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Extended abstract: This talk intends to put a few PhD theses, research publications and projects of the York University's Laboratory for Industrial and Applied Mathematics in a coherent framework about information processing delay, high dimension data clustering, and nonlinear neural dynamics. The objective is to develop both mathematical foundation and(More)
Data clustering has been discussed extensively, but almost all known conventional clustering algorithms tend to break down in high dimensional spaces because of the inherent sparsity of the data points. Existing subspace clustering algorithms for handling high-dimensional data focus on numerical dimensions. In this paper, we designed an iterative algorithm(More)
We develop some techniques to prove analytically the existence and stability of long period oscillations of stem cell populations in the case of periodic chronic myelogenous leukemia. Such a periodic oscillation $p_\infty $ can be analytically constructed when the hill coefficient involved in the nonlinear feedback is infinite, and we show it is possible to(More)
We consider the effect of the effective timing of a delayed feedback on the excitatory neuron in a recurrent inhibitory loop, when biological realities of firing and absolute refractory period are incorporated into a phenomenological spiking linear or quadratic integrate-and-fire neuron model. We show that such models are capable of generating a large(More)
A new neural network architecture (PART) and the resulting algorithm are proposed to find projected clusters for data sets in high dimensional spaces. The architecture is based on the well known ART developed by Carpenter and Grossberg, and a major modification (selective output signaling) is provided in order to deal with the inherent sparsity in the full(More)