This paper introduces an analysis technique, commutativity analysis, for automatically parallelizing computations that manipulate dynamic, pointer-based data structures. Commutativity analysis views computations as composed of operations on objects. It then analyzes the program to discover when operations commute, i.e. leave the objects in the same state regardless of the order in which they ex...

Paul Seymour conjectured that any graph G of order n and minimum degree at least k k+1n contains the k th power of a Hamilton cycle. We prove the following approximate version. For any > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least ( k k+1 + )n, then G contains the kth power of a Hamilton cycle. c © 1998 John Wiley & Sons, Inc. J Graph Th...

We exploit the Galois symmetries of little disks operads to show that many differentials in Goodwillie–Weiss spectral sequences approximating homology and homotopy knot spaces vanish at a prime $p$ . Combined with recent results on relationship between embedding calculus finite-type theory, we deduce $(n+1)$ th approximation is -local universal Vassiliev invariant degree $\leq n$ for every $n \...

This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinear problem wi...