Fast algorithm for detecting the most unusual part of 2d and 3d digital images. Application to large medical databases

In this paper we introduce a fast algorithm that can detect the most unusual part of a digital image. The most unusual part of a given shape is de ned as a part of the image that has the maximal distance to all non intersecting shapes with the same form. The method is tested on two and three-dimensional images and have shown very good results without any prede ned model. The results can be used to scan large image databases, as for example medical databasesThe work is financially supported by Spanish Grants TIN 2004 07676-G01-01, TIN 2007 66862 (K.K.) and DGI.M.CyT.FIS2005- 1729 (E.K.

Spatial asymmetric retrieval states in binary attractor neural network

Copyright 2005 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.In this paper we show that during the retrieval process in a binary Hebb attractor neural network, spatial localized states can be observed when the connectivity of the network is distancedependent and there is an asymmetry between the retrieval and the learning statesThis work is nancial supported by Departamento de Fìsica Fundamental, UNED and by Spanish Grants CICyT, TIC 01 572, TIN 2004 07676, DGI.M.CyT.BFM2001-291- C02-01 and Promoción de la Investigación UNED'0

Bump formations in attractor neural network and their application in image reconstruction

Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.In this paper we analyze the bump formations in binary attractor neural networks with distance dependent connectivity. We show that by introducing a two stage learning procedure an increase of the critical storage capacity of the network is observed. The procedure has been tested on a network with N = 64K neurons by using a selection of 3700 natural images. Our analysis shows that the bumps can be regarded as intrinsic characteristics of the image and the topology of the network and they can be used to improve the performance of the network by increasing its capacity.The authors acknowledge the financial support from the Spanish Grants DGI.M. CyT. FIS 2005-1729 and TIN 2004-07676-G01-0

Power accretion in social systems

We consider a model of power distribution in a social system where a set of agents plays a simple game on a graph: The probability of winning each round is proportional to the agent’s current power, and the winner gets more power as a result. We show that when the agents are distributed on simple one-dimensional and two-dimensional networks, inequality grows naturally up to a certain stationary value characterized by a clear division between a higher and a lower class of agents. High class agents are separated by one or several lower class agents which serve as a geometrical barrier preventing further flow of power between them. Moreover, we consider the effect of redistributive mechanisms, such as proportional (nonprogressive) taxation. Sufficient taxation will induce a sharp transition towards a more equal society, and we argue that the critical taxation level is uniquely determined by the system geometry. Interestingly, we find that the roughness and Shannon entropy of the power distributions are a very useful complement to the standard measures of inequality, such as the Gini index and the Lorenz curveWe acknowledge financial support from the Spanish Government through Grants No. FIS2015-69167-C2-1-P, No. FIS2015-66020-C2- 1-P, and No. PGC2018-094763-B-I0

Statistics of natural images using hash fractal image compression

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in CompSysTech '03 Proceedings of the 4th international conference conference on Computer systems and technologies: e-Learning, http://dx.doi.org/10.1145/973620.973661.Natural images form very small subset of all images. In spite of the fact, the direct computation of their block densities is not possible. On the other hand, the existence of various successful image compression methods, in particularly, the fractal compression, indicates that the compression somehow is able to capture and use at least part of the natural image statistics. In this work we show how hash based fractal image compression can be used to derive quite precise the entropies of 4 × 4 patches of the natural images. We state that the probability density in first order factorize to the probability densities of the contrast, the brightness and the index of the codebook blocks