Системи диференциални уравнения и невронни мрежи със закъснения и импулси

Department of Mathematics & Statistics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman и ИМИ-БАН, 16.06.2014 г., присъждане на научна степен "доктор на науките" на Валерий Ковачев по научна специалност 01.01.13. математическо моделиране и приложение на математиката. [Covachev Valery Hristov; Ковачев Валерий Христов

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Sliding intermittent control for BAM neural networks with delays

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/615947 Open AccessThis paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuous feedback control, the impulsive control, the periodically intermittent control, and the semi-impulsive control. By using analysis techniques and the Lyapunov function methods, some sufficient criteria are derived for the closed-loop delayed BAM neural networks to be globally exponentially stable. Finally, two illustrative examples are given to show the effectiveness of the proposed control scheme and the obtained theoretical results

Synaptic plasticity and memory addressing in biological and artificial neural networks

Biological brains are composed of neurons, interconnected by synapses to create large complex networks. Learning and memory occur, in large part, due to synaptic plasticity -- modifications in the efficacy of information transmission through these synaptic connections. Artificial neural networks model these with neural "units" which communicate through synaptic weights. Models of learning and memory propose synaptic plasticity rules that describe and predict the weight modifications. An equally important but under-evaluated question is the selection of \textit{which} synapses should be updated in response to a memory event. In this work, we attempt to separate the questions of synaptic plasticity from that of memory addressing. Chapter 1 provides an overview of the problem of memory addressing and a summary of the solutions that have been considered in computational neuroscience and artificial intelligence, as well as those that may exist in biology. Chapter 2 presents in detail a solution to memory addressing and synaptic plasticity in the context of familiarity detection, suggesting strong feedforward weights and anti-Hebbian plasticity as the respective mechanisms. Chapter 3 proposes a model of recall, with storage performed by addressing through local third factors and neo-Hebbian plasticity, and retrieval by content-based addressing. In Chapter 4, we consider the problem of concurrent memory consolidation and memorization. Both storage and retrieval are performed by content-based addressing, but the plasticity rule itself is implemented by gradient descent, modulated according to whether an item should be stored in a distributed manner or memorized verbatim. However, the classical method for computing gradients in recurrent neural networks, backpropagation through time, is generally considered unbiological. In Chapter 5 we suggest a more realistic implementation through an approximation of recurrent backpropagation. Taken together, these results propose a number of potential mechanisms for memory storage and retrieval, each of which separates the mechanism of synaptic updating -- plasticity -- from that of synapse selection -- addressing. Explicit studies of memory addressing may find applications not only in artificial intelligence but also in biology. In artificial networks, for example, selectively updating memories in large language models can help improve user privacy and security. In biological ones, understanding memory addressing can help with health outcomes and treating memory-based illnesses such as Alzheimers or PTSD

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Power Quality Issues in Distributed Generation

This book deals with several selected aspects of electric power quality issues typically faced during grid integration processes of contemporary renewable energy sources. In subsequent chapters of this book the reader will be familiarized with the issues related to voltage and current harmonics and inter-harmonics generation and elimination, harmonic emission of switch-mode rectifiers, reactive power flow control in power system with non-linear loads, modeling and simulation of power quality issues in power grid, advanced algorithms used for estimating harmonic components, and new methods of measurement and analysis of real time accessible power quality related data

Institute of Safety Research, Annual Report 1995

The report gives an overview on the scientific work of the Institute of Safety Research in 1995