An Abstraction of Whitney's Broken Circuit Theorem

We establish a broad generalization of Whitney's broken circuit theorem on the chromatic polynomial of a graph to sums of type $\sum_{A\subseteq S} f(A)$ where $S$ is a finite set and $f$ is a mapping from the power set of $S$ into an abelian group. We give applications to the domination polynomial and the subgraph component polynomial of a graph, the chromatic polynomial of a hypergraph, the characteristic polynomial and Crapo's beta invariant of a matroid, and the principle of inclusion-exclusion. Thus, we discover several known and new results in a concise and unified way. As further applications of our main result, we derive a new generalization of the maximums-minimums identity and of a theorem due to Blass and Sagan on the M\"obius function of a finite lattice, which generalizes Rota's crosscut theorem. For the classical M\"obius function, both Euler's totient function and its Dirichlet inverse, and the reciprocal of the Riemann zeta function we obtain new expansions involving the greatest common divisor resp. least common multiple. We finally establish an even broader generalization of Whitney's broken circuit theorem in the context of convex geometries (antimatroids).Comment: 18 page

Hepatitis C virus pharmacogenomics in Latin American populations: implications in the era of direct-acting antivirals

In recent years, great progress has been made in the field of new therapeutic options for hepatitis C virus (HCV) infection. The new direct-acting antiviral agents (DAAs) represent a great hope for millions of chronically infected individuals because their use may lead to excellent cure rates with fewer side effects. In Latin America, the high prevalence of HCV genotype 1 infection and the significant association of Native American ancestry with risk predictive single-nucleotide polymorphisms (SNPs) in IFNL4 and ITPA genes highlight the need to implement new treatment regimens in these populations. However, the universal accessibility to DAAs is still not a reality in the region as their high cost is one of the major, although not the only, limiting factors for their broad implementation. Therefore, under these circumstances, could the assessment of host genetic markers be a useful tool to prioritize DAA treatment until global access to these new drugs can be achieved? This review will summarize the scientific evidences and the potential implications of HCV pharmacogenomics in this rapidly evolving era of anti-HCV drug development.Fil: Trinks, Julieta. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Caputo, Mariela. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hulaniuk, María L.. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; ArgentinaFil: Corach, Daniel. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Flichman, Diego Martin. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Multidisciplinary investigation of the pit circuit at Durrington Walls, UK

ISBN: 9782753585874.– Comprehensive geophysical assessment of huge pits; ERT, GPR, mag and EM. – Novel approach to testing and interpreting pits via coring. – Largest pit circuit confirmed in both the Stonehenge landscape and the UK.Publisher PDFPeer reviewe