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.

Multi-scale lines and edges in V1 and beyond: brightness, object categorization and recognition, and consciousness

In this paper we present an improved model for line and edge detection in cortical area V1. This model is based on responses of simple and complex cells, and it is multi-scale with no free parameters. We illustrate the use of the multi-scale line/edge representation in different processes: visual reconstruction or brightness perception, automatic scale selection and object segregation. A two-level object categorization scenario is tested in which pre-categorization is based on coarse scales only and final categorization on coarse plus fine scales. We also present a multi-scale object and face recognition model. Processing schemes are discussed in the framework of a complete cortical architecture. The fact that brightness perception and object recognition may be based on the same symbolic image representation is an indication that the entire (visual) cortex is involved in consciousness.

Repply to: Brito, A.C., Brotas, V., Caetano, M., Coutinho, T.P., Bordalo, A.A., Icely, J., Neto, J.M., Serôdio, J., Moita, T. (2012) "Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive" [Ecological Indicators 19, 5-14]

We write to comment on the recently published paper “Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive” (Brito et al., 2012). This paper presents an integrated methodology to analyse the ecological quality status of several Portuguese transitional waters, using phytoplanktonrelated metrics. One of the systems analysed, the Guadiana estuary in southern Portugal, is considered the most problematic estuary, with its upstream water bodies classified as Poor in terms of ecological status. We strongly disagree with this conclusion and we would like to raise awareness to some methodological constraints that, in our opinion, are the basis of such deceptive conclusions and should therefore not be neglected when using phytoplankton to assess the ecological status of natural waters.