3,391 research outputs found
Lattice Dynamics in the Half-Space, II. Energy Transport Equation
We consider the lattice dynamics in the half-space. The initial data are
random according to a probability measure which enforces slow spatial variation
on the linear scale . We establish two time regimes. For
times of order , , locally the measure
converges to a Gaussian measure which is time stationary with a covariance
inherited from the initial measure (non-Gaussian, in general). For times of
order , this covariance changes in time and is governed by a
semiclassical transport equation.Comment: 35 page
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
Exponential and moment inequalities for U-statistics
A Bernstein-type exponential inequality for (generalized) canonical
U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen
inequalities for sums of independent random variables are extended to
(generalized) U-statistics of any order whose kernels are either nonnegative or
canonicalComment: 22 page
On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios
Different change-point type models encountered in statistical inference for
stochastic processes give rise to different limiting likelihood ratio
processes. In a previous paper of one of the authors it was established that
one of these likelihood ratios, which is an exponential functional of a
two-sided Poisson process driven by some parameter, can be approximated (for
sufficiently small values of the parameter) by another one, which is an
exponential functional of a two-sided Brownian motion. In this paper we
consider yet another likelihood ratio, which is the exponent of a two-sided
compound Poisson process driven by some parameter. We establish, that similarly
to the Poisson type one, the compound Poisson type likelihood ratio can be
approximated by the Brownian type one for sufficiently small values of the
parameter. We equally discuss the asymptotics for large values of the parameter
and illustrate the results by numerical simulations
Gamma-ray lines and neutrons from solar flares
The energy spectrum of accelerated protons and nuclei at the site of a limb flare was derived by a technique, using observations of the time dependent flux of high energy neutrons at the Earth. This energy spectrum is very similar to the energy spectra of 7 disk flares for which the accelerated particle spectra was previously derived using observations of 4 to 7 MeV to 2.223 MeV fluence ratios. The implied spectra for all of these flares are too steep to produce any significant amount of radiation from pi meson decay. It is suggested that the observed 10 MeV gamma rays from the flare are bremsstrahlung of relativistic electrons
Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations
The linearization of complex ordinary differential equations is studied by
extending Lie's criteria for linearizability to complex functions of complex
variables. It is shown that the linearization of complex ordinary differential
equations implies the linearizability of systems of partial differential
equations corresponding to those complex ordinary differential equations. The
invertible complex transformations can be used to obtain invertible real
transformations that map a system of nonlinear partial differential equations
into a system of linear partial differential equation. Explicit invariant
criteria are given that provide procedures for writing down the solutions of
the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single
research paper "Linearizability criteria for systems of two second-order
differential equations by complex methods" which has been published in
Nonlinear Dynamics. Due to citations of both parts I and II these are not
replaced with the above published articl
Equivalence of conservation laws and equivalence of potential systems
We study conservation laws and potential symmetries of (systems of)
differential equations applying equivalence relations generated by point
transformations between the equations. A Fokker-Planck equation and the Burgers
equation are considered as examples. Using reducibility of them to the
one-dimensional linear heat equation, we construct complete hierarchies of
local and potential conservation laws for them and describe, in some sense, all
their potential symmetries. Known results on the subject are interpreted in the
proposed framework. This paper is an extended comment on the paper of J.-q. Mei
and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press].Comment: 10 page
Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
Two-frequency Wigner distribution is introduced to capture the asymptotic
behavior of the space-frequency correlation of paraxial waves in the radiative
transfer limits. The scaling limits give rises to deterministic transport-like
equations. Depending on the ratio of the wavelength to the correlation length
the limiting equation is either a Boltzmann-like integral equation or a
Fokker-Planck-like differential equation in the phase space. The solutions to
these equations have a probabilistic representation which can be simulated by
Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal
direction, the corresponding Fokker-Planck-like equation can be solved exactly.Comment: typos correcte
Classification of Generalized Symmetries for the Vacuum Einstein Equations
A generalized symmetry of a system of differential equations is an
infinitesimal transformation depending locally upon the fields and their
derivatives which carries solutions to solutions. We classify all generalized
symmetries of the vacuum Einstein equations in four spacetime dimensions. To
begin, we analyze symmetries that can be built from the metric, curvature, and
covariant derivatives of the curvature to any order; these are called natural
symmetries and are globally defined on any spacetime manifold. We next classify
first-order generalized symmetries, that is, symmetries that depend on the
metric and its first derivatives. Finally, using results from the
classification of natural symmetries, we reduce the classification of all
higher-order generalized symmetries to the first-order case. In each case we
find that the generalized symmetries are infinitesimal generalized
diffeomorphisms and constant metric scalings. There are no non-trivial
conservation laws associated with these symmetries. A novel feature of our
analysis is the use of a fundamental set of spinorial coordinates on the
infinite jet space of Ricci-flat metrics, which are derived from Penrose's
``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te
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Landmark detection in 2D bioimages for geometric morphometrics: a multi-resolution tree-based approach
The detection of anatomical landmarks in bioimages is a necessary but tedious step for geometric morphometrics studies in many research domains. We propose variants of a multi-resolution tree-based approach to speed-up the detection of landmarks in bioimages. We extensively evaluate our method variants on three different datasets (cephalometric, zebrafish, and drosophila images). We identify the key method parameters (notably the multi-resolution) and report results with respect to human ground truths and existing methods. Our method achieves recognition performances competitive with current existing approaches while being generic and fast. The algorithms are integrated in the open-source Cytomine software and we provide parameter configuration guidelines so that they can be easily exploited by end-users. Finally, datasets are readily available through a Cytomine server to foster future research
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