36,039 research outputs found
Saddle Points Stability in the Replica Approach Off Equilibrium
We study the replica free energy surface for a spin glass model near the
glassy temperature. In this model the simplicity of the equilibrium solution
hides non trivial metastable saddle points. By means of the stability analysis
performed for one and two real replicas constrained, an interpretation for some
of them is achieved.Comment: 10 pages and 3 figures upon request, Univerista` di Roma I preprint
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Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
We compute the phenomenological signatures of a model (Watanabe et al' 09) of
anisotropic inflation driven by a scalar and a vector field. The action for the
vector is U(1) invariant, and the model is free of ghost instabilities. A
suitable coupling of the scalar to the kinetic term of the vector allows for a
slow roll evolution of the vector vev, and hence for a prolonged anisotropic
expansion; this provides a counter example to the cosmic no hair conjecture. We
compute the nonvanishing two point correlation functions between physical modes
of the system, and express them in terms of power spectra with angular
dependence. The anisotropy parameter g_* for the scalar-scalar spectrum
(defined as in the Ackerman et al '07 parametrization) turns out to be negative
in the simplest realization of the model, which, therefore, cannot account for
the angular dependence emerged in some analyses of the WMAP data. A g_* of
order -0.1 is achieved when the energy of the vector is about 6-7 orders of
magnitude smaller than that of the scalar during inflation. For such values of
the parameters, the scalar-tensor correlation (which is in principle a
distinctive signature of anisotropic spaces) is smaller than the tensor-tensor
correlation
CMB Anomalies from Relic Anisotropy
Most of the analysis of the Cosmic Microwave Background relies on the
assumption of statistical isotropy. However, given some recent evidence
pointing against isotropy, as for instance the observed alignment of different
multipoles on large scales, it is worth testing this assumption against the
increasing amount of available data. As a pivot model, we assume that the
spectrum of the primordial perturbations depends also on their directionality
(rather than just on the magnitude of their momentum, as in the standard case).
We explicitly compute the correlation matrix for the temperature anisotropies
in the simpler case in which there is a residual isotropy between two spatial
directions. As a concrete example, we consider a different initial expansion
rate along one direction, and the following isotropization which takes place
during inflation. Depending on the amount of inflation, this can lead to broken
statistical isotropy on the largest observable scales.Comment: 6 pages, 2 .ps figure
Approximate Canonical Quantization for Cosmological Models
In cosmology minisuperspace models are described by nonlinear
time-reparametrization invariant systems with a finite number of degrees of
freedom. Often these models are not explicitly integrable and cannot be
quantized exactly. Having this in mind, we present a scheme for the
(approximate) quantization of perturbed, nonintegrable, time-reparametrization
invariant systems that uses (approximate) gauge invariant quantities. We apply
the scheme to a couple of simple quantum cosmological models.Comment: 16 pages, Latex, accepted for publication in Int. Jou. Mod. Phys.
Optimal Clustering under Uncertainty
Classical clustering algorithms typically either lack an underlying
probability framework to make them predictive or focus on parameter estimation
rather than defining and minimizing a notion of error. Recent work addresses
these issues by developing a probabilistic framework based on the theory of
random labeled point processes and characterizing a Bayes clusterer that
minimizes the number of misclustered points. The Bayes clusterer is analogous
to the Bayes classifier. Whereas determining a Bayes classifier requires full
knowledge of the feature-label distribution, deriving a Bayes clusterer
requires full knowledge of the point process. When uncertain of the point
process, one would like to find a robust clusterer that is optimal over the
uncertainty, just as one may find optimal robust classifiers with uncertain
feature-label distributions. Herein, we derive an optimal robust clusterer by
first finding an effective random point process that incorporates all
randomness within its own probabilistic structure and from which a Bayes
clusterer can be derived that provides an optimal robust clusterer relative to
the uncertainty. This is analogous to the use of effective class-conditional
distributions in robust classification. After evaluating the performance of
robust clusterers in synthetic mixtures of Gaussians models, we apply the
framework to granular imaging, where we make use of the asymptotic
granulometric moment theory for granular images to relate robust clustering
theory to the application.Comment: 19 pages, 5 eps figures, 1 tabl
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