7,055 research outputs found
Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds
Let (S(t)) be a one-parameter family S = (S(t)) of positive integral
operators on a locally compact space L. For a possibly non-uniform partition of
[0,1] define a measure on the path space C([0,1],L) by using a) S(dt) for the
transition between cosecutive partition times of distance dt, and b) a suitable
continuous interpolation scheme (e.g. Brownian bridges or geodesics). If
necessary normalize to get a probability measure. We prove a version of
Chernoff's theorem of semigroup theory and tighness results which together
yield convergence in law of such measures as the partition gets finer. In
particular let L be a closed smooth submanifold of a Riemannian manifold M. We
prove convergence of Brownian motion on M, conditioned to visit L at all
partition times, to a process on L whose law has a Radon-Nikodym density with
repect to Brownian motion on L which contains scalar, mean and sectional
curvature terms. Various approximation schemes for Brownian motion are also
given. These results substantially extend earlier work by the authors and by
Andersson and Driver.Comment: 35 pages, revised version for publication, more detailed expositio
Annotated bibliography of gender in agriculture - A reference resource for Africa RISING researchers
Kondo effect of Co adatoms on Ag monolayers on noble metal surfaces
The Kondo temperature of single Co adatoms on monolayers of Ag on Cu
and Au(111) is determined using Scanning Tunneling Spectroscopy. of Co on
a single monolayer of Ag on either substrate is essentially the same as that of
Co on a homogenous Ag(111) crystal. This gives strong evidence that the
interaction of surface Kondo impurities with the substrate is very local in
nature. By comparing found for Co on Cu, Ag, and Au (111)-surfaces we
show that the energy scale of the many-electron Kondo state is insensitive to
the properties of surface states and to the energetic position of the projected
bulk band edges.Comment: 4 pages, 3 figure
Scale space consistency of piecewise constant least squares estimators -- another look at the regressogram
We study the asymptotic behavior of piecewise constant least squares
regression estimates, when the number of partitions of the estimate is
penalized. We show that the estimator is consistent in the relevant metric if
the signal is in , the space of c\`{a}dl\`{a}g functions equipped
with the Skorokhod metric or equipped with the supremum metric.
Moreover, we consider the family of estimates under a varying smoothing
parameter, also called scale space. We prove convergence of the empirical scale
space towards its deterministic target.Comment: Published at http://dx.doi.org/10.1214/074921707000000274 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
Kondo temperature of magnetic impurities at surfaces
Based on the experimental observation, that only the close vicinity of a
magnetic impurity at metal surfaces determines its Kondo behaviour, we
introduce a simple model which explains the Kondo temperatures observed for
cobalt adatoms at the (111) and (100) surfaces of Cu, Ag, and Au. Excellent
agreement between the model and scanning tunneling spectroscopy (STS)
experiments is demonstrated. The Kondo temperature is shown to depend on the
occupation of the d-level determined by the hybridization between adatom and
substrate with a minimum around single occupancy.Comment: 4 pages, 2 figure
Implications of the introduction of forage chopper machines
United States Agency for International Developmen
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