Remarks on the Nonexistence of Doubling Measures

Remarks on collision manifolds and nonexistence of non self-similar collision solutions in the 3-vortex problem

Dynamic Bayesian Information Measures

This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t>=0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings...

Some remarks on dimensional dual hyperovals of polar type

A notion of dimensional dual polar spaces of polar type is given with a family of new examples. Nonexistence is shown for those of dimension 3, while there are just two isomorphism classes for those of dimension 2.

Some Remarks about Metric Spaces, Spherical Mappings, Functions and Their Derivatives

If p ∈ Rn, then we have the radial projection map from Rn\{p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a funct...

Remarks on Interpolation and Recognition Using Neural Nets

We consider different types of single-hidden-Iayer feedforward nets: with or without direct input to output connections, and using either threshold or sigmoidal activation functions. The main results show that direct connections in threshold nets double the recognition but not the interpolation power, while using sigmoids rather than thresholds allows (at least) doubling both. Various results a...