Robust Bounds on Choosing from Large Tournaments

Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out any alternative in large random tournaments. Nevertheless, all analytical results thus far have assumed a rigid probabilistic model, in which either a tournament is chosen uniformly at random, or there is a linear order of alternatives and the orientation of all edges in the tournament is chosen with the same probabilities according to the linear order. In this work, we consider a significantly more general model where the orientation of different edges can be chosen with different probabilities. We show that a number of common tournament solutions, including the top cycle and the uncovered set, are still unlikely to rule out any alternative under this model. This corresponds to natural graph-theoretic conditions such as irreducibility of the tournament. In addition, we provide tight asymptotic bounds on the boundary of the probability range for which the tournament solutions select all alternatives with high probability.Comment: Appears in the 14th Conference on Web and Internet Economics (WINE), 201

Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types

A Tri-Oceanic Perspective: DNA Barcoding Reveals Geographic Structure and Cryptic Diversity in Canadian Polychaetes

Although polychaetes are one of the dominant taxa in marine communities, their distributions and taxonomic diversity are poorly understood. Recent studies have shown that many species thought to have broad distributions are actually a complex of allied species. In Canada, 12% of polychaete species are thought to occur in Atlantic, Arctic, and Pacific Oceans, but the extent of gene flow among their populations has not been tested.Sequence variation in a segment of the mitochondrial cytochrome c oxidase I (COI) gene was employed to compare morphological versus molecular diversity estimates, to examine gene flow among populations of widespread species, and to explore connectivity patterns among Canada's three oceans. Analysis of 1876 specimens, representing 333 provisional species, revealed 40 times more sequence divergence between than within species (16.5% versus 0.38%). Genetic data suggest that one quarter of previously recognized species actually include two or more divergent lineages, indicating that richness in this region is currently underestimated. Few species with a tri-oceanic distribution showed genetic cohesion. Instead, large genetic breaks occur between Pacific and Atlantic-Arctic lineages, suggesting their long-term separation. High connectivity among Arctic and Atlantic regions and low connectivity with the Pacific further supports the conclusion that Canadian polychaetes are partitioned into two distinct faunas.Results of this study confirm that COI sequences are an effective tool for species identification in polychaetes, and suggest that DNA barcoding will aid the recognition of species overlooked by the current taxonomic system. The consistent geographic structuring within presumed widespread species suggests that historical range fragmentation during the Pleistocene ultimately increased Canadian polychaete diversity and that the coastal British Columbia fauna played a minor role in Arctic recolonization following deglaciation. This study highlights the value of DNA barcoding for providing rapid insights into species distributions and biogeographic patterns in understudied groups

Change Point Analysis based on Empirical Characteristic Functions

62G20, 62E20, 60F17, Empirical characteristic function, Change point analysis,