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-$P$ 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

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

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

Correction to: Health-related qualify of life, angina type and coronary artery disease in patients with stable chest pain

The original article [1] contained an error in coauthor, Balazs Ruzsics’s name which has since been corrected