On an analogue of L2-Betti numbers for finite field coefficients and a question of Atiyah

We construct a dimension function for modules over the group ring of an amenable group. This may replace the von Neumann dimension in the definition of L2-Betti numbers and thus allows an analogue definition for finite field coefficients. Furthermore we construct examples for characteristic 2 in answer to Atiyah question of irrational L2-Betti numbers

Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis

In many geodetic engineering applications it is necessary to solve the problem of describing a measured data point cloud, measured, e. g. by laser scanner, by means of free-form curves or surfaces, e. g., with B-Splines as basis functions. The state of the art approaches to determine B-Splines yields results which are seriously manipulated by the occurrence of data gaps and outliers. Optimal and robust B-Spline fitting depend, however, on optimal selection of the knot vector. Hence we combine in our approach Monte-Carlo methods and the location and curvature of the measured data in order to determine the knot vector of the B-Spline in such a way that no oscillating effects at the edges of data gaps occur. We introduce an optimized approach based on computed weights by means of resampling techniques. In order to minimize the effect of outliers, we apply robust M-estimators for the estimation of control points. The above mentioned approach will be applied to a multi-sensor system based on kinematic terrestrial laserscanning in the field of rail track inspection. © 2016 Walter de Gruyter GmbH, Berlin/Munich/Boston

Topology optimisation under uncertainties with neural networks

Topology optimisation is a mathematical approach relevant to different engineering problems where the distribution of material in a defined domain is distributed in some optimal way, subject to a predefined cost function representing desired (e.g., mechanical) properties and constraints. The computation of such an optimal distribution depends on the numerical solution of some physical model (in our case linear elasticity) and robustness is achieved by introducing uncertainties into the model data, namely the forces acting on the structure and variations of the material stiffness, rendering the task high-dimensional and computationally expensive. To alleviate this computational burden, we develop two neural network architectures (NN) that are capable of predicting the gradient step of the optimisation procedure. Since state-of-the-art methods use adaptive mesh refinement, the neural networks are designed to use a sufficiently fine reference mesh such that only one training phase of the neural network suffices. As a first architecture, a convolutional neural network is adapted to the task. To include sequential information of the optimisation process, a recurrent neural network is constructed as a second architecture. A common 2D bridge benchmark is used to illustrate the performance of the proposed architectures. It is observed that the NN prediction of the gradient step clearly outperforms the classical optimisation method, in particular since larger iteration steps become viable

Aspects of quaranteed error control in CPDEs

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretisation error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bounds (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects. First, the variational crimes from a nonconforming finite element discretisation and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB. Second, the reliable approximation of the discretisation error on curved boundaries and, finally, the reliable bounds of the error with respect to some goal-functional, namely, the error in the approximation of the directional derivative at a given poin

Crime Mapping through Geo-Spatial Social Media Activity

The presence of crime is one of the major challenges for societies all over the World, especially in metropolitan areas. As indicated by prior research, Information Systems can contribute greatly to cope with the complex factors that influence the emergence and location of delinquencies. In this work, we combine commonly used approaches of static environmental characteristics with Social Media. We expect that blending in such dynamic information of public behavior is a valuable addition to explain and predict criminal activity. Consequently, we employ Zero-Inflated Poisson Regressions and Geographically Weighted Regressions to examine how suitable Social Media data actually is for this purpose. Our results unveil geographic variation of explanatory power throughout a metropolitan area. Furthermore, we find that Social Media works exceptionally well for description of certain crime types and thus is also likely to enhance the accuracy of delinquency prediction

Aspects of guaranteed error control in CPDEs

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretisation error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bounds (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects. First, the variational crimes from a nonconforming finite element discretisation and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB. Second, the reliable approximation of the discretisation error on curved boundaries and, finally, the reliable bounds of the error with respect to some goal-functional, namely, the error in the approximation of the directional derivative at a given point

AN OPEN DOOR MAY TEMPT A SAINT – DATA ANALYTICS FOR SPATIAL CRIMINOLOGY

The vast amounts of data that are generated and collected in today’s world bear immense potential for businesses and authorities. Innovative companies already adopt novel analytics methods driven by competition and the urge of constantly gaining new insights into business operations, customer preferences, and strategic decision making. Nonetheless, local authorities have been slow to embrace the opportunities enabled by data analytics. In this paper, we demonstrate and discuss how latent structures unveil valuable information on an aspect of public life and communities we all face: criminal activity. On city-scale, we analyze the spatial correspondence of recorded crime to its physical environment, the public presence, and the demographical structure in its vicinity. Our results show that Big Data in fact is able to identify and quantify the main spatial drivers of criminal activity. At the same time, we are able to maintain interpretability by design, which ultimately allows deep informational insights

Exponential signaling gain at the receptor level enhances signal-to-noise ratio in bacterial chemotaxis

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