This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.
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This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
This book presents a class of novel optimal control methods and games schemes based on adaptive dynamic programming techniques. For systems with one control input, the ADP-based optimal control is designed for different objectives, while for systems with multi-players, the optimal control inputs are proposed based on games. In order to verify the effectiveness of the proposed methods, the book analyzes the properties of the adaptive dynamic programming methods, including convergence of the iterative value functions and the stability of the system under the iterative control laws. Further, to substantiate the mathematical analysis, it presents various application examples, which provide reference to real-world practices.
This volume documents the contributions presented at The ICRTMPCS II International Conference on Advances in Mathematical and Computational Sciences. Entries focus on modern trends and techniques in branches of pure and applied mathematics, statistics, and computer science. Highlighting applications in coding theory, cryptography, graph theory, fuzzy theory, variance analysis, data analysis, and sampling theory.
The concepts and techniques presented in this volume originated from the fields of dynamics, statistics, control theory, computer science and informatics, and are applied to novel and innovative real-world applications. Over the past few decades, the use of dynamic systems, control theory, computing, data mining, machine learning and simulation has gained the attention of numerous researchers from all over the world. Admirable scientific projects using both model-free and model-based methods coevolved at today’s research centers and are introduced in conferences around the world, yielding new scientific advances and helping to solve important real-world problems. One important area of progress is the bioeconomy, where advances in the life sciences are used to produce new products in a sustainable and clean manner. In this book, scientists from all over the world share their latest insights and important findings in the field. The majority of the contributed papers for this volume were written by participants of the 3rd International Conference on Dynamics, Games and Science, DGSIII, held at the University of Porto in February 2014, and at the Berkeley Bioeconomy Conference at the University of California at Berkeley in March 2014. The aim of the project of this book “Modeling, Dynamics, Optimization and Bioeconomics II” follows the same aim as its companion piece, “Modeling, Dynamics, Optimization and Bioeconomics I,” namely, the exploration of emerging and cutting-edge theories and methods for modeling, optimization, dynamics and bioeconomy.
This book constitutes the refereed proceedings of the 13th International Symposium on Neural Networks, ISNN 2016, held in St. Petersburg, Russia in July 2016. The 84 revised full papers presented in this volume were carefully reviewed and selected from 104 submissions. The papers cover many topics of neural network-related research including signal and image processing; dynamical behaviors of recurrent neural networks; intelligent control; clustering, classification, modeling, and forecasting; evolutionary computation; and cognition computation and spiking neural networks.
This book focuses on the stability of the dynamical neural system, synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined concept of stability, synchronization and consensus are adopted to provide a better explanation of the complex neural network. Researchers in the fields of dynamical systems, computer science, electrical engineering and mathematics will benefit from the discussions on complex systems. The book will also help readers to better understand the theory behind the control technique and its design.
Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.
This book briefly covers internationally contributed chapters with artificial intelligence and applied mathematics-oriented background-details. Nowadays, the world is under attack of intelligent systems covering all fields to make them practical and meaningful for humans. In this sense, this edited book provides the most recent research on use of engineering capabilities for developing intelligent systems. The chapters are a collection from the works presented at the 2nd International Conference on Artificial Intelligence and Applied Mathematics in Engineering held within 09-10-11 October 2020 at the Antalya, Manavgat (Turkey). The target audience of the book covers scientists, experts, M.Sc. and Ph.D. students, post-docs, and anyone interested in intelligent systems and their usage in different problem domains. The book is suitable to be used as a reference work in the courses associated with artificial intelligence and applied mathematics.
