21,953 research outputs found
A percolation system with extremely long range connections and node dilution
We study the very long-range bond-percolation problem on a linear chain with
both sites and bonds dilution. Very long range means that the probability
for a connection between two occupied sites at a distance
decays as a power law, i.e. when , and
when . Site dilution means that the occupancy probability of a site
is . The behavior of this model results from the competition
between long-range connectivity, which enhances the percolation, and site
dilution, which weakens percolation. The case with is
well-known, being the exactly solvable mean-field model. The percolation order
parameter is investigated numerically for different values of
, and . We show that in the ranges
and the percolation order parameter depends only on
the average connectivity of sites, which can be explicitly computed in
terms of the three parameters , and
Overview of Constrained PARAFAC Models
In this paper, we present an overview of constrained PARAFAC models where the
constraints model linear dependencies among columns of the factor matrices of
the tensor decomposition, or alternatively, the pattern of interactions between
different modes of the tensor which are captured by the equivalent core tensor.
Some tensor prerequisites with a particular emphasis on mode combination using
Kronecker products of canonical vectors that makes easier matricization
operations, are first introduced. This Kronecker product based approach is also
formulated in terms of the index notation, which provides an original and
concise formalism for both matricizing tensors and writing tensor models. Then,
after a brief reminder of PARAFAC and Tucker models, two families of
constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models,
are described in a unified framework, for order tensors. New tensor
models, called nested Tucker models and block PARALIND/CONFAC models, are also
introduced. A link between PARATUCK models and constrained PARAFAC models is
then established. Finally, new uniqueness properties of PARATUCK models are
deduced from sufficient conditions for essential uniqueness of their associated
constrained PARAFAC models
Microlensing path parametrization for Earth-like Exoplanet detection around solar mass stars
We propose a new parametrization of the impact parameter u0 and impact angle
{\alpha} for microlensing systems composed by an Earth-like Exoplanet around a
Solar mass Star at 1 AU. We present the caustic topology of such system, as
well as the related light curves generated by using such a new parametrization.
Based on the same density of points and accuracy of regular methods, we obtain
results 5 times faster for discovering Earth-like exoplanet. In this big data
revolution of photometric astronomy, our method will impact future missions
like WFIRST (NASA) and Euclid (ESA) and they data pipelines, providing a rapid
and deep detection of exoplanets for this specific class of microlensing event
that might otherwise be lost.Comment: 8 pages, 7 figures, accepted to be published in The Astronomical
Journa
Spin-glass behaviour on random lattices
The ground-state phase diagram of an Ising spin-glass model on a random graph
with an arbitrary fraction of ferromagnetic interactions is analysed in the
presence of an external field. Using the replica method, and performing an
analysis of stability of the replica-symmetric solution, it is shown that
, correponding to an unbiased spin glass, is a singular point in the
phase diagram, separating a region with a spin-glass phase () from a
region with spin-glass, ferromagnetic, mixed, and paramagnetic phases
()
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
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