Representation by Integrating Reproducing Kernels

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel whose corresponding Hilbert space is given as the image of the direct integral of the individual Hilbert spaces under the summation operator. This generalises the well-known results for finite sums of reproducing kernels; however, many more special cases are subsumed under this approach: so-called Mercer kernels obtained through series expansions; kernels generated by integral transforms; mixtures of positive definite functions; and in particular scale-mixtures of radial basis functions. This opens new vistas into known results, e.g. generalising the Kramer sampling theorem; it also offers interesting connections between measurements and integral transforms, e.g. allowing to apply the representer theorem in certain inverse problems, or bounding the pointwise error in the image domain when observing the pre-image under an integral transform

Sparsity Order Estimation from a Single Compressed Observation Vector

We investigate the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. We show that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, we prove that matrices which are composed of a Khatri-Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix which may incur in a degradation in the achievable coherence. We thus also address suitable choices of the measurement matrices. In particular, we analyze Khatri-Rao and Vandermonde matrices in terms of their coherence and provide a new design for Vandermonde matrices that achieves a low coherence

Analytic machines

In this paper we present some results about it analytic machines regarding th power of computations over sf bf Q and sf bf R, solutions of differential equations and the stability problem of dynamical systems. We first explain the machine model, wich is a kind of sc Blum-Shub-Smale machine enhanced by infinite convergent computiations. Next, we compare the computional power of such machinesofer the fields sf bf Q and sf bf R showing that finite computations with real numbers can be simulated by infinite converging computations on rational numbers, but the precision of the approximation is not known during the process. Our attention is then shifted to it ordinary differential equations (ODEs), dynamical systems described by ODEs and the undecidability of a class of stability problems for dynamical syste

Modeling the growth of fingerprints improves matching for adolescents

We study the effect of growth on the fingerprints of adolescents, based on which we suggest a simple method to adjust for growth when trying to recover a juvenile's fingerprint in a database years later. Based on longitudinal data sets in juveniles' criminal records, we show that growth essentially leads to an isotropic rescaling, so that we can use the strong correlation between growth in stature and limbs to model the growth of fingerprints proportional to stature growth as documented in growth charts. The proposed rescaling leads to a 72% reduction of the distances between corresponding minutiae for the data set analyzed. These findings were corroborated by several verification tests. In an identification test on a database containing 3.25 million right index fingers at the Federal Criminal Police Office of Germany, the identification error rate of 20.8% was reduced to 2.1% by rescaling. The presented method is of striking simplicity and can easily be integrated into existing automated fingerprint identification systems

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

HLA-Ligandenanalysen im Kontext der Tumorimmunologie, der Autoimmunität und der parasitären Onchozerkose

Auf der Oberfläche aller kernhaltigen Zellen befinden sich spezielle membranständige Proteinkomplexe, die sogenannten Haupthistokompatibilitätskomplexe (engl. Major Histo-compatibility Complex, MHC). Die Funktion der MHC-Moleküle besteht in der Präsentation aller in einer Zelle exprimierten Proteine (Proteom) in Form von kurzen Peptiden, den MHC-Liganden, auf der Zelloberfläche. MHC-Liganden sind von zentraler Bedeutung in der Immunologie, da sie sowohl bei der Erkennung und Bekämpfung von Krankheiten, als Zielstruktur in der Krebsimmuntherapie aber auch bei der Entstehung von Autoimmun-erkrankungen eine wichtige Rolle spielen. Ziel dieser Arbeit war die Identifikation und Validation von MHC-Liganden im Kontext der Prostatakrebsimmuntherapie, der Autoimmunität bei der Multiplen Sklerose sowie die Identifikation parasitärer und bakterieller MHC-Liganden aus Gewebe mit Onchozerkose. Insgesamt wurden 21 Prostatagewebe, 2 MHC-Klasse-II-transfizierte Zelllinien sowie 8 Gewebeproben aus Patienten mit Onchozerkose bearbeitet und die MHC-Liganden mas-senspektrometrisch analysiert. Aufgrund der unterschiedlichen Fragestellungen war es notwendig, die Parameter für die Identifikation und Bewertung der MHC-Liganden anzu-passen, um so die Anzahl möglicher Kandidatenpeptide zu erhöhen oder die Zahl falsch positiver Peptididentifikationen zu erniedrigen. Aus über 38 000 identifizierten Sequenzen auf Prostatagewebe wurden 63 Peptidsequenzen aus 28 tumorassoziierten Antigenen (TAA) der Prostata selektiert und in vitro auf Immunogenität getestet. Neben ubiquitär exprimierten TAA wurden zusätzlich auch Liganden aus Differenzierungsantigenen der Prostata, wie PSA, PAP und PSMA identifiziert. Alle MHC-Klasse-I-Liganden wurden über synthetische Peptide der entsprechenden Sequenz verifiziert sowie die HLA-Restriktion über Epitopvorhersage bestätigt. Zusätzlich wurde eine Methode entwickelt, die es erlaubt, die wahrscheinlichste HLA-Restriktion einer bereits analysierten Gewebeprobe auf-zuklären. Im Rahmen des Multiplen Sklerose-Projekts wurden HLA-Klasse-II-Liganden aus dem relevanten HLA-DR15 in Präsentation auf selbigem Molekül erfolgreich identifiziert. Über die MHC-Ligandenanalyse der humanen Gewebeproben mit Onchozerkose wurden insgesamt 9 Peptide aus Onchocerca volvulus oder Wolbachia eindeutig identifiziert und ihre Sequenz über synthetische Peptide bestätigt