51,057 research outputs found
Parallel computation of optimized arrays for 2-D electrical imaging surveys
Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The Sherman–Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrix–vector multiplications for a single add-on array were replaced with matrix–matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on commonly available microcomputers
MAP Estimators for Piecewise Continuous Inversion
We study the inverse problem of estimating a field from data comprising a
finite set of nonlinear functionals of , subject to additive noise; we
denote this observed data by . Our interest is in the reconstruction of
piecewise continuous fields in which the discontinuity set is described by a
finite number of geometric parameters. Natural applications include groundwater
flow and electrical impedance tomography. We take a Bayesian approach, placing
a prior distribution on and determining the conditional distribution on
given the data . It is then natural to study maximum a posterior (MAP)
estimators. Recently (Dashti et al 2013) it has been shown that MAP estimators
can be characterised as minimisers of a generalised Onsager-Machlup functional,
in the case where the prior measure is a Gaussian random field. We extend this
theory to a more general class of prior distributions which allows for
piecewise continuous fields. Specifically, the prior field is assumed to be
piecewise Gaussian with random interfaces between the different Gaussians
defined by a finite number of parameters. We also make connections with recent
work on MAP estimators for linear problems and possibly non-Gaussian priors
(Helin, Burger 2015) which employs the notion of Fomin derivative.
In showing applicability of our theory we focus on the groundwater flow and
EIT models, though the theory holds more generally. Numerical experiments are
implemented for the groundwater flow model, demonstrating the feasibility of
determining MAP estimators for these piecewise continuous models, but also that
the geometric formulation can lead to multiple nearby (local) MAP estimators.
We relate these MAP estimators to the behaviour of output from MCMC samples of
the posterior, obtained using a state-of-the-art function space
Metropolis-Hastings method.Comment: 53 pages, 21 figure
Nucleon-Nucleon Optical Model for Energies to 3 GeV
Several nucleon-nucleon potentials, Paris, Nijmegen, Argonne, and those
derived by quantum inversion, which describe the NN interaction for T-lab below
300$ MeV are extended in their range of application as NN optical models.
Extensions are made in r-space using complex separable potentials definable
with a wide range of form factor options including those of boundary condition
models. We use the latest phase shift analyses SP00 (FA00, WI00) of Arndt et
al. from 300 MeV to 3 GeV to determine these extensions. The imaginary parts of
the optical model interactions account for loss of flux into direct or resonant
production processes. The optical potential approach is of particular value as
it permits one to visualize fusion, and subsequent fission, of nucleons when
T-lab above 2 GeV. We do so by calculating the scattering wave functions to
specify the energy and radial dependences of flux losses and of probability
distributions. Furthermore, half-off the energy shell t-matrices are presented
as they are readily deduced with this approach. Such t-matrices are required
for studies of few- and many-body nuclear reactions.Comment: Latex, 40 postscript pages including 17 figure
The Design and Implementation of a Bayesian CAD Modeler for Robotic Applications
We present a Bayesian CAD modeler for robotic applications. We address the problem of taking into account the propagation of geometric uncertainties when solving inverse geometric problems. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements, instead of a simple equality or inequality. To solve geometric problems in this framework, we propose an original resolution method able to adapt to problem complexity.
Using two examples, we show how to apply our approach by providing simulation results using our modeler
A Robotic CAD System using a Bayesian Framework
We present in this paper a Bayesian CAD system
for robotic applications. We address the problem of the
propagation of geometric uncertainties and how esian
CAD system for robotic applications. We address the
problem of the propagation of geometric uncertainties
and how to take this propagation into account when
solving inverse problems. We describe the methodology
we use to represent and handle uncertainties using
probability distributions on the system's parameters
and sensor measurements. It may be seen as a
generalization of constraint-based approaches where we
express a constraint as a probability distribution instead
of a simple equality or inequality. Appropriate
numerical algorithms used to apply this methodology
are also described. Using an example, we show how
to apply our approach by providing simulation results
using our CAD system
A Monte Carlo study of the triangular lattice gas with the first- and the second-neighbor exclusions
We formulate a Swendsen-Wang-like version of the geometric cluster algorithm.
As an application,we study the hard-core lattice gas on the triangular lattice
with the first- and the second-neighbor exclusions. The data are analyzed by
finite-size scaling, but the possible existence of logarithmic corrections is
not considered due to the limited data. We determine the critical chemical
potential as and the critical particle density as
. The thermal and magnetic exponents
and , estimated from Binder ratio and
susceptibility , strongly support the general belief that the model is in
the 4-state Potts universality class. On the other hand, the analyses of
energy-like quantities yield the thermal exponent ranging from
to . These values differ significantly from the expected value 3/2,
and thus imply the existence of logarithmic corrections.Comment: 4 figures 2 table
- …