510 research outputs found
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
Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas
Plant diseases are responsible for substantial and sometimes devastating economic and societal costs and thus are a major limiting factor for stable and sustainable agricultural production. Diseases of crops are particular crippling in developing countries that are heavily dependent on agriculture for food security and income. Various techniques have been developed to reduce the negative impact of plant diseases and eliminate the associated parasites, but the success of these approaches strongly depends on population awareness and the degree of engagement with disease control and prevention programs. In this paper we derive and analyse a mathematical model of mosaic disease of Jatropha curcas, an important biofuel plant, with particular emphasis on the effects of interventions in the form of nutrients and insecticides, whose use depends on the level of population awareness. Two contributions to disease awareness are considered in the model: global awareness campaigns, and awareness from observing infected plants. All steady states of the model are found, and their stability is analysed in terms of system parameters. We identify parameter regions associated with eradication of disease, stable endemic infection, and periodic oscillations in the level of infection. Analytical results are supported by numerical simulations that illustrate the behaviour of the model in different dynamical regimes. Implications of theoretical results for practical implementation of disease control are discussed
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