In a complete graph with independent uniform (or exponential) edge weights, let be the minimum-weight spanning tree (MST), and MST after deleting edges of all previous trees. We show that each tree's weight converges in probability to constant , we conjecture . The problem is distinct from Frieze Johansson's minimum combined k edge-disjoint trees; indeed, With an w “arriving” at time Kruskal's ...

The dimer model is a statistical mechanical model on a graph, where configurations consist of perfect matchings of the vertices. For planar graphs, expressions for the partition function and local statistics can be obtained using determinants. The planar dimer model can be used to model a number of other statistical mechanical processes such as the planar Ising model and free fermions. It is al...

Current IDSs usually have several shortcomings. First, the speed and sensitivity of detection are not so ideal. Secondly, the response system lacks the ability to correct errors. Thirdly, the cost of intrusion detection is not considered, that is, the response policy is static. This paper applies fuzzy default theory to transform reasoning and response engine of IDS, based on the proving of IDS...