4,070 research outputs found
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 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
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