practitioners who need to characterize the capabilities of measurement systems and evaluate measurement data. It will also be of interest to scientists and engineers concerned with the reliability, trustworthiness and reproducibility of data and data analytics in data-driven systems in engineering, environmental and life sciences.

This volume will interest researchers and others involved with high-precision measurements and the development of mathematical tools for this purpose. Advances in metrology depend on improvements in scientific and technical knowledge, the quality of instruments, a better use of advanced mathematical tools and the development of new ones.A tradition of close cooperation between metrologists and mathematicians, while found elsewhere, is lacking in Italy. This workshop wishes to start such a cooperation by providing a common meeting ground. Several industrial sectors, particularly those of instrumentation and software, are likely to benefit from this process, since metrology has a high impact on the overall quality of industrial products and applied mathematics is becoming increasingly important in industrial processes.

This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments Relations Part II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master’s degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).