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1 Topological and Geometrical Combinatorics Martin Tancer Abstract The task of the thesis is to present several new results on topological methods in combinatorics. The results can be split into two main streams. The first stream regards intersection patterns of convex sets. It is shown in the thesis that finite projective planes cannot be intersection patterns of convex sets of fixed dimension which answers a question of Alon, Kalai, Matoušek and Meshulam. Another result shows that d-collapsibility (a necessary condition on properties of in- tersection patterns of convex sets in dimension d) is NP-complete for recognition if d ≥ 4. In addition it is shown that d-collapsibility is not a necessary condition on properties of intersection patterns of good covers, which disproves a conjecture of G. Wegner from 1975. The second stream considers algorithmic hardness of recognition of simplicial com- plexes embeddable into Rd . The following results are proved: It is algorithmically un- decidable whether a k-dimensional simplicial complex piecewise-linearly embeds into Rd for d ≥ 5 and k ∈ {d−1, d}; and this problem is NP-hard if d ≥ 4 and d ≥ k ≥ 2d−2 3 .

Over the course of an organism's life, its genome is exposed to endogenous and exogenous chemical, physical and biological agents - genotoxins. These genotoxins alter its basic structural components - sugar residues, phosphodiester bonds, and nitrogenous bases. Organisms have therefore evolved a plethora of different strategies to both repair DNA lesions and maintain genomic stability. These DNA repair pathways are linked with several other cell pathways, including chromatin remodelling, DNA replication, transcription, cell cycle control, apoptosis - programmed cell death (PCD), thereby providing a coordinated cellular response to DNA damage. Biochemical mechanisms of DNA repair are relatively well understood in yeast and mammals, however, far less so in plants. While these repair mechanisms are evolutionary conserved, significant differences still remain. Therefore, further investigation is required. This thesis summarises the introduction of a novel plant model - the moss, Physcomitrella patens (Physcomitrella). As a haploid gametophyte with unique characteristics of high frequency of homologous recombination (HR), and apical growth of filaments, it is an ideal organism to study DNA repair in plants. Previous research on Physcomitrella regarding mechanisms of DNA lesion repair induced by...

Der DNA-Verpackungsmechanismus des humanen Cytomegalievirus (HCMV) ist charakteristisch für große DNA-Viren wie Herpesviren und ds-Bakteriophagen. Er beruht auf der Spaltung der konkatemeren DNA durch einen viralen, hetero-oligomeren Proteinkomplex, der Terminase. In der vorliegenden Arbeit konnten die funktionellen Domänen der Terminase-Untereinheit pUL89 in vitro identifiziert und charakterisiert werden. Neben einer Nuklease-Aktivität besitzt pUL89 auch die Fähigkeit dsDNA sequenz-unabhängig zu binden. Durch Nuklease-Untersuchungen konnte gezeigt werden, dass pUL89 sowohl dsDNA, als auch lineare DNA spaltet. PUL89 weist dabei eine größere Spezifität zu dsDNA auf. Des Weiteren konnte nachgewiesen werden, dass die Aminosäure D463 eine zentrale Funktion innerhalb der Nuklease-Aktivität besitzt. Durch kolorimetrische DNA-Bindungsuntersuchungen konnte die Aminosäure R544 als essenziell für die dsDNA-Bindungsfähigkeit von pUL89 identifiziert werden. Basierend auf den in vitro Ergebnissen wurden rekombinanten TB40/E-Virusmutanten mit Mutationen im ORF UL89 durch die En Passant Mutagenese generiert. Mit Hilfe dieser Viren sollte der Einfluss der Mutationen auf die Replikation des Virus charakterisiert werden. Es war möglich nachzuweisen, dass die Aminosäuren E534 und R544 eine essenzielle Aufgabe innerhalb von HCMV erfüllen, da die Mutation einer dieser Aminosäure zu nicht wachstums-fähigen BAC-Mutanten führte. Zur Charakterisierung dieser Konstrukte wurden die Zelllinien HELF Fi301-UL89 und HELF Fi301-vProm-UL89 verwendet. Durch Untersuchungen hinsichtlich der Wachstumseigenschaften, Proteinexpression, DNA-Spaltung, DNA-Bindung sowie elektronenmikroskopischen Aufnahmen, konnte gezeigt werden, dass die wachstums-kompetenten BAC-Mutanten keinen signifikanten Unterschied zum Wildtyp-Virus TB40/E zeigten. Sodass nachgewiesen werden konnte, dass die basischen Aminosäuren H565 und H571 keine essenzielle Funktion in pUL89 erfüllen. / The human cytomegalovirus DNA packaging mechanism is characteristic for large DNA viruses like Herpes viruses and ds bacteriophages. This mechanism is based on the cleavage of concatemeric DNA by the viral heterooligomeric protein complex terminase. This dissertation includes the identification and characterization of functional domains of the HCMV terminase subunit pUL89. PUL89 contain a nuclease activity and the ability to bind dsDNA. This protein shows the property to cut as well dsDNA as linear DNA. The amino acid D463 shows a significant role in this cleavage event. Colorimetric DNA binding experiments show the central role of R544 in DNA binding by pUL89. Based of the in vitro results recombinant TB40/E viruses with mutations in the ORF UL89 were generated. These viruses allow a characterization of the impact of virus replication. It was possible to show that the amino acids E534 and R544 have a functional role in HCMV. The mutation of one of these amino acids was enough to generate a growth deficient mutant. The stable cell lines HELF Fi301-UL89 and HELF Fi301-vProm UL89 were used for the characterization of the growth deficient mutants. The growth competent mutants H656A and H571A show no significant differences in comparison with the wild type TB40/E virus. This was verified by growth kinetics, protein expression characterizations, pulse field gel electrophoresis, DNA binding assays and electron microscopy.

The topic of diploma thesis is to design a "city house", in a form of the intensive urban structure, using the area with the greatest efficiency in terms of housing, services and jobs on a relatively small area. The main function of the new complex is housing supplemented by services, as well as, leisure and education facilities. The art school, the gallery, the office space and other facilities serve not only the residents of the "intensive house", but also the rest of the public, with the possibility of getting new jobs at an accessible distance, which is the main task of an intensive structure. The aim is to create a multifunctional urban building that revitalizes the inefficiently used area and at the same time brings green spaces designed for relaxation that are missing in this area.

This diploma thesis is focused on the history of the construction development of the residential real estates in the locality of Brno - Komin. The locality is described in this thesis in the basic information form, range of the cadastral area and demography. In addition, the historical events which had influence on the development of this locality are outlined. Further, also the economy structure, public facility and amenities throughout the history are mentioned. Another part of this thesis outlines this locality development, changes and growth during each time period. Further, the characteristic building elements and types of the real estate are described for each time period. The final part of this work is focused on the analysis of development possibilities of construction in this locality.

Within this work, a set of depositions induced by focused electron beam was prepared. The depositions were prepared in the presence of water vapours from trimethyl(methylcyclopentadienyl)platinum(IV) precursor. The dependence of prepared materials purity on beam accelerating voltage and water vapour pressure was measured. The best platinum content was achieved at (27,2 ± 0,4) at. %, with beam accelerating voltage 5 kV, beam current 1600 pA and water vapour pressure 100 Pa. Due to subsequent long-term exposure to light, air humidity and air oxygen, the platinum content was increased to (39,2 ± 2,1) at. %.

This diploma thesis deals with cluster analysis for long-term electrocardiograms (ECG) clustering. The linear filtration is used for ECG preprocessing. The ECG sign segmenting in single heart cycles is based on the detection QRS complex and consequently to an application of dynamic time warping algorithms. To an application of all these mentioned processes and to results interpretation, a program called Cluster analysis has been created in the Matlab background. The results of this diploma thesis confirm that cluster analysis is able to distinguish cardiac arrhythmias which are typical with their shape distinctness of normal heart cycles.

This project investigates methods of construction the wavelet-based QRS-complex detector. QRS-complex detection is very important, because it helps automatically calculate heart rate and in some cases it is used for compression ECG signal. The design of QRS detector can be made with many methods, in this project were mentioned and consequently tested only a few variants. The principle of designed detector used a wavelet-based decomposition of the original ECG signal to several frequency-coded bands. These bands are consequently transformed to absolute values and with the help of the threshold value are marked positions of assumed QRS complexes. Then are these assumed positions from all bands compared between themselves. If the position is confirmed at least at one nearby band, then is this position marked as true QRS complex. To increase efficiency of designed detector, two modifications were additionally mentioned. The first one, using the envelope of the signal, had rather negative effect on detectors efficiency. The second modification, using combined signal from three pseudoorthogonal leads, had reversely very good effect on detectors efficiency. In the end, the designed detector and all its modifications were tested on signals from CSE library (exactly on leads II, V2 and V6).

The topic of this master's thesis is the analysis of ECG signals using wavelet transform. In the introductory chapters there is a brief description of heart anatomy, the emergence and spread of potentials, which evocating activities of myocardium. There is an overview of techniques used for ECG signals analysis and explanation of ECG curve diagnostic importance. Work also containts an ECG signal analysis common procedure explanation and different approaches brief overview. The main part of this work is an application detecting significant intervals in the ECG signal, developed in Matlab. In several chapters the detection procedure is described in more details and gave reasons for chosen methods. In the last chapter there is a preview of several signals as a result of developed application, together with evaluation of the tests carried out at the CSE database. Detector sensitivity was quantified over 99,10%.