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Approximating the Stability Region for a Differential Equation with a Distributed Delay

S. A. Campbell, R. Jessop (2009)

Mathematical Modelling of Natural Phenomena

We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a distribution independent stability region may be obtained in a similar way that delay independent...

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network

Maciej Huk (2012)

International Journal of Applied Mathematics and Computer Science

In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....

Comparison of supervised learning methods for spike time coding in spiking neural networks

Andrzej Kasiński, Filip Ponulak (2006)

International Journal of Applied Mathematics and Computer Science

In this review we focus our attention on supervised learning methods for spike time coding in Spiking Neural Networks (SNNs). This study is motivated by recent experimental results regarding information coding in biological neural systems, which suggest that precise timing of individual spikes may be essential for efficient computation in the brain. We are concerned with the fundamental question: What paradigms of neural temporal coding can be implemented with the recent learning methods? In order...

Convergence analysis for principal component flows

Shintaro Yoshizawa, Uwe Helmke, Konstantin Starkov (2001)

International Journal of Applied Mathematics and Computer Science

A common framework for analyzing the global convergence of several flows for principal component analysis is developed. It is shown that flows proposed by Brockett, Oja, Xu and others are all gradient flows and the global convergence of these flows to single equilibrium points is established. The signature of the Hessian at each critical point is determined.

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