63,948 research outputs found
Comparison of Gaussian process modeling software
Gaussian process fitting, or kriging, is often used to create a model from a
set of data. Many available software packages do this, but we show that very
different results can be obtained from different packages even when using the
same data and model. We describe the parameterization, features, and
optimization used by eight different fitting packages that run on four
different platforms. We then compare these eight packages using various data
functions and data sets, revealing that there are stark differences between the
packages. In addition to comparing the prediction accuracy, the predictive
variance--which is important for evaluating precision of predictions and is
often used in stopping criteria--is also evaluated
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
On micro-structural effects in dielectric mixtures
The paper presents numerical simulations performed on dielectric properties
of two-dimensional binary composites on eleven regular space filling
tessellations. First, significant contributions of different parameters, which
play an important role in the electrical properties of the composite, are
introduced both for designing and analyzing material mixtures. Later, influence
of structural differences and intrinsic electrical properties of constituents
on the composite's over all electrical properties are investigated. The
structural differences are resolved by the spectral density representation
approach. The numerical technique, without any {\em a-priori} assumptions, for
extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions
on Dielectrics and Electrical Insulatio
MATSuMoTo: The MATLAB Surrogate Model Toolbox For Computationally Expensive Black-Box Global Optimization Problems
MATSuMoTo is the MATLAB Surrogate Model Toolbox for computationally
expensive, black-box, global optimization problems that may have continuous,
mixed-integer, or pure integer variables. Due to the black-box nature of the
objective function, derivatives are not available. Hence, surrogate models are
used as computationally cheap approximations of the expensive objective
function in order to guide the search for improved solutions. Due to the
computational expense of doing a single function evaluation, the goal is to
find optimal solutions within very few expensive evaluations. The multimodality
of the expensive black-box function requires an algorithm that is able to
search locally as well as globally. MATSuMoTo is able to address these
challenges. MATSuMoTo offers various choices for surrogate models and surrogate
model mixtures, initial experimental design strategies, and sampling
strategies. MATSuMoTo is able to do several function evaluations in parallel by
exploiting MATLAB's Parallel Computing Toolbox.Comment: 13 pages, 7 figure
Filling a silo with a mixture of grains: Friction-induced segregation
We study the filling process of a two-dimensional silo with inelastic
particles by simulation of a granular media lattice gas (GMLG) model. We
calculate the surface shape and flow profiles for a monodisperse system and we
introduce a novel generalization of the GMLG model for a binary mixture of
particles of different friction properties where, for the first time, we
measure the segregation process on the surface. The results are in good
agreement with a recent theory, and we explain the observed small deviations by
the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let
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