L2-Homogenization of Heat Equations on Tubular Neighborhoods

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.Comment: 34 page

Multiple testing, uncertainty and realistic pictures

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.Comment: This paper initially appeared in January 2011 as EURANDOM Report 2011-004. Link to the abstract at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd

Which one to choose? New evidence on the choice and success of job search methods

This paper provides new evidence on the choice and success of six different job search channels comprising the public employment agency, advertisements in newspapers and journals, internet job search, recruitment agencies, direct applications, and the social network. In addition, job search intensity and its effects are regarded. Relying on panel data for Germany, we are able to consider observed and unobserved heterogeneity in the estimation. In line with findings for other countries, the results show that consideration of various channels in individual job search increases the employment chances. With regard to the determinants, the estimates exhibit clear differences between the job search channels and with respect to search intensity. The results for success of the job search channels reveal that the public employment agency is ineffective and even harms the employment chances of the unemployed job seekers. In contrast, direct application for jobs and internet job search provide successful channels and increase the employment chances.job search, unemployment, job placement, Germany, SOEP

Product variety and technical change

Several trade-based measures of product variety have recently been used implicitly to represent states of technology, promoting long-run growth. In this paper, we define the state of technology as the range of specialised production processes and propose the variety of capital goods available for production as a direct measure of technology. Within a simple growth framework, we derive a testable “conditional technological convergence” hypothesis on this measure. The hypothesis is tested with highly disaggregated trade data by economic categories, using tools from the income convergence literature. The results suggest that trade-based count measures of the variety of available capital goods indeed behave “as if” they were representing technology and that there is conditional technological convergence among our panel of mainly OECD and transition economies.Product variety, diffusion, adoption, technical change

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

Parsimonious Segmentation of Time Series' by Potts Models

Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics

Segmentation of Time Series: Parameter Dependence of Blake-Zisserman and Mumford-Shah Functionals and the Transition from Discrete to Continuous

The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in continuous time are the Mumford-Shah functionals. Time series which minimise these functionals are proper estimates or representations of the signals behind recorded data. We focus on consistent behaviour of the functionals and the estimates, as parameters vary or as the sampling rate increases. For each time continuous time series $f\in L^2 (\lbrack 0,1\rbrack)$ we take conditional expectations w.r.t. to $\sigma$-algebras generated by finer and finer partitions of the time domain into intervals, and thereby construct a sequence $(f_n)_{n\in\N}$ of discrete time series. As $n$ increases this amounts to sampling the continuous time series with more and more accuracy. Our main result is consistent behaviour of segmentations w.r.t. to variation of parameters and increasing sampling rate