Dans cette thèse, nous cherchons à reconstruire une approximation d'une variété connue seulement à partir d'un nuage de points de grande dimension l'échantillonnant. Nous nous efforçons de trouver des méthodes de reconstructions efficaces et produisant des approximations ayant la même topologie que la variété échantillonnée. Une attention particulière est consacrée aux flag-complexes et particulièrement aux complexes de Rips. Nous montrons que le complexe de Rips capture la topologie d'une variété échantillonnée en supposant de bonnes conditions d'échantillonnage. En tirant avantage de la compacité des flags-complexes qui peuvent être représentés de manière compacte avec un graphe, nous présentons une structure de données appelée squelette/bloqueurs pour complexes simpliciaux. Nous étudions ensuite deux opérations de simplifications, la contraction d'arête et le collapse simplicial, qui s'avèrent utiles pour réduire un complexe simplicial sans en changer sa topologie. / In this thesis, we look for methods for reconstructing an approximation of a manifold known only through a high-dimensional point cloud. Especially, we are interested in efficient methods that produce approximations that share the same topology as the sampled manifold. A particular attention is devoted to flag-complexes and more specially to Rips complexes due to their compactedness. We show that the Rips complex shares the topology of a sampled manifold under good sampling conditions. By taking advantage of the compactedness of flag-complexes, we present a data structure for simplicial complexes called skeleton/blockers. We then study two simplification operations, the edge contraction and the simplicial collapse, that turn out to be useful for reducing a simplicial complex without changing its topology.

Ricin and Shiga toxin type 1 are potent cytotoxins known as ribosome inhibition proteins, abbreviated RIPs. Proteins of this family shut down protein synthesis by removing a critical adenine in the conserved stem-loop structure of 28S rRNA. Due to its exquisite cytotoxicity, the plant toxin ricin has been used as a biological warfare agent. Although great achievement has been made on ricin research, including catalytic mechanism and structure analysis, there is still no specific treatment available for ricin exposure. In addition, ricin A chain inhibitors may also be useful against the homologous bacterial proteins shiga toxins, which are responsible for dysentery, and diseases related to food poisoning, including hemolytic uremic syndrome. Previous study on RTA inhibitor search has provided a number of substrate analog inhibitors, all of which, however, are weaker inhibitors. Therefore, the goal of this work is to improve the binding affinity of known inhibitors and to discovery new scaffolds for inhibitor discovery and development. In this work, multiple approaches were employed for this purpose, including optimizing known inhibitors and searching new inhibitors by Virtual Drug Screening (VDS) and High Throughput Screening (HTS). A number of new RTA inhibitors were discovered by these strategies, which provide a variety of pharmacophores for RTA inhibitor design, and also added a new line of evidence for VDS as an advanced technology for drug discovery and development. / text

Thesis (M.Ing. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010.

The ability to localise objects and persons is a useful ability, that is currently used in everyday life in the form of Global Positioning System (GPS) navigation. Localisation is also useful in data networks. The ability to localise nodes in a network paves the way for applications such as location based services, beamforming and geographic routing. The Radio Interferometric Positioning System (RIPS), is a method originally designed for localisation in wireless sensor networks. RIPS is a promising method due to the fact that it is capable of localisation with high accuracy over long ranges. This is something which other existing methods are not capable of. RIPS makes localisation measurements in a different manner from conventional methods. Instead of making pairwise measurements between a transmitter and receiver, RIPS uses sets of four nodes in each of its measurements. Furthermore, RIPS requires multiple measurements to obtain the correct RIPS measurement value. This value is referred to as a q–range. Multiple q–ranges are required in order to localise a node. This creates overhead in terms of co–operation between the nodes participating in a RIPS measurement. The focus of this research is to provide a possible solution to this problem of overhead. In this dissertation an investigation is launched into the considerations and benefits of implementing RIPS on a single node. This is done by creating a conceptual design for a single wireless node capable of implementing RIPS through the use of multiple antennas. In order to test this conceptual device, a simulation model is created. This simulation model is then validated, verified and used in experiments designed to test the effects of certain design considerations and variables on the conceptual device’s localisation accuracy. The analysis of the results from these experiments shows that the conceptual device’s use of multiple antennas makes RIPS sensitive to errors. Increasing the distances separating the conceptual device’s antennas is found to decrease this sensitivity to errors. This is shown to be caused by the distances separating the antennas imposing limits on the range of q–ranges values that are possible, with smaller distances resulting in smaller ranges of possible q–range values. It is also found that the use of higher frequencies in RIPS measurements results in greater accuracy. This is with the assumption that these frequencies can be accurately transmitted. / Thesis (M.Ing. (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2012.

Thesis (M.Ing. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010.

The ability to localise objects and persons is a useful ability, that is currently used in everyday life in the form of Global Positioning System (GPS) navigation. Localisation is also useful in data networks. The ability to localise nodes in a network paves the way for applications such as location based services, beamforming and geographic routing. The Radio Interferometric Positioning System (RIPS), is a method originally designed for localisation in wireless sensor networks. RIPS is a promising method due to the fact that it is capable of localisation with high accuracy over long ranges. This is something which other existing methods are not capable of. RIPS makes localisation measurements in a different manner from conventional methods. Instead of making pairwise measurements between a transmitter and receiver, RIPS uses sets of four nodes in each of its measurements. Furthermore, RIPS requires multiple measurements to obtain the correct RIPS measurement value. This value is referred to as a q–range. Multiple q–ranges are required in order to localise a node. This creates overhead in terms of co–operation between the nodes participating in a RIPS measurement. The focus of this research is to provide a possible solution to this problem of overhead. In this dissertation an investigation is launched into the considerations and benefits of implementing RIPS on a single node. This is done by creating a conceptual design for a single wireless node capable of implementing RIPS through the use of multiple antennas. In order to test this conceptual device, a simulation model is created. This simulation model is then validated, verified and used in experiments designed to test the effects of certain design considerations and variables on the conceptual device’s localisation accuracy. The analysis of the results from these experiments shows that the conceptual device’s use of multiple antennas makes RIPS sensitive to errors. Increasing the distances separating the conceptual device’s antennas is found to decrease this sensitivity to errors. This is shown to be caused by the distances separating the antennas imposing limits on the range of q–ranges values that are possible, with smaller distances resulting in smaller ranges of possible q–range values. It is also found that the use of higher frequencies in RIPS measurements results in greater accuracy. This is with the assumption that these frequencies can be accurately transmitted. / Thesis (M.Ing. (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2012.

Dans cette thèse, nous cherchons à reconstruire une approximation d'une variété connue seulement à partir d'un nuage de points de grande dimension l'échantillonnant. Nous nous efforçons de trouver des méthodes de reconstructions efficaces et produisant des approximations ayant la même topologie que la variété échantillonnée. Une attention particulière est consacrée aux flag-complexes et particulièrement aux complexes de Rips. Nous montrons que le complexe de Rips capture la topologie d'une variété échantillonnée en supposant de bonnes conditions d'échantillonnage. En tirant avantage de la compacité des flags-complexes qui peuvent être représentés de manière compacte avec un graphe, nous présentons une structure de données appelée squelette/bloqueurs pour complexes simpliciaux. Nous étudions ensuite deux opérations de simplifications, la contraction d'arête et le collapse simplicial, qui s'avèrent utiles pour réduire un complexe simplicial sans en changer sa topologie.

No description available.

A ciliate is a phylum of protozoa that has two types of nuclei, macronuclei and micronuclei. There may be more than one of each type of nucleus in the organism [1]. The macronucleus is the structure where protein synthesis and cell metabolism occur [1]. The micronucleus stores genetic information and is mobilized during a sexual reproduction process called conjugation [1]. The somatic macronucleus (MAC) is developed from the germ-line micronucleus (MIC) through genome rearrangement during a sexual reproduction process called conjugation [6, 8]. Segments of the MIC that form the MAC during conjugation are called macronuclear destined sequences (MDSs) [8]. During sequencing each MDS is given coordinates where the MDS sequences begin and end in the MIC. The orientation of a MDS in the MIC can be taken to be positive or negative. If the direction of the MDS in the MIC agrees with the direction in the MAC then the orientation is positive otherwise it is a negative orientation. In this thesis we analyze various aspects of the gene assembly during the rearrangment process of the ciliate Oxytricha trifallax that were recently sequenced [15]. Some of the properties analyzed include overlapping MDSs, orientation, MDSs starting and ending position in the MIC and the gaps of overlapping MDS pairs. A gap of an overlapping MDS pair is the order difference of two MDSs for a particular MAC contig that overlap in the MIC contig. We use 120 MAC contigs from [15] that have overlaps among their own MDSs. These 120 MAC contigs make up the data set we call D4. We explore the patterns of overlapping MDSs in the MIC in D4. To quantify such patterns, we associate a vector V (An) to each MAC contig An, where V (An) = (v1(An), v2(An), v3(An)) is a vector in R3. The first entry is the number of overlapping MDS pairs divided by the number of MDSs. The second entry is the sum of gaps of overlapping MDS pairs divided by the sum of all possible gaps. The final entry is the total number of overlapping base pairs divided by the total length of the MAC contig. We computed the distance matrixM = (dij) where dij is the Euclidean distance between V (Ai) and V (Aj). The MAC contig vectors and M were computed using Python. To analyze D4 we applied Topological Data Analysis (TDA). TDA uses topological constructs to assess shapes in data [3, 12]. From the data entries of the distance matrix M = (dij) we applied a Vietoris-Rips filtration to generate the barcodes of the persistent homology in dimensions 0, 1 and 2. The persistence barcode of 0-dimensional homology illustrates clusters of the data while the 1-dimensional homology represents non-trivial loops in the simplicial complex [3, 13]. The application of TDA on the ciliate Oxytricha trifallax identified ten MAC contig clusters at epsilon= 0.1 in D4 and several loops that were persistent for two or three epsilon values. Other TDA methods can be applied to the Vietoris-Rips filtration to further identify which MAC contigs appear in each cluster.

No description available.