The Floyd-Warshall algorithm is a simple and widely used algorithm to compute shortest paths between all pairs of vertices in an edge weighted directed graph. It can also be used to detect the presence of negative cycles. We will show that for this task many existing implementations of the Floyd-Warshall algorithm will fail because exponentially large numbers can appear during its execution.

Floyd languages (FL), alias Operator Precedence Languages, have recently received renewed attention thanks to their closure properties and local parsability which allow one to apply automatic verification techniques (e.g. model checking) and parallel and incremental parsing. They properly include various other classes, noticeably Visual Pushdown languages. In this paper we provide a characteriz...

For thousands of years mankind lived just like the animals And then something happened that unleashed the power of his imagination He learned to talk Pink Floyd I Introduction I-A What is a Cognitive Map? Cognitive maps or Cause maps were first used in 1948 by Edward C. Tolman. The idea however, of cognitive maps dates back to 1913, where Trowbridge carried out investigations in cognitive maps,...

Objective: There has been a growing interest in finding plants with biological active ingredients for medicinal application. Materials and Methods: Three colors of petals of Althaea officinalis (A. officinalis) flowers, i.e., pink, reddish pink, and white were examined for total antioxidant activity and flavonoids content. Results: The reddish pink flowers of A. officinalis have more antioxidant...

We prove that in characteristic p > 0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method o...

For a random walk on finitely generated group G we obtain generalization of classical inequality Ancona. We deduce as corollary that the identity map extends to continuous equivariant surjection from Martin boundary Floyd boundary, with preimages conical points being singletons. This provides new results for compactifications relatively hyperbolic groups.

We show that several versions of Floyd and Rivest’s algorithm Select for finding the kth smallest of n elements require at most n+min{k, n− k}+ o(n) comparisons on average and with high probability. This rectifies the analysis of Floyd and Rivest, and extends it to the case of nondistinct elements. Our computational results confirm that Select may be the best algorithm in practice.

Investigating the Fate of Pre-neoplastic Cells in a Mouse Model of Medulloblastoma by Jessica Dawn Kessler Department of Pharmacology and Cancer Biology Duke University Date:_______________________ Approved: ___________________________ Robert J. Wechsler-Reya, Ph.D. Supervisor ___________________________ Dennis Thiele, Ph.D. ___________________________ Fan Wang, Ph.D. __________________________...