33,690 research outputs found
Comparison of two-dimensional binned data distributions using the energy test
For the purposes of monitoring HEP experiments, comparison is often made between regularly acquired histograms of data and reference histograms which represent the ideal state of the equipment. With the larger experiments now starting up, there is a need for automation of this task since the volume of comparisons would overwhelm human operators. However, the two-dimensional histogram comparison tools currently available in ROOT have noticeable shortcomings. We present a new comparison test for 2D histograms, based on the Energy Test of Aslan and Zech, which provides more decisive discrimination between histograms of data coming from different distributions
A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography
Photoacoustic tomography is a hybrid imaging technique that combines high
optical tissue contrast with high ultrasound resolution. Direct reconstruction
methods such as filtered backprojection, time reversal and least squares suffer
from curved line artefacts and blurring, especially in case of limited angles
or strong noise. In recent years, there has been great interest in regularised
iterative methods. These methods employ prior knowledge on the image to provide
higher quality reconstructions. However, easy comparisons between regularisers
and their properties are limited, since many tomography implementations heavily
rely on the specific regulariser chosen. To overcome this bottleneck, we
present a modular reconstruction framework for photoacoustic tomography. It
enables easy comparisons between regularisers with different properties, e.g.
nonlinear, higher-order or directional. We solve the underlying minimisation
problem with an efficient first-order primal-dual algorithm. Convergence rates
are optimised by choosing an operator dependent preconditioning strategy. Our
reconstruction methods are tested on challenging 2D synthetic and experimental
data sets. They outperform direct reconstruction approaches for strong noise
levels and limited angle measurements, offering immediate benefits in terms of
acquisition time and quality. This work provides a basic platform for the
investigation of future advanced regularisation methods in photoacoustic
tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to
v2: regularisation with directional wavelet has been added; new experimental
tests have been include
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
Non parametric reconstruction of distribution functions from observed galactic disks
A general inversion technique for the recovery of the underlying distribution
function for observed galactic disks is presented and illustrated. Under the
assumption that these disks are axi-symmetric and thin, the proposed method
yields the unique distribution compatible with all the observables available.
The derivation may be carried out from the measurement of the azimuthal
velocity distribution arising from positioning the slit of a spectrograph along
the major axis of the galaxy. More generally, it may account for the
simultaneous measurements of velocity distributions corresponding to slits
presenting arbitrary orientations with respect to the major axis. The approach
is non-parametric, i.e. it does not rely on a particular algebraic model for
the distribution function. Special care is taken to account for the fraction of
counter-rotating stars which strongly affects the stability of the disk. An
optimisation algorithm is devised -- generalising the work of Skilling & Bryan
(1984) -- to carry this truly two-dimensional ill-conditioned inversion
efficiently. The performances of the overall inversion technique with respect
to the noise level and truncation in the data set is investigated with
simulated data. Reliable results are obtained up to a mean signal to noise
ratio of~5 and when measurements are available up to . A discussion of
the residual biases involved in non parametric inversions is presented.
Prospects of application to observed galaxies and other inversion problems are
discussed.Comment: 11 pages, 13 figures; accepted for publication by MNRA
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
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