BURA Collection:http://bura.brunel.ac.uk/handle/2438/2352014-08-31T10:16:42Z2014-08-31T10:16:42ZThe geometric measure of entanglement for a symmetric pure state with non-negative amplitudesHayashi, MMarkham, DMurao, MOwari, MVirmani, Shttp://bura.brunel.ac.uk/handle/2438/89622014-08-26T15:31:24Z2009-01-01T00:00:00ZTitle: The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes
Authors: Hayashi, M; Markham, D; Murao, M; Owari, M; Virmani, S
Abstract: In this paper for a class of symmetric multiparty pure states, we consider a conjecture
related to the geometric measure of entanglement: “for a symmetric pure state,
the closest product state in terms of the fidelity can be chosen as a symmetric
product state.” We show that this conjecture is true for symmetric pure states whose
amplitudes are all non-negative in a computational basis. The more general conjecture
is still open.
Description: Copyright @ 2009 American Institute of Physics.2009-01-01T00:00:00ZStability of cluster solutions in a cooperative consumer chain modelWei, JWinter, Mhttp://bura.brunel.ac.uk/handle/2438/89522014-08-26T11:29:40Z2014-01-01T00:00:00ZTitle: Stability of cluster solutions in a cooperative consumer chain model
Authors: Wei, J; Winter, M
Abstract: We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.
Description: This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.2014-01-01T00:00:00ZRobust methods for inferring sparse network structuresVinciotti, VHashem, Hhttp://bura.brunel.ac.uk/handle/2438/89412014-08-22T13:34:34Z2013-01-01T00:00:00ZTitle: Robust methods for inferring sparse network structures
Authors: Vinciotti, V; Hashem, H
Abstract: Networks appear in many fields, from finance to medicine, engineering, biology and social science. They often comprise of a very large number of entities, the nodes, and the interest lies in inferring the interactions between these entities, the edges, from relatively limited data. If the underlying network of interactions is sparse, two main statistical approaches are used to retrieve such a structure: covariance modeling approaches with a penalty constraint that encourages sparsity of the network, and nodewise regression approaches with sparse regression methods applied at each node. In the presence of outliers or departures from normality, robust approaches have been developed which relax the assumption of normality. Robust covariance modeling approaches are reviewed and compared with novel nodewise approaches where robust methods are used at each node. For low-dimensional problems, classical deviance tests are also included and compared with penalized likelihood approaches. Overall, copula approaches are found to perform best: they are comparable to the other methods under an assumption of normality or mild departures from this, but they are superior to the other methods when the assumption of normality is strongly violated.
Description: This is the post-print version of the final paper published in Computational Statistics & Data Analysis. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2013 Elsevier B.V.2013-01-01T00:00:00ZComplex scale-free networks with tunable power-law exponent and clusteringColman, ERRodgers, GJhttp://bura.brunel.ac.uk/handle/2438/89292014-08-22T13:17:11Z2013-01-01T00:00:00ZTitle: Complex scale-free networks with tunable power-law exponent and clustering
Authors: Colman, ER; Rodgers, GJ
Abstract: We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes mm “ambassador” nodes and ll of each ambassador’s descendants where mm and ll are random variables selected from any choice of distributions plpl and qmqm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant mm and the number of selected descendants from each ambassador is the constant ll, the power-law exponent is (2l+1)/l(2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of ll and mm. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.
Description: This article is made available through the Brunel Open Access Publishing Fund. It is distributed under a Creative Commons License (http://creativecommons.org/licenses/by/3.0/). Copyright @ 2013 Elsevier B.V.2013-01-01T00:00:00Z