This paper presents a complete analysis of a new model of market share dynamics under advertising effort, taking into account word-of-mouth (WOM) interactions between satisfied customers, dissatisfied defectors, as well as undecided customers. The populations of satisfied customers and defectors are both modeled as competing predators preying on a population of undecided customers, using Lotka-Volterra-type interaction terms, which have also been used in a related, but different, class of WOM and electronic WOM models. The proposed model describes the dynamics of market share from arbitrary nonnegative initial conditions, up to and including the market in which there are no longer any undecided customers, thereby extending both the classical Vidale-Wolfe model in which the market with no undecided customers is never reached at equilibrium due to the positive decay term, as well as the Lanchester model which only deals with the market with no undecided customers. Another new feature of the proposed model is that, even under constant advertising effort, and fixed values of interaction coefficients, different outcomes can arise, depending on the initial fractions of satisfied customers and defectors. The design of a class of advertising policies that attain a desired market share is also presented, with corresponding numerical simulations.

This paper introduces an ACO model and associated algorithm, called Coupled EigenAnt, for the problem of finding the shortest of N paths between a source and a destination node. It is based on the recently introduced EigenAnt algorithm, the novelty being that it allows probabilistic path choice on both the forward and return journeys, as well as the fact that it introduces decay of pheromone deposition following a geometric progression. Equilibrium points of the model are calculated and the local stability of the two path synchronous version analyzed. Simulations illustrate the main features of the algorithm.

This paper presents a Hill-climbing technique applied to a residential energy system control and management, based on battery energy storage connected to power grids. The main focus is to develop an optimal controller that is both easy to implement and capable of minimizing the electricity cost for residential customers. Simulation results corroborate the advantages of the proposed method.

This paper presents a unified way to design neural networks characterized as second-order ordinary differential equations (ODE), the trajectories of which can converge to the global minimum of nonconvex scalar functions. These neural networks, sometimes also called continuous-time algorithms, are interpreted as closed-loop control systems and the state feedback design is based on control Lyapunov functions. The focus is on a new family of continuous-time versions of conjugate gradient method, named controlled conjugate gradient (CCG) nets, that generalize heavy ball with friction (HBF) nets. For nonconvex functions, the goal of these nets is to produce trajectories that start from an arbitrary initial point and can escape from local minima, thereby increasing the chances of converging to the global minimum. Several numerical examples are given, using benchmark problems, showing that this escape and subsequent convergence to the global minimum occurs.

This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex functions that have continuous first- and second-order derivatives and a unique global minimum. The approach is based on interpreting the function as a controlled object, namely one that has an output (the function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov function (CLF) technique, well known in systems and control theory. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its competitors, such as the heavy ball with friction method or the more recent dynamic inertial Newton-like method.

The problem of restoring images degraded by linear position invariant distortions and noise is solved by means of a L1-norm regularization, which is equivalent to determining a L1-norm solution of an overdetermined system of linear equations, which results from a data-fitting term plus a regularization term that are both in L1norm. This system is solved by means of a gradient-based neural network with a discontinuous activation function, which is ensured to converge to a L1-norm solution of the corresponding system of linear equations.

A solution for the load balancing problem in local clusters of heterogeneous processors is proposed within the setting of delayed artificial neural networks, optimal control and linear matrix inequalities (LMI) theory. Based on a mathematical model that includes delays and processors with different processing velocities, this model is transformed into a special case of delayed cellular neural networks model. A systematic method of controller synthesis is derived, based on two coupled linear matrix inequalities - one guaranteeing global convergence and the other guaranteeing performance in the linear region of operation. Simulations and computational experiments show the efficiency of this approach, reducing load balancing time.

This paper presents the implementation of two neural networks for SVM training in parallel computers. The results obtained are compared with two well known packages for SVM training and the parallel implementation shows that the neural network approach can be as accurate as the traditional packages and, since the proposed gradient-based neural networks can be easily parallelized, the proposed approach is scalable and the training times can be considerably reduced.

A gradient system with discontinuous righthand side that solves an underdetermined system of linear equations in the L/sub 1/ norm is presented. An upper bound estimate for finite time convergence to a solution set of the system of linear equations is shown by means of the Persidskii form of the gradient system and the corresponding nonsmooth diagonal type Lyapunov function. This class of systems can be interpreted as a recurrent neural network and an application devoted to solving least squares support vector machines (LS-SVM) is used as an example.

This paper implements support vector machines (SVM) for the discrimination of nonseparable classes using gradient systems with discontinuous righthand sides. The gradient systems are obtained from an exact penalty method applied to the constrained quadratic optimization problems. Global convergence to the solution of the corresponding constrained problems is shown to be independent of the penalty parameters and of the regularization parameter of the SVM.

A k-winners-take-all (KWTA) problem is formulated as a linear programming (LP) problem with bounded variables. The solution set of the LP problem determines the winners. The LP problem is converted into an unconstrained optimization problem with two exact penalty functions, that is solved by using a gradient descent method implemented as a neural network. Theoretical results ensuring the convergence to the correct solution are provided.

A new analog inhibitory Hopfield based winner-take-all (WTA) circuit is proposed. The general circuit structure is a binary tree arrangement of second order Hopfield networks and logic nodes. The connection matrix belongs to the class of diagonally stable block diagonal matrices and the activation functions are piecewise linear or sigmoidal. The mathematical justification of the WTA circuit functioning, on the basis of the uniqueness and global asymptotic stability of the equilibrium, is given. Simulation examples are also provided.

It is shown that the assumption of D-stability of the interconnection matrix, together with the standard assumptions on the activation functions, guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes. For the synchronous mode, these assumptions are also shown to imply local asymptotic stability of the equilibrium. For the asynchronous mode of operation, two results are derived. First, it is shown that symmetry and stability of the interconnection matrix guarantee local asymptotic stability of the equilibrium under a class of asynchronous modes-this is referred to as local absolute asymptotic stability. Second, it is shown that, under the standard assumptions, if the nonnegative matrix whose elements are the absolute values of the corresponding elements of the interconnection matrix is stable, then the equilibrium is globally absolutely asymptotically stable under a class of asynchronous modes. The results obtained are discussed from the points of view of their applications, robustness, and their relationship to earlier results.

This paper formalizes a general technique to combine different methods in the solution of large systems of nonlinear equations using parallel asynchronous implementations on distributed-memory multiprocessor systems. Such combinations of methods, referred to as team algorithms, are evaluated as a way of obtaining desirable properties of different methods and a sufficient condition for their convergence is derived. The load flow problem of electrical power networks is presented as an example problem that, under certain conditions, has the characteristics to make a team algorithm an appealing choice for its solution. Experimental results of an implementation on an Intel iPSC/860 Hypercube are reported, showing that considerable speedup and robustness can be obtained using team algorithms.

This paper investigates a continuous-valued discrete-time analog of the well-known continuous-valued continuous-time Hopfield neural network model, first proposed by Takeda and Goodman (1986). It is shown that the assumption of D-stability of the interconnection matrix, together with the standard assumptions on the activation functions, guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes. Conditions for local and global asymptotic stability are also derived, for both synchronous and asynchronous modes of operation. The results obtained are discussed both from the points of view of applications and robustness.