Semi-definite programming and functional inequalities for Distributed Parameter Systems

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration. For the case of polynomial function matrices, sufficient conditions for positivity of the matrix inequality and, therefore, for the integral inequalities are cast as semi-definite programs. The inequalities are used to study stability of linear partial differential equations.Comment: 8 pages, 5 figure

Quantum walks on general graphs

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.Comment: 8 pages, v2: substantial rewrite improves clarity, corrects errors and omissions; v3: removes major error in final section and integrates remainder into other sections, figures remove

Experimental investigation of optical atom traps with a frequency jump

We study the evolution of a trapped atomic cloud subject to a trapping frequency jump for two cases: stationary and moving center of mass. In the first case, the frequency jump initiates oscillations in the cloud's momentum and size. At certain times we find the temperature is significantly reduced. When the oscillation amplitude becomes large enough, local density increases induced by the anharmonicity of the trapping potential are observed. In the second case, the oscillations are coupled to the center of mass motion through the anharmonicity of the potential. This induces oscillations with even larger amplitudes, enhancing the temperature reduction effects and leading to nonisotropic expansion rates while expanding freely.Comment: 8 figures, Journal of Physics B: At. Mol. Op. Phy

Web Usage Mining with Evolutionary Extraction of Temporal Fuzzy Association Rules

In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets' boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries. The GA-based approach is enhanced from previous work by including a graph representation and an improved fitness function. A comparison of the GA-based approach with a traditional approach on real-world Web log data discovered rules that were lost with the traditional approach. The GA-based approach is recommended as complementary to existing algorithms, because it discovers extra rules. (C) 2013 Elsevier B.V. All rights reserved

Temporal fuzzy association rule mining with 2-tuple linguistic representation

This paper reports on an approach that contributes towards the problem of discovering fuzzy association rules that exhibit a temporal pattern. The novel application of the 2-tuple linguistic representation identifies fuzzy association rules in a temporal context, whilst maintaining the interpretability of linguistic terms. Iterative Rule Learning (IRL) with a Genetic Algorithm (GA) simultaneously induces rules and tunes the membership functions. The discovered rules were compared with those from a traditional method of discovering fuzzy association rules and results demonstrate how the traditional method can loose information because rules occur at the intersection of membership function boundaries. New information can be mined from the proposed approach by improving upon rules discovered with the traditional method and by discovering new rules

Shear flow induced isotropic to nematic transition in a suspension of active filaments

We study the effects of externally applied shear flow on a model of suspensions of motors and filaments, via the equations of active hydrodynamics [PRL {\bf 89} (2002) 058101; {\bf 92} (2004) 118101]. In the absence of shear, the orientationally ordered phase of {\it both} polar and apolar active particles is always unstable at zero-wavenumber. An imposed steady shear large enough to overcome the active stresses stabilises both apolar and moving polar phases. Our work is relevant to {\it in vitro} studies of active filaments, the reorientation of endothelial cells subject to shear flow and shear-induced motility of attached cells.Comment: 8 pages, 4 figures submitted to Europhysics Letter

Photoassociation spectroscopy of a Spin-1 Bose-Einstein condensate

We report on the high resolution photoassociation spectroscopy of a $^{87}$Rb spin-1 Bose-Einstein condensate to the $1_\mathrm{g} (P_{3/2}) v = 152$ excited molecular states. We demonstrate the use of spin dependent photoassociation to experimentally identify the molecular states and their corresponding initial scattering channel. These identifications are in excellent agreement with the eigenvalues of a hyperfine-rotational Hamiltonian. Using the observed spectra we estimate the change in scattering length and identify photoassociation laser light frequency ranges that maximize the change in the spin-dependent mean-field interaction energy.Comment: 5 pages, 4 figure