Modular design of data-parallel graph algorithms

Amorphous Data Parallelism has proven to be a suitable vehicle for implementing concurrent graph algorithms effectively on multi-core architectures. In view of the growing complexity of graph algorithms for information analysis, there is a need to facilitate modular design techniques in the context of Amorphous Data Parallelism. In this paper, we investigate what it takes to formulate algorithms possessing Amorphous Data Parallelism in a modular fashion enabling a large degree of code re-use. Using the betweenness centrality algorithm, a widely popular algorithm in the analysis of social networks, we demonstrate that a single optimisation technique can suffice to enable a modular programming style without loosing the efficiency of a tailor-made monolithic implementation

Standard noncommuting and commuting dilations of commuting tuples

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on Boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of Cuntz algebra O_n coming from dilations of commuting tuples.Comment: 18 pages, Latex, 1 commuting diagra

Directed Acyclic Graphs

This code is copyright (2015) by the University of Hertfordshire and is made available to third parties for research or private study, criticism or review, and for the purpose of reporting the state of the art, under the normal fair use/fair dealing exceptions in Sections 29 and 30 of the Copyright, Designs and Patents Act 1988. Use of the code under this provision is limited to non-commercial use: please contact us if you wish to arrange a licence covering commercial use of the code.This source code implements a unified framework for pre-processing Directed Acyclic Graphs (DAGs) to lookup reachability between two vertices as well as compute the least upper bound of two vertices in constant time. Our framework builds on the adaptive pre-processing algorithm for constant time reachability lookups and extends this to compute the least upper bound of a vertex-pair in constant time. The theoretical details of this work can be found in the research paper which is available at http://uhra.herts.ac.uk/handle/2299/1215

Metal-insulator transition in an aperiodic ladder network: an exact result

We show, in a completely analytical way, that a tight binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we calculate the two-terminal conductance numerically. The numerical results corroborate the analytical findings and yield a richer variety of spectrum showing multiple mobility edges.Comment: 4 pages, 3 figure

Got water? Social divisions and access to public goods in rural India

We use data for 436 rural districts from the 2001 Census of India to examine whether different aspects of social divisions help explain the wide variation in access to tap water across rural India. Studies linking social fragmentation to public goods usually aggregate different types of fragmentation into one index. In contrast, we use disaggregated measures of social fragmentation to show that different types of social fragmentation are associated with dramatically different outcomes for access to tap water in rural India. Communities that are heterogeneous in terms of caste (within the majority Hindu religion) have lower access to tap water than correspondingly homogeneous communities. Communities that are fragmented across religions have higher access to tap water than correspondingly homogeneous communities. This underscores the importance of heterogeneity both within and across religions. Therefore, relying on aggregate measures of social fragmentation may conceal different effects of the component measures and obscure important information regarding the design of policies related to public goods