59,712 research outputs found
Smoothed Analysis of Dynamic Networks
We generalize the technique of smoothed analysis to distributed algorithms in
dynamic network models. Whereas standard smoothed analysis studies the impact
of small random perturbations of input values on algorithm performance metrics,
dynamic graph smoothed analysis studies the impact of random perturbations of
the underlying changing network graph topologies. Similar to the original
application of smoothed analysis, our goal is to study whether known strong
lower bounds in dynamic network models are robust or fragile: do they withstand
small (random) perturbations, or do such deviations push the graphs far enough
from a precise pathological instance to enable much better performance? Fragile
lower bounds are likely not relevant for real-world deployment, while robust
lower bounds represent a true difficulty caused by dynamic behavior. We apply
this technique to three standard dynamic network problems with known strong
worst-case lower bounds: random walks, flooding, and aggregation. We prove that
these bounds provide a spectrum of robustness when subjected to
smoothing---some are extremely fragile (random walks), some are moderately
fragile / robust (flooding), and some are extremely robust (aggregation).Comment: 20 page
Random walk on random walks: low densities
We consider a random walker in a dynamic random environment given by a system
of independent simple symmetric random walks. We obtain ballisticity results
under two types of perturbations: low particle density, and strong local drift
on particles. Surprisingly, the random walker may behave very differently
depending on whether the underlying environment particles perform lazy or
non-lazy random walks, which is related to a notion of permeability of the
system. We also provide a strong law of large numbers, a functional central
limit theorem and large deviation bounds under an ellipticity condition.Comment: 28 page
The Radius of Metric Subregularity
There is a basic paradigm, called here the radius of well-posedness, which
quantifies the "distance" from a given well-posed problem to the set of
ill-posed problems of the same kind. In variational analysis, well-posedness is
often understood as a regularity property, which is usually employed to measure
the effect of perturbations and approximations of a problem on its solutions.
In this paper we focus on evaluating the radius of the property of metric
subregularity which, in contrast to its siblings, metric regularity, strong
regularity and strong subregularity, exhibits a more complicated behavior under
various perturbations. We consider three kinds of perturbations: by Lipschitz
continuous functions, by semismooth functions, and by smooth functions,
obtaining different expressions/bounds for the radius of subregularity, which
involve generalized derivatives of set-valued mappings. We also obtain
different expressions when using either Frobenius or Euclidean norm to measure
the radius. As an application, we evaluate the radius of subregularity of a
general constraint system. Examples illustrate the theoretical findings.Comment: 20 page
Duality in cosmological perturbation theory
Cosmological perturbation equations derived from low-energy effective actions
are shown to be invariant under a duality transformation reminiscent of
electric-magnetic, strong-weak coupling, S-duality. A manifestly
duality-invariant approximation for perturbations far outside the horizon is
introduced, and it is argued to be useful even during a high curvature epoch.
Duality manifests itself through a remnant symmetry acting on the classical
moduli of cosmological models, and implying lower bounds on the number and
energy density of produced particles.Comment: 14 pages, LATEX, no figure
Approximation Limits of Linear Programs (Beyond Hierarchies)
We develop a framework for approximation limits of polynomial-size linear
programs from lower bounds on the nonnegative ranks of suitably defined
matrices. This framework yields unconditional impossibility results that are
applicable to any linear program as opposed to only programs generated by
hierarchies. Using our framework, we prove that O(n^{1/2-eps})-approximations
for CLIQUE require linear programs of size 2^{n^\Omega(eps)}. (This lower bound
applies to linear programs using a certain encoding of CLIQUE as a linear
optimization problem.) Moreover, we establish a similar result for
approximations of semidefinite programs by linear programs. Our main ingredient
is a quantitative improvement of Razborov's rectangle corruption lemma for the
high error regime, which gives strong lower bounds on the nonnegative rank of
certain perturbations of the unique disjointness matrix.Comment: 23 pages, 2 figure
The moduli problem at the perturbative level
Moduli fields generically produce strong dark matter -- radiation and baryon
-- radiation isocurvature perturbations through their decay if they remain
light during inflation. We show that existing upper bounds on the magnitude of
such fluctuations can thus be translated into stringent constraints on the
moduli parameter space m_\sigma (modulus mass) -- \sigma_{inf} (modulus vacuum
expectation value at the end of inflation). These constraints are complementary
to previously existing bounds so that the moduli problem becomes worse at the
perturbative level. In particular, if the inflationary scale H_{inf}~10^{13}
GeV, particle physics scenarios which predict high moduli masses m_\sigma >
10-100 TeV are plagued by the perturbative moduli problem, even though they
evade big-bang nucleosynthesis constraints.Comment: 4 pages, 3 figures (revtex) -- v2: an important correction on the
amplitude/transfer of isocurvature modes at the end of inflation, typos
corrected, references added, basic result unchange
Horava Gravity in the Effective Field Theory formalism: from cosmology to observational constraints
We consider Horava gravity within the framework of the effective field theory
(EFT) of dark energy and modified gravity. We work out a complete mapping of
the theory into the EFT language for an action including all the operators
which are relevant for linear perturbations with up to sixth order spatial
derivatives. We then employ an updated version of the EFTCAMB/EFTCosmoMC
package to study the cosmology of the low-energy limit of Horava gravity and
place constraints on its parameters using several cosmological data sets. In
particular we use cosmic microwave background (CMB) temperature-temperature and
lensing power spectra by Planck 2013, WMAP low-l polarization spectra, WiggleZ
galaxy power spectrum, local Hubble measurements, Supernovae data from SNLS,
SDSS and HST and the baryon acoustic oscillations measurements from BOSS, SDSS
and 6dFGS. We get improved upper bounds, with respect to those from Big Bang
Nucleosynthesis, on the deviation of the cosmological gravitational constant
from the local Newtonian one. At the level of the background phenomenology, we
find a relevant rescaling of the Hubble rate at all epoch, which has a strong
impact on the cosmological observables; at the level of perturbations, we
discuss in details all the relevant effects on the observables and find that in
general the quasi-static approximation is not safe to describe the evolution of
perturbations. Overall we find that the effects of the modifications induced by
the low-energy Horava gravity action are quite dramatic and current data place
tight bounds on the theory parameters.Comment: v1: 27 pages, 7 figures. v2: 28 pages, 7 figures. Changes in Figs.
2,3,4,6,7 and Tabs. 1,2. Matches published version in Phys. Dark Uni
Bounds on isocurvature perturbations from CMB and LSS data
We obtain very stringent bounds on the possible cold dark matter, baryon and
neutrino isocurvature contributions to the primordial fluctuations in the
Universe, using recent cosmic microwave background and large scale structure
data. In particular, we include the measured temperature and polarization power
spectra from WMAP and ACBAR, as well as the matter power spectrum from the 2dF
galaxy redshift survey. Neglecting the possible effects of spatial curvature,
tensor perturbations and reionization, we perform a Bayesian likelihood
analysis with nine free parameters, and find that the amplitude of the
isocurvature component cannot be larger than about 31% for the cold dark matter
mode, 91% for the baryon mode, 76% for the neutrino density mode, and 60% for
the neutrino velocity mode, at 2-sigma, for uncorrelated models. On the other
hand, for correlated adiabatic and isocurvature components, the fraction could
be slightly larger. However, the cross-correlation coefficient is strongly
constrained, and maximally correlated/anticorrelated models are disfavored.
This puts strong bounds on the curvaton model, independently of the bounds on
non-Gaussianity.Comment: 4 pages, 1 figure, some minor corrections; version accepted in PR
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