9,855 research outputs found
A trivariate interpolation algorithm using a cube-partition searching procedure
In this paper we propose a fast algorithm for trivariate interpolation, which
is based on the partition of unity method for constructing a global interpolant
by blending local radial basis function interpolants and using locally
supported weight functions. The partition of unity algorithm is efficiently
implemented and optimized by connecting the method with an effective
cube-partition searching procedure. More precisely, we construct a cube
structure, which partitions the domain and strictly depends on the size of its
subdomains, so that the new searching procedure and, accordingly, the resulting
algorithm enable us to efficiently deal with a large number of nodes.
Complexity analysis and numerical experiments show high efficiency and accuracy
of the proposed interpolation algorithm
The High Density Region of QCD from an Effective Model
We study the high density region of QCD within an effective model obtained in
the frame of the hopping parameter expansion and choosing Polyakov-type loops
as the main dynamical variables representing the fermionic matter. This model
still shows the so-called sign problem, a difficulty peculiar to non-zero
chemical potential, but it permits the development of algorithms which ensure a
good overlap of the simulated Monte Carlo ensemble with the true one. We review
the main features of the model and present results concerning the dependence of
various observables on the chemical potential and on the temperature, in
particular of the charge density and the Polykov loop susceptibility, which may
be used to characterize the various phases expected at high baryonic density.
In this way, we obtain information about the phase structure of the model and
the corresponding phase transitions and cross over regions, which can be
considered as hints about the behaviour of non-zero density QCD.Comment: 7 pages, 5 figures, talk presented at the XXVth International
Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg,
German
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds
We consider the problem of interpolating a function given on scattered points
using Hermite-Birkhoff formulas on the sphere and other manifolds. We express
each proposed interpolant as a linear combination of basis functions, the
combination coefficients being incomplete Taylor expansions of the interpolated
function at the interpolation points. The basis functions have the following
features: (i) depend on the geodesic distance; (ii) are orthonormal with
respect to the point-evaluation functionals; and (iii) have all derivatives
equal zero up to a certain order at the interpolation points. Moreover, the
construction of such interpolants, which belong to the class of partition of
unity methods, takes advantage of not requiring any solution of linear systems
Fast and flexible interpolation via PUM with applications in population dynamics
In this paper the Partition of Unity Method (PUM) is efficiently performed
using Radial Basis Functions (RBFs) as local approximants. In particular, we
present a new space-partitioning data structure extremely useful in
applications because of its independence from the problem geometry. Moreover,
we study, in the context of wild herbivores in forests, an application of such
algorithm. This investigation shows that the ecosystem of the considered
natural park is in a very delicate situation, for which the animal population
could become extinguished. The determination of the so-called sensitivity
surfaces, obtained with the new fast and flexible interpolation tool, indicates
some possible preventive measures to the park administrators
Partition of Unity Interpolation on Multivariate Convex Domains
In this paper we present a new algorithm for multivariate interpolation of
scattered data sets lying in convex domains \Omega \subseteq \RR^N, for any
. To organize the points in a multidimensional space, we build a
-tree space-partitioning data structure, which is used to efficiently apply
a partition of unity interpolant. This global scheme is combined with local
radial basis function approximants and compactly supported weight functions. A
detailed description of the algorithm for convex domains and a complexity
analysis of the computational procedures are also considered. Several numerical
experiments show the performances of the interpolation algorithm on various
sets of Halton data points contained in , where can be any
convex domain like a 2D polygon or a 3D polyhedron
Car Sharing and Relocation Strategies: a Case Study Comparison in the Italian Market
The sharing economy represents an economic model based on the sharing of goods and services. In particular, this paper examines car sharing model, an attractive alternative to a self-owned car which has found large interest in the recent literature in different research fields. This study aims to investigate innovative and effective relocation strategies based on the analysis of data on users’ consumptions, for the constantly growing car sharing system. For this purpose, after a literature review, the paper presents a case study focused on the car repositioning algorithm developed by one of the market leader in this sector: car2go. More in detail, the paper evaluates differences and similarities in the strategic management of this model within the Italian context, through a comparison among the cities of Rome and Milan. Empirical results and practical implications for users will be provided, by highlighting opportunities and threats concerning the different settings
The East model: recent results and new progresses
The East model is a particular one dimensional interacting particle system in
which certain transitions are forbidden according to some constraints depending
on the configuration of the system. As such it has received particular
attention in the physics literature as a special case of a more general class
of systems referred to as kinetically constrained models, which play a key role
in explaining some features of the dynamics of glasses. In this paper we give
an extensive overview of recent rigorous results concerning the equilibrium and
non-equilibrium dynamics of the East model together with some new improvements
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