Volkmar Liebscher

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We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0,1]) as well(More)
Somitogenesis describes the segmentation of vertebrate embryonic bodies, which is thought to be induced by ultradian clocks (i.e., clocks with relatively short cycles compared to circadian clocks). One candidate for such a clock is the bHLH factor Hes1, forming dimers which repress the transcription of its own encoding gene. Most models for such small(More)
Whole-genome analysis using high-density single-nucleotide-polymorphism oligonucleotide arrays allows identification of microdeletions, microduplications, and uniparental disomies. We studied 67 children with unexplained mental retardation with normal karyotypes, as assessed by G-banded chromosome analyses. Their DNAs were analyzed with Affymetrix 100K(More)
First we explain the interplay between robust loss functions non linear lters and Bayes smoothers for edge preserving image recon struction Then we prove the surprising fact that maximum posterior smoothers are nonlinear lters A generalized Potts prior for segmen tation and piecewise smoothing of noisy signals and images is adopted For one dimensional(More)
The cDNA-chip technology is a highly versatile tool for the comprehensive analysis of gene expression at the transcript level. Although it has been applied successfully in expression profiling projects, there is an ongoing dispute concerning the quality of such expression data. The latter critically depends on the specificity of hybridisation. SAFE(More)
In a series of papers [66, 65, 62, 63, 64] TSIRELSON constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by ARVESON [4] for classifying E0-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So we connect(More)
The authors propose piecewise deterministic Markov processes as an alternative approach to model gene regulatory networks. A hybrid simulation algorithm is presented and discussed, and several standard regulatory modules are analysed by numerical means. It is shown that despite of the partial simplification of the mesoscopic nature of regulatory networks(More)
We study special Quantum Markov chains on a Fock space related to iterated beam splittings as introduced in [23]. Besides a characterizatioin of the position distributions of the chain, we show some kind of weak convergence of such discrete time Quantum Markov chains to a kind of continuous time Quantum Markov process. Furthermore, we provide existence and(More)