Master's Thesis
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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.
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.
In dieser Masterarbeit wurde die Entwicklung des Erregerspektrums und der Resistenz der Erreger gegen spezielle Antibiotika von 2010-2017 untersucht. Die untersuchten Proben wurden vom Medizinischen Zentrallabor Altenburg ausgewertet und stammten dabei aus Urinen, pulmonalen Materialien oder Blutkulturen. Innerhalb der Arbeit wurden mit dem assoziativen Datenanalyse-Tool und Reporting-System QlikView die Labordaten der untersuchten Jahre hinsichtlich der Entwicklung der Erregeranteile und deren Resistenz ausgewertet. Es wurden die häufigsten bakteriellen Erreger bei klinisch relevanten Infektionen ermittelt und ihr Verhalten gegen leitliniengerechte Antibiotika untersucht. Das Auftreten von multiresistenten Erregern konnte detektiert und deren Entwicklung analysiert werden. Die Materialien wurden getrennt voneinander untersucht und deren Ergebnisse gegenübergestellt.
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).