Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6

The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions.Comment: 43 pages and 44 figure

Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

To be or not to be: the importance of attendance in integrated physiology teaching using non-traditional approaches

<p>Abstract</p> <p>Background</p> <p>There is increasing use of non-traditional methods like problem-based learning, team-working and several other active-learning techniques in Physiology teaching. While several studies have investigated the impact of class attendance on the academic performance in traditional teaching, there is limited information regarding whether the new modalities are especially sensible to this factor.</p> <p>Methods</p> <p>Here, we performed a comparative study between a control group receiving information through traditional methods and an experimental group submitted to new methodologies in Physiology teaching.</p> <p>Results</p> <p>We found that while mean examination scores were similar in the control and the experimental groups, a different picture emerge when data are organized according to four categorical attendance levels. In the experimental group, scores were not different between the 1st and the 2nd exams (P = 0.429) nor between the 2nd and the 3^rdexams (P = 0.225) for students that never or poorly attend classes, in contrast to the control group (P < 0.001). A score difference between attending students versus the absentees was maximal in the experimental versus the control group all along the different exams and in the final score.</p> <p>Conclusion</p> <p>We suggest that class attendance is critical for learning using non-traditional methods.</p

Epistatic Roles for Pseudomonas aeruginosa MutS and DinB (DNA Pol IV) in Coping with Reactive Oxygen Species-Induced DNA Damage

Pseudomonas aeruginosa is especially adept at colonizing the airways of individuals afflicted with the autosomal recessive disease cystic fibrosis (CF). CF patients suffer from chronic airway inflammation, which contributes to lung deterioration. Once established in the airways, P. aeruginosa continuously adapts to the changing environment, in part through acquisition of beneficial mutations via a process termed pathoadaptation. MutS and DinB are proposed to play opposing roles in P. aeruginosa pathoadaptation: MutS acts in replication-coupled mismatch repair, which acts to limit spontaneous mutations; in contrast, DinB (DNA polymerase IV) catalyzes error-prone bypass of DNA lesions, contributing to mutations. As part of an ongoing effort to understand mechanisms underlying P. aeruginosa pathoadaptation, we characterized hydrogen peroxide (H2O2)-induced phenotypes of isogenic P. aeruginosa strains bearing different combinations of mutS and dinB alleles. Our results demonstrate an unexpected epistatic relationship between mutS and dinB with respect to H2O2-induced cell killing involving error-prone repair and/or tolerance of oxidized DNA lesions. In striking contrast to these error-prone roles, both MutS and DinB played largely accurate roles in coping with DNA lesions induced by ultraviolet light, mitomycin C, or 4-nitroquinilone 1-oxide. Models discussing roles for MutS and DinB functionality in DNA damage-induced mutagenesis, particularly during CF airway colonization and subsequent P. aeruginosa pathoadaptation are discussed

CD36 deficiency attenuates experimental mycobacterial infection

<p>Abstract</p> <p>Background</p> <p>Members of the CD36 scavenger receptor family have been implicated as sensors of microbial products that mediate phagocytosis and inflammation in response to a broad range of pathogens. We investigated the role of CD36 in host response to mycobacterial infection.</p> <p>Methods</p> <p>Experimental <it>Mycobacterium bovis </it>Bacillus Calmette-Guérin (BCG) infection in <it>Cd36^+/+</it>and <it>Cd36^-/-</it>mice, and <it>in vitro </it>co-cultivation of <it>M. tuberculosis</it>, BCG and <it>M. marinum </it>with <it>Cd36^+/+</it>and <it>Cd36^-/-</it>murine macrophages.</p> <p>Results</p> <p>Using an <it>in vivo </it>model of BCG infection in <it>Cd36^+/+</it>and <it>Cd36^-/-</it>mice, we found that mycobacterial burden in liver and spleen is reduced (83% lower peak splenic colony forming units, p < 0.001), as well as the density of granulomas, and circulating tumor necrosis factor (TNF) levels in <it>Cd36^-/-</it>animals. Intracellular growth of all three mycobacterial species was reduced in <it>Cd36^-/-</it>relative to wild type <it>Cd36^+/+</it>macrophages <it>in vitro</it>. This difference was not attributable to alterations in mycobacterial uptake, macrophage viability, rate of macrophage apoptosis, production of reactive oxygen and/or nitrogen species, TNF or interleukin-10. Using an <it>in vitro </it>model designed to recapitulate cellular events implicated in mycobacterial infection and dissemination <it>in vivo </it>(i.e., phagocytosis of apoptotic macrophages containing mycobacteria), we demonstrated reduced recovery of viable mycobacteria within <it>Cd36^-/-</it>macrophages.</p> <p>Conclusions</p> <p>Together, these data indicate that CD36 deficiency confers resistance to mycobacterial infection. This observation is best explained by reduced intracellular survival of mycobacteria in the <it>Cd36^-/-</it>macrophage and a role for CD36 in the cellular events involved in granuloma formation that promote early bacterial expansion and dissemination.</p