Optimal Timer Based Selection Schemes

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on Communications, uses stackrel.st

A note on Schubert varieties in G/B

This article does not have an abstract

On some Frobenius restriction theorems for semistable sheaves

We prove a version of an effective Frobenius restriction theorem for semistable bundles in characteristic p. The main novelty is in restricting the bundle to the p-fold thickening of a hypersurface section. The base variety is G/P, an abelian variety or a smooth projective toric variety

The variety of circular complexes and F-splitting

This article does not have an abstract

Restriction theorems for homogeneous bundles

We prove that for an irreducible representation τ: GL(n) → GL(W), the associated homogeneous Pnk-vector bundle Wτ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in Pnk, where k is an algebraically closed field of characteristic ≠2,3 respectively. In particular Wτ is semistable when restricted to general hypersurfaces of degree ≥2 and is strongly semistable when restricted to the generic hypersurface of degree ≥2