Since the outstanding and pioneering research work of Hopfield on recurrent neural networks (RNNs) in the early 80s of the last century, neural networks have rekindled strong interests in scientists and researchers. Recent years have recorded a remarkable advance in research and development work on RNNs, both in theoretical research as weIl as actual applications. The field of RNNs is now transforming into a complete and independent subject. From theory to application, from software to hardware, new and exciting results are emerging day after day, reflecting the keen interest RNNs have instilled in everyone, from researchers to practitioners. RNNs contain feedback connections among the neurons, a phenomenon which has led rather naturally to RNNs being regarded as dynamical systems. RNNs can be described by continuous time differential systems, discrete time systems, or functional differential systems, and more generally, in terms of non linear systems. Thus, RNNs have to their disposal, a huge set of mathematical tools relating to dynamical system theory which has tumed out to be very useful in enabling a rigorous analysis of RNNs.

Abstract: "Max and min operations have interesting properties that facilitate the exchange of information between the symbolic and real- valued domains. As such, neural networks that employ max-min activation functions have been a subject of interest in recent years. Since max-min functions are not strictly differentiable, many ad hoc learning methods for such max-min neural networks have been proposed in the literature. In this technical report, we propose a mathematically sound learning method based on using Fourier convergence analysis to derive a gradient descent technique for max-min error functions. This method is then applied to two models: a feedforward fuzzy-neural network and a recurrent max-min neural network. We show how a 'typical' fuzzy-neural network model employing max- min activation functions can be trained to perform function approximation; its performance was found to be better than that of a conventional feedforward neural network. We also propose a novel recurrent max-min neural network model which is trained to perform grammatical inference as an application example. Comparisons are made between this model and recurrent neural networks that use conventional sigmoidal activation fuctions; such recurrent sigmoidal networks are known to be difficult to train and generalize poorly on long strings. The comparisons show that our model not only performs better in terms of learning speed and generalization, its final weight configuration allows a DFQ to be extracted in a straighforward manner. However, it has a potential drawback: the minimal network size required for successful convergence grows with increasing language depth and complexity. Nevertheless, we are able to demonstrate that our proposed gradient descent technique does allow max-min neural networks to learn effectively. Our leaning method should be extensible to other neural networks that have non-differentiable activation functions."

Zeroing Neural Networks Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps. Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book: Describes how to design, analyze, and apply FTZNN models for solving computational problems Presents multiple FTZNN models for solving time-varying computational problems Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.

This book presents the latest, innovative research findings on P2P, Parallel, Grid, Cloud, and Internet Computing. It gathers the Proceedings of the 12th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing, held on November 8–10, 2017 in Barcelona, Spain. These computing technologies have rapidly established themselves as breakthrough paradigms for solving complex problems by enabling the aggregation and sharing of an increasing variety of distributed computational resources at large scale. Grid Computing originated as a paradigm for high-performance computing, offering an alternative to expensive supercomputers through different forms of large-scale distributed computing, while P2P Computing emerged as a new paradigm after client-server and web-based computing and has shown to be useful in the development of social networking, B2B (Business to Business), B2C (Business to Consumer), B2G (Business to Government), B2E (Business to Employee), and so on. Cloud Computing has been defined as a “computing paradigm where the boundaries of computing are determined by economic rationale rather than technical limits”. Cloud computing has quickly been adopted in a broad range of application domains and provides utility computing at large scale. Lastly, Internet Computing is the basis of any large-scale distributed computing paradigm; it has very rapidly developed into a flourishing field with an enormous impact on today’s information societies, serving as a universal platform comprising a large variety of computing forms such as Grid, P2P, Cloud and Mobile computing. The aim of the book “Advances on P2P, Parallel, Grid, Cloud and Internet Computing” is to provide the latest findings, methods and development techniques from both theoretical and practical perspectives, and to reveal synergies between these large-scale computing paradigms.

This book presents deep learning techniques, concepts, and algorithms to classify and analyze big data. Further, it offers an introductory level understanding of the new programming languages and tools used to analyze big data in real-time, such as Hadoop, SPARK, and GRAPHX. Big data analytics using traditional techniques face various challenges, such as fast, accurate and efficient processing of big data in real-time. In addition, the Internet of Things is progressively increasing in various fields, like smart cities, smart homes, and e-health. As the enormous number of connected devices generate huge amounts of data every day, we need sophisticated algorithms to deal, organize, and classify this data in less processing time and space. Similarly, existing techniques and algorithms for deep learning in big data field have several advantages thanks to the two main branches of the deep learning, i.e. convolution and deep belief networks. This book offers insights into these techniques and applications based on these two types of deep learning. Further, it helps students, researchers, and newcomers understand big data analytics based on deep learning approaches. It also discusses various machine learning techniques in concatenation with the deep learning paradigm to support high-end data processing, data classifications, and real-time data processing issues. The classification and presentation are kept quite simple to help the readers and students grasp the basics concepts of various deep learning paradigms and frameworks. It mainly focuses on theory rather than the mathematical background of the deep learning concepts. The book consists of 5 chapters, beginning with an introductory explanation of big data and deep learning techniques, followed by integration of big data and deep learning techniques and lastly the future directions.

This book uses numerical analysis as the main tool to investigate methods in machine learning and A.I. The efficiency of neural network representation on for polynomial functions is studied in detail, together with an original description of the Latin hypercube method. In addition, unique features include the use of Tensorflow for implementation on session and the application n to the construction of new optimized numerical schemes.