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Search Results: 1 - 10 of 200522 matches for " P. Wittich "
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Smooth Homogenization of Heat Equations on Tubular Neighborhoods
O. Wittich
Mathematics , 2008,
Abstract: We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube diameter tends to zero, a suitably rescaled and renormalized semigroup converges to a limit semigroup in Sobolev spaces of arbitrarily large Sobolev index.
L2-Homogenization of Heat Equations on Tubular Neighborhoods
O. Wittich
Mathematics , 2008,
Abstract: We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can be effectively described by a Hamiltonian on the submanifold with a potential that depends on the geometry of the submanifold and of the embedding.
Kondo temperature of magnetic impurities at surfaces
P. Wahl,L. Diekh?ner,M. A. Schneider,L. Vitali,G. Wittich,K. Kern
Physics , 2004, DOI: 10.1103/PhysRevLett.93.176603
Abstract: 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.
An artificial neural network based $b$ jet identification algorithm at the CDF Experiment
J. Freeman,W. Ketchum,J. D. Lewis,S. Poprocki,A. Pronko,V. Rusu,P. Wittich
Physics , 2011, DOI: 10.1016/j.nima.2011.10.024
Abstract: We present the development and validation of a new multivariate $b$ jet identification algorithm ("$b$ tagger") used at the CDF experiment at the Fermilab Tevatron. At collider experiments, $b$ taggers allow one to distinguish particle jets containing $B$ hadrons from other jets. Employing feed-forward neural network architectures, this tagger is unique in its emphasis on using information from individual tracks. This tagger not only contains the usual advantages of a multivariate technique such as maximal use of information in a jet and tunable purity/efficiency operating points, but is also capable of evaluating jets with only a single track. To demonstrate the effectiveness of the tagger, we employ a novel method wherein we calculate the false tag rate and tag efficiency as a function of the placement of a lower threshold on a jet's neural network output value in $Z+1$ jet and $t\bar{t}$ candidate samples, rich in light flavor and $b$ jets, respectively.
Kondo effect of Co adatoms on Ag monolayers on noble metal surfaces
M. A. Schneider,P. Wahl,L. Diekh?ner,L. Vitali,G. Wittich,K. Kern
Physics , 2004, DOI: 10.1143/JJAP.44.5328
Abstract: The Kondo temperature $T_K$ of single Co adatoms on monolayers of Ag on Cu and Au(111) is determined using Scanning Tunneling Spectroscopy. $T_K$ 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 $T_K$ 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.
Non-Uniqueness of Gibbs measures relative to Brownian motion
Volker Betz,Olaf Wittich
Mathematics , 2007,
Abstract: We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V. We show that for a large class of V, including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.
Detection of objects in noisy images and site percolation on square lattices
Mikhail A. Langovoy,Olaf Wittich
Computer Science , 2011,
Abstract: We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.
Computationally efficient algorithms for statistical image processing. Implementation in R
Mikhail A. Langovoy,Olaf Wittich
Computer Science , 2011,
Abstract: In the series of our earlier papers on the subject, we proposed 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 developed algorithms that allowed to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints were imposed on the objects, only a weak bulk condition for the object's interior was required. Our algorithms have linear complexity and exponential accuracy. In the present paper, we describe an implementation of our nonparametric hypothesis testing method. We provide a program that can be used for statistical experiments in image processing. This program is written in the statistical programming language R.
Multiple testing, uncertainty and realistic pictures
Mikhail A. Langovoy,Olaf Wittich
Statistics , 2011,
Abstract: We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on finite lattices.
Randomized algorithms for statistical image analysis and site percolation on square lattices
Mikhail A. Langovoy,Olaf Wittich
Statistics , 2011, DOI: 10.1111/stan.12010
Abstract: We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.
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