Upper Bounds on Number of Steals in Rooted Trees

Inspired by applications in parallel computing, we analyze the setting of work stealing in multithreaded computations. We obtain tight upper bounds on the number of steals when the computation can be modeled by rooted trees. In particular, we show that if the computation with n processors starts with one processor having a complete k-ary tree of height h (and the remaining n ? 1 processors having nothing), the maximum possible number of steals is \({\sum }_{i=1}^{n}(k-1)^{i}\binom {h}{i}\).     

The effects of physical and chemical interactions in the formation of cellulose aerogels

Aerogels are low density materials which are produced from wet gels, and find a variety of potential uses. The relative importance of shape/geometry and self-association of the starting materials for the production of aerogels is studied herein. Aerogels were produced from microcrystalline cellulose (MCC) and its functionalized analog, carboxymethyl cellulose (CMC). With increasing functionalization, CMC gains the potential for self-association, differentiating itself from MCC. The present study explores the preparation of aerogels from MCC and CMC, comparing performance with and without significant self-association potential, and more broadly evaluating the production of low density structural materials from renewable cellulose. It was observed that the self-association present in CMC substantially increases aerogel mechanical properties when compared those of non-interactive MCC. Aspect ratio is proposed to also be an import parameter in the structure–property relationship for these materials.     

Generalized kings and single-elimination winners in random tournaments

Autonomous Agents and Multi-Agent Systems - For cooperative games with externalities, the problem of optimally partitioning a set of players into disjoint exhaustive coalitions is called coalition...