Localization and its consequences for quantum walk algorithms and quantum communication

The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that quantum mechanics can also lead, through the phenomenon of localization, to exponential suppression of motion on these graphs (even in the absence of decoherence). In fact, for physical embodiments of graphs, this will be the generic behaviour. It also has implications for proposals for using spin networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v

What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

A new correlator in quantum spin chains

We propose a new correlator in one-dimensional quantum spin chains, the $s-$Emptiness Formation Probability ($s-$EFP). This is a natural generalization of the Emptiness Formation Probability (EFP), which is the probability that the first $n$ spins of the chain are all aligned downwards. In the $s-$EFP we let the spins in question be separated by $s$ sites. The usual EFP corresponds to the special case when $s=1$, and taking $s>1$ allows us to quantify non-local correlations. We express the $s-$EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur

Search for Electromagnetic Counterparts to LIGO-Virgo Candidates: Expanded Very Large Array

This paper summarizes a search for radio wavelength counterparts to candidate gravitational wave events. The identification of an electromagnetic counterpart could provide a more complete understanding of a gravitational wave event, including such characteristics as the location and the nature of the progenitor. We used the Expanded Very Large Array (EVLA) to search six galaxies which were identified as potential hosts for two candidate gravitational wave events. We summarize our procedures and discuss preliminary results.Comment: 4 pages; to appear in the New Horizons in Time Domain Astronomy, Proceedings of IAU Symposium 285, eds. R. E. M. Griffin, R. J. Hanisch & R. Seama

SBML models and MathSBML

MathSBML is an open-source, freely-downloadable Mathematica package that facilitates working with Systems Biology Markup Language (SBML) models. SBML is a toolneutral,computer-readable format for representing models of biochemical reaction networks, applicable to metabolic networks, cell-signaling pathways, genomic regulatory networks, and other modeling problems in systems biology that is widely supported by the systems biology community. SBML is based on XML, a standard medium for representing and transporting data that is widely supported on the internet as well as in computational biology and bioinformatics. Because SBML is tool-independent, it enables model transportability, reuse, publication and survival. In addition to MathSBML, a number of other tools that support SBML model examination and manipulation are provided on the sbml.org website, including libSBML, a C/C++ library for reading SBML models; an SBML Toolbox for MatLab; file conversion programs; an SBML model validator and visualizer; and SBML specifications and schemas. MathSBML enables SBML file import to and export from Mathematica as well as providing an API for model manipulation and simulation

Random matrix theory, the exceptional Lie groups, and L-functions

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are here extended to non-classical groups. We focus on an explicit example: the exceptional Lie group G_2. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_2, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the 7-dimensional representation of G_2. The random matrix calculations extend to all exceptional Lie groupsComment: 14 page

Scotland, Catalonia and the “right” to self-determination: a comment suggested by Kathryn Crameri’s “Do Catalans Have the Right to Decide?

No abstract available

Regional differences in nutrient-induced secretion of gut serotonin

Enterochromaffin (EC) cells located in the gastrointestinal (GI) tract provide the vast majority of serotonin (5-HT) in the body and constitute half of all enteroendocrine cells. EC cells respond to an array of stimuli, including various ingested nutrients. Ensuing 5-HT release from these cells plays a diverse role in regulating gut motility as well as other important responses to nutrient ingestion such as glucose absorption and fluid balance. Recent data also highlight the role of peripheral 5-HT in various pathways related to metabolic control. Details related to the manner by which EC cells respond to ingested nutrients are scarce and as that the nutrient environment changes along the length of the gut, it is unknown whether the response of EC cells to nutrients is dependent on their GI location. The aim of the present study was to identify whether regional differences in nutrient sensing capability exist in mouse EC cells. We isolated mouse EC cells from duodenum and colon to demonstrate differential responses to sugars depending on location. Measurements of intracellular calcium concentration and 5-HT secretion demonstrated that colonic EC cells are more sensitive to glucose, while duodenal EC cells are more sensitive to fructose and sucrose. Short-chain fatty acids (SCFAs), which are predominantly synthesized by intestinal bacteria, have been previously associated with an increase in circulating 5-HT; however, we find that SCFAs do not acutely stimulate EC cell 5-HT release. Thus, we highlight that EC cell physiology is dictated by regional location within the GI tract, and identify differences in the regional responsiveness of EC cells to dietary sugars.Alyce M. Martin, Amanda L. Lumsden, Richard L. Young, Claire F. Jessup, Nick J. Spencer, Damien J. Keatin

The Intrinsic Dimensionality of Attractiveness: A Study in Face Profiles

The study of human attractiveness with pattern analysis techniques is an emerging research field. One still largely unresolved problem is which are the facial features relevant to attractiveness, how they combine together, and the number of independent parameters required for describing and identifying harmonious faces. In this paper, we present a first study about this problem, applied to face profiles. First, according to several empirical results, we hypothesize the existence of two well separated manifolds of attractive and unattractive face profiles. Then, we analyze with manifold learning techniques their intrinsic dimensionality. Finally, we show that the profile data can be reduced, with various techniques, to the intrinsic dimensions, largely without loosing their ability to discriminate between attractive and unattractive face