Levy ratchets with dichotomic random flashing

Additive symmetric L\'evy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such L\'evy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the L\'evy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static L\'evy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive L\'evy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.Comment: 15 pages, 6 figure

Statistical Mechanics of Soft Margin Classifiers

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin Support Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review

The dynamics of opinion in hierarchical organizations

We study the mutual influence of authority and persuasion in the flow of opinion. Many social organizations are characterized by a hierarchical structure where the propagation of opinion is asymmetric. In the normal flow of opinion formation a high-rank agent uses its authority (or its persuasion when necessary) to impose its opinion on others. However, agents with no authority may only use the force of its persuasion to propagate their opinions. In this contribution we describe a simple model with no social mobility, where each agent belongs to a class in the hierarchy and has also a persuasion capability. The model is studied numerically for a three levels case, and analytically within a mean field approximation, with a very good agreement between the two approaches. The stratum where the dominant opinion arises from is strongly dependent on the percentage of agents in each hierarchy level, and we obtain a phase diagram identifying the relative frequency of prevailing opinions. We also find that the time evolution of the conflicting opinions polarizes after a short transient.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Ground-state topology of the Edwards-Anderson +/-J spin glass model

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.Comment: 16 pages and 21 figure

Bound State and Order Parameter Mixing Effect by Nonmagnetic Impurity Scattering in Two-band Superconductors

We investigate nonmagnetic impurity effects in two-band superconductors, focusing on the effects of interband scatterings. Within the Born approximation, it is known that interband scatterings mix order parameters in the two bands. In particular, only one averaged energy gap appears in the excitation spectrum in the dirty limit. [G. Gusman: J. Phys. Chem. Solids {\bf 28} (1967) 2327.] In this paper, we take into account the interband scattering within the $t$-matrix approximation beyond the Born approximation in the previous work. We show that, although the interband scattering is responsible for the mixing effect, this effect becomes weak when the interband scattering becomes very strong. In the strong interband scattering limit, a two-gap structure corresponding to two order parameters recovers in the superconducting density of states. We also show that a bound state appears around a nonmagnetic impurity depending on the phase of interband scattering potential.Comment: 28pages, 10 figure

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog