Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities

An extensive list of results for the ground state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are being tested on mean-field models at low connectivity. Comparison with existing replica results for such models verifies the strength of those techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe lattices) exhibit a richer phenomenology than has been anticipated by theory. Our data prove to be sufficiently accurate to speculate about some exact results.Comment: 4 pages, RevTex4, 5 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Jamming Model for the Extremal Optimization Heuristic

Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin system on a fixed-valence graph. The numerical results for the spin system exhibit the same phenomena found in all earlier studies of extremal optimization, and our analytical results for the model reproduce many of these features.Comment: 9 pages, RevTex4, 7 ps-figures included, as to appear in J. Phys. A, related papers available at http://www.physics.emory.edu/faculty/boettcher

Extremal Optimization of Graph Partitioning at the Percolation Threshold

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of Physics

A self-organizing random immigrants genetic algorithm for dynamic optimization problems

This is the post-print version of the article. The official published version can be obtained from the link below - Copyright @ 2007 SpringerIn this paper a genetic algorithm is proposed where the worst individual and individuals with indices close to its index are replaced in every generation by randomly generated individuals for dynamic optimization problems. In the proposed genetic algorithm, the replacement of an individual can affect other individuals in a chain reaction. The new individuals are preserved in a subpopulation which is defined by the number of individuals created in the current chain reaction. If the values of fitness are similar, as is the case with small diversity, one single replacement can affect a large number of individuals in the population. This simple approach can take the system to a self-organizing behavior, which can be useful to control the diversity level of the population and hence allows the genetic algorithm to escape from local optima once the problem changes due to the dynamics.This work was supported by FAPESP (Proc. 04/04289-6)

RADAR-base: A Novel Open Source m-Health Platform

Smartphones with embedded and connected sensors are playing vital role in healthcare through various apps and mHealth platforms. RADAR-base is a modern mHealth data collection platform built around Confluent and Apache Kafka. RADAR-base enables study design and set up, active and passive remote data collection. It provides secure data transmission, and scalable solutions for data storage, management and access. The application is used presently in RADAR-CNS study to collect data from patients suffering from Multiples Sclerosis, Depression and Epilepsy. Beyond RADAR-CNS, RADAR-base is being deployed across a number of other funded research programmes

RADAR-base: Epilepsy Case Study

The traditional hospital set-up is not appropriate for long-term epilepsy seizure detection in naturalistic ambulatory settings. To explore the feasibility of seizure detection in such a setting, an in-hospital study was conducted to evaluate three wearable devices and a data collection platform for ambulatory seizure detection. The platform collects and processes data for study administrators, clinicians and data scientists, who use it to create models to detect seizures. For that purpose, all data collected from the wearable devices is additionally synchronized with the hospital EEG and video, with gold-standard seizure labels provided by trained clinicians. Data collected by wearable devices shows potential for seizure detection in out-of-hospital based and ambulatory settings

Genetic algorithms with self-organizing behaviour in dynamic environments

Copyright @ 2007 Springer-VerlagIn recent years, researchers from the genetic algorithm (GA) community have developed several approaches to enhance the performance of traditional GAs for dynamic optimization problems (DOPs). Among these approaches, one technique is to maintain the diversity of the population by inserting random immigrants into the population. This chapter investigates a self-organizing random immigrants scheme for GAs to address DOPs, where the worst individual and its next neighbours are replaced by random immigrants. In order to protect the newly introduced immigrants from being replaced by fitter individuals, they are placed in a subpopulation. In this way, individuals start to interact between themselves and, when the fitness of the individuals are close, one single replacement of an individual can affect a large number of individuals of the population in a chain reaction. The individuals in a subpopulation are not allowed to be replaced by individuals of the main population during the current chain reaction. The number of individuals in the subpopulation is given by the number of individuals created in the current chain reaction. It is important to observe that this simple approach can take the system to a self-organization behaviour, which can be useful for GAs in dynamic environments.Financial support was obtained from FAPESP (Proc. 04/04289-6)

Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and random couplings $J_{ij}=\pm \tilde{J}$. We confirm these expectation by means of various analytical results. In particular we unveil the connection between the spatial fluctuations of the populations of populations of fields defined at different sites of the lattice and the Gaussian nature of the free-energy fluctuations. On the contrary on locally homogeneous lattices the populations do not fluctuate over the sites and as a consequence the small-deviations of the free energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model

Random Graph Coloring - a Statistical Physics Approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the 2-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges.Comment: 17 pages, 9 figure