Message passing and Monte Carlo algorithms: connecting fixed points with metastable states

Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in the Edwards-Anderson model in 2-dimensions these approximations predict a spin glass transition at finite $T$. Here we show that the spin glass solutions of the Cluster Variational Method (CVM) at plaquette level do describe well actual metastable states of the system. Moreover, we prove that these states can be used to predict non trivial statistical quantities, like the distribution of the overlap between two replicas. Our results support the idea that message passing algorithms can be helpful to accelerate Monte Carlo simulations in finite dimensional systems.Comment: 6 pages, 6 figure

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.Comment: 16 pages, 1 figur

Adaptive drivers in a model of urban traffic

We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers' behavioral parameters via numerical simulations and mean-field analytical arguments. We identify a phase transition between a low- and a high-density regime. In the latter, inductive drivers may surprisingly behave worse than randomly selecting drivers.Comment: 7 pages, final versio

Gas Chromatography-Mass Spectrometry Study of the Essential Oils of Schinus longifolia (Lindl.) Speg., Schinus fasciculata (Griseb.) I. M. Johnst., and Schinus areira L.

The essential oil composition from the aerial parts of three Anacardiaceae growing in Bah¨ªa Blanca, Argentina was studied by gas chromatography and gas chromatography-mass spectrometry. The essential oils of S. longifolia and S. fasciculata have been studied for the first time. The major constituents were ¦Á-pinene (46.5%), ¦Â-pinene (15.1%) and ¦Á-phellandrene (10.1%) for S. longifolia and limonene (10.9%), ¦Â-phellandrene (6.16%) and ¦Á-phellandrene (5.6%) for S. fasciculata. The major components of the essential oil of S. areira were limonene (28.6%), ¦Á-phellandrene (10.1%), sabinene (9.2%) and camphene (9.2%) differing from the literature data. The essential oils from S. areira and S. longifolia exhibited a high biotoxicity in a brine shrimp assay with Artemia persimilis.Fil: Murray, Ana Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Química del Sur. Universidad Nacional del Sur. Departamento de Química. Instituto de Química del Sur; Argentina. Universidad Nacional del Sur. Departamento de Química. Instituto de Investigaciones en Química Orgánica; ArgentinaFil: Frontera, Maria Eugenia. Universidad Nacional del Sur. Departamento de Química. Instituto de Investigaciones en Química Orgánica; ArgentinaFil: Tomas, María A.. Universidad Nacional del Sur. Departamento de Química. Instituto de Investigaciones en Química Orgánica; ArgentinaFil: Mulet, María Cristina. Universidad Nacional del Sur. Departamento de Química. Instituto de Investigaciones en Química Orgánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Química del Sur. Universidad Nacional del Sur. Departamento de Química. Instituto de Química del Sur; Argentin

Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

We solve the Edwards-Anderson model (EA) in different Husimi lattices. We show that, at T=0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes have always a trivial paramagnetic solution stable under 1RSB perturbations while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We compute the free-energy, the complexity and the ground state energy of different Husimi lattices at the level of the 1RSB approximation. We also show, when the fraction of ferromagnetic couplings increases, the existence, first, of a discontinuous transition from a paramagnetic to a spin glass phase and latter of a continuous transition from a spin glass to a ferromagnetic phase.Comment: 20 pages, 10 figures (v3: Corrected analysis of transitions. Appendix proof fixed

Computing a Knot Invariant as a Constraint Satisfaction Problem

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.Comment: 6 pages, 3 figures, submitted to short note in Journal of Physical Society of Japa

A New Simulated Annealing Algorithm for the Multiple Sequence Alignment Problem: The approach of Polymers in a Random Media

We proposed a probabilistic algorithm to solve the Multiple Sequence Alignment problem. The algorithm is a Simulated Annealing (SA) that exploits the representation of the Multiple Alignment between $D$ sequences as a directed polymer in $D$ dimensions. Within this representation we can easily track the evolution in the configuration space of the alignment through local moves of low computational cost. At variance with other probabilistic algorithms proposed to solve this problem, our approach allows for the creation and deletion of gaps without extra computational cost. The algorithm was tested aligning proteins from the kinases family. When D=3 the results are consistent with those obtained using a complete algorithm. For $D>3$ where the complete algorithm fails, we show that our algorithm still converges to reasonable alignments. Moreover, we study the space of solutions obtained and show that depending on the number of sequences aligned the solutions are organized in different ways, suggesting a possible source of errors for progressive algorithms.Comment: 7 pages and 11 figure

Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of replicas. In the scheme, survey propagation (SP), which is an efficient algorithm developed recently for analyzing the microscopic properties of glassy states for a fixed sample of disordered systems, can be reproduced by assuming the simplest replica symmetry on stationary points of the replicated Bethe free energy. Belief propagation and generalized SP can also be offered in the identical framework under assumptions of the highest and broken replica symmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136 (2005

Polynomial iterative algorithms for coloring and analyzing random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This lead us to propose a new algorithm able to color in polynomial time random graphs in the hard but colorable region, i.e when $c\in [c_d,c_q]$.Comment: 23 pages, 10 eps figure