91 research outputs found
Evaluating Matrix Functions by Resummations on Graphs: the Method of Path-Sums
We introduce the method of path-sums which is a tool for exactly evaluating a
function of a discrete matrix with possibly non-commuting entries, based on the
closed-form resummation of infinite families of terms in the corresponding
Taylor series. If the matrix is finite, our approach yields the exact result in
a finite number of steps. We achieve this by combining a mapping between matrix
powers and walks on a weighted directed graph with a universal graph-theoretic
result on the structure of such walks. We present path-sum expressions for a
matrix raised to a complex power, the matrix exponential, matrix inverse, and
matrix logarithm. We show that the quasideterminants of a matrix can be
naturally formulated in terms of a path-sum, and present examples of the
application of the path-sum method. We show that obtaining the inversion height
of a matrix inverse and of quasideterminants is an NP-complete problem.Comment: 23 pages, light version submitted to SIAM Journal on Matrix Analysis
and Applications (SIMAX). A separate paper with the graph theoretic results
is available at: arXiv:1202.5523v1. Results for matrices over division rings
will be published separately as wel
Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates
We develop a pairing mean-field theory to describe the quantum dynamics of
the dissociation of molecular Bose-Einstein condensates into their constituent
bosonic or fermionic atoms. We apply the theory to one, two, and
three-dimensional geometries and analyze the role of dimensionality on the atom
production rate as a function of the dissociation energy. As well as
determining the populations and coherences of the atoms, we calculate the
correlations that exist between atoms of opposite momenta, including the column
density correlations in 3D systems. We compare the results with those of the
undepleted molecular field approximation and argue that the latter is most
reliable in fermionic systems and in lower dimensions. In the bosonic case we
compare the pairing mean-field results with exact calculations using the
positive- stochastic method and estimate the range of validity of the
pairing mean-field theory. Comparisons with similar first-principle simulations
in the fermionic case are currently not available, however, we argue that the
range of validity of the present approach should be broader for fermions than
for bosons in the regime where Pauli blocking prevents complete depletion of
the molecular condensate.Comment: 16 pages, 10 figure
Ultra-large Rydberg dimers in optical lattices
We investigate the dynamics of Rydberg electrons excited from the ground
state of ultracold atoms trapped in an optical lattice. We first consider a
lattice comprising an array of double-well potentials, where each double well
is occupied by two ultracold atoms. We demonstrate the existence of molecular
states with equilibrium distances of the order of experimentally attainable
inter-well spacings and binding energies of the order of 10^3 GHz. We also
consider the situation whereby ground-state atoms trapped in an optical lattice
are collectively excited to Rydberg levels, such that the charge-density
distributions of neighbouring atoms overlap. We compute the hopping rate and
interaction matrix elements between highly-excited electrons separated by
distances comparable to typical lattice spacings. Such systems have tunable
interaction parameters and a temperature ~10^{-4} times smaller than the Fermi
temperature, making them potentially attractive for the study and simulation of
strongly correlated electronic systems.Comment: 10 pages, 6 figures, PRA format, version to be published in PR
Exact Inference on Gaussian Graphical Models of Arbitrary Topology using Path-Sums
We present the path-sum formulation for exact statistical inference of
marginals on Gaussian graphical models of arbitrary topology. The path-sum
formulation gives the covariance between each pair of variables as a branched
continued fraction of finite depth and breadth. Our method originates from the
closed-form resummation of infinite families of terms of the walk-sum
representation of the covariance matrix. We prove that the path-sum formulation
always exists for models whose covariance matrix is positive definite: i.e.~it
is valid for both walk-summable and non-walk-summable graphical models of
arbitrary topology. We show that for graphical models on trees the path-sum
formulation is equivalent to Gaussian belief propagation. We also recover, as a
corollary, an existing result that uses determinants to calculate the
covariance matrix. We show that the path-sum formulation formulation is valid
for arbitrary partitions of the inverse covariance matrix. We give detailed
examples demonstrating our results
Breaking habits or breaking habitual behaviours? Old habits as a neglected factor in weight loss maintenance.
Maintaining weight loss requires long-term behaviour change. Theory and evidence around habitual behaviour - i.e., action triggered by impulses that are automatically activated upon exposure to cues, due to learned cue-action associations - can aid development of interventions to support weight loss maintenance. Specifically, weight loss is more likely to be sustained where people develop new habits that support weight management, and break old habits that may undermine such efforts. Interventions seeking to break 'bad' weight-related habits have focused on inhibiting unwanted impulses or avoiding cues. This paper draws attention to the possibility that while such approaches may discontinue habitual behaviour, underlying habit associations may remain. We use evidence from existing qualitative studies to demonstrate that, left unchecked, unwanted habit associations can render people prone to lapsing into old patterns of unhealthy behaviours when motivation or willpower is momentarily weakened, or when returning to familiar settings following temporarily discontinued exposure. We highlight six behaviour change techniques especially suited to disrupting habit associations, but show that these techniques have been underused in weight loss maintenance interventions to date. We call for intervention developers and practitioners to adopt techniques conducive to forming new habit associations to directly override old habits, and to use the persistence of unwanted habit associations as a potential indicator of long-term weight loss intervention effectiveness
Mobile Robot Localization using Panoramic Vision and Combinations of Feature Region Detectors
IEEE International Conference on Robotics and Automation (ICRA 2008, Pasadena, California, May 19-23, 2008), pp. 538-543.This paper presents a vision-based approach for
mobile robot localization. The environmental model is topological. The new approach uses a constellation of different types of affine covariant regions to characterize a place. This type of representation permits a reliable and distinctive environment modeling. The performance of the proposed approach is evaluated using a database of panoramic images from different rooms. Additionally, we compare different combinations of complementary feature region detectors to find the one that achieves the best results. Our experimental results show promising results for this new localization method. Additionally, similarly to what happens with single detectors, different combinations exhibit different strengths and weaknesses depending on the situation, suggesting that a context-aware method to combine
the different detectors would improve the localization results.This work was partially supported by USC Women in Science and Engineering (WiSE), the FI grant from the Generalitat de Catalunya, the European Social Fund, and the MID-CBR project grant TIN2006-15140-C03-01 and FEDER funds and the grant 2005-SGR-00093
Pre-service teachers linking their metalinguistic knowledge to their practice: A functional approach
Existing work in Anglophone countries has raised concerns regarding teachers’ knowledge about language (KAL); this may well be an issue in other countries also, with notable exceptions such as Finland. In Australia, with the introduction of the new Australian Curriculum, the question of teacher KAL has become crucial. Teachers, both practising and pre-service, generally have some knowledge about language as an object, usually including the text structures of particular school genres and information about sentence structure and word classes. This knowledge may be based on traditional grammar and may not be well applied above the sentence level. Teachers may also have an intuitive knowledge of discourse structures and are beginning to reflect on their own discourse using understandings of dialogic teaching. This paper provides an example of how first-year pre-service teachers (PSTs) were introduced to KAL at both the grammatical and the discourse levels, as part of an introductory unit on spoken language. A range of approaches was used, including a functional view of discourse. The PSTs then applied their KAL by putting it into a context that was meaningful for them: discussing their own practice. The paper gives an illustration of some of the work they produced that demonstrates their emerging understandings
Oral administration of a Salmonella enterica-based vaccine expressing Bacillus anthracis protective antigen confers protection against aerosolized B. anthracis.
Bacillus anthracis is the causative agent of anthrax, a disease that affects wildlife, livestock, and humans. Protection against anthrax is primarily afforded by immunity to the B. anthracis protective antigen (PA), particularly PA domains 4 and 1. To further the development of an orally delivered human vaccine for mass vaccination against anthrax, we produced Salmonella enterica serovar Typhimurium expressing full-length PA, PA domains 1 and 4, or PA domain 4 using codon-optimized PA DNA fused to the S. enterica serovar Typhi ClyA and under the control of the ompC promoter. Oral immunization of A/J mice with Salmonella expressing full-length PA protected five of six mice against a challenge with 10(5) CFU of aerosolized B. anthracis STI spores, whereas Salmonella expressing PA domains 1 and 4 provided only 25% protection (two of eight mice), and Salmonella expressing PA domain 4 or a Salmonella-only control afforded no measurable protection. However, a purified recombinant fusion protein of domains 1 and 4 provided 100% protection, and purified recombinant 4 provided protection in three of eight immunized mice. Thus, we demonstrate for the first time the efficacy of an oral S. enterica-based vaccine against aerosolized B. anthracis spores
Science in neo-Victorian poetry
This article considers the work of three contemporary poets and their engagement, in verse, with Victorian science. Beginning with the outlandish ‘theories’ of Mick Imlah’s ‘The Zoologist’s Bath’ (1983), it moves on to two works of biografiction – Anthony Thwaite’s poem ‘At Marychurch’ (1980), which outlines Philip Henry Gosse’s doomed attempts to unite evolution and Christianity, and Ruth Padel’s Darwin: A Life in Poems (2009). Starting off with John Glendening’s idea that science in neo-Victorian fiction, if fully embraced, provides an opportunity for self-revelation to characters, this article explores the rather less happy resolutions of each of these poems, while in addition discussing the ways in which these poems perform the formal changes and mutability discussed within them
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