Invariant multi-scale object categorisation and recognition

Object recognition requires that templates with canonical views are stored in memory. Such templates must somehow be normalised. In this paper we present a novel method for obtaining 2D translation, rotation and size invariance. Cortical simple, complex and end-stopped cells provide multi-scale maps of lines, edges and keypoints. These maps are combined such that objects are characterised. Dynamic routing in neighbouring neural layers allows feature maps of input objects and stored templates to converge. We illustrate the construction of group templates and the invariance method for object categorisation and recognition in the context of a cortical architecture, which can be applied in computer vision.

Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

Neuro-genetic PID autotuning: time invariant case

The Proportional, Integral and Derivative (PID) controllers are widely used in induxtrial applications. Their popularity comes from their robust performance and also from their functional simplicity.