Fakultät Informatik und Mathematik
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We compute the Fourier expansion of Hecke operators on vector-valued modular forms for the Weil representation associated to a lattice L. The Hecke operators considered in this paper include operators T(p^2l) where p is a prime dividing the level of the lattice L. Additionally, an explicit formula for a general type of Gauss sum associated to a lattice L drops out as a by-product.
Today, ubiquitous mobile devices have not only arrived but entered the safety critical domain. There, systems are about to be controlled where human health or even human life is put at risk. For example, in automation systems first ideas surface to control parts of the system via a COTS smartphone. Another example is the idea to control the autonomous parking function of a car via a COTS smartphone too. As beneficial and convenient these ideas are on the first thought, on the second thought, dangers of these approaches become obvious. Especially in case of failures the system’s safety has to be maintained. The open question is how to achieve this mandatory requirement with COTS components, e.g. smartphones that are not developed following the development process necessary for safetycritical systems. This paper presents a concept to reliably detect human interaction while activating safety critical functions via COTS mobile devices. Thus a means is provided to detect erroneous activation requests for the safetycritical function.
The performance of cognitive models often depends on the settings of specific model parameters, such as the rate of memory decay or the speed of motor responses. The systematic exploration of a model’s parameter space can yield relevant insights into model behavior and can also be used to improve the fit of a model to human data. However, exhaustive parameter space searches quickly run into a combinatorial explosion as the number of parameters investigated increases. Taking an established instance-based learning task as example, we show
how simulation using parallel computing and derivative-free optimization methods can be applied to investigate the effects
of different parameter settings. We find that both global optimization methods involving genetic algorithms as well as local methods yield satisfactory results in this case. Furthermore, we show how a model implemented in a specific cognitive architecture (ACT-R) can be mathematically reformulated to prepare the application of derivative-based optimization methods which promise further efficiency gains for quantitative analysis.
It is simple to query a relational database because all columns of the tables are known and the language SQL is easily applicable. In NoSQL, there usually is no fixed schema and no query language. In this article, we present NotaQL, a data-transformation language for wide-column stores. NotaQL is easy to use and powerful. Many MapReduce algorithms like filtering, grouping, aggregation and even breadth-first-search, PageRank and other graph and text algorithms can be expressed in two or three short lines of code.
PURPOSE
Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography.
METHODS
In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization.
RESULTS
Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection.
CONCLUSIONS
The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.
A Step Towards the Automated Diagnosis of Parkinson's Disease: Analyzing Handwriting Movements
(2015)
Parkinson’s disease (PD) has affected millions of people world-wide, being its major problem the loss of movements and, consequently, the ability of working and locomotion. Although we can find several works that attempt at dealing with this problem out there, most of them make use of datasets composed by a few subjects only. In this work, we present some results toward the automated diagnosis of PD by means of computer vision-based techniques in a dataset composed by dozens of patients, which is one of the main contributions of this work. The dataset is part of a joint research project that aims at extracting both visual and signal-based information from healthy and PD patients in order to go forward the early diagnosis of PD patients. The dataset is composed by handwriting clinical exams that are analyzed by means of image processing and machine learning techniques, being the preliminary results encouraging and promising. Additionally, a new quantitative feature to measure the amount of tremor of an individual’s handwritten trace called Mean Relative Tremor is also presented.
Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar
(2015)
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photoacoustic and thermoacoustic tomography and sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.
We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford–Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp–Logan phantom from seven angular views only. We illustrate the practical applicability on a real positron emission tomography dataset. As further applications, we consider spherical Radon data as well as blurred data.
Analysen auf NoSQL-Datenbanken sind oft langdauernd und die Ergebnisse fur den Benutzer haufig schwer verst ̈andlich. Wir prasentieren eine Möglichkeit, Datenmengen aus Wide-Column Stores mittels der Transformationssprache NotaQL zu transformieren sowie zu aggregieren und die Ergebnisse in Form von Diagrammen dem Benutzer darzustellen. Dabei kommen Sampling-Techniken zum Einsatz, um die Berechnung auf Kosten der Genauigkeit zu beschleunigen. Das von uns verwendete iterative Samplingverfahren sorgt fur eine kontinuierliche Verbesserung der Berechnungsgenauigkeit und bietet zudem Möglichkeiten zur Genauigkeitsabschätzung, die in Form von Konfidenzintervallen in den Diagrammen dargestellt werden kann.
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