Fast algorithm for border bases of Artinian Gorenstein algebras

Given a multi-index sequence $$\sigma$$, we present a new efficient algorithm to compute generators of the linear recurrence relations between the terms of $$\sigma$$. We transform this problem into an algebraic one, by identifying multi-index sequences, multivariate formal power series and linear functionals on the ring of multivariate polynomials. In this setting, the recurrence relations are the elements of the kerne l$I$\sigma of the Hankel operator $H$\sigma associated to $$\sigma$$. We describe the correspondence between multi-index sequences with a Hankel operator of finite rank and Artinian Gorenstein Algebras. We show how the algebraic structure of the Artinian Gorenstein algebra $A$\sigma$$associated to the sequence$$\sigma yields the structure of the terms $\sigma\alpha$for all$$\alpha$ $\in$ N n$. This structure is explicitly given by a border basis of$A$\sigma$$, which is presented as a quotient of the polynomial ring$K[x 1 ,. .. , xn$] by the kernel$I$\sigma$$of the Hankel operator$H$\sigma$$. The algorithm provides generators of$I$\sigma$$constituting a border basis, pairwise orthogonal bases of$A$\sigma$$ and the tables of multiplication by the variables in these bases. It is an extension of Berlekamp-Massey-Sakata (BMS) algorithm, with improved complexity bounds. We present applications of the method to different problems such as the decomposition of functions into weighted sums of exponential functions, sparse interpolation, fast decoding of algebraic codes, computing the vanishing ideal of points, and tensor decomposition. Some benchmarks illustrate the practical behavior of the algorithm

Beyond Worst-Case Analysis for Joins with Minesweeper

We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is developing a framework to measure this stronger notion of complexity, which we call {\it certificate complexity}, that extends notions of Barbay et al. and Demaine et al.; a certificate is a set of propositional formulae that certifies that the output is correct. This notion captures a natural class of join algorithms. In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees. Our second contribution is to develop a dichotomy theorem for the certificate-based notion of complexity. Roughly, we show that Minesweeper evaluates $\beta$-acyclic queries in time linear in the certificate plus the output size, while for any $\beta$-cyclic query there is some instance that takes superlinear time in the certificate (and for which the output is no larger than the certificate size). We also extend our certificate-complexity analysis to queries with bounded treewidth and the triangle query.Comment: [This is the full version of our PODS'2014 paper.

Bond stretching phonon softening and angle-resolved photoemission kinks in optimally doped Bi2Sr1.6La0.4Cu2O6 superconductors

We report the first measurement of the optical phonon dispersion in optimally doped single layer Bi2Sr1.6La0.4Cu2O6+delta using inelastic x-ray scattering. We found a strong softening of the Cu-O bond stretching phonon at about q=(0.25,0,0) from 76 to 60 meV, similar to the one reported in other cuprates. A direct comparison with angle-resolved photoemission spectroscopy measurements taken on the same sample, revealed an excellent agreement in terms of energy and momentum between the ARPES nodal kink and the soft part of the bond stretching phonon. Indeed, we find that the momentum space where a 63 meV kink is observed can be connected with a vector q=(xi,0,0) with xi~0.22, which corresponds exactly to the soft part of the bond stretching phonon mode. This result supports an interpretation of the ARPES kink in terms of electron-phonon coupling.Comment: submited to PR

Brief report: how adolescents with ASD process social information in complex scenes. Combining evidence from eye movements and verbal descriptions

We investigated attention, encoding and processing of social aspects of complex photographic scenes. Twenty-four high-functioning adolescents (aged 11–16) with ASD and 24 typically developing matched control participants viewed and then described a series of scenes, each containing a person. Analyses of eye movements and verbal descriptions provided converging evidence that both groups displayed general interest in the person in each scene but the salience of the person was reduced for the ASD participants. Nevertheless, the verbal descriptions revealed that participants with ASD frequently processed the observed person’s emotion or mental state without prompting. They also often mentioned eye-gaze direction, and there was evidence from eye movements and verbal descriptions that gaze was followed accurately. The combination of evidence from eye movements and verbal descriptions provides a rich insight into the way stimuli are processed overall. The merits of using these methods within the same paradigm are discussed

Helium Emission in the Type Ic SN 1999cq

We present the first unambiguous detection of helium emission lines in spectra of Type Ic supernovae (SNe Ic). The presence of He I lines, with full width at half maximum ~ 2000 km/s, and the distinct absence of any other intermediate-width emission (e.g., Halpha), implies that the ejecta of SN Ic 1999cq are interacting with dense circumstellar material composed of almost pure helium. This strengthens the argument that the progenitors of SNe Ic are core-collapse events in stars that have lost both their hydrogen and helium envelopes, either through a dense wind or mass-transfer to a companion. In this way, SN 1999cq is similar to supernovae such as SN 1987K and SN 1993J that helped firmly establish a physical connection between Type Ib and Type II supernovae. The light curve of SN 1999cq is very fast, with an extremely rapid rise followed by a quick decline. SN 1999cq is also found to exhibit a high level of emission at blue wavelengths (< 5500 A), likely resulting from either an unusually large amount of iron and iron-group element emission or uncharacteristically low reddening compared with other SNe Ic.Comment: 17 pages (AASTeX V5.0), 4 figures, accepted for publication in the Astronomical Journa

Spectral and spatial imaging of the Be+sdO binary phi Persei

The rapidly rotating Be star phi Persei was spun up by mass and angular momentum transfer from a now stripped-down, hot subdwarf companion. Here we present the first high angular resolution images of phi Persei made possible by new capabilities in longbaseline interferometry at near-IR and visible wavelengths. We observed phi Persei with the MIRC and VEGA instruments of the CHARA Array. Additional MIRC-only observations were performed to track the orbital motion of the companion, and these were fit together with new and existing radial velocity measurements of both stars to derive the complete orbital elements and distance. The hot subdwarf companion is clearly detected in the near-IR data at each epoch of observation with a flux contribution of 1.5% in the H band, and restricted fits indicate that its flux contribution rises to 3.3% in the visible. A new binary orbital solution is determined by combining the astrometric and radial velocity measurements. The derived stellar masses are 9.6+-0.3Msol and 1.2+-0.2Msol for the Be primary and subdwarf secondary, respectively. The inferred distance (186 +- 3 pc), kinematical properties, and evolutionary state are consistent with membership of phi Persei in the alpha Per cluster. From the cluster age we deduce significant constraints on the initial masses and evolutionary mass transfer processes that transformed the phi Persei binary system. The interferometric data place strong constraints on the Be disk elongation, orientation, and kinematics, and the disk angular momentum vector is coaligned with and has the same sense of rotation as the orbital angular momentum vector. The VEGA visible continuum data indicate an elongated shape for the Be star itself, due to the combined effects of rapid rotation, partial obscuration of the photosphere by the circumstellar disk, and flux from the bright inner disk.Comment: 16 pages, 6 figures, 1 Anne

Do adults with high functioning autism or Asperger Syndrome differ in empathy and emotion recognition?

The present study examined whether adults with high functioning autism (HFA) showed greater difficulties in (i) their self-reported ability to empathise with others and/or (ii) their ability to read mental states in others’ eyes than adults with Asperger syndrome (AS). The Empathy Quotient (EQ) and ‘Reading the Mind in the Eyes’ Test (Eyes Test) were compared in 43 adults with AS and 43 adults with HFA. No significant difference was observed on EQ score between groups, while adults with AS performed significantly better on the Eyes Test than those with HFA. This suggests that adults with HFA may need more support, particularly in mentalizing and complex emotion recognition, and raises questions about the existence of subgroups within autism spectrum conditions