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

Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings

Type 0A string theory in the (2,4k) superconformal minimal model backgrounds and the bosonic string in the (2,2k-1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using double scaled matrix models. The resolvent of an associated Schrodinger operator plays three very important interconnected roles, which we explore perturbatively and non-perturbatively. On one hand, it acts as a source for placing D-branes and fluxes into the background, while on the other, it acts as a probe of the background, its first integral yielding the effective force on a scaled eigenvalue. We study this probe at disc, torus and annulus order in perturbation theory, in order to characterize the effects of D-branes and fluxes on the matrix eigenvalues. On a third hand, the integrated resolvent forms a representation of a twisted boson in an associated conformal field theory. The entire content of the closed string theory can be expressed in terms of Virasoro constraints on the partition function, which is realized as wavefunction in a coherent state of the boson. Remarkably, the D-brane or flux background is simply prepared by acting with a vertex operator of the twisted boson. This generates a number of sharp examples of open-closed duality, both old and new. We discuss whether the twisted boson conformal field theory can usefully be thought of as another holographic dual of the non-critical string theory.Comment: 37 pages, some figures, LaTe

The Cap in the Hat: Unoriented 2D Strings and Matrix(-Vector) Models

We classify the possible bosonic and Type 0 unoriented string theories in two dimensions, and find their dual matrix(-vector) models. There are no RP^2 R-R tadpoles in any of the models, but many of them possess a massless tachyon tadpole. Thus all the models we find are consistent two-dimensional string vacua, but some get quantum corrections to their classical tachyon background. Where possible, we solve the tadpole cancellation condition, and find all the tachyon tadpole-free theories.Comment: 34 pages, LaTeX; Errors corrected in some of the open string representations in tables 1, 2 and 3. References and acknowledgments adde

Distributed power control for wireless networks via the alternating direction method of multipliers

Utility-based power control in wireless networks has been widely recognized as an effective mechanism to managing co-channel interferences. It is based on the maximization of system utility subject to power constraints, which is referred to as power control optimization problem. Global coupling between the mutual interference of wireless channels increases the difficulty of searching global optimum significantly. In this paper, we decouple the optimization problems with concave and non-concave utility functions; and transform them into a global consensus problem by introducing locally slack variables. We then propose two distributed iterative optimization algorithms for the global consensus problems with concave and non-concave objective functions, respectively, based on an alternating direction method of multipliers. Furthermore, we prove that both algorithms converge to the global optimum of the total network utility. Simulation results show the effectiveness of the algorithms. Comparison experiments show that the developed algorithms compare favourably against some other well-known algorithms

Two-Dimensional Unoriented Strings And Matrix Models

We investigate unoriented strings and superstrings in two dimensions and their dual matrix quantum mechanics. Most of the models we study have a tachyon tadpole coming from the RP^2 worldsheet which needs to be cancelled by a renormalization of the worldsheet theory. We find evidence that the dual matrix models describe the renormalized theory. The singlet sector of the matrix models is integrable and can be formulated in terms of fermions moving in an external potential and interacting via the Calogero-Moser potential. We show that in the double-scaling limit the latter system exhibits particle-hole duality and interpret it in terms of the dual string theory. We also show that oriented string theories in two dimensions can be continuously deformed into unoriented ones by turning on non-local interactions on the worldsheet. We find two unoriented superstring models for which only oriented worldsheets contribute to the S-matrix. A simple explanation for this is found in the dual matrix model.Comment: 36 pages, harvmac, 2 eps figure

Wave transmission, phonon localization and heat conduction of 1D Frenkel-Kontorova chain

We study the transmission coefficient of a plane wave through a 1D finite quasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in an infinite uniform harmonic chain. By varying the mass of atoms in the infinite uniform chain, we obtain the transmission coefficients for {\it all} eigenfrequencies. The phonon localization of the incommensurated FK chain is also studied in terms of the transmission coefficients and the Thouless exponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chain at low temperature is calculated. It is found that the stationary heat flux $J(N)\sim N^{\alpha}$, and $\alpha$ depends on the strength of the external potential.Comment: 15 pages in Revtex, 8 EPS figure

Closed String Tachyon Condensation at c=1

The c=1 matrix model, with or without a type 0 hat, has an exact quantum solution corresponding to closed string tachyon condensation along a null surface. The condensation occurs, and spacetime dissolves, at a finite retarded time on I^+. The outgoing quantum state of tachyon fluctuations in this time-dependent background is computed using both the collective field and exact fermion pictures. Perturbative particle production induced by the moving tachyon wall is shown to be similar to that induced by a soft moving mirror. Hence, despite the fact that I^+ for the tachyon is geodesicaly incomplete, quantum correlations in the incoming state are unitarily transmitted to the outgoing state in perturbation theory. It is also shown that, non-perturbatively, information can leak across the tachyon wall, and tachyon scattering is not unitary. Exact unitarity remains intact only in the free fermion picture.Comment: Minor corrections; References added; 24 pages, 2 figures, harvma

The Trouble with de Sitter Space

In this paper we assume the de Sitter Space version of Black Hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter space should be implemented. Then we prove a no go theorem for implementing the symmetries if the entropy is finite. Thus we must either give up the finiteness of the de Sitter entropy or the exact symmetry of the classical space. Each has interesting implications for the very long time behavior. We argue that the lifetime of a de Sitter phase can not exceed the Poincare recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.Comment: 15 pages, 1 figure. v2: added fifth section with comments on long time stability of de Sitter space, in which we argue that the lifetime can not exceed the Poincare recurrence time. v3: corrected a minor error in the appendi

Nonperturbative aspects of ABJM theory

Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published in JHE