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In this master thesis, we define a new bivariate polynomial which we call the defensive alliance polynomial and denote it by da(G; x; y). It is a generalization of the alliance polynomial and the strong alliance polynomial. We show the relation between da(G; x; y) and the alliance, the strong alliance, the induced connected subgraph polynomials as well as the cut vertex sets polynomial. We investigate information encoded about G in da(G; x; y). We discuss the defensive alliance polynomial for the path graphs, the cycle graphs, the star graphs, the double star graphs, the complete graphs, the complete bipartite graphs, the regular graphs, the wheel graphs, the open wheel graphs, the friendship graphs, the triangular book graphs and the quadrilateral book graphs. Also, we prove that the above classes of graphs are characterized by its defensive alliance polynomial. We present the defensive alliance polynomial of the graph formed of attaching a vertex to a complete graph. We show two pairs of graphs which are not characterized by the alliance polynomial but characterized by the defensive alliance polynomial.
Also, we present three notes on results in the literature. The first one is improving a bound and the other two are counterexamples.
This study presents an analysis of the coverage made by the journals El País (Spain), Folha de S. Paulo (Brazil) and Süddeutsche Zeitung (Germany) about the protests in Brazil against the 2013 Confederations Cup and the 2014 FIFA World Cup to establish a comparison between them and see which topics were emphasized by the newspapers and which tone they use in their reporting. Based on the research questions, four categories were developed for the analysis of the journals: article structure; topic of the article; actors/group of persons and tone of the reporting, all of them composed by several subcategories. It was concluded that the themes highlighted by the European newspapers were different from those stressed on the Brazilian diary. Nonetheless, all the reviewed newspapers made a neutral coverage of the protests.
kein Abstract vorhanden
Path decomposition of a graph has received an important amount of interest over the past decades because of its applications in algorithmic graph theory and in real life problems. For the computation of a path decomposition of small width, we use different heuritics approaches. One of the most useful method is by Bodlaender and Kloks. In this thesis, we focus on the computation, applications, transformation and approximation of a path decomposition of small width.
It is easy to convert a path decomposition in to nice path decomposition with same width, which is more convinent to use to find the graph parameters like independent sets, chromatic polynomials etc. Inspired by [28], we find an algorithm to compute the chromatic polynomial of a graph via nice path decomposition with small width.
Community acquired pneumonia (CAP) is a very common, yet infectious and sometimes lethal disease. Therefor, this disease is connected to high costs of diagnosis and treatment. To actually reduce the costs for health care in this matter, diagnosis and treatment must get cheaper to conduct with no loss in predictive accuracy. One effective way in doing so would be the identification of easy detectable and highly specific transcriptomic markers, which would reduce the amount of work required for laboratory tests by possibly enhanced diagnosis capability.
Transcriptomic whole blood data, derived from the PROGRESS study was combined with several documented features like age, smoking status or the SOFA score. The analysis pipeline included processing by self organizing maps for dimensionality and noise reduction, as well as diffusion pseudotime (DPT). Pseudotime enabled modelling a disease run of CAP, where each sample represented a state/time in the modelled run. Both methods combined resulted in a proposed disease run of CAP, described by 1476 marker genes. The additional conduction of a geneset analysis also provided information about the immune related functions of these marker genes.
In the following study we evaluated capabilities of how a simple autoencoder can be used to trainGeneralized Learning Vector Quantization classifier. Specifically, we proved that the bottlenecks of an autoencoder serve as an "information filter" which tries to best represent the desired output in that particular layer in the statistical sense of mutual information.
Autoencoder model was trained for purely unsupervised task and leveraged the advantages by learning feature representations. As a result, the model got the significant value of the accuracy. Implementation and tuning of the model was carried out using Tensor Flow [1].
An extra study has been dedicated to improve traditional GLVQ algorithm taken from sklearn-lvg [2] using the bottleneck from an autoencoder.
The study has revealed potential of bottlenecks of an autoencoder as pre-processing tool in improving the accuracy of GLVQ. Specifically, the model was capable to identify 75% improvements of accuracy in GLVQ comparing to original one, which has about 62%. Consequently, the research exposed the need for further improvement of the model in the present problem case.
Internationalization and business expansion appear to be the most challenging processes in business conduction today. Every step of the foreign market entry process and overseas operations establishment is full of obvious risks and hidden pitfalls. Theoretical background, multiplied with the vital practice, is playing the key role in such a complicated business process; such information can be used as a guideline by further market entrants and players. At present, Germany with its well-developed engineering industry represents a broad space for research of internationalization process in its different forms, as well as can show both successful and negative results of foreign market entries.
Soft Learning Vector Quantisation (SLVQ) andRobust Soft Learning Vector Quantisation (RSLVQ) are supervised data classification methods, that have been applied successfully to real world classification problems. The performance of SLVQ and RSLVQ, however, reduces, when they are applied tomore complicated classification problems. In this thesis, we have introducedmodi-fications to SLVQand RSLVQ, in order to havemore capable versions of them. A few possibilities to modify SLVQ and RSLVQ are considered, some of them are not successful enough and they have been included for the sake of completeness. The fruits of the thesis are plenty, including Tangent Soft Learning Vector Quantisation-Strong (TSLVQ-S), together with its more stable version Tangent Robust Soft Learning Vector Quantisation-Strong (TRSLVQ-S), Attraction Soft Learning Vector Quantisation (ASLVQ) and Grassmannian Soft Learning Vector Quantisation (GSLVQ).
This thesis focuses on the introduction of a process for the fracture toughness testing of epoxy resin systems, in the light of the linear elastic fracture mechanic approach. Based on the requirements of ISO 13586, SENB-specimen were designed and especially the precracking process was analysed and the tapping process was optimized by designing and testing a drop-weight device. After successful validating the test process using specimen made of Araldite LY556, the in uence of GNP loading on the fracture toughness was analysed. The pure epoxy showed a KIc of 0.73 MPap
m, being perfectly in line with the manufacturers datasheet. A peak in fracture toughness of 0.83 MPap
m was archived at 1 wt% and a loading rate of 10 mm/min, showing a decreasing trend as the loading is increased further. As the loading rate is increased, the fracture toughness reduces slightly for 0.5 wt% and 2 wt% GNP, but
drops signicantly for 1 wt% GNP obliterating the peak. The load vs. displacement curves showed quasi-brittle material behaviour. The fracture surfaces were analysed using SEM and while the neat resin did not show any features, did the reinforced samples show pattern of crack pinning in connection with bridging and pull-out. The resulting improvement is less signicant as observed by other researchers for larger GNPs. This is in line with the general idea, that small particles are not able to yield as high improvements, but the signicant decrease for higher loading rates is not observed or described so far. It is suspected that tests at lower loading rates (e.g. 1 or 0.5 mm/min) show an even higher fracture toughness.