Mathematics Commons^™

Prestructuring Neural Networks Via Extended Dependency Analysis With Application To Pattern Classification, George G. Lendaris, Thaddeus T. Shannon, Martin Zwick

Systems Science Faculty Publications and Presentations

We consider the problem of matching domain-specific statistical structure to neural-network (NN) architecture. In past work we have considered this problem in the function approximation context; here we consider the pattern classification context. General Systems Methodology tools for finding problem-domain structure suffer exponential scaling of computation with respect to the number of variables considered. Therefore we introduce the use of Extended Dependency Analysis (EDA), which scales only polynomially in the number of variables, for the desired analysis. Based on EDA, we demonstrate a number of NN pre-structuring techniques applicable for building neural classifiers. An example is provided in which EDA …

Sensory And Motor Interdependence In Postural Adjustments, Gin Mccollum

Gin McCollum

The sensory reafference from a movement depends upon the movement, and the movement chosen depends upon the available senses, as demonstrated by vestibular patients who abandon certain movements. Often, one variable is assumed to be dependent whereas the other is independent; however, sensory and motor dynamics in posture are interdependent as conditions upon each other. This paper applies conditional dynamics to characterize the global structure of interdependence between sensory states and motor strategies in fast postural adjustments. The mathematical formalism incorporates rich but disparate experimental, clinical, and theoretical results about sensory and motor control of posture.

The control structures presented …

Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study models for the gravity-driven, dissipative motion of a single grain on an inclined rough surface. Imposing some conditions on the momentum loss due to the collisions between the particle and the surface, we arrive at a class of models in which the grain dynamics is described by one-dimensional maps. The dynamics of these maps is studied in detail. We prove the existence of various dynamical phases and show that the presence of these phases is independent of the restitution law (within the class considered).