We introduce a renormalization group scheme that applies to vector fields on Td×Rm with frequency vectors that satisfy a Brjuno condition. Earlier approaches were restricted to Diophantine frequencies, due to a limited control of multidimensional continued fractions. We get around this restriction by avoiding the use of a continued fractions expansion. Our results concerning invariant tori gene...

These lecture notes were written to accompany a minicourse given at the School and Workshop on Dynamical Systems at IMPA (Rio de Janeiro), January 2006. Warning: These notes are unedited lecture notes and do contain errors! Proceed with caution... Let f : M → M be a (pointwise) partially hyperbolic diffeomor-phism. Recall what partially hyperbolic means. At every point in M , there exist tangen...

Identificaiton of people using a set of gait image sequences in varing situations is a challenging problem. We use a bilinear model to separate two independent factors, gait style and phase. N-normalized gait poses is defined and generated by embedding gait image sequences to a standard lower dimensional manifold and learning mapping from the manifold to every pixel. This normalized gait phase ...

Presented approach in polynomial time calculates large number of invariants for each vertex, which won’t change with graph isomorphism and should fully determine the graph. For example numbers of closed paths of length k for given starting vertex, what can be though as the diagonal terms of k-th power of the adjacency matrix. For k = 2 we would get degree of verities invariant, higher describes...

The capacity of a quantum gate to produce entangled states on bipartite system is quantified in terms the entangling power. This quantity defined as average linear entropy entanglement produced after applying over whole set separable states. Here we focus symmetric two-qubit gates, acting space, and calculate power appropriate local-invariant. A geometric description local equivalence classes g...

An Adaptive-Subspace Self-Organizing Map (ASSOM) can learn a set of ordered linear subspaces which correspond to invariant classes. However the basic ASSOM cannot properly learn linear manifolds that are shifted away from the origin of the input space. In this paper, we propose an improvement on ASSOM to amend this deficiency. The new network, named AOSSOM for Adaptive Offset Subspace Self-Orga...

A state-of-the-art system for finding objects in images has recently been developed by David Lowe. The algorithm is termed the Scale-Invariant Feature Transform (SIFT) and intends to detect similar feature points in each of the available images and then describe these points with a feature vector which is independent of image scale and orientation. Thus feature points which correspond to differ...

This paper introduces a novel scheme which works on symbolizing every line in an object image for object recognition. Symbolizing is accomplished in terms of angles of intersection with regard to a line under consideration. Spatial relationship existing among the symbolized lines is represented using the notion of Triangular Spatial Relationship (TSR). A set of quadruples which preserves the TS...

Interactions in complex solutions that consist of multiple components can be quantified via number correlations observed within an isochoric subsystem. The fluctuation solution theory carries out a conversion between experimental data (usually measured under isobaric conditions) and the through cumbersome thermodynamic variable transformations. In contrast, we have recently demonstrated heurist...

let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for t...