47,354 research outputs found
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estimation
procedures for metric estimation from landmark configurations distributed
according to the transition distribution of a Riemannian Brownian motion
arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.
The distribution possesses properties similar to the regular Euclidean normal
distribution but its transition density is governed by a high-dimensional PDE
with no closed-form solution in the nonlinear case. We show how the density can
be numerically approximated by Monte Carlo sampling of conditioned Brownian
bridges, and we use this to estimate parameters of the LDDMM kernel and thus
the metric structure by maximum likelihood
A graphical, scalable and intuitive method for the placement and the connection of biological cells
We introduce a graphical method originating from the computer graphics domain
that is used for the arbitrary and intuitive placement of cells over a
two-dimensional manifold. Using a bitmap image as input, where the color
indicates the identity of the different structures and the alpha channel
indicates the local cell density, this method guarantees a discrete
distribution of cell position respecting the local density function. This
method scales to any number of cells, allows to specify several different
structures at once with arbitrary shapes and provides a scalable and versatile
alternative to the more classical assumption of a uniform non-spatial
distribution. Furthermore, several connection schemes can be derived from the
paired distances between cells using either an automatic mapping or a
user-defined local reference frame, providing new computational properties for
the underlying model. The method is illustrated on a discrete homogeneous
neural field, on the distribution of cones and rods in the retina and on a
coronal view of the basal ganglia.Comment: Corresponding code at https://github.com/rougier/spatial-computatio
Calculation of time resolution of the J-PET tomograph using the Kernel Density Estimation
In this paper we estimate the time resolution of the J-PET scanner built from
plastic scintillators. We incorporate the method of signal processing using the
Tikhonov regularization framework and the Kernel Density Estimation method. We
obtain simple, closed-form analytical formulas for time resolutions. The
proposed method is validated using signals registered by means of the single
detection unit of the J-PET tomograph built out from 30 cm long plastic
scintillator strip. It is shown that the experimental and theoretical results,
obtained for the J-PET scanner equipped with vacuum tube photomultipliers, are
consistent.Comment: 25 pages, 11 figure
Fine Tuning Classical and Quantum Molecular Dynamics using a Generalized Langevin Equation
Generalized Langevin Equation (GLE) thermostats have been used very
effectively as a tool to manipulate and optimize the sampling of thermodynamic
ensembles and the associated static properties. Here we show that a similar,
exquisite level of control can be achieved for the dynamical properties
computed from thermostatted trajectories. By developing quantitative measures
of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic
oscillator, we show that these analytical results accurately predict the
behavior of strongly anharmonic systems. We also show that it is possible to
correct, to a significant extent, the effects of the GLE term onto the
corresponding microcanonical dynamics, which puts on more solid grounds the use
of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and
could help improve the prediction of dynamical quantities from techniques that
use a Langevin term to stabilize dynamics. Finally we address the use of
thermostats in the context of approximate path-integral-based models of quantum
nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some
of the artifacts associated with these techniques, improving the quality of
results for the modelling of vibrational dynamics of molecules, liquids and
solids
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