775 research outputs found
Generalized Spatial Regression with Differential Regularization
We aim at analyzing geostatistical and areal data observed over irregularly
shaped spatial domains and having a distribution within the exponential family.
We propose a generalized additive model that allows to account for
spatially-varying covariate information. The model is fitted by maximizing a
penalized log-likelihood function, with a roughness penalty term that involves
a differential quantity of the spatial field, computed over the domain of
interest. Efficient estimation of the spatial field is achieved resorting to
the finite element method, which provides a basis for piecewise polynomial
surfaces. The proposed model is illustrated by an application to the study of
criminality in the city of Portland, Oregon, USA
IGS: an IsoGeometric approach for Smoothing on surfaces
We propose an Isogeometric approach for smoothing on surfaces, namely
estimating a function starting from noisy and discrete measurements. More
precisely, we aim at estimating functions lying on a surface represented by
NURBS, which are geometrical representations commonly used in industrial
applications. The estimation is based on the minimization of a penalized
least-square functional. The latter is equivalent to solve a 4th-order Partial
Differential Equation (PDE). In this context, we use Isogeometric Analysis
(IGA) for the numerical approximation of such surface PDE, leading to an
IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a
surface. Indeed, IGA facilitates encapsulating the exact geometrical
representation of the surface in the analysis and also allows the use of at
least globally continuous NURBS basis functions for which the 4th-order
PDE can be solved using the standard Galerkin method. We show the performance
of the proposed IGS method by means of numerical simulations and we apply it to
the estimation of the pressure coefficient, and associated aerodynamic force on
a winglet of the SOAR space shuttle
Optical properties of periodic systems within the current-current response framework: pitfalls and remedies
We compare the optical absorption of extended systems using the
density-density and current-current linear response functions calculated within
many-body perturbation theory. The two approaches are formally equivalent for a
finite momentum of the external perturbation. At
, however, the equivalence is maintained only if a small
expansion of the density-density response function is used. Moreover, in
practical calculations this equivalence can be lost if one naively extends the
strategies usually employed in the density-based approach to the current-based
approach. Specifically we discuss the use of a smearing parameter or of the
quasiparticle lifetimes to describe the finite width of the spectral peaks and
the inclusion of electron-hole interaction. In those instances we show that the
incorrect definition of the velocity operator and the violation of the
conductivity sum rule introduce unphysical features in the optical absorption
spectra of three paradigmatic systems: silicon (semiconductor), copper (metal)
and lithium fluoride (insulator). We then demonstrate how to correctly
introduce lifetime effects and electron-hole interactions within the
current-based approach.Comment: 17 pages, 6 figure
Exciton-Exciton transitions involving strongly bound Frenkel excitons: an ab initio approach
In pump-probe spectroscopy, two laser pulses are employed to garner dynamical
information from the sample of interest. The pump initiates the optical process
by exciting a portion of the sample from the electronic ground state to an
accessible electronic excited state, an exciton. Thereafter, the probe
interacts with the already excited sample. The change in the absorbance after
pump provides information on transitions between the excited states and their
dynamics. In this work we study these exciton-exciton transitions by means of
an ab initio real time propagation scheme based on dynamical Berry phase
formulation. The results are then analyzed taking advantage of a Fermi-golden
rule approach formulated in the excitonic basis-set and in terms of the
symmetries of the excitonic states. Using bulk LiF and 2D hBN as two prototype
materials, we discuss the selection rules for transitions involving strongly
bound Frenkel excitons, for which the hydrogen model cannot be used
A PDE-regularized smoothing method for space-time data over manifolds with application to medical data
We propose an innovative statistical-numerical method to model spatio- temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regu- larizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in prac- tical contexts, by dealing with neuroimaging and hemodynamic data
Integrated Depths for Partially Observed Functional Data
Partially observed functional data are frequently encountered in applications and are the object of an increasing interest by the literature. We here address the problem of measuring the centrality of a datum in a partially observed functional sample. We propose an integrated functional depth for partially observed functional data, dealing with the very challenging case where partial observability can occur systematically on any observation of the functional dataset. In particular, differently from many techniques for partially observed functional data, we do not request that some functional datum is fully observed, nor we require that a common domain exist, where all of the functional data are recorded. Because of this, our proposal can also be used in those frequent situations where reconstructions methods and other techniques for partially observed functional data are inapplicable. By means of simulation studies, we demonstrate the very good performances of the proposed depth on finite samples. Our proposal enables the use of benchmark methods based on depths, originally introduced for fully observed data, in the case of partially observed functional data. This includes the functional boxplot, the outliergram and the depth versus depth classifiers. We illustrate our proposal on two case studies, the first concerning a problem of outlier detection in German electricity supply functions, the second regarding a classification problem with data obtained from medical imaging. for this article are available online
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