13,997 research outputs found
Fast algorithm for border bases of Artinian Gorenstein algebras
Given a multi-index sequence , we present a new efficient algorithm
to compute generators of the linear recurrence relations between the terms of
. 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\sigma of the Hankel operator
$H$\sigma associated to . 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 \sigma\sigma yields the
structure of the terms $\sigma\alpha N nAK[x 1 ,. .. , xnIHIA$ 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 -acyclic queries in time linear in the certificate
plus the output size, while for any -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
Active and driven hydrodynamic crystals
Motivated by the experimental ability to produce monodisperse particles in
microfluidic devices, we study theoretically the hydrodynamic stability of
driven and active crystals. We first recall the theoretical tools allowing to
quantify the dynamics of elongated particles in a confined fluid. In this
regime hydrodynamic interactions between particles arise from a superposition
of potential dipolar singularities. We exploit this feature to derive the
equations of motion for the particle positions and orientations. After showing
that all five planar Bravais lattices are stationary solutions of the equations
of motion, we consider separately the case where the particles are passively
driven by an external force, and the situation where they are self-propelling.
We first demonstrate that phonon modes propagate in driven crystals, which are
always marginally stable. The spatial structure of the eigenmodes depend solely
on the symmetries of the lattices, and on the orientation of the driving force.
For active crystals, the stability of the particle positions and orientations
depends not only on the symmetry of the crystals but also on the perturbation
wavelengths and on the crystal density. Unlike unconfined fluids, the stability
of active crystals is independent of the nature of the propulsion mechanism at
the single particle level. The square and rectangular lattices are found to be
linearly unstable at short wavelengths provided the volume fraction of the
crystals is high enough. Differently, hexagonal, oblique, and face-centered
crystals are always unstable. Our work provides a theoretical basis for future
experimental work on flowing microfluidic crystals.Comment: 10 pages, 10 figure
Rotating Constricted Switching Arcs Burning in Gas and in Vacuum
The method of controlling high-current switching arcs by transverse magnetic fields (TMF) forcing the constricted arc to rotate in a contact system is being applied successfully to improve the breaking capability of vacuum interrupters and gas circuit breakers. We describe the behavior of magnetically driven switching arcs in vacuum and in gas environment. We report on experiments using high-velocity videography, magnetic probes, and spectroscopy; they deliver the velocity, the temperature and the voltage of an arc. We present models and simulations of the moving constricted arc burning in metal vapor and in air. And we describe a particular switching application of TMF arc control and explain a scaling law of the contact size with the current interruption capability
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
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