Impulse response model for a class of distributed parameter systems

Article Abstract:

A mathematical model is developed here for the impulse response of a class of systems represented by a general linear parabolic partial differential equation. Using a generalized eigenfunction expansion and the concept of a sampled-data system, a canonical set of state equations is obtained in discrete form. The impulse inputs may be any known time-varying functions on the given boundaries of the system or may be assumed to be distributed over a finite boundary region. For this computer model, no spatial discretization is required. Each discrete-time equation represents the dynamic behavior of each eigenvalue of the system and the response variable of any discrete location is given by a spatial linear combination of these state variables. Due to the discrete formulation of the system equations, numerical stability is assured. The equations are stable for any sampling time selected and the solution at any particular time desired may be simply obtained by incorporating this value directly into the model equations. The application of this method is demonstrated by solving a two-dimensional heat transfer problem subject to a single impulse input and comparisons were made to the finite element method of solution. (Reprinted by permission from the publisher.)

Mathematical models, Difference Equations, Equation Analysis

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A general purpose simulation environment for neural models

Article Abstract:

Current interest in neural networks has produced a diverse set of algorithms and architectures that vary in connectivity pattern, temporal behavior, update rules, and convergence properties. We have designed a flexible simulation system that can support the implementation of a wide range of neural network approaches. The UCLA-SFINX simulator is especially suited for the exploration of structured, irregular, and layered connectivity patterns. Functions, such as those in early vision, are modeled using the regular connectivity of center/surround antagonistic receptive fields and can be implemented as the difference of concentric gaussians. Higher level cognitive functions, such as supervised and unsupervised learning, have more irregular, dynamic connectivity structures and update mechanisms that are also supported. To visualize weight spaces, input/output training sets, image data, or other network characteristics, SFINX provides an X-windows based graphical output that assists in rapidly assessing the consequences of altering connectivity patterns, parameter tuning, and other experiments. (Reprinted with permission of the publisher.)

Systems analysis, Neural networks, Computer science, Cognitive science, Connectivity, System Design, Neural Network

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