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.

Correlates of facial expressions in the primary visual cortex

Face detection and recognition should be complemented by recognition of facial expression, for example for social robots which must react to human emotions. Our framework is based on two multi-scale representations in cortical area V1: keypoints at eyes, nose and mouth are grouped for face detection [1]; lines and edges provide information for face recognition [2].

Recognition of facial expressions by cortical multi-scale line and edge coding

Empirical studies concerning face recognition suggest that faces may be stored in memory by a few canonical representations. Models of visual perception are based on image representations in cortical area V1 and beyond, which contain many cell layers for feature extraction. Simple, complex and end-stopped cells provide input for line, edge and keypoint detection. Detected events provide a rich, multi-scale object representation, and this representation can be stored in memory in order to identify objects. In this paper, the above context is applied to face recognition. The multi-scale line/edge representation is explored in conjunction with keypoint-based saliency maps for Focus-of-Attention. Recognition rates of up to 96% were achieved by combining frontal and 3/4 views, and recognition was quite robust against partial occlusions.