We present an O(n4)-time algorithm for the following problem: Given a set of items with known access frequencies, find the optimal binary search tree under the realistic assumption that each comparison can only result in a two-way decision: either an equality comparison or a less-than comparisons. This improves the best known result of O(n5) time, which is based on split tree algorithms. Our al...

The Orbit Problem consists of determining, given a linear transformation A on Q, together with vectors x and y, whether the orbit of x under repeated applications of A can ever reach y. This problem was famously shown to be decidable by Kannan and Lipton in the 1980s. In this paper, we are concerned with the problem of synthesising suitable invariants P ⊆ R, i.e., sets that are stable under A a...

Let K be a convex subset of a uniformly convex Banach space. It is proved that if K is compact, then the fixed points of a continuous generalized nonexpansive self-mapping T on K can be approximated by the iterates of T, with t B (0,1), T,(x) = (1 t)x + tT(x), x e K; T, is asymptotically regular if T has a fixed point. Let (X, d) be a (nonempty) metric space. A function a of X X X into [0, oo) ...

We consider polyhedral versions of Kannan and Lipton's Orbit Problem [14, 13] determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector space Q. In the context of program veri cation, very similar reachability questions were also considered and left open by Lee and Yannakakis in [15], and by Bra...

There exists extensive literature on fixed points of self-mappings in metric and Banach spaces. But in many applications the mappings under examination may not always be self-mappings, therefore fixed point theorems for nonself-mappings form a natural subject for investigation. Assad and Kirk [2] initiated the study of fixed point of nonselfmappings in metrically convex spaces. Indeed while doi...

Hunain Alam ([email protected]) Amruta V Bhate ([email protected]) Prakash Gangadaran ([email protected]) Sharda S Sawant ([email protected]) Shimul Salot ([email protected]) Lalit Sehgal ([email protected]) Prerana P Dange ([email protected]) Devendra A Chaukar ([email protected]) Anil K D’cruz ([email protected]) Sadhna Kannan ([email protected]) ...

Shenyang Li, Nithya Mariappan, Judit Megyesi, Brian Shank, Krishnaswamy Kannan, Sue Theus, Peter M. Price, Jeremy S. Duffield, and Didier Portilla Division of Nephrology, University of Arkansas for Medical Sciences, Little Rock, Arkansas; Division of Rheumatology, Department of Internal Medicine, University of Arkansas for Medical Sciences, Little Rock, Arkansas; Central Arkansas Veterans Healt...

First drafts prepared by Dr Germaine Buck Louis, Bethesda, USA; Dr Terri Damstra, Research Triangle Park, USA; Dr Fernando DíazBarriga, San Luis Potosi, Mexico; Dr Elaine Faustman, Washington, USA; Dr Ulla Hass, Soborg, Denmark; Dr Robert Kavlock, Research Triangle Park, USA; Dr Carole Kimmel, Washington, USA; Dr Gary Kimmel, Silver Spring, USA; Dr Kannan Krishnan, Montreal, Canada; Dr Ulrike L...