Mathematics

  2010 MAY 4 - (VerticalNews.com) -- According to recent research published in the journal Advances in Applied Mathematics, "The biologist Rene Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for this system to produce sustained oscillations."

  "In this paper, we state and prove this conjecture for asynchronous automata networks, a class of discrete dynamical systems extensively used to model the behaviors of gene networks," wrote A. Richard and colleagues ...read more

  2010 MAY 4 - (VerticalNews.com) -- According to a study from Milan, Italy, "We consider the Sobolev (Bessel potential) spaces H-l(R-d, C), and their standard norms parallel to parallel to(l) (with e integer or non-integer). We are interested in the unknown sharp constant K-lmnd in the inequality parallel to fg parallel to e<= K-lmnd parallel to f parallel to(m)parallel to g parallel to(n) (f is an element of H-m(R-d, C), g is an element of H-n(R-d, C); 0<= l<= m<= n, m + n - l> d/2); we derive upper and lower bounds K-lmnd +/- for this constant. ...read more

  2010 MAY 4 - (VerticalNews.com) -- 'We consider a local edge-connectivity hypergraph augmentation problem. Specifically, we are given a hypergraph G = (V, E) and a subpartition of V. We are asked to find the smallest possible integer gamma, for which there exists a set of size-two edges F, with vertical bar F vertical bar = gamma, such that in G' = (V, E boolean OR F), the local edge-connectivity between any pair of vertices lying in the same part of the subpartition is at least a given value k. Using a transformation from the bin-packing problem, we show that the associated decision problem is NP-complete, even when k = 2 ...read more