Analysis of a Reputation System for Mobile Ad-Hoc Networks with Liars

The application of decentralized reputation systems is a promising approach to ensure cooperation and fairness, as well as to address random failures and malicious attacks in Mobile Ad-Hoc Networks. However, they are potentially vulnerable to liars. With our work, we provide a first step to analyzing robustness of a reputation system based on a deviation test. Using a mean-field approach to our stochastic process model, we show that liars have no impact unless their number exceeds a certain threshold (phase transition). We give precise formulae for the critical values and thus provide guidelines for an optimal choice of parameters.Comment: 17 pages, 6 figure

A module-theoretic approach to matroids

Speyer recognized that matroids encode the same data as a special class of tropical linear spaces and Shaw interpreted tropically certain basic matroid constructions; additionally, Frenk developed the perspective of tropical linear spaces as modules over an idempotent semifield. All together, this provides bridges between the combinatorics of matroids, the algebra of idempotent modules, and the geometry of tropical linear spaces. The goal of this paper is to strengthen and expand these bridges by systematically developing the idempotent module theory of matroids. Applications include a geometric interpretation of strong matroid maps and the factorization theorem; a generalized notion of strong matroid maps, via an embedding of the category of matroids into a category of module homomorphisms; a monotonicity property for the stable sum and stable intersection of tropical linear spaces; a novel perspective of fundamental transversal matroids; and a tropical analogue of reduced row echelon form.Comment: 22 pages; v3 minor corrections/clarifications; to appear in JPA

Twisting the Infinitesimal Site

We classify twistings of Grothendieck's differential operators on a smooth variety $X$ in prime characteristic $p$. We prove isomorphism classes of twistings are in bijection with $H^2(X,\mathbb{Z}_p(1))$, the degree 2, weight 1 syntomic cohomology of $X$. We also discuss the relationship between twistings of crystalline and Grothendieck differential operators. Twistings in mixed characteristic are also analyzed.Comment: 20 pages. Comments welcom

Quantization of restricted Lagrangian subvarieties in positive characteristic

Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on X with the structure of a restricted Lie algebra. We consider deformation quantization of line bundles on Lagrangian subvarieties Y of X to modules over such quantizations. If the ideal sheaf of Y is a restricted Lie subalgebra of the structure sheaf of X, we show that there is a certain cohomology class which vanishes if and only if a line bundle on Y admits a quantization.Comment: Comments welcome! 22 page

Species interactions within and between the inquiline larval fauna of Sarracenia purpurea L.: competition or commensalism?

Species interactions such as commensalism and competition greatly affect community structure and composition. The small and diverse communities present in the northern pitcher-plant Sarracenia purpurea L. (Sarraceniaceae) are ideal for the study of species interactions. This study investigated the relationships within and between the inquiline populations of the mosquito Wyeomyia smithii and the midge Metriocnemus knabi contained within the leaves of S. purpurea. Samples of pitcher-plant leaf contents were taken from Waldron Fen, Emmet County, Michigan. The larvae present in each sample were identified, counted and measured. Average densities and larval lengths per unit volume were calculated by species type and dipteran association (i.e., cohabitation with other fly species). The data indicated that both interspecific competition and intraspecific competition may be present in the larval populations of Metriocnemus knabi and Wyeomyia smithii. The co-habitation of M. knabi and W. smithii resulted in reduced M. knabi mean larval length per unit volume when compared with the mean larval length per unit volume of M. knabi found alone, indicating the presence of interspecific competition (1.35 +- 0.15 vs. 2.64 +- 0.40, U=747.5, p<0.05, n=59). The singly-occurring average length of W. smithii decreased with increasing density, indicating the presence of intraspecific competition within the population of W. smithii (Spearman's = -0.302, p<0.05).http://deepblue.lib.umich.edu/bitstream/2027.42/54844/1/3285.pd