Consider a simple random walk on a connected graph G = (V; E). Let C(u; v) be the expected time taken for the walk starting at vertex u to reach vertex v and then go back to u again, i.e. the commute time for u and v, and

We give an example showing that tight closure does not commute with localization. Mathematical Subject Classification (2000): 13A35, 14H60

Let A and B be n × n matrices, let C = ABA−1B−1 be the multiplicative commutator of A and B, and assume AC = CA. Olga Taussky (1961) examined the structure of A and B for the case where A and B are unitary. Marcus and Thompson (1966) generalized her results to the case where A and C are assumed normal. We look at this problem for general A, with particular attention to the cases where A is diag...

Abstract. Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V (KG)be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V (KG) commute with each other if and only if G is isomorphic to one of the groups on this list. In particular, this property depends only on G and not ...

Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster’s rule, relative plausibility and belief transforms form one such “epistemic” family, and possess natural rationales within Shafer’s formulation of the theory of evidence. However, the relative belief transform only e...

The exterior degree d∧(G) of a finite group G has been recently introduced by Rezaei and Niroomand in order to study the probability that two given elements x and y of G commute in the nonabelian exterior square G ∧ G. This notion is related with the probability d(G) that two elements of G commute in the usual sense. Motivated by a paper of Erovenko and Sury of 2008, we compute the exterior deg...

The traces of the quantum powers of a generic quantum matrix pairwise commute. This was conjectured by Kaoru Ikeda, in connection with certain Hamiltonian systems. The proof involves Newton’s formulae for quantum matrices, relating traces of quantum powers with sums of principal minors. 2000 Mathematics Subject Classification. 81R50, 16W35, 20G42, 70H06

1077-3142/$ see front matter Crown Copyright 2 doi:10.1016/j.cviu.2011.11.002 ⇑ Corresponding author. Address: Room 725, Cen University, Beijing 100084, China. Fax: +86 10 62788 E-mail address: [email protected] (Q. D This paper presents a random-walk-based feature extraction method called commute time guided transformation (CTG) in the graph embedding framework. The paper contributes...