571 research outputs found
A Shape Theorem for Riemannian First-Passage Percolation
Riemannian first-passage percolation (FPP) is a continuum model, with a
distance function arising from a random Riemannian metric in . Our main
result is a shape theorem for this model, which says that large balls under
this metric converge to a deterministic shape under rescaling. As a
consequence, we show that smooth random Riemannian metrics are geodesically
complete with probability one
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
Mitochondrial Dna Replacement Versus Nuclear Dna Persistence
In this paper we consider two populations whose generations are not
overlapping and whose size is large. The number of males and females in both
populations is constant. Any generation is replaced by a new one and any
individual has two parents for what concerns nuclear DNA and a single one (the
mother) for what concerns mtDNA. Moreover, at any generation some individuals
migrate from the first population to the second.
In a finite random time , the mtDNA of the second population is completely
replaced by the mtDNA of the first. In the same time, the nuclear DNA is not
completely replaced and a fraction of the ancient nuclear DNA persists. We
compute both and . Since this study shows that complete replacement of
mtDNA in a population is compatible with the persistence of a large fraction of
nuclear DNA, it may have some relevance for the Out of Africa/Multiregional
debate in Paleoanthropology
Information and (co-)variances in discrete evolutionary genetics involving solely selection
The purpose of this Note is twofold: First, we introduce the general
formalism of evolutionary genetics dynamics involving fitnesses, under both the
deterministic and stochastic setups, and chiefly in discrete-time. In the
process, we particularize it to a one-parameter model where only a selection
parameter is unknown. Then and in a parallel manner, we discuss the estimation
problems of the selection parameter based on a single-generation frequency
distribution shift under both deterministic and stochastic evolutionary
dynamics. In the stochastics, we consider both the celebrated Wright-Fisher and
Moran models.Comment: a paraitre dans Journal of Statistical Mechanics: Theory and
Application
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization
We consider a family of models describing the evolution under selection of a
population whose dynamics can be related to the propagation of noisy traveling
waves. For one particular model, that we shall call the exponential model, the
properties of the traveling wave front can be calculated exactly, as well as
the statistics of the genealogy of the population. One striking result is that,
for this particular model, the genealogical trees have the same statistics as
the trees of replicas in the Parisi mean-field theory of spin glasses. We also
find that in the exponential model, the coalescence times along these trees
grow like the logarithm of the population size. A phenomenological picture of
the propagation of wave fronts that we introduced in a previous work, as well
as our numerical data, suggest that these statistics remain valid for a larger
class of models, while the coalescence times grow like the cube of the
logarithm of the population size.Comment: 26 page
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
In this paper we study a Tikhonov-type method for ill-posed nonlinear
operator equations \gdag = F(
ag) where \gdag is an integrable,
non-negative function. We assume that data are drawn from a Poisson process
with density t\gdag where may be interpreted as an exposure time. Such
problems occur in many photonic imaging applications including positron
emission tomography, confocal fluorescence microscopy, astronomic observations,
and phase retrieval problems in optics. Our approach uses a
Kullback-Leibler-type data fidelity functional and allows for general convex
penalty terms. We prove convergence rates of the expectation of the
reconstruction error under a variational source condition as both
for an a priori and for a Lepski{\u\i}-type parameter choice rule
On exact time-averages of a massive Poisson particle
In this work we study, under the Stratonovich definition, the problem of the
damped oscillatory massive particle subject to a heterogeneous Poisson noise
characterised by a rate of events, \lambda (t), and a magnitude, \Phi,
following an exponential distribution. We tackle the problem by performing
exact time-averages over the noise in a similar way to previous works analysing
the problem of the Brownian particle. From this procedure we obtain the
long-term equilibrium distributions of position and velocity as well as
analytical asymptotic expressions for the injection and dissipation of energy
terms. Considerations on the emergence of stochastic resonance in this type of
system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical
Mechanics: Theory and Experimen
The Random Discrete Action for 2-Dimensional Spacetime
A one-parameter family of random variables, called the Discrete Action, is
defined for a 2-dimensional Lorentzian spacetime of finite volume. The single
parameter is a discreteness scale. The expectation value of this Discrete
Action is calculated for various regions of 2D Minkowski spacetime. When a
causally convex region of 2D Minkowski spacetime is divided into subregions
using null lines the mean of the Discrete Action is equal to the alternating
sum of the numbers of vertices, edges and faces of the null tiling, up to
corrections that tend to zero as the discreteness scale is taken to zero. This
result is used to predict that the mean of the Discrete Action of the flat
Lorentzian cylinder is zero up to corrections, which is verified. The
``topological'' character of the Discrete Action breaks down for causally
convex regions of the flat trousers spacetime that contain the singularity and
for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte
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