582 research outputs found
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
, and 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
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