The mechanism of DNA mismatch repair has been modeled upon biochemical studies of the E. coli DNA adenine methylation-instructed pathway where the initial recognition of mismatched nucleotides is performed by the MutS protein. MutS homologs (MSH) have been identified based on a highly conserved region containing a Walker-A adenine nucleotide binding motif. Here we show that adenine nucleotide b...

The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a ds 2 e+1 blog2(Ds+1)c+1 -approximation algorithm for MVRST where Ds is the minimum diameter of spanning trees of G.

The goal of this paper is to find a competitive algorithm for the following problem. We are given a hypergraph G = (X,E), |E| = n, with weighted edges and maximum edge size k. We wish to maximize the weight of a matching M ⊆ E of G, given that edges are revealed in a random order, and that when an edge e is revealed the algorithm must decide either e ∈ M or e / ∈M . Note that this is a generali...

Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on N vertices. Assume further that D → ∞ as N → ∞ and that co-degrees of pairs of vertices in H are at most L where L = o(D/ log N). We consider the random greedy algorithm for forming a matching in H. We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all e...

We have recently suggested a new quantum gravity theory that can be unified with mechanics. coined this collision space-time. This seems to fully consistent 3-dimensional space-time, is, three space dimensions and time-dimensions, so some would call it six-dimensional. However, we shown collision-time collision-length (space) are just two different sides of the same “coin” (space-time), is more...