Moduli spaces of (G,h)-constellations

Given an infinite reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G \to N_0, we construct the moduli space M_{\theta}(X) of \theta-stable (G,h)-constellations on X, which is a generalization of the invariant Hilbert scheme after Alexeev and Brion and an analogue of the moduli space of \theta-stable G-constellations for finite groups introduced by Craw and Ishii. Our construction of a morphism M_{\theta}(X) \to X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G.Comment: 30 pages, published version and erratu

Moduli spaces of (G,h)-constellations

Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_Ө(X) of Ө-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of Ө-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_Ө(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.Für eine reduktive Gruppe G, die auf einem affinen C-Schema X wirkt, und eine Hilbertfunktion h: Irr G → N_0 konstruieren wir den Modulraum M_Ө(X) der Ө-stabilen (G,h)-Konstellationen auf X, der eine gemeinsame Verallgemeinerung des invarianten Hilbertschemas nach Alexeev und Brion und des von Craw und Ishii eingeführten Modulraumes von Ө-stabilen G-Konstellationen für endliche Gruppen G ist. Unsere Konstruktion eines Morphismus M_Ө(X) → X//G macht diesen Modulraum zu einem Kandidaten einer Auflösung der Singularitäten des Quotienten X//G. Außerdem bestimmen wir das invariante Hilbertschema der Nullfaser der Impulsabbildung einer Wirkung von Sl_2 auf (C²)⁶ als eines der ersten Beispiele von invarianten Hilbertschemata mit Multiplizitäten. Dabei beschreiben wir eine allgemeine Vorgehensweise für derartige Berechnungen. Ferner zeigen wir, dass unser Hilbertschema glatt und zusammenhängend ist und daher eine Auflösung der Singularitäten der symplektischen Reduktion der Wirkung darstellt.92 S

Casino gambling in Germany : development, legal conditions and the exclusion system

The aim of this paper is to provide an overview about the German casino gambling industry as a whole and the identification of its particularities, while putting a special focus on the present exclusion system. To achieve that, the foundations were laid by examining general developments on the market as well as pointing out recent legal changes, like the introduction of the Interstate treaty on gambling and its consequences for the casinos. Additionally, the application process and the basis for regulation of the establishments have been presented in detail. This general part is then followed by an extensive description of the German exclusion system. The program was set in contrast to those present in other, especially North American jurisdictions, in order to illuminate its unique features. Secondly, the focus is shifted on the development of a profile of excluders from German casinos by examining whether the established risk factors are also significant predictors for the number of bans in German communities. To our knowledge, there is no work explicitly analyzing casino patrons. Using a unique dataset, the approach brought some interesting insights. Some of the considered variables can be confirmed to serve this task in the given framework, whilst others did not yield a statistically significant impact. The most important sociodemographic factors are male gender, being between 30 and 39 years old, and not living in a partnership. The shares of the first two variables have a positive, the latter one a negative influence. Education, unemployment, and migration status, which are usually agreed on to be good predictors, did not exhibit significant results. However, it would be wrong to neglect them, as the outcome is probably owed to noise in the data, which lowers the precision of the estimation and could lead to insignificance. The coefficients of the variables that have been included to capture proximity turn out to be significant and bigger in magnitude than those of the sociodemographic factors. Distance to the next casino and the share of exclusions are inversely related, if the distance increases, the share of bans will decrease. The dummy variables capturing immediate proximity to gambling establishments also provide evidence for this pattern. If a classical casino or an annex is present in a community, this has a positive impact on the share of excluders. Considering only the proximity dimension of availability, the results are in favor of the hypothesis that higher availability could be a predictor for an increase of bans, which serve as a proxy for PG. The additionally included control variables also yield significant results. The coefficient of the indicator for a sparsely populated region shows that the share of excluders in said areas is on average higher than in dense ones. Furthermore, the share of assistance centers in a county positively drives the share of bans. The dummy variable indicating communities in the former GDR turns out to be negatively associated with the dependent variable. This makes absolute sense, considering the different developments of the gambling markets in these two regions between 1950 and 1990. However, the magnitude of the distinct effects on the amount of exclusions is rather small and the model is only able to explain about 10% of the variation in the number of bans, which is a rather small fraction. This is very likely owed to the fact that although problematic or pathological gambling is in parts driven by external sociodemographic factors like age, gender or the marital status, a lot of the behavior is facilitated by internal predisposition which cannot be captured with this type of analysis. Nevertheless, many of the proposed risk or, more neutrally stated, influence factors can be confirmed by this approach, which has been specifically adapted to the German terrestrial casino patrons

A Hardware Perspective on the ChaCha Ciphers: Scalable Chacha8/12/20 Implementations Ranging from 476 Slices to Bitrates of 175 Gbit/s

AES (Advanced Encryption Standard) accelerators are commonly used in high-throughput applications, but they have notable resource requirements. We investigate replacing the AES cipher with ChaCha ciphers and propose the first ChaCha FPGA implementations optimized for data throughput. In consequence, we compare implementations of three different system architectures and analyze which aspects dominate the performance of those.Our experimental results indicate that a bandwidth of 175 Gbit/s can be reached with as little as 2982 slices, whereas comparable state of the art AES accelerators require 10 times as many slices. Taking advantage of the flexibility inherent in the ChaCha cipher, we also demonstrate how our implementation scales to even higher throughputs or lower resource usage (down to 476 slices), benefiting applications which previously could not employ cryptography because of resource limitations

Cosmic Rays VI - Starburst galaxies at multiwavelengths

We propose an explanation for the far-infrared/radio correlation of galaxies in terms of the energy balance of the interstellar medium and determine the flux from high-energy photons and neutrinos from starburst galaxies. We present a catalog of the 127 brightest starburst galaxies with redshifts of z<0.03. In order to investigate the correlation between radio- and far-infrared emission, we apply the leaky box approximation. Further, we derive photon- and neutrino spectra from proton-proton interactions in supernova remnants (SNRs). Here, we assume that a fraction of the SNR's energy is transferred to the acceleration of cosmic rays. We also investigate the possibility of detecting Gamma Ray Bursts from nearby starburst galaxies, using the catalog defined here. We show that the radio emission is only weakly dependent on the magnetic field. It turns out that the intensity of the radio signal is directly proportional to the number of supernova explosions, which scales with the far-infrared luminosity. In addition, we find that high-energy photons from proton-proton interactions in SNRs in starbursts can make up several percent of the diffuse gamma-ray background. The neutrino flux from the same sources has a maximum energy of ~1e5 GeV. Neutrinos can, on the other hand, can be observed if a Gamma Ray Burst happens in a nearby starburst. About 0.03 GRBs per year are expected to occur in the entire catalog. The true number is expected to be even higher, since we only include the brightest sources. The number of events per burst in IceCube varies between about one event and more than 1000 events. This provides good prospects for IceCube to detect a significant event, since the background for a GRB search is close to zero.Comment: 27 pages, 13 figure

Identifying predictive features of autism spectrum disorders in a clinical sample of adolescents and adults using machine learning

Diagnosing autism spectrum disorders (ASD) is a complicated, time-consuming process which is particularly challenging in older individuals. One of the most widely used behavioral diagnostic tools is the Autism Diagnostic Observation Schedule (ADOS). Previous work using machine learning techniques suggested that ASD detection in children can be achieved with substantially fewer items than the original ADOS. Here, we expand on this work with a specific focus on adolescents and adults as assessed with the ADOS Module 4. We used a machine learning algorithm (support vector machine) to examine whether ASD detection can be improved by identifying a subset of behavioral features from the ADOS Module 4 in a routine clinical sample of N = 673 high-functioning adolescents and adults with ASD (n = 385) and individuals with suspected ASD but other best-estimate or no psychiatric diagnoses (n = 288). We identified reduced subsets of 5 behavioral features for the whole sample as well as age subgroups (adolescents vs. adults) that showed good specificity and sensitivity and reached performance close to that of the existing ADOS algorithm and the full ADOS, with no significant differences in overall performance. These results may help to improve the complicated diagnostic process of ASD by encouraging future efforts to develop novel diagnostic instruments for ASD detection based on the identified constructs as well as aiding clinicians in the difficult question of differential diagnosis

An Analytical Model of Configurable Systolic Arrays to find the Best-Fitting Accelerator for a given DNN Workload

Since their breakthrough, complexity of Deep Neural Networks (DNNs) is rising steadily. As a result, accelerators for DNNs are now used in many domains. However, designing and configuring an accelerator that meets the requirements of a given application perfectly is a challenging task. In this paper, we therefore present our approach to support the accelerator design process. With an analytical model of a systolic array we can estimate performance, energy consumption and area for each design option. To determine these metrics, usually a cycle accurate simulation is performed, which is a time-consuming task. Hence, the design space has to be restricted heavily. Analytical modelling, however, allows for fast evaluation of a design using a mathematical abstraction of the accelerator. For DNNs, this works especially well since the dataflow and memory accesses have high regularity. To show the correctness of our model, we perform an exemplary realization with the state-of-the-art systolic array generator Gemmini and compare it with a cycle accurate simulation and state-of-the-art modelling tools, showing less than 1% deviation. We also conducted a design space exploration, showing the analytical model’s capabilities to support an accelerator design. In a case study on ResNet-34, we can demonstrate that our model and DSE tool reduces the time to find the best-fitting solution by four or two orders of magnitude compared to a cycle-accurate simulation or state-of-the-art modelling tools, respectively

EFFECT: An End-to-End Framework for Evaluating Strategies for Parallel AI Anomaly Detection

Neural networks achieve high accuracy in tasks like image recognition or segmentation. However, their application in safety-critical domains is limited due to their black-box nature and vulnerability to specific types of attacks. To mitigate this, methods detecting out-of-distribution or adversarial attacks in parallel to the network inference were introduced. These methods are hard to compare because they were developed for different use cases, datasets, and networks. To fill this gap, we introduce EFFECT, an end-to-end framework to evaluate and compare new methods for anomaly detection, without the need for retraining and by using traces of intermediate inference results. The presented workflow works with every preexisting neural network architecture and evaluates the considered anomaly detection methods in terms of accuracy and computational complexity. We demonstrate EFFECT\u27s capabilities, by creating new detectors for ShuffleNet and MobileNetV2 for anomaly detection as well as fault origin detection. EFFECT allows us to design an anomaly detector, based on the Mahalanobis distance as well as CNN based detectors. For both use cases, we achieve accuracies of over 85 %, classifying inferences as normal or abnormal, and thus beating existing methods