Ergodic Dynamics : From Basic Theory to Applications
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms.
Related Books
New challenges in software engineering ; Vol 1
Explores the key challenges shaping the future of software development, including automation, AI-driven development, security-focused engineering, resilient and autonomous architectures, business process optimization, cloud computing, microservices, high-performance distributed systems, and sustainable technologies. Software engineering is undergoing a constant transformation, driven by rapid technological advances and evolving market demands. additionally, it delves into the ethical considerations of AI, the evolution of intuitive user interfaces, and the importance of multidisciplinary collaboration.
Fundamentals of manufacturing engineering using digital visualization
Offers a guide to core principles and practices of manufacturing engineering. It covers the design of, together with technological and measurement issues for, technical systems. Locating charts and setup schemes describing different machining processes are included. Concepts of product quality, with a focus on accuracy indicators, machining accuracy, roughness, and the impact of surface quality on exploitation properties are also explained. Furthermore, key machining methods, including turning, milling, hole machining, grinding, and gear machining, are analyzed in depth, covering their principles, applications, and techniques. The book is enriched by QR codes, linking to a mobile application presenting additional information about the content, for an interactive and extended learning experience. It also uses illustrations visualized with digital tools to promote a better understanding of the concepts.
AI in drug discovery
Constitutes the refereed proceedings of the First international workshop on ai in Drug Discovery, AIDD 2024, held as a part of the 33rd International Conference on Artificial Neural Networks, ICANN 2024, in Lugano, Switzerland, on September 19, 2024. These papers focus on various aspects of the rapidly evolving field of Artificial Intelligence (AI)-driven drug discovery in chemistry, including Big Data and advanced Machine Learning, eXplainable AI (XAI), Chemoinformatics, Use of deep learning to predict molecular properties, Modeling and prediction of chemical reaction data and Generative models.
AI in banking : Practical applications and case studies
Delves into the application of AI from theory to practice, offering detailed insights into AI project design and code implementation across eleven business scenarios in four major sectors: retail banking, e-banking, bank credit, and tech operations. it provides hands-on examples of various technologies, including automatic machine learning, integrated learning, graph computation, recommendation systems, causal inference, generative adversarial networks, supervised learning, unsupervised learning, computer vision, reinforcement learning, fuzzy control, automatic control, speech recognition, semantic understanding, bayesian networks, edge computing, and more. this book stands as a rare and practical guide to AI projects in the banking industry.
