Recurrent neural networks for solving matrix algebra problems

The aim of this dissertation is the application of recurrent neural networks (RNNs) to solving some problems from a matrix algebra with particular reference to the computations of the generalized inverses as well as solving the matrix equations of constant (timeinvariant) matrices. We examine the ability to exploit the correlation between the dynamic state equations of recurrent neural networks for computing generalized inverses and integral representations of these generalized inverses. Recurrent neural networks are composed of independent parts (sub-networks). These sub-networks can work simultaneously, so parallel and distributed processing can be accomplished. In this way, the computational advantages over the existing sequential algorithms can be attained in real-time applications. We investigate and exploit an analogy between the scaled hyperpower family (SHPI family) of iterative methods for computing the matrix inverse and the discretization of Zhang Neural Network (ZNN) models. A class of ZNN models corresponding to the family of hyperpower iterative methods for computing the generalized inverses on the basis of the discovered analogy is defined. The Matlab Simulink implementation of the introduced ZNN models is described in the case of scaled hyperpower methods of the order 2 and 3. We present the Matlab Simulink model of a hybrid recursive neural implicit dynamics and give a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model

MATLAB SIMULATION OF THE HYBRID OF RECURSIVE NEURAL DYNAMICS FOR ONLINE MATRIX INVERSION

A novel kind of a hybrid recursive neural implicit dynamics for real-time matrix inversion has been recently proposed and investigated. Our goal is to compare the hybrid recursive neural implicit dynamics on the one hand, and conventional explicit neural dynamics on the other hand. Simulation results show that the hybrid model can coincide better with systems in practice and has higher abilities in representing dynamic systems. More importantly, hybrid model can achieve superior convergence performance in comparison with the existing dynamic systems, specifically recently-proposed Zhang dynamics. This paper presents the Simulink model of a hybrid recursive neural implicit dynamics and gives a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model

A novel quaternion linear matrix equation solver through zeroing neural networks with applications to acoustic source tracking

Due to its significance in science and engineering, time-varying linear matrix equation (LME) problems have received a lot of attention from scholars. It is for this reason that the issue of finding the minimum-norm least-squares solution of the time-varying quaternion LME (ML-TQ-LME) is addressed in this study. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. In light of that, two new ZNN models are introduced to solve the ML-TQ-LME problem for time-varying quaternion matrices of arbitrary dimension. Two simulation experiments and two practical acoustic source tracking applications show that the models function superbly

Applications of Zhang neural networks to economics

Τα υποδείγματα Leontief, γνωστά και ως μοντέλα Εισροών-Εκροών, περιγράφουν την αλληλεξάρτηση μεταξύ των διαφόρων βιομηχανικών τομέων σε μια οικονομία και αποτελούν ένα ευρέως χρησιμοποιούμενο ανα τον κόσμο μακροοικονομικό εργαλείο. Στην βιβλιογραφία συναντώνται διάφορες βελτιστοποιημένες εκδοχές των αρχικού μοντέλου Leontief με σκοπό την ρεαλιστικότερη και ακριβέστερη δυνατή πληροφόρηση και συμπερασματολογία ως προς τις διαβιομηχανικές αλληλεπιδράσεις. Στην παρούσα διπλωματική εργασία γίνεται μια προσέγγιση στο εκτενές χρονικά μεταβαλλόμενο σε συνεχή χρόνο δυναμικό μοντέλο Leontief, για το οποίο δεν προσφέρεται λύση στην εώς τωρα διεθνή βιβλιογραφία, έχοντας ως στόχο την επίλυση αυτού μέσω της χρήσης των Zhang νευρωνικών δικτύων. Στο μοντέλο αυτό είναι χρονικά μεταβαλλόμενοι και οι συντελεστές του πίνακα Εισροών-Εκροών αλλά και οι συντελεστές του πίνακα κεφαλαίών. Επιτυγχάνεται λύση μέσω της επίλυσης χρονικά μεταβαλλόμενου γραμμικού συστήματως αλλά και μέσω της εύρεσης αντιστρόφου ενός χρονικά μεταβαλλόμενου πίνακα για την ειδική περίπτωση όπου ο πίνακας κεφαλαίων είναι ο μηδενικός πίνακας, διασφαλίζοντας επίσης την ύπαρξη αποδεκτών λύσεων για το ειδικό αυτό μοντέλο.Leontief models, also known as Input-Output models, describe the interdependence between different industrial sectors in an economy and are a widely used macroeconomic tool for the world. Several improved versions of Leontief’s analytical framework meet in the literature to provide more realistic and accurate information, thus, perception on the interactions of the industry. In this thesis we come across an effort to approach the extended time-varying Leontief model in continuous time, for which no solution is proposed in the general literature. Our goal is to provide an online solution for the aforementioned dynamic model by using Zhang neural networks. In this model the coefficients of Input-Output matrix as so the coefficients of the capital matrix are time-varying. Solution is obtained by solving time-varying linear system of equations during which we need to obtain also the inverse of time-varying matrix, for the special case where the capital coefficients matrix is the zero matrix, while also ensuring the existence of acceptable solutions for this special model

Novel decoupling networks for small antenna arrays

Ph.DDOCTOR OF PHILOSOPH

On the concentration properties of Interacting particle processes

These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. We illustrate these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling and the quantitative performance analysis of a series of advanced Monte Carlo methods, including particle filters, genetic type island models, Markov bridge models, interacting particle Markov chain Monte Carlo methodologies

Intelligent Transportation Related Complex Systems and Sensors

Building around innovative services related to different modes of transport and traffic management, intelligent transport systems (ITS) are being widely adopted worldwide to improve the efficiency and safety of the transportation system. They enable users to be better informed and make safer, more coordinated, and smarter decisions on the use of transport networks. Current ITSs are complex systems, made up of several components/sub-systems characterized by time-dependent interactions among themselves. Some examples of these transportation-related complex systems include: road traffic sensors, autonomous/automated cars, smart cities, smart sensors, virtual sensors, traffic control systems, smart roads, logistics systems, smart mobility systems, and many others that are emerging from niche areas. The efficient operation of these complex systems requires: i) efficient solutions to the issues of sensors/actuators used to capture and control the physical parameters of these systems, as well as the quality of data collected from these systems; ii) tackling complexities using simulations and analytical modelling techniques; and iii) applying optimization techniques to improve the performance of these systems. It includes twenty-four papers, which cover scientific concepts, frameworks, architectures and various other ideas on analytics, trends and applications of transportation-related data

Developing New Methods for Efficient Container Stacking Operations

Containerized transportation has become an essential part of the intermodal freight transport. Millions of containers pass through container terminals on an annual basis. Handling a large number of containers arriving and leaving terminals by different modalities including the new mega-size ships significantly affects the performance of terminals. Container terminal operators are always looking for new technologies and smart solutions to maintain efficiency. They need to know how different operations at the terminal interact and affect the performance of the terminal as a whole. Among all operations, the stacking area is of special importance since almost every container must be stacked in this area for a period of time. If the stacking operations of the terminal are not well managed, then the response time of the terminal significantly increases and consequently the performance decreases. In this dissertation, we propose, develop, and test optimization methods to support the decisions of container terminal operators in the stacking area. First, we study how to sequence storage and retrieval containers to be carried out by a single or two automated stacking cranes in a block of containers. The objective is to minimize the makespan of the cranes. Finally, we study how to minimize the expected number of reshuffles when incoming containers have to be stacked in a block of containers. A reshuffle is the removal of a container stacked on top of a desired container. Reshuffling containers is one of the daily operations at a container terminal which is time consuming and increases a ship's berthing time

Maximally localized Wannier functions: Theory and applications

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.Comment: 62 pages. Accepted for publication in Reviews of Modern Physic

Hybrid GNN-ZNN models for solving linear matrix equations

New dynamical models for solving the matrix equations BX=D and XC=D are developed in time-invariant case. These models are derived as a combination of GNN and ZNN models. They do not posses GNN dynamic due to their implicit dynamics. Formally observed, they can be derived by multiplying the right hand side in the ZNN dynamics by an appropriate symmetric positive definite matrix which improves the convergence rate. For this purpose, these models are termed as HZNN. The convergence of HZNN models is global and exponential. Also, the convergence rate of HZNN models is superior with respect to the convergence rate of the classical GNN model as well as with respect to ZNN models in time-invariant case. Capability of the HZNN models to overcome unavoidable implementation noises is considered theoretically and numerically. The Matlab implementation of HZNN models is proposed and used in numerical experiments for solving matrix equations and computing various appearances of outer inverses with prescribed range and null space. © 2018 Elsevier B.V