Phase Transition with the Berezinskii--Kosterlitz--Thouless Singularity in the Ising Model on a Growing Network

We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterised by the Berezinskii--Kosterlitz--Thouless singularity, although critical fluctuations are absent, and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as $exp(-const/\sqrt{T_c-T})$. We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range inhomogeneity. {\em Note added}.--After this paper had been published, we have learnt that the infinite order phase transition in the effective model we arrived at was discovered by O. Costin, R.D. Costin and C.P. Grunfeld in 1990. This phase transition was considered in the papers: [1] O. Costin, R.D. Costin and C.P. Grunfeld, J. Stat. Phys. 59, 1531 (1990); [2] O. Costin and R.D. Costin, J. Stat. Phys. 64, 193 (1991); [3] M. Bundaru and C.P. Grunfeld, J. Phys. A 32, 875 (1999); [4] S. Romano, Mod. Phys. Lett. B 9, 1447 (1995). We would like to note that Costin, Costin and Grunfeld treated this model as a one-dimensional inhomogeneous system. We have arrived at the same model as a one-replica ansatz for a random growing network where expected to find a phase transition of this sort based on earlier results for random networks (see the text). We have also obtained the distribution of the linear response to a local field, which characterises correlations in this system. We thank O. Costin and S. Romano for indicating these publications of 90s.Comment: 5 pages, 2 figures. We have added a note indicating that the infinite order phase transition in the effective model we arrived at was discovered in the work: O. Costin, R.D. Costin and C.P. Grunfeld, J. Stat. Phys. 59, 1531 (1990). Appropriate references to the papers of 90s have been adde

miRNA profiles as a predictor of chemoresponsiveness in Wilms' tumor blastema.

The current SIOP treatment protocol for Wilms' tumor involves pre-operative chemotherapy followed by nephrectomy. Not all patients benefit equally from such chemotherapy. The aim of this study was to generate a miRNA profile of chemo resistant blastemal cells in high risk Wilms' tumors which might serve as predictive markers of therapeutic response at the pre-treatment biopsy stage. We have shown here that unsupervised hierarchical clustering of genome-wide miRNA expression profiles can clearly separate intermediate risk tumors from high risk tumors. A total of 29 miRNAs were significantly differentially expressed between post-treatment intermediate risk and high risk groups, including miRNAs that have been previously linked to chemo resistance in other cancer types. Furthermore, 7 of these 29 miRNAs were already at the pre-treatment biopsy stage differentially expressed between cases ultimately deemed intermediate risk compared to high risk. These miRNA alterations include down-regulation in high risk cases of miR-193a.5p, miR-27a and the up-regulation of miR-483.5p, miR-628.5p, miR-590.5p, miR-302a and miR-367. The demonstration of such miRNA markers at the pre-treatment biopsy stage could permit stratification of patients to more tailored treatment regimens

Logarithmic rate dependence in deforming granular materials

Rate-independence for stresses within a granular material is a basic tenet of many models for slow dense granular flows. By contrast, logarithmic rate dependence of stresses is found in solid-on-solid friction, in geological settings, and elsewhere. In this work, we show that logarithmic rate-dependence occurs in granular materials for plastic (irreversible) deformations that occur during shearing but not for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate, \Omega, leads to an increase in the stress and the stress fluctuations that at least qualitatively resemble what occurs due to an increase in the density. Increases in \Omega also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is stopped at t=0, stress relaxations occur with \sigma(t)/ \sigma(t=0) \simeq A \log(t/t_0). This collective relaxation of the stress network over logarithmically long times provides a mechanism for rate-dependent strengthening.Comment: 4 pages, 5 figures. RevTeX

Stress in frictionless granular material: Adaptive Network Simulations

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure

Finite-time fluctuations in the degree statistics of growing networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barab\'asi-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.Comment: 33 pages, 7 figures, 1 tabl

Dissipation of vibration in rough contact

The relationship which links the normal vibration occurring during the sliding of rough surfaces and the nominal contact area is investigated. Two regimes are found. In the first one, the vibrational level does not depend on the contact area, while in the second one, it is propor- tional to the contact area. A theoretical model is proposed. It is based on the assumption that the vibrational level results from a competition between two processes of vibration damping, the internal damping of the material and the contact damping occurring at the interface

Influence of degree correlations on network structure and stability in protein-protein interaction networks

<p>Abstract</p> <p>Background</p> <p>The existence of negative correlations between degrees of interacting proteins is being discussed since such negative degree correlations were found for the large-scale <it>yeast </it>protein-protein interaction (PPI) network of Ito et al. More recent studies observed no such negative correlations for high-confidence interaction sets. In this article, we analyzed a range of experimentally derived interaction networks to understand the role and prevalence of degree correlations in PPI networks. We investigated how degree correlations influence the structure of networks and their tolerance against perturbations such as the targeted deletion of hubs.</p> <p>Results</p> <p>For each PPI network, we simulated uncorrelated, positively and negatively correlated reference networks. Here, a simple model was developed which can create different types of degree correlations in a network without changing the degree distribution. Differences in static properties associated with degree correlations were compared by analyzing the network characteristics of the original PPI and reference networks. Dynamics were compared by simulating the effect of a selective deletion of hubs in all networks.</p> <p>Conclusion</p> <p>Considerable differences between the network types were found for the number of components in the original networks. Negatively correlated networks are fragmented into significantly less components than observed for positively correlated networks. On the other hand, the selective deletion of hubs showed an increased structural tolerance to these deletions for the positively correlated networks. This results in a lower rate of interaction loss in these networks compared to the negatively correlated networks and a decreased disintegration rate. Interestingly, real PPI networks are most similar to the randomly correlated references with respect to all properties analyzed. Thus, although structural properties of networks can be modified considerably by degree correlations, biological PPI networks do not actually seem to make use of this possibility.</p

A model for collisions in granular gases

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.Comment: 11 pages, 2 figure