Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs

Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs

Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs

A Collection of Problems in Extremal Combinatorics

PhDExtremal combinatorics is concerned with how large or small a combinatorial structure can be if we insist it satis es certain properties. In this thesis we investigate four different problems in extremal combinatorics, each with its own unique flavour. We begin by examining a graph saturation problem. We say a graph G is H-saturated if G contains no copy of H as a subgraph, but the addition of any new edge to G creates a copy of H. We look at how few edges a Kp- saturated graph can have when we place certain conditions on its minimum degree. We look at a problem in Ramsey Theory. The k-colour Ramsey number Rk(H) of a graph H is de ned as the least integer n such that every k- colouring of Kn contains a monochromatic copy of H. For an integer r > 3 let Cr denote the cycle on r vertices. By studying a problem related to colourings without short odd cycles, we prove new lower bounds for Rk(Cr) when r is odd. Bootstrap percolation is a process in graphs that can be used to model how infection spreads through a community. We say a set of vertices in a graph percolates if, when this set of vertices start off as infected, the whole graph ends up infected. We study minimal percolating sets, that is, percolating sets with no proper percolating subsets. In particular, we investigate if there is any relation between the smallest and the largest minimal percolating sets in bounded degree graph sequences. A tournament is a complete graph where every edge has been given an orientation. We look at the maximum number of directed k-cycles a tournament can have and investigate when there exist tournaments with many more k-cycles than expected in a random tournament.Engineering and Physical Sciences Research Council, grant number EP/K50290X/1

Algorithmic Graph Theory

The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions

Economic and impact modeling to guide introduction of new tools against malaria

Background Tremendous gains have been made over the last decades in scaling-up malaria preventive and curative interventions. Through this effort, new partnerships and funding streams were mobilized to support innovation toward global malaria targets. As a result, there are many promising new tools to detect, treat, and prevent the disease in clinical development and under evaluation for regulatory approval and eventual adoption by programs. The aim of this thesis was to generate evidence on costs and impact of a new vaccine against malaria (RTS,S AS/01) and to inform downstream policy decisions on its implementation in Plasmodium falciparum (Pf) malaria endemic African countries. Methods A micro-costing methodology was proposed to estimate costs of the vaccine implementation and several other interventions currently deployed by malaria programs (e.g. mass drug administration, indoor residual spraying, rapid reporting, and reactive case detection). The costing models were developed around regionally relevant implementation scenarios informed with program operational documents and inputs from local partners. The vaccine implementation costs derived were then linked to an individual-based model of malaria transmission dynamics that included a vaccine model parameterized to data from the phase 3 trials. Taking into account country epidemiological and health systems features, the model predicted the incremental impact and cost-effectiveness of the new vaccine when added on top of routine prevention and treatment for each of the 43 Pf endemic countries in Africa. Finally, nationally representative data from the Demographic and Health Surveys (DHS) were analyzed to evaluate the scale-up and the distribution of routine malaria interventions with respect to equity. The analysis sought to identify delivery channels for deployment of the new vaccine that might offer a comparative advantage by expanding access and or by fostering equity in malaria prevention. Results and significance The costing studies demonstrated how prospective micro-costing approaches drawing on secondary data could be used to estimate costs of new interventions prior to their implementation in countries. The methodology developed within the thesis yielded highly contextualized and programmatically relevant costs of existing and new interventions to inform decisions at global, country, or other levels. It demonstrated large differences in cost of RTS,S service delivery between Sub-Saharan African (SSA) countries: ranging from 0.72 USD per dose in Burkina Faso to 2.34 USD in Kenya. The impact and cost-effectiveness evaluation of RTS,S indicated that the vaccine was likely to be cost-effective under conventional GDP-based thresholds in most moderate transmission countries; the estimated cost-effectiveness varied with country vaccination coverage, within country heterogeneity in transmission, and cost of service delivery. The analyses of the DHS data further underscored the importance of monitoring adoption and scale-up of new health technologies for equity. Failure to do so could lead to lasting gradients in access to prevention and undermine effectiveness of interventions missing populations at highest risk where the benefits are likely to be greatest. These considerations are immediately relevant for RTS,S currently being evaluated for deployment through the Expanded Program for Immunization that was shown to have higher coverage than other routine malaria interventions but was also more pro-rich than interventions deployed via campaigns (i.e. long-lasting insecticide treated nets (LLINs), IRS). In addition to clinical and field trials, models of transmission dynamics are increasingly used to support evaluation of interventions against malaria. Parameterized with field data the models adequately capture long-term effects of interventions and interactions between properties of new interventions, immunity, and features of the setting on clinical outcomes. The methodologies and the workflows developed within this thesis to support the evaluation of RTS,S for global policy recommendation can be readily adapted to other interventions against malaria. As malaria endemic countries diversify with respect to prevalence, health systems, and economic development, modeling combined with economic analysis become increasingly useful tools to inform unique prioritization of interventions within country malaria programs, including for adoption of new tools

Cumulative index to NASA Tech Briefs, 1986-1990, volumes 10-14

Tech Briefs are short announcements of new technology derived from the R&D activities of the National Aeronautics and Space Administration. These briefs emphasize information considered likely to be transferrable across industrial, regional, or disciplinary lines and are issued to encourage commercial application. This cumulative index of Tech Briefs contains abstracts and four indexes (subject, personal author, originating center, and Tech Brief number) and covers the period 1986 to 1990. The abstract section is organized by the following subject categories: electronic components and circuits, electronic systems, physical sciences, materials, computer programs, life sciences, mechanics, machinery, fabrication technology, and mathematics and information sciences