A Quantitative Clustering Approach to Ultrametricity in Spin Glasses

We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the elimination of the (in this context accidental) spin flip symmetry plays a crucial role in the analysis, since the symmetry hides the real nature of the data. We are able to use in the analysis disorder averaged quantities. We are able to exhibit a number of features of the low $T$ phase of the mean field theory, and to claim that the full hierarchical structure can be observed without ambiguities only on very large lattice volumes, not currently accessible by numerical simulations.Comment: 15 pages with color figure

Numerical evidences of universal trap-like aging dynamics

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.Comment: 25 pages, 15 figure

Numerical Simulations of the Dynamical Behavior of the SK Model

We study the dynamical behavior of the Sherrington Kirkpatrick model. Thanks to the APE supercomputer we are able to analyze large lattice volumes, and to investigate the low $T$ region. We present a determination of the remnant magnetization and of its time decay exponent, of the energy time decay exponent, and we discuss aging phenomena in the model.Comment: 11 pages including 8 figures. Revised version with major restructurin

Numerical Simulations of Spin Glass Systems

We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach.Comment: Contribution to the volume: "Spin Glasses and Random Fields", edited by P. Young. 40 pages including 13 figure

RNA-based regulation: dynamics and response to perturbations of competing RNAs

The observation that, through a titration mechanism, microRNAs (miRNAs) can act as mediators of effective interactions among their common targets (competing endogenous RNAs or ceRNAs) has brought forward the idea ('ceRNA hypothesis') that RNAs can regulate each other in extended 'cross-talk' networks. Such an ability might play a major role in post-transcriptional regulation (PTR) in shaping a cell's protein repertoire. Recent work focusing on the emergent properties of the cross-talk networks has emphasized the high flexibility and selectivity that may be achieved at stationarity. On the other hand, dynamical aspects, possibly crucial on the relevant time scales, are far less clear. We have carried out a dynamical study of the ceRNA hypothesis on a model of PTR. Sensitivity analysis shows that ceRNA cross-talk is dynamically extended, i.e. it may take place on time scales shorter than those required to achieve stationairity even in cases where no cross-talk occurs in the steady state, and is possibly amplified. Besides, in case of large, transfection-like perturbations the system may develop strongly non-linear, threshold response. Finally, we show that the ceRNA effect provides a very efficient way for a cell to achieve fast positive shifts in the level of a ceRNA when necessary. These results indicate that competition for miRNAs may indeed provide an elementary mechanism to achieve system-level regulatory effects on the transcriptome over physiologically relevant time scales.Comment: Main text: 10 pages, 13 figures. Supporting Text: 3 pages, 6 figure