arXiv subjects

Roberto Mulet

Publications and source records attributed to Roberto Mulet.

45 records · Page 3Linked to original sources

arXiv2011

Stochastic approximation to the specific response of the immune system

We develop a stochastic model to study the specific response of the immune system. The model is based on the dynamical interaction between Regulatory and Effector CD4+ T cells in the presence of Antigen Presenting Cells inside a lymphatic node. At a mean field level the model predicts the existence of different regimes where active, tolerant, or cyclic immune responses are possible. To study the model beyond mean field and to understand the specific responses of the immune system we use the Linear Noise Approximation and show that fluctuations due to finite size effects may strongly alter the mean field scenario. Moreover, it was found the existence of a certain characteristic frequency for the fluctuations. All the analytical predictions were compared with simulations using the Gillespie's algorithm.

q-bio.CB↗

arXiv2011

A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice

Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.

cond-mat.dis-nn↗

arXiv2010

Symmetry breaking in frustrated systems: effective fluctuation spectrum due to coupling effects

We study the Langevin dynamics of a d-dimensional Ginzburg-Landau Hamiltonian with isotropic long range repulsive interactions. We show that, once the symmetry is broken, there is a coupling between the mean value of the local field and its fluctuations, generating an anisotropic effective fluctuation spectrum. This anisotropy has many interesting dynamical consequences. In the infinite time limit, static results are recovered which can be compared with the well known Brazovskii's transition to a state with modulated order. Our study reveals that the modulated solution appears continuously in d = 3 contrary to what is found in the usual approach neglecting coupling of modes, while for d < 3 transitions are still discontinuous. Analytical results for positional and orientational order parameters are also obtained and interpreted in the context of recent discussions.

cond-mat.mtrl-sci↗

arXiv2010

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$.

cond-mat.mtrl-sci↗

arXiv2010

H-T phase diagram of the bi-dimensional Ising model with exchange and dipolar interactions

We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exchange and long-range dipolar interactions as a function of the applied magnetic field H. The model is studied through extensive Monte Carlo simulations that show the existence of many modulated phases with long range orientational order for a wide range of fields. These phases are characterized by different wave vectors that change discontinuously with the magnetic field. We provide numerical evidence supporting the existence of first order transitions between these phases. At higher fields our results suggest a Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic phase.

cond-mat.mtrl-sci↗

arXiv2007

Estimating the size of the solution space of metabolic networks

In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation, allows the computation in polynomial time of the volume of a non full-dimensional convex polytope in high dimensions. The result of our algorithm match closely the prediction of Monte Carlo based estimations of the flux distributions of the Red Blood Cell metabolic network but in incomparably shorter time. We also analyze the statistical properties of the average fluxes of the reactions in the E-Coli metabolic network and finally to test the effect of gene knock-outs on the size of the solution space of the E-Coli central metabolism.

cond-mat.dis-nn↗

arXiv2006

Langevin dynamics of fluctuation induced first order phase transitions: self consistent Hartree Approximation

The Langevin dynamics of a system exhibiting a Fluctuation Induced First Order Phase Transition is solved within the self consistent Hartree Approximation. Competition between interactions at short and long length scales gives rise to spatial modulations in the order parameter, like stripes in 2d and lamellae in 3d. We show that when the time scale of observation is small compared with the time needed to the formation of modulated structures, the dynamics is dominated by a standard ferromagnetic contribution plus a correction term. However, once these structures are formed, the long time dynamics is no longer pure ferromagnetic. After a quench from a disordered state to low temperatures the system develops growing domains of stripes (lamellae). Due to the character of the transition, the paramagnetic phase is metastable at all finite temperatures, and the correlation length diverges only at T=0. Consequently, the temperature is a relevant variable, for $T>0$ the system exhibits interrupted aging while for T=0 the system ages for all time scales. Furthermore, for all $T$, the exponent associated with the aging phenomena is independent of the dimension of the system.

cond-mat.soft↗

arXiv2006

On the flexibility of complex systems

Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the system must satisfy a set of random dense linear constraints. By statistical mechanics techniques, we describe the transition between a non-flexible system in which the constraints are not fully satisfied, to a flexible system, in which the constraints can be satisfied in many ways. This phase transition is described in terms of the appearance of zeros modes in the statistical mechanics problem.

cond-mat.dis-nn↗

arXiv2005

The marriage problem: from the bar of appointments to the agency

We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that lead the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of the Nash equilibrium states of the system that agree very well with the results of Monte Carlo simulations. Finally, through large scale numerical simulations we compare the Global Optimum of the society with the stable marriage of lower energy. We showed that both states are strongly correlated and that the selffish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the Global Optimum of the society.

physics.soc-ph↗