Some Multicolor Ramsey Numbers Involving Cycles

Establishing the values of Ramsey numbers is, in general, a difficult task from the computational point of view. Over the years, researchers have developed methods to tackle this problem exhaustively in ways that require intensive computations. These methods are often backed by theoretical results that allow us to cut the search space down to a size that is within the limits of current computing capacity. This thesis focuses on developing algorithms and applying them to generate Ramsey colorings avoiding cycles. It adds to a recent trend of interest in this particular area of finite Ramsey theory. Our main contributions are the enumeration of all (C_5,C_5,C_5;n) Ramsey colorings and the study of the Ramsey numbers R(C_4,C_4,K_4) and R4(C_5)

Constraint Satisfaction Techniques for Combinatorial Problems

The last two decades have seen extraordinary advances in tools and techniques for constraint satisfaction. These advances have in turn created great interest in their industrial applications. As a result, tools and techniques are often tailored to meet the needs of industrial applications out of the box. We claim that in the case of abstract combinatorial problems in discrete mathematics, the standard tools and techniques require special considerations in order to be applied effectively. The main objective of this thesis is to help researchers in discrete mathematics weave through the landscape of constraint satisfaction techniques in order to pick the right tool for the job. We consider constraint satisfaction paradigms like satisfiability of Boolean formulas and answer set programming, and techniques like symmetry breaking. Our contributions range from theoretical results to practical issues regarding tool applications to combinatorial problems. We prove search-versus-decision complexity results for problems about backbones and backdoors of Boolean formulas. We consider applications of constraint satisfaction techniques to problems in graph arrowing (specifically in Ramsey and Folkman theory) and computational social choice. Our contributions show how applying constraint satisfaction techniques to abstract combinatorial problems poses additional challenges. We show how these challenges can be addressed. Additionally, we consider the issue of trusting the results of applying constraint satisfaction techniques to combinatorial problems by relying on verified computations

Understanding How Disease and Environment Combine to Structure Resistance in Estuarine Bivalve Populations

Delaware Bay oyster (Crassostrea virginica) populations are influenced by two lethal parasites that cause Dermo and MSX diseases. As part of the US National Science Foundation Ecology of Infectious Diseases initiative, a program developed for Delaware Bay focuses on understanding how oyster population genetics and population dynamics interact with the environment and these parasites to structure he host populations, and how these interactions might modified by climate change. Laboratory and field studies undertaken during this program include identifying genes related to MSX and Dermo disease resistance, potential regions for refugia and the mechanisms that allow them to exist, phenotypic and genotypic differences in oysters from putative refugia and high-disease areas, and spatial and temporal variability in the effective size of the spawning populations. Resulting data provide inputs to oyster genetics, population dynamics, and larval growth models that interface with a three-dimensional circulation model developed for Delaware Bay. Reconstruction of Lagrangian particle tracks is used to infer transport pathways of oyster larvae and MSX and Dermo disease pathogens. Results emerging from laboratory, field, and modeling studies are providing an understanding of long-term changes in Delaware Bay oyster populations that occur as the oyster population responds to climate, environmental, and biological variability

Allosteric modulation of AURKA kinase activity by a small-molecule inhibitor of its protein-protein interaction with TPX2.

The essential mitotic kinase Aurora A (AURKA) is controlled during cell cycle progression via two distinct mechanisms. Following activation loop autophosphorylation early in mitosis when it localizes to centrosomes, AURKA is allosterically activated on the mitotic spindle via binding to the microtubule-associated protein, TPX2. Here, we report the discovery of AurkinA, a novel chemical inhibitor of the AURKA-TPX2 interaction, which acts via an unexpected structural mechanism to inhibit AURKA activity and mitotic localization. In crystal structures, AurkinA binds to a hydrophobic pocket (the 'Y pocket') that normally accommodates a conserved Tyr-Ser-Tyr motif from TPX2, blocking the AURKA-TPX2 interaction. AurkinA binding to the Y- pocket induces structural changes in AURKA that inhibit catalytic activity in vitro and in cells, without affecting ATP binding to the active site, defining a novel mechanism of allosteric inhibition. Consistent with this mechanism, cells exposed to AurkinA mislocalise AURKA from mitotic spindle microtubules. Thus, our findings provide fresh insight into the catalytic mechanism of AURKA, and identify a key structural feature as the target for a new class of dual-mode AURKA inhibitors, with implications for the chemical biology and selective therapeutic targeting of structurally related kinases.We are grateful for the access and support at beamlines i02, i03 and i04-1 at Diamond Light Source at Harwell, UK (proposal MX9007 and MX9537) and at beamline Proxima1 at the SOLEIL Synchrotron, Gif-sur-Yvette, France. We are grateful for access and support from the X-ray and biophysics facilities (Dept. of Biochemistry) and the screening/imaging facility (MRC Cancer Unit). M.J. was supported by a Cancer Research UK studentship held in the labs of DS and ARV, PS and MR by a Wellcome Trust Strategic Award to ARV and MH, and DJH, BH, AJN and GM by grants from the UK Medical Research Council to ARV.This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/srep2852

Molecular typing of ST239-MRSA-III from diverse geographic locations and the evolution of the SCCmec III element during its intercontinental spread

ST239-MRSA-III is probably the oldest truly pandemic MRSA strain, circulating in many countries since the 1970s. It is still frequently isolated in some parts of the world although it has been replaced by other MRSA strains in, e.g., most of Europe. Previous genotyping work (Harris et al., 2010; Castillo-Ramírez et al., 2012) suggested a split in geographically defined clades. In the present study, a collection of 184 ST239-MRSA-III isolates, mainly from countries not covered by the previous studies were characterized using two DNA microarrays (i) targeting an extensive range of typing markers, virulence and resistance genes and (ii) a SCCmec subtyping array. Thirty additional isolates underwent whole-genome sequencing (WGS) and, together with published WGS data for 215 ST239-MRSA-III isolates, were analyzed using in-silico analysis for comparison with the microarray data and with special regard to variation within SCCmec elements. This permitted the assignment of isolates and sequences to 39 different SCCmec III subtypes, and to three major and several minor clades. One clade, characterized by the integration of a transposon into nsaB and by the loss of fnbB and splE was detected among isolates from Turkey, Romania and other Eastern European countries, Russia, Pakistan, and (mainly Northern) China. Another clade, harboring sasX/sesI is widespread in South-East Asia including China/Hong Kong, and surprisingly also in Trinidad & Tobago. A third, related, but sasX/sesI-negative clade occurs not only in Latin America but also in Russia and in the Middle East from where it apparently originated and from where it also was transferred to Ireland. Minor clades exist or existed in Western Europe and Greece, in Portugal, in Australia and New Zealand as well as in the Middle East. Isolates from countries where this strain is not epidemic (such as Germany) frequently are associated with foreign travel and/or hospitalization abroad. The wide dissemination of this strain and the fact that it was able to cause a hospital-borne pandemic that lasted nearly 50 years emphasizes the need for stringent infection prevention and control and admission screening

Characterizing Genetic Susceptibility to Breast Cancer in Women of African Ancestry

Background: Genome-wide association studies have identified approximately 100 common genetic variants associated with breast cancer risk, the majority of which were discovered in women of European ancestry. Because of different patterns of linkage disequilibrium, many of these genetic markers may not represent signals in populations of African ancestry. Methods: We tested 74 breast cancer risk variants and conducted fine-mapping of these susceptibility regions in 6,522 breast cancer cases and 7,643 controls of African ancestry from three genetic consortia (AABC, AMBER, and ROOT). Results: Fifty-four of the 74 variants (73%) were found to have ORs that were directionally consistent with those previously reported, of which 12 were nominally statistically significant ( P < 0.05). Through fine-mapping, in six regions ( 3p24, 12p11, 14q13, 16q12/FTO, 16q23, 19p13 ), we observed seven markers that better represent the underlying risk variant for overall breast cancer or breast cancer subtypes, whereas in another two regions ( 11q13, 16q12/TOX3 ), we identified suggestive evidence of signals that are independent of the reported index variant. Overlapping chromatin features and regulatory elements suggest that many of the risk alleles lie in regions with biological functionality. Conclusions: Through fine-mapping of known susceptibility regions, we have revealed alleles that better characterize breast cancer risk in women of African ancestry. Impact: The risk alleles identified represent genetic markers for modeling and stratifying breast cancer risk in women of African ancestry. Cancer Epidemiol Biomarkers Prev; 26(7); 1-11. ©2017 AACR

A Genetic Locus within the FMN1/GREM1 Gene Region Interacts with Body Mass Index in Colorectal Cancer Risk

Colorectal cancer risk can be impacted by genetic, environmental, and lifestyle factors, including diet and obesity. Geneenvironment interactions (G x E) can provide biological insights into the effects of obesity on colorectal cancer risk. Here, we assessed potential genome-wide G x E interactions between body mass index (BMI) and common SNPs for colorectal cancer risk using data from 36,415 colorectal cancer cases and 48,451 controls from three international colorectal cancer consortia (CCFR, CORECT, and GECCO). The G x E tests included the conventional logistic regression using multiplicative terms (one degree of freedom, 1DF test), the two-step EDGE method, and the joint 3DF test, each of which is powerful for detecting G x E interactions under specific conditions. BMI was associated with higher colorectal cancer risk. The two-step approach revealed a statistically significant GxBMI interaction located within the Formin 1/Gremlin 1 (FMN1/GREM1) gene region (rs58349661). This SNP was also identified by the 3DF test, with a suggestive statistical significance in the 1DF test. Among participants with the CC genotype of rs58349661, overweight and obesity categories were associated with higher colorectal cancer risk, whereas null associations were observed across BMI categories in those with the TT genotype. Using data from three large international consortia, this study discovered a locus in the FMN1/GREM1 gene region that interacts with BMI on the association with colorectal cancer risk. Further studies should examine the potential mechanisms through which this locus modifies the etiologic link between obesity and colorectal cancer