Avalanche Polynomials of some Families of Graphs

We study the abelian sandpile model on different families of graphs. We introduced the avalanche polynomial which enumerates the size of the avalanches triggered by the addition of a particle on a recurrent configuration. This polynomial is calculated for several families of graphs. In the case of the complete graph, the result involves some known result on Parking function

Cuts and flows of cell complexes

We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory of cuts and flows in graphs, most notably the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and give sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.Comment: 30 pages. Final version, to appear in Journal of Algebraic Combinatoric

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

A differential equation for a class of discrete lifetime distributions with an application in reliability: A demonstration of the utility of computer algebra

YesIt is shown that the probability generating function of a lifetime random variable T on a finite lattice with polynomial failure rate satisfies a certain differential equation. The interrelationship with Markov chain theory is highlighted. The differential equation gives rise to a system of differential equations which, when inverted, can be used in the limit to express the polynomial coefficients in terms of the factorial moments of T. This then can be used to estimate the polynomial coefficients. Some special cases are worked through symbolically using Computer Algebra. A simulation study is used to validate the approach and to explore its potential in the reliability context

A new framework for designing programmes of assessment

Research on assessment in medical education has strongly focused on individual measurement instruments and their psychometric quality. Without detracting from the value of this research, such an approach is not sufficient to high quality assessment of competence as a whole. A programmatic approach is advocated which presupposes criteria for designing comprehensive assessment programmes and for assuring their quality. The paucity of research with relevance to programmatic assessment, and especially its development, prompted us to embark on a research project to develop design principles for programmes of assessment. We conducted focus group interviews to explore the experiences and views of nine assessment experts concerning good practices and new ideas about theoretical and practical issues in programmes of assessment. The discussion was analysed, mapping all aspects relevant for design onto a framework, which was iteratively adjusted to fit the data until saturation was reached. The overarching framework for designing programmes of assessment consists of six assessment programme dimensions: Goals, Programme in Action, Support, Documenting, Improving and Accounting. The model described in this paper can help to frame programmes of assessment; it not only provides a common language, but also a comprehensive picture of the dimensions to be covered when formulating design principles. It helps identifying areas concerning assessment in which ample research and development has been done. But, more importantly, it also helps to detect underserved areas. A guiding principle in design of assessment programmes is fitness for purpose. High quality assessment can only be defined in terms of its goals

Genetic and Anatomic Determinants of Enzootic Venezuelan Equine Encephalitis Virus Infection of Culex (Melanoconion) taeniopus

Venezuelan equine encephalitis (VEE) is a re-emerging, mosquito-borne viral disease with the potential to cause fatal encephalitis in both humans and equids. Recently, detection of endemic VEE caused by enzootic strains has escalated in Mexico, Peru, Bolivia, Colombia and Ecuador, emphasizing the importance of understanding the enzootic transmission cycle of the etiologic agent, VEE virus (VEEV). The majority of work examining the viral determinants of vector infection has been performed in the epizootic mosquito vector, Aedes (Ochlerotatus) taeniorhynchus. Based on the fundamental differences between the epizootic and enzootic cycles, we hypothesized that the virus-vector interaction of the enzootic cycle is fundamentally different from that of the epizootic model. We therefore examined the determinants for VEEV IE infection in the enzootic vector, Culex (Melanoconion) taeniopus, and determined the number and susceptibility of midgut epithelial cells initially infected and their distribution compared to the epizootic virus-vector interaction. Using chimeric viruses, we demonstrated that the determinants of infection for the enzootic vector are different than those observed for the epizootic vector. Similarly, we showed that, unlike A. taeniorhynchus infection with subtype IC VEEV, C. taeniopus does not have a limited subpopulation of midgut cells susceptible to subtype IE VEEV. These findings support the hypothesis that the enzootic VEEV relationship with C. taeniopus differs from the epizootic virus-vector interaction in that the determinants appear to be found in both the nonstructural and structural regions, and initial midgut infection is not limited to a small population of susceptible cells

Comparative proteomic analysis of metabolically labelled proteins from Plasmodium falciparum isolates with different adhesion properties

The virulence of Plasmodium falciparum relates in part to the cytoadhesion characteristics of parasitized erythrocytes but the molecular basis of the different qualitative and quantitative binding phenotypes is incompletely understood. This paucity of information is due partly to the difficulty in working with membrane proteins, the variant nature of these surface antigens and their relatively low abundance. To address this two-dimensional (2D) protein profiles of closely related, but phenotypically different laboratory strains of P. falciparum have been characterized using proteomic approaches. Since the mature erythrocyte has no nucleus and no protein synthesis capability, metabolic labelling of proteins was used to selectively identify parasite proteins and increase detection sensitivity. A small number of changes (less than 10) were observed between four different P. falciparum laboratory strains with distinctive cytoadherence properties using metabolic labelling, with more parasite protein changes found in trophozoite iRBCs than ring stage. The combination of metabolic labelling and autoradiography can therefore be used to identify parasite protein differences, including quantitative ones, and in some cases to obtain protein identifications by mass spectrometry. The results support the suggestion that the membrane protein profile may be related to cytoadherent properties of the iRBCs. Most changes between parasite variants were differences in iso-electric point indicating differential protein modification rather than the presence or absence of a specific peptide