Tangent Codes

The present article studies the finite Zariski tangent spaces to an affine variety X as linear codes, in order to characterize their typical or exceptional properties by global geometric conditions on X. The discussion concerns the generic minimum distance of a tangent code to X, its lower semi-continuity under a deformation of X, as well as the existence of Zariski tangent spaces to X with exceptional minimum distance. Tangent codes are shown to admit simultaneous decoding. The duals of the tangent codes to X are realized by gradients of polynomials from the ideal of X. We provide constructions of affine varieties with near MDS, cyclic or Hamming tangent codes. Puncturing, shortening and extending finite Zariski tangent spaces are related to the corresponding operations on affine varieties. The (u|u+v) construction of tangent codes is associated with a fibered product of varieties. Explicit constructions realize linear Hamming isometries as differentials of morphisms of affine varieties

Formal Definition of the Concept “Infos”

The concept INFOS is very important for understanding the information phenomena. Because of this, it is basic for the General Information Theory. The more precise formal definition of this concept is given in the paper

16 International Journal "Information Theories & Applications " Vol.11 FORMAL DEFINITION OF THE CONCEPT “INFOS”

Abstract: The concept INFOS is very important for understanding the information phenomena. Because of this, it is basic for the General Information Theory. The more precise formal definition of this concept is given in the paper

Local Features in APICAS Analyzing of Added Value of the Descriptors Based on MPEG-7 Vector Quantization

Abstract- An approach for extracting higher-level visual features for art painting classification based on MPEG-7 descriptors was implemented in the system “Art Painting Image Colour Aesthetics and Semantics ” (APICAS). The approach consists of the following steps: (1) tiling images into non-overlapping rectangles in order to capture more detailed local information; (2) the tiles of the images are clustered for each MPEG-7 descriptor; (3) vector quantization is used to assign a unique value to each tile, which corresponds to the number of the cluster where the tile belongs, in order to reduce the dimensionality of the data. The distribution of significance of the attributes, the importance of the underlying MPEG-7 descriptors as well as analysis of spatial granularity for class prediction in this domain are analyzed