miguel angel cruz

We analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three-state square lattice divided into spatial cells (districts). In the spirit of the statistical mechanics of social impact, we introduce a dominant influence rule (DIR), according to which, in a single update step, a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres. In contrast to models based on some form of majority rule (MR), a system governed by the DIR is easily trapped in a stable non-consensus state, if all nodes of the discussion group have the same weight of influence. To ensure that a consensus in the DIR system is necessarily reached, we need to put a stochastic process in the update rule. Further, the stochastic DIR model is used as a starting point for understanding the effect of spatial heterogeneity of active agent (non-zero spin) distribution on the exit probabilities. Initially, the positive and negative spins (active agents) are assigned to some nodes with non-uniform spatial distributions; while the rest of the nodes remain in the state with spin zero (uncommitted voters). By varying the relative means and skewness of the initial spin distributions, we observe critical behaviors of exit probabilities in finite size systems. The critical exponents are obtained by Monte Carlo simulations. The results of numerical simulations are discussed in the context of social dynamics.

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

We study the statistical topology of folding configurations of hand folded paper balls. Specifically, we are studying the distribution of two sides of the sheet along the ball surface and the distribution of sheet fragments when the ball is cut in half. We found that patterns obtained by mapping of ball surface into unfolded flat sheet exhibit the fractal properties characterized by two fractal dimensions which are independent on the sheet size and the ball diameter. The mosaic patterns obtained by sheet reconstruction from fragments of two parts (painted in two different colors) of the ball cut in half also possess a fractal scale invariance characterized by the box fractal dimension DBF=1.68±0.04 , which is independent on the sheet size. Furthermore, we noted that DBF , at least numerically, coincide with the universal fractal dimension of the intersection of hand folded paper ball with a plane. Some other fractal properties of folding configurations are recognized.

About 25–50% of women with Cowden disease, a syndrome associated with germ-line mutations of the PTEN gene (at 10q23), develop breast cancer (BC), but PTEN mutations have been found in only 5% of sporadic BCs. However, 29–48% of BCs display loss of heterozygosity in 10q23, and about 40% of BCs show a decrease or absence of PTEN protein levels at the time of diagnosis. Promoter hypermethylation has been identified as an alternative mechanism of tumor-suppressor gene inactivation, but its importance in PTEN silencing in sporadic BC is unknown. We investigated PTEN promoter hypermethylation in 90 sporadic BCs and its correlations with 11 molecular and pathologic parameters, including mRNA levels of PTEN. The study, a methylation-specific PCR assay, was carried out with methylated specific primers designed in a region with scarce homology with the psiPTEN pseudogene. Expression was analyzed by real-time PCR. We found that the PTEN promoter was hypermethylated in 43 BCs (48%). PTEN hypermethylation was associated with ERBB2 overexpression, larger size, and higher histologic grade (P = 0.012, 0.03, and 0.009, respectively). We concluded that PTEN promoter hypermethylation is a common event in sporadic BC, correlating with other well-established prognostic factors of this malignancy. Additionally, PTEN mRNA expression was lower in tumors with aberrant methylation. © 2004 Wiley-Liss, Inc.