6 research outputs found
Spatially Indexed Functional Data
The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation. A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations. To detect global changes in the ionosphere, we present a novel statistical methodology that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle unevenly spaced, partially observed curves. While this research makes a solid contribution to the space physics community, our statistical methodology is very flexible and can be useful in other applied problems
Random Sequential Adsorption of Objects of Decreasing Size
We consider the model of random sequential adsorption, with depositing
objects, as well as those already at the surface, decreasing in size according
to a specified time dependence, from a larger initial value to a finite value
in the large time limit. Numerical Monte Carlo simulations of two-dimensional
deposition of disks and one-dimensional deposition of segments are reported for
the density-density correlation function and gap-size distribution function,
respectively. Analytical considerations supplement numerical results in the
one-dimensional case. We investigate the correlation hole - the depletion of
correlation functions near contact and, for the present model, their vanishing
at contact - that opens up at finite times, as well as its closing and
reemergence of the logarithmic divergence of correlation properties at contact
in the large time limit.Comment: Submitted for publicatio
Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends
We develop methodology for the estimation of the functional mean and the
functional principal components when the functions form a spatial process. The
data consist of curves observed at spatial
locations . We propose several
methods, and evaluate them by means of a simulation study. Next, we develop a
significance test for the correlation of two such functional spatial fields.
After validating the finite sample performance of this test by means of a
simulation study, we apply it to determine if there is correlation between
long-term trends in the so-called critical ionospheric frequency and decadal
changes in the direction of the internal magnetic field of the Earth. The test
provides conclusive evidence for correlation, thus solving a long-standing
space physics conjecture. This conclusion is not apparent if the spatial
dependence of the curves is neglected.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS524 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Random Sequential Adsorption of Oriented Superdisks
In this work we extend recent study of the properties of the dense packing of
"superdisks," by Y. Jiao, F. H. Stillinger and S. Torquato, Phys. Rev. Lett.
100, 245504 (2008), to the jammed state formed by these objects in random
sequential adsorption. The superdisks are two-dimensional shapes bound by the
curves of the form |x|^(2p) + |y|^(2p) = 1, with p > 0. We use Monte Carlo
simulations and theoretical arguments to establish that p = 1/2 is a special
point at which the jamming density has a discontinuous derivative as a function
of p. The existence of this point can be also argued for by geometrical
arguments
Deterministic reaction models with power-law forces
We study a one-dimensional particles system, in the overdamped limit, where
nearest particles attract with a force inversely proportional to a power of
their distance and coalesce upon encounter. The detailed shape of the
distribution function for the gap between neighbouring particles serves to
discriminate between different laws of attraction. We develop an exact
Fokker-Planck approach for the infinite hierarchy of distribution functions for
multiple adjacent gaps and solve it exactly, at the mean-field level, where
correlations are ignored. The crucial role of correlations and their effect on
the gap distribution function is explored both numerically and analytically.
Finally, we analyse a random input of particles, which results in a stationary
state where the effect of correlations is largely diminished