Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs

The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. Similarly, greedy algorithms deliver very good approximations to the optimal solution in practice. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that, on real instances, this leads to better approximations than the standard greedy approach within reasonable time

Passive radar on moving platforms exploiting DVB-T transmitters of opportunity

The work, effort, and research put into passive radar for stationary receivers have shown significant developments and progress in recent years. The next challenge is mounting a passive radar on moving platforms for the purpose of target detection and ground imaging, e.g. for covert border control. A passive radar on a moving platform has many advantages and offers many benefits, however there is also a considerable drawback that has limited its application so far. Due to the movement the clutter returns are spread in Doppler and may overlap moving targets, which are then difficult to detect. While this problem is common for an active radar as well, with a passive radar a further problem arises: It is impossible to control the exploited time-varying waveform emitted from a telecommunication transmitter. A conventional processing approach is ineffective as the time-varying waveform leads to residuals all over the processed data. Therefore a dedicated clutter cancellation method, e.g. the displaced phase centre antenna (DPCA) approach, does not have the ability to completely remove the clutter, so that target detection is considerably limited. The aim must be therefore to overcome this limitation by exploiting a processing technique, which is able to remove these residuals in order to cope with the clutter returns thus making target detection feasible. The findings of this research and thesis show that a reciprocal filtering based stage is able to provide a time-invariant impulse response similar to the transmissions of an active radar. Due to this benefit it is possible to achieve an overall complete clutter removal together with a dedicated DPCA stage, so that moving target detection is considerably improved, making it possible in the first place. Based on mathematical analysis and on simulations it is proven, that by exploiting this processing in principle an infinite clutter cancellation can be achieved. This result shows that the reciprocal filter is an essential processing stage. Applications on real data acquired from two different measurement campaigns prove these results. By the proposed approach, the limiting factor (i.e. the time-varying waveform) for target detection is negotiated, and in principle any clutter cancellation technique known from active radar can be applied. Therefore this analysis and the results provide a substantial contribution to the passive radar research community and enables it to address the next questions

Transforming Growth Factor Alpha Stimulation of Mucosal Tissue Cultures from Head and Neck Squamous Cell Carcinoma Patients Increases Chemoresistance to Cisplatin

The monoclonal epidermal growth factor receptor ( EGFR) antibody cetuximab (Erbitux(TM)) was recently approved by the European Medicines Agency for the treatment of recurrent and/or metastatic head and neck squamous cell carcinoma (HNSCC) in combination with a platinum-based chemotherapy. Since the antibody has only a limited effect as a monotherapy, possible explanations for the synergistic effect with cisplatin are enhanced antibody-dependent cytoxicity and increased sensitivity to the drug. Most of our knowledge of EGFR biology in HNSCC is based on studies using EGFR inhibitors and/or antibodies. Our study was designed to evaluate the impact of EGFR stimulation on cisplatin-induced DNA damage. Therefore, tissue cultures were produced of tumor-free oropharyngeal mucosa biopsies of HNSCC patients and controls. In a previous study, overexpression of EGFR in tissue cultures from tumor patients compared to controls was confirmed by immunohistochemical staining. Twenty-four-hour stimulation of tissue cultures with transforming growth factor alpha (TGF-alpha), a specific EGFR ligand, resulted in a reduction of cisplatin-induced DNA damage by 35% in cases, whereas in controls TGF-alpha had no effect. This reflects a statistically significant increase in cellular chemoresistance to cisplatin following TGF-alpha stimulation and helps to further understand effects of EGFR antisense therapy in combination with chemotherapy. Copyright (C) 2010 S. Karger AG, Base

Multi-loop investigations of strong interactions at high temperatures

Matter alters its properties remarkably when confronted with extreme conditions such as temperatures as high as in the early universe. The emergence of the Quark-Gluon Plasma and restoration of electroweak symmetry through phase transitions are but the most prominent phenomena to invigorate studies of gauge theories at finite temperatures. If the temperature is sufficiently high, static observables are effectively described in a reduced dimension by a framework known as Dimensional Reduction. The computer algebraic multi-loop treatment of perturbation theory for finite-temperature theories is at the core of this thesis. It adopts sophisticated tools from zero temperature to decimate typically vast numbers of Feynman integrals with the objective to automate the dimensional reduction. To accomplish this, integration-by-parts identities pertinent to both massless and massive loops at finite temperature are illuminated. Additionally, an inclusion of higher-dimensional operators in these theories is first motivated and then generalised. The developed tools are applied to review the advancements of [1] in chapter 4 and [2] in chapter 5. There, we analyse the dimensionally reduced theories of high-temperature QCD, namely electrostatic and magnetostatic QCD. We inspect three-loop contributions stemming from non-static modes to the magnetostatic coupling in dimensionally reduced hot Yang-Mills theory [1]. By including dimension-six operators the result is found to be infrared finite and influenced by all scales in the QCD hierarchy. Incorporating also electrostatic effects indicates a non-perturbative ultrasoft gauge coupling at O(as^3/2). Based on its relevance in cosmology, we determine another low-energy coefficient in electrostatic QCD, the Debye mass. By including effects from massive fermions up to two loops [2], energy ranges of (1 GeV–10 TeV) are scanned to show the smooth crossing of quark mass thresholds

Information-Theoretic Trust Regions for Stochastic Gradient-Based Optimization

Stochastic gradient-based optimization is crucial to optimize neural networks. While popular approaches heuristically adapt the step size and direction by rescaling gradients, a more principled approach to improve optimizers requires second-order information. Such methods precondition the gradient using the objective’s Hessian. Yet, computing the Hessian is usually expensive and effectively using second-order information in the stochastic gradient setting is non-trivial. We propose using Information-Theoretic Trust Region Optimization (arTuRO) for improved updates with uncertain second-order information. By modeling the network parameters as a Gaussian distribution and using a Kullback-Leibler divergence-based trust region, our approach takes bounded steps accounting for the objective’s curvature and uncertainty in the parameters. Before each update, it solves the trust region problem for an optimal step size, resulting in a more stable and faster optimization process. We approximate the diagonal elements of the Hessian from stochastic gradients using a simple recursive least squares approach, constructing a model of the expected Hessian over time using only first-order information. We show that arTuRO combines the fast convergence of adaptive moment-based optimization with the generalization capabilities of SGD

Information-Theoretic Trust Regions for Stochastic Gradient-Based Optimization

Stochastic gradient-based optimization is crucial to optimize neural networks. While popular approaches heuristically adapt the step size and direction by rescaling gradients, a more principled approach to improve optimizers requires second-order information. Such methods precondition the gradient using the objective's Hessian. Yet, computing the Hessian is usually expensive and effectively using second-order information in the stochastic gradient setting is non-trivial. We propose using Information-Theoretic Trust Region Optimization (arTuRO) for improved updates with uncertain second-order information. By modeling the network parameters as a Gaussian distribution and using a Kullback-Leibler divergence-based trust region, our approach takes bounded steps accounting for the objective's curvature and uncertainty in the parameters. Before each update, it solves the trust region problem for an optimal step size, resulting in a more stable and faster optimization process. We approximate the diagonal elements of the Hessian from stochastic gradients using a simple recursive least squares approach, constructing a model of the expected Hessian over time using only first-order information. We show that arTuRO combines the fast convergence of adaptive moment-based optimization with the generalization capabilities of SGD

Human Activity Classification with Online Growing Neural Gas

Panzner M, Beyer O, Cimiano P. Human Activity Classification with Online Growing Neural Gas. In: Workshop on New Challenges in Neural Computation (NC2). 2013: 106-113.In this paper we present an online approach to human ac- tivity classification based on Online Growing Neural Gas (OGNG). In contrast to state-of-the-art approaches that perform training in an offline fashion, our approach is online in the sense that it circumvents the need to store any training examples, processing the data on the fly and in one pass. The approach is thus particularly suitable in life-long learning settings where never-ending streams of data arise. We propose an archi- tecture that consists of two layers, allowing the storage of human actions in a more memory efficient structure. While the first layer (feature map) dynamically clusters Space-Time Interest Points (STIP) and serves as basis for the creation of histogram-based signatures of human actions, the second layer (class map) builds a classification model that relies on these human action signatures. We present experimental results on the KTH activity dataset showing that our approach has comparable per- formance to a Support Vector Machine (SVM) while performing online and avoiding to store examples explicitly