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- ItemAdaptive smoothing of digital images: The R package adimpro(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2007) Polzehl, J.; Tabelow, K.Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.
- ItemA propagation-separation approach to estimate the autocorrelation in a time-series(Göttingen : Copernicus, 2008) Divine, D.V.; Polzehl, J.; Godtliebsen, F.The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.
- ItemClassification and clustering: models, software and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mucha, Hans-Joachim; Ritter, GunterWe are pleased to present the report on the 30th Fall Meeting of the working group ``Data Analysis and Numerical Classification'' (AG-DANK) of the German Classification Society. The meeting took place at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, from Friday Nov. 14 till Saturday Nov. 15, 2008. Already 12 years ago, WIAS had hosted a traditional Fall Meeting with special focus on classification and multivariate graphics (Mucha and Bock, 1996). This time, the special topics were stability of clustering and classification, mixture decomposition, visualization, and statistical software.
- ItemOptimal and robust a posteriori error estimates in L∞(L2) for the approximation of Allen-Cahn equations past singularities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Bartels, Sören; Müller, RüdigerOptimal a posteriori error estimates in L∞(L2) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of conforming, nonconforming, mixed, and discontinuous Galerkin methods. Numerical experiments illustrate the theoretical results.
- ItemAnisotropic growth of random surfaces in 2 + 1 dimensions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Borodin, Alexei; Ferrari, Patrik L.We construct a family of stochastic growth models in $2+1$ dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield $1+1$ dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models. The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece. (2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order $ln(t)$ for time $tgg 1$. (3) There is a map of the $(2+1)$-dimensional space-time to the upper half-plane $H$ such that on space-like submanifolds the multi-point fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on $H$.
- ItemParameter estimation in time series analysis(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Spokoiny, VladimirThe paper offers a novel unified approach to studying the accuracy of parameter estimation for a time series. Important features of the approach are: (1) The underlying model is not assumed to be parametric. (2) The imposed conditions on the model are very mild and can be easily checked in specific applications. (3) The considered time series need not to be ergodic or stationary. The approach is equally applicable to ergodic, unit root and explosive cases. (4) The parameter set can be unbounded and non-compact. (5) No conditions on parameter identifiability are required. (6) The established risk bounds are nonasymptotic and valid for large, moderate and small samples. (7) The results describe confidence and concentration sets rather than the accuracy of point estimation. The whole approach can be viewed as complementary to the classical one based on the asymptotic expansion of the log-likelihood. In particular, it claims a consistency of the considered estimate in a rather general sense, which usually is assumed to be fulfilled in the asymptotic analysis. In standard situations under ergodicity conditions, the usual rate results can be easily obtained as corollaries from the established risk bounds. The approach and the results are illustrated on a number of popular time series models including autoregressive, Generalized Linear time series, ARCH and GARCH models and meadian/quantile regression.
- ItemAnalysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Henrion, René; Outrata, Jií̌; Surowiec, ThomasWe consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify M-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration.
- ItemImpact of size, shape and composition on piezoelectric effects and the electronic properties of InGaAs/GaAs quantum dots(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Schliwa, Andrei; Winkelnkemper, Momme; Bimberg, DieterThe strain fields in and around self-organized In(Ga)As/GaAs quantum dots (QD) sensitively depend on QD geometry, average InGaAs composition and the In/Ga distribution profile. Piezoelectric fields of varying size are one result of these strain fields. We study systematically a large variety of realistic QD geometries and composition profiles, and calculate the linear and quadratic parts of the piezoelectric field. The balance of the two orders depends strongly on the QD shape and composition. For pyramidal InAs QDs with sharp interfaces a strong dominance of the second order fields is found. Upon annealing the first order terms become dominant, resulting in a reordering of the electron p- and d-states and a reorientation of the hole wavefunctions.
- ItemEscaping the Brownian stalkers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Weiß, AlexanderWe propose a simple model for the behaviour of long-time investors on stock markets, consisting of three particles, which represent the current price of the stock, and the opinion of the buyers, or sellers resp., about the right trading price. As time evolves both groups of traders update their opinions with respect to the current price. The update speed is controled by a parameter $gamma$, the price process is described by a geometric Brownian motion. The stability of the market is governed by the difference of the buyers' opinion and the sellers' opinion.
- ItemStationary solutions to an energy model for semiconductor devices where the equations are defined on different domains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, Annegret; Hünlich, RolfWe discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain $Omega_0$ of the domain of definition $Omega$ of the energy balance equation and of the Poisson equation. Here $Omega_0$ corresponds to the region of semiconducting material, $OmegasetminusOmega_0$ represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two-dimensional stationary energy model. For this purpose we derive a $W^1,p$-regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem.