23,836 research outputs found
Testing Distributions of Huge Objects
We initiate a study of a new model of property testing that is a hybrid of
testing properties of distributions and testing properties of strings.
Specifically, the new model refers to testing properties of distributions, but
these are distributions over huge objects (i.e., very long strings).
Accordingly, the model accounts for the total number of local probes into these
objects (resp., queries to the strings) as well as for the distance between
objects (resp., strings), and the distance between distributions is defined as
the earth mover's distance with respect to the relative Hamming distance
between strings.
We study the query complexity of testing in this new model, focusing on three
directions. First, we try to relate the query complexity of testing properties
in the new model to the sample complexity of testing these properties in the
standard distribution testing model. Second, we consider the complexity of
testing properties that arise naturally in the new model (e.g., distributions
that capture random variations of fixed strings). Third, we consider the
complexity of testing properties that were extensively studied in the standard
distribution testing model: Two such cases are uniform distributions and pairs
of identical distributions
Testing Distributions of Huge Objects
We initiate a study of a new model of property testing that is a hybrid of
testing properties of distributions and testing properties of strings.
Specifically, the new model refers to testing properties of distributions, but
these are distributions over huge objects (i.e., very long strings).
Accordingly, the model accounts for the total number of local probes into these
objects (resp., queries to the strings) as well as for the distance between
objects (resp., strings), and the distance between distributions is defined as
the earth mover's distance with respect to the relative Hamming distance
between strings.
We study the query complexity of testing in this new model, focusing on three
directions. First, we try to relate the query complexity of testing properties
in the new model to the sample complexity of testing these properties in the
standard distribution testing model. Second, we consider the complexity of
testing properties that arise naturally in the new model (e.g., distributions
that capture random variations of fixed strings). Third, we consider the
complexity of testing properties that were extensively studied in the standard
distribution testing model: Two such cases are uniform distributions and pairs
of identical distributions
Gravitational Waves from Abelian Gauge Fields and Cosmic Strings at Preheating
Primordial gravitational waves provide a very important stochastic background
that could be detected soon with interferometric gravitational wave antennas or
indirectly via the induced patterns in the polarization anisotropies of the
cosmic microwave background. The detection of these waves will open a new
window into the early Universe, and therefore it is important to characterize
in detail all possible sources of primordial gravitational waves. In this paper
we develop theoretical and numerical methods to study the production of
gravitational waves from out-of-equilibrium gauge fields at preheating. We then
consider models of preheating after hybrid inflation, where the symmetry
breaking field is charged under a local U(1) symmetry. We analyze in detail the
dynamics of the system in both momentum and configuration space, and show that
gauge fields leave specific imprints in the resulting gravitational wave
spectra, mainly through the appearence of new peaks at characteristic
frequencies that are related to the mass scales in the problem. We also show
how these new features in the spectra correlate with string-like spatial
configurations in both the Higgs and gauge fields that arise due to the
appearance of topological winding numbers of the Higgs around Nielsen-Olesen
strings. We study in detail the time evolution of the spectrum of gauge fields
and gravitational waves as these strings evolve and decay before entering a
turbulent regime where the gravitational wave energy density saturates.Comment: This paper is dedicated to the memory of Lev Kofman. Added references
and comments in Sec. III.B. Version accepted in PR
Asymptotics of Discrete MDL for Online Prediction
Minimum Description Length (MDL) is an important principle for induction and
prediction, with strong relations to optimal Bayesian learning. This paper
deals with learning non-i.i.d. processes by means of two-part MDL, where the
underlying model class is countable. We consider the online learning framework,
i.e. observations come in one by one, and the predictor is allowed to update
his state of mind after each time step. We identify two ways of predicting by
MDL for this setup, namely a static} and a dynamic one. (A third variant,
hybrid MDL, will turn out inferior.) We will prove that under the only
assumption that the data is generated by a distribution contained in the model
class, the MDL predictions converge to the true values almost surely. This is
accomplished by proving finite bounds on the quadratic, the Hellinger, and the
Kullback-Leibler loss of the MDL learner, which are however exponentially worse
than for Bayesian prediction. We demonstrate that these bounds are sharp, even
for model classes containing only Bernoulli distributions. We show how these
bounds imply regret bounds for arbitrary loss functions. Our results apply to a
wide range of setups, namely sequence prediction, pattern classification,
regression, and universal induction in the sense of Algorithmic Information
Theory among others.Comment: 34 page
Anamorphosis in hybrid inflation: How to avoid fine-tuning of initial conditions?
In order to generate more than 60 e-folds of accelerated expansion in
original hybrid inflation, 2-fields trajectories are usually required to be
initially fine-tuned in a very narrow band along the inflationary valley or in
some isolated points outside it. From a more precise investigation of the
dynamics, these points which can cover a non-negligible proportion of the space
of sub-planckian initial field values, depending on the potential parameters,
are shown to be organised in connected domains with fractal boundaries. They
correspond to trajectories first falling towards the bottom of the potential,
then climbing and slow-rolling back along the inflationary valley. The full
parameter space, including initial velocities and all the potential parameters,
is then explored by using Monte-Carlo-Markov-Chains (MCMC) methods. Results
indicate that successful initial conditions (IC) outside the valley are not
localized in the parameter space and are the dominant way to realise inflation,
independently of initial field velocities. Natural bounds on parameters are
deduced. The genericity of our results is confirmed in 5 other hybrid models
from various framework.Comment: AIP Proceedings of the "Invisible Universe" conference, Palais de
l'Unesco, Paris, 29 June - 4 July 200
Fractal initial conditions and natural parameter values in hybrid inflation
We show that the initial field values required to produce inflation in the
two fields original hybrid model, and its supergravity F-term extension, do not
suffer from any fine-tuning problem, even when the fields are restricted to be
sub-planckian and for almost all potential parameter values. This is due to the
existence of an initial slow-roll violating evolution which has been overlooked
so far. Due to the attractor nature of the inflationary valley, these
trajectories end up producing enough accelerated expansion of the universe. By
numerically solving the full non-linear dynamics, we show that the set of such
successful initial field values is connected, of dimension two and possesses a
fractal boundary of infinite length exploring the whole field space. We then
perform a Monte-Carlo-Markov-Chain analysis of the whole parameter space
consisting of the initial field values, field velocities and potential
parameters. We give the marginalised posterior probability distributions for
each of these quantities such that the universe inflates long enough to solve
the usual cosmological problems. Inflation in the original hybrid model and its
supergravity version appears to be generic and more probable by starting
outside of the inflationary valley. Finally, the implication of our findings in
the context of the eternal inflationary scenario are discussed.Comment: 16 pages, 16 figures, uses RevTeX. Lyapunov exponents and references
added, matches published versio
Evolution of the Mean Jet Shape and Dijet Asymmetry Distribution of an Ensemble of Holographic Jets in Strongly Coupled Plasma
Some of the most important probes of the quark-gluon plasma (QGP) produced in
heavy ion collisions come from the analysis of how the shape and energy of jets
are modified by passage through QGP. We model an ensemble of back-to-back
dijets to gain a qualitative understanding of how the shapes of the individual
jets and the asymmetry in the energy of the pairs of jets are modified by
passage through an expanding droplet of strongly coupled plasma, as modeled in
a holographic gauge theory. We do so by constructing an ensemble of strings in
the gravitational description of the gauge theory. We model QCD jets in vacuum
using strings whose endpoints move "downward" into the gravitational bulk
spacetime with some fixed small angle that represents the opening angle (ratio
of jet mass to jet energy) that the QCD jet would have in vacuum. Such strings
must be moving through the gravitational bulk at (close to) the speed of light;
they must be (close to) null. This condition does not specify the energy
distribution along the string, meaning that it does not specify the shape of
the jet being modeled. We study the dynamics of strings that are initially not
null and show that strings with a wide range of initial conditions rapidly
accelerate and become null and, as they do, develop a similar distribution of
their energy density. We use this distribution of the energy density along the
string, choose an ensemble of strings whose opening angles and energies are
distributed as in perturbative QCD, and show that we can then fix one model
parameter such that the mean jet shape in our ensemble matches that measured in
p-p collisions reasonably well. We send our strings through the plasma,
choosing the second model parameter to get a reasonable suppression in the
number of jets, and study how the mean jet shape and the dijet asymmetry are
modified, comparing both to data from LHC heavy ion collisions.Comment: References added; 34 pages, 11 figure
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