An algorithm to discover the k-clique cover in networks

In social network analysis, a k-clique is a relaxed clique, i.e., a k-clique is a quasi-complete sub-graph. A k-clique in a graph is a sub-graph where the distance between any two vertices is no greater than k. The visualization of a small number of vertices can be easily performed in a graph. However, when the number of vertices and edges increases the visualization becomes incomprehensible. In this paper, we propose a new graph mining approach based on k-cliques. The concept of relaxed clique is extended to the whole graph, to achieve a general view, by covering the network with k-cliques. The sequence of k-clique covers is presented, combining small world concepts with community structure components. Computational results and examples are presented

Symmetric invariants and cohomology of groups

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46235/1/208_2005_Article_BF01446902.pd

Quantum Tomography under Prior Information

We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the system. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that 4d-4 measurement outcomes (POVM elements) is enough in order to identify all pure states in a d-dimensional Hilbert space, and that the minimal number is at most 2 log_2(d) smaller than this upper bound.Comment: v3: There was a mistake in the derived finer upper bound in Theorem 3. The corrected upper bound is +1 to the earlier versio

Social environmental impacts on survey cooperation

Social environmental influences on survey cooperation are explored using data from six national household surveys in the United States matched to 1990 decennial census data. Consistent with the past literature on prosocial behavior, cooperation rates in these six surveys are found to be lower in urban, densely populated, high crime rate areas. Measures of social cohesion show no evidence of influencing cooperation. The influence of the environmental variables is then observed after introducing statistical controls for household structure, race, age of household members, presence of children, and socioeconomic attributes of households. Over half of the measured influence of the environmental variables is explained by these household-level attributes. These findings have practical import for survey administrators and are informative for the construction of a theory of survey participation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43559/1/11135_2004_Article_BF00153986.pd