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

Segregation in spatially structured cities

Half of the world population resides in cities and urban segregation is becoming a global issue. One of the best known attempts to understand it is the Schelling model, which considers two types of agents that relocate whenever a transfer rule depending on the neighbor distribution is verified. The main aim of the present study is to broaden our understanding of segregated neighborhoods in the city, i.e. ghettos, extending the Schelling model to consider economic aspects and their spatial distribution. To this end we have considered a monetary gap between the two social groups and five types of urban structures, defined by the house pricing city map. The results show that ghetto sizes tend to follow a power law distribution in all the considered cases. For each city framework the interplay between economical aspects and the geometrical features determine the location where ghettos reach their maximum size. The system first steps shape greatly the city's final appearance. Moreover, the segregated population ratios depends largely on the monetary gap and not on the city type, implying that ghettos are able to adapt to different urban frameworks.Comment: 16 pages, 8 figure

Dynamical properties of the Landau-Ginzburg model with long-range correlated quenched impurities

We investigate the critical dynamics of the time-dependent Landau-Ginzburg model with non conserved n-component order parameter (Model A) in the presence of long-range correlated quenched impurities. We use a special kind of long-range correlations, previously introduced by Weinrib and Halperin. Using a double expansion in \epsilon and \delta we calculate the critical exponent z up to second order on the small parameters. We show that the quenched impurities of this kind affect the critical dynamics already in first order of \epsilon and \delta, leading to a relevant correction for the mean field value of the exponent zComment: 7 pages, REVTEX, to be published in Phys. Rev.