Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Equilibration through local information exchange in networks

We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.Comment: v1: 7 pages, 1 figure, v2: 4 pages, 2 figures, simplified analysis and more organized results, v3: minor change

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure

Statistical mechanics of image restoration and error-correcting codes

We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties. For image restoration in mean-field system a line of optimal performance is shown to exist in the parameter space. These results are illustrated by solving exactly the infinite-range model. The solutions enable us to determine how precisely one should estimate unknown parameters. Monte Carlo simulations are carried out to see how far the conclusions from the infinite-range model are applicable to the more realistic two-dimensional case in image restoration.Comment: 20 pages, 9 figures, ReVTe

High plasma leptin levels confer increased risk of atherosclerosis in women with systemic lupus erythematosus, and are associated with inflammatory oxidised lipids.

BackgroundPatients with systemic lupus erythematosus (SLE) are at increased risk of atherosclerosis, even after accounting for traditional risk factors. High levels of leptin and low levels of adiponectin are associated with both atherosclerosis and immunomodulatory functions in the general population.ObjectiveTo examine the association between these adipokines and subclinical atherosclerosis in SLE, and also with other known inflammatory biomarkers of atherosclerosis.MethodsCarotid ultrasonography was performed in 250 women with SLE and 122 controls. Plasma leptin and adiponectin levels were measured. Lipoprotein a (Lp(a)), oxidised phospholipids on apoB100 (OxPL/apoB100), paraoxonase, apoA-1 and inflammatory high-density lipoprotein (HDL) function were also assessed.ResultsLeptin levels were significantly higher in patients with SLE than in controls (23.7±28.0 vs 13.3±12.9 ng/ml, p<0.001). Leptin was also higher in the 43 patients with SLE with plaque than without plaque (36.4±32.3 vs 20.9±26.4 ng/ml, p=0.002). After multivariate analysis, the only significant factors associated with plaque in SLE were leptin levels in the highest quartile (≥29.5 ng/ml) (OR=2.8, p=0.03), proinflammatory HDL (piHDL) (OR=12.8, p<0.001), age (OR=1.1, p<0.001), tobacco use (OR=7.7, p=0.03) and hypertension (OR=3.0, p=0.01). Adiponectin levels were not significantly associated with plaque in our cohort. A significant correlation between leptin and piHDL function (p<0.001), Lp(a) (p=0.01) and OxPL/apoB100 (p=0.02) was also present.ConclusionsHigh leptin levels greatly increase the risk of subclinical atherosclerosis in SLE, and are also associated with an increase in inflammatory biomarkers of atherosclerosis such as piHDL, Lp(a) and OxPL/apoB100. High leptin levels may help to identify patients with SLE at risk of atherosclerosis

Supersymmetry Breaking in the Early Universe

Supersymmetry breaking in the early universe induces scalar soft potentials with curvature of order the Hubble constant. This has a dramatic effect on the coherent production of scalar fields along flat directions. For the moduli problem it generically gives a concrete realization of the problem by determining the field value subsequent to inflation. However it might suggest a solution if the minimum of the induced potential coincides with the true minimum. The induced Hubble scale mass also has important implications for the Affleck-Dine mechanism of baryogenesis. This mechanism requires large squark or slepton expectation values to develop along flat directions in the early universe. This is generally not the case if the induced mass squared is positive, but does occur if it is negative. The resulting baryon to entropy ratio depends mainly on the dimension of the nonrenormalizable operator in the superpotential which stabilizes the flat direction, and the reheat temperature after inflation. Unlike the original scenario, it is possible to obtain an acceptable baryon asymmetry without subsequent entropy releases.Comment: 11 pages, requires phyzz

Entanglement and Timing-Based Mechanisms in the Coherent Control of Scattering Processes

The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies