2,334 research outputs found
Neutrino Observatories Can Characterize Cosmic Sources and Neutrino Properties
Neutrino telescopes that measure relative fluxes of ultrahigh-energy
can give information about the location and
characteristics of sources, about neutrino mixing, and can test for neutrino
instability and for departures from CPT invariance in the neutrino sector. We
investigate consequences of neutrino mixing for the neutrino flux arriving at
Earth, and consider how terrestrial measurements can characterize distant
sources. We contrast mixtures that arise from neutrino oscillations with those
signaling neutrino decays. We stress the importance of measuring fluxes in neutrino observatories.Comment: 9 RevTeX pages, 4 figure
S4Net: Single Stage Salient-Instance Segmentation
We consider an interesting problem-salient instance segmentation in this
paper. Other than producing bounding boxes, our network also outputs
high-quality instance-level segments. Taking into account the
category-independent property of each target, we design a single stage salient
instance segmentation framework, with a novel segmentation branch. Our new
branch regards not only local context inside each detection window but also its
surrounding context, enabling us to distinguish the instances in the same scope
even with obstruction. Our network is end-to-end trainable and runs at a fast
speed (40 fps when processing an image with resolution 320x320). We evaluate
our approach on a publicly available benchmark and show that it outperforms
other alternative solutions. We also provide a thorough analysis of the design
choices to help readers better understand the functions of each part of our
network. The source code can be found at
\url{https://github.com/RuochenFan/S4Net}
Supernova neutrinos and antineutrinos: ternary luminosity diagram and spectral split patterns
In core-collapse supernovae, the nu_e and anti-nu_e species may experience
collective flavor swaps to non-electron species nu_x, within energy intervals
limited by relatively sharp boundaries ("splits"). These phenomena appear to
depend sensitively upon the initial energy spectra and luminosities. We
investigate the effect of generic variations of the fractional luminosities
(l_e, l_{anti-e}, l_x) with respect to the usual "energy equipartition" case
(1/6, 1/6, 1/6), within an early-time supernova scenario with fixed thermal
spectra and total luminosity. We represent the constraint l_e+l_{anti-e}+4l_x=1
in a ternary diagram, which is explored via numerical experiments (in
single-angle approximation) over an evenly-spaced grid of points. In inverted
hierarchy, single splits arise in most cases, but an abrupt transition to
double splits is observed for a few points surrounding the equipartition one.
In normal hierarchy, collective effects turn out to be unobservable at all grid
points but one, where single splits occur. Admissible deviations from
equipartition may thus induce dramatic changes in the shape of supernova
(anti)neutrino spectra. The observed patterns are interpreted in terms of
initial flavor polarization vectors (defining boundaries for the single/double
split transitions), lepton number conservation, and minimization of potential
energy.Comment: 24 pages, including 14 figures (1 section with 2 figures added).
Accepted for publication in JCA
Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism Problem
The ellipsoid method is an algorithm that solves the (weak) feasibility and
linear optimization problems for convex sets by making oracle calls to their
(weak) separation problem. We observe that the previously known method for
showing that this reduction can be done in fixed-point logic with counting
(FPC) for linear and semidefinite programs applies to any family of explicitly
bounded convex sets. We use this observation to show that the exact feasibility
problem for semidefinite programs is expressible in the infinitary version of
FPC. As a corollary we get that, for the isomorphism problem, the
Lasserre/Sums-of-Squares semidefinite programming hierarchy of relaxations
collapses to the Sherali-Adams linear programming hierarchy, up to a small loss
in the degree
Definable ellipsoid method, sums-of-squares proofs, and the isomorphism problem
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that this reduction can be done in fixed-point logic with counting (FPC) for linear and semidefinite programs applies to any family of explicitly bounded convex sets. We use this observation to show that the exact feasibility problem for semidefinite programs is expressible in the infinitary version of FPC. As a corollary we get that, for the graph isomorphism problem, the Lasserre/Sums-of-Squares semidefinite programming hierarchy of relaxations collapses to the Sherali-Adams linear programming hierarchy, up to a small loss in the degree. © 2018 ACM.Peer ReviewedPostprint (author's final draft
On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies
We derive Cayley's type conditions for periodical trajectories for the
billiard within an ellipsoid in the Lobachevsky space. It appears that these
new conditions are of the same form as those obtained before for the Euclidean
case. We explain this coincidence by using theory of geodesically equivalent
metrics and show that Lobachevsky and Euclidean elliptic billiards can be
naturally considered as a part of a hierarchy of integrable elliptical
billiards.Comment: 14 pages, to appear in Journal of Geometry and Physic
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