For n > r > 1, let f,(n) denote the minimum number q, such that it is possible to partition all edges of the complete r-graph on n vertices into q complete r-partite r-graphs. Graham and Pollak showed that fz(n) = n-1. Here we observe that f3(n) = n-2 and show that for every fixed r > 2, there are positive constants cx(r) and c2(r) such that q(r) < f,(n)" n-f'/2J < c2(r) for all n > r. This sol...

De Paoli-Iseppi, R., Johansson, P., Menzies, A., Dias, K., Pupo, G., Kakavand, H., Wilmott, J., Mann, G., Hayward, N., Dinger, M., Long, G., Scolyer, R. (2016). Comparison of whole-exome sequencing of matched fresh and formalin fixed paraffin embedded melanoma tumours: implications for clinical decision making. Pathology, 48(3), 261-266. ...

We prove that Thompson’s group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman–Thompson groups Vn,r with the homology of the zeroth component of the infinite loop space of the mod n− 1 Moore spectrum. As V = V2,1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect t...

A Mixed Media Reality (MMR) system and associated techniques are disclosed. The MMR system provides mechanisms for forming a mixed media document that includes media of at least two types (e.g., printed paper as a first medium and digital content and/or web link as a second medium). In one embodiment, an MMR document is retrieved based on recognition of a paper document. Responsive to a compari...

Billy Graham was one of the world’s most famous Christian evangelists in twentieth century. He visited Scotland 1955 and led a six week Crusade at Kelvin Hall Glasgow. Thousands people attended these rallies listened to preach. At end campaign, it calculated that 26,457 had responded Gospel message proclaimed by Graham. This paper, based upon critical examination twenty four sermons delivered G...

For finite graphs F and G, let Nr(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. I f g and c?? are families of graphs, it is natural to ask then whether or not the quantities NF(G), FE F, are linearly independent when G is restricted to Q. For example, if P = (K1, &} (where K, denotes the complete graph on n vertices) and 9 is the fa...