Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some elaborated splitting techniques, all of the operators occurring in the problem formulation are processed individually via forward or backward steps. The treatment of parallel sums of linearly composed maximally monotone operators is motivated by applications in imaging which involve first- and second-order total variation functionals, to which a special attention is given.Comment: 25 page

Topoisomerase-II mediated biochemical mapping of centromeres and nitroreductase mediated drug metabolism in Trypanosomatids

PhDThe protozoan parasites Trypanosoma cruzi and Trypanosoma brucei are the causative agents of Chagas disease and Human African sleeping sickness respectively. Existing therapies are toxic and ineffective against the later stages of the two diseases, consequently safer, improved therapies are urgently required. Here, two areas of trypanosome biology are explored. In the first section, the process of cell division is approached from a fundamental biology perspective. Centromeres are the region of DNA where kinetochore structures form, allowing the attachment of microtubules to facilitate chromosome segregation. In T. brucei we have characterized the nature and location of centromeres by exploiting the localized activity of topoisomerase-II, a cancer chemotherapy target, at the centromere. Etoposide mediated DNA cleavage mapping revealed the presence of signature AT-rich repeat regions coupled with adjacent retrotransposons at the centromere. Further experiments demonstrate that of the two nuclear T. brucei topoisomerase-II isoforms, only topoisomerase-IIα is essential and active at the centromere. The second section centres on pro-drug development against a trypanosome type I nitroreductase. This enzyme has previously been implicated in activation of nifurtimox and benznidazole, the two therapies in clinical use against Chagas disease. Initially we have developed a luciferase based drug assay system in the clinically relevant intracellular T. cruzi stage and rapidly screened a range of nitroaromatic based compounds for trypanocidal activity. A series of derived nitrofuryl compounds previously developed against Chagas disease were also screened against T. brucei, where most demonstrate trypanocidal activities of less than 1 μM. Further we show that these compounds are active substrates of nitroreductase, and act as pro-drugs within the parasite by specific activation of nitroreductase to generate cytotoxic moieties

Inertial Douglas-Rachford splitting for monotone inclusion problems

We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel'ski\u{\i}--Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal-dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory.Comment: arXiv admin note: text overlap with arXiv:1402.529

Repetitive DNA is associated with centromeric domains in Trypanosoma brucei but not Trypanosoma cruzi

Centromeres in Trypanosoma cruzi and Trypanosoma brucei can be localised to regions between directional gene clusters that contain degenerate retroelements, and in the case of T. brucei, repetitive DNA