Neural Computing in Quaternion Algebra

兵庫県立大学201

Selected aspects of complex, hypercomplex and fuzzy neural networks

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.Comment: 46 page

Learning Schemes for Recurrent Neural Networks

兵庫県立大学大学院202

Learning Schemes for Recurrent Neural Networks

兵庫県立大学大学院202

Advanced Information Processing Methods and Their Applications

This Special Issue has collected and presented breakthrough research on information processing methods and their applications. Particular attention is paid to the study of the mathematical foundations of information processing methods, quantum computing, artificial intelligence, digital image processing, and the use of information technologies in medicine

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Modeling and Simulation in Engineering

The Special Issue Modeling and Simulation in Engineering, belonging to the section Engineering Mathematics of the Journal Mathematics, publishes original research papers dealing with advanced simulation and modeling techniques. The present book, “Modeling and Simulation in Engineering I, 2022”, contains 14 papers accepted after peer review by recognized specialists in the field. The papers address different topics occurring in engineering, such as ferrofluid transport in magnetic fields, non-fractal signal analysis, fractional derivatives, applications of swarm algorithms and evolutionary algorithms (genetic algorithms), inverse methods for inverse problems, numerical analysis of heat and mass transfer, numerical solutions for fractional differential equations, Kriging modelling, theory of the modelling methodology, and artificial neural networks for fault diagnosis in electric circuits. It is hoped that the papers selected for this issue will attract a significant audience in the scientific community and will further stimulate research involving modelling and simulation in mathematical physics and in engineering