431 research outputs found
Almost Optimal Streaming Algorithms for Coverage Problems
Maximum coverage and minimum set cover problems --collectively called
coverage problems-- have been studied extensively in streaming models. However,
previous research not only achieve sub-optimal approximation factors and space
complexities, but also study a restricted set arrival model which makes an
explicit or implicit assumption on oracle access to the sets, ignoring the
complexity of reading and storing the whole set at once. In this paper, we
address the above shortcomings, and present algorithms with improved
approximation factor and improved space complexity, and prove that our results
are almost tight. Moreover, unlike most of previous work, our results hold on a
more general edge arrival model. More specifically, we present (almost) optimal
approximation algorithms for maximum coverage and minimum set cover problems in
the streaming model with an (almost) optimal space complexity of
, i.e., the space is {\em independent of the size of the sets or
the size of the ground set of elements}. These results not only improve over
the best known algorithms for the set arrival model, but also are the first
such algorithms for the more powerful {\em edge arrival} model. In order to
achieve the above results, we introduce a new general sketching technique for
coverage functions: This sketching scheme can be applied to convert an
-approximation algorithm for a coverage problem to a
(1-\eps)\alpha-approximation algorithm for the same problem in streaming, or
RAM models. We show the significance of our sketching technique by ruling out
the possibility of solving coverage problems via accessing (as a black box) a
(1 \pm \eps)-approximate oracle (e.g., a sketch function) that estimates the
coverage function on any subfamily of the sets
Magnetic field effects on neutrino production in microquasars
We investigate the effects of magnetic fields on neutrino production in
microquasars. We calculate the steady particle distributions for the pions and
muons generated in p-gamma and p-p interactions in the jet taking the effects
of all energy losses into account. The obtained neutrino emission is
significantly modified due to the synchrotron losses suffered by secondary
pions and muons. The estimates made for neutrino fluxes arriving on the Earth
imply that detection of high-energy neutrinos from the vicinity of the compact
object can be difficult. However, in the case of windy microquasars, the
interaction of energetic protons in the jet with matter of dense clumps of the
wind could produce detectable neutrinos. This is because the pions and muons at
larger distances from the compact object will not be affected by synchrotron
losses.Comment: 12 pages, 11 figures, accepted for publication in A&
Electronic Structures of SiC Nanoribbons
Electronic structures of SiC nanoribbons have been studied by spin-polarized
density functional calculations. The armchair nanoribbons are nonmagnetic
semiconductor, while the zigzag nanoribbons are magnetic metal. The spin
polarization in zigzag SiC nanoribbons is originated from the unpaired
electrons localized on the ribbon edges. Interestingly, the zigzag nanoribbons
narrower than 4 nm present half-metallic behavior. Without the aid of
external field or chemical modification, the metal-free half-metallicity
predicted for narrow SiC zigzag nanoribbons opens a facile way for nanomaterial
spintronics applications.Comment: 10 pages, 5 figure
On the nature of the AGILE galactic transient sources
The Italian gamma-ray satellite AGILE has recently reported the detection of
some variable high-energy sources likely of galactic origin. These sources do
not have any obvious counterpart at lower energies. We propose that these
sources are produced in proton-dominated jets of galactic microquasars. We
develop a model for microquasar jets that takes into account both primary
leptons and protons and all relevant radiative processes, including secondary
particle emission and gamma-ray attenuation due to pair creation in the jet. We
obtain spectral energy distributions that correspond to what is observed by
AGILE, with most of the power concentrated between 100 MeV and 10 GeV and
reaching luminosities of erg s. We make detailed spectral
predictions that can be tested by the Fermi gamma-ray telescope in the
immediate future. We conclude that hadronic jets in galactic accreting sources
can be responsible for the variable unidentified gamma-ray sources detected by
AGILE.Comment: 4 pages, 2 figures. Accepted for publication in Astronomy &
Astrophysics (Letters
Gamma-ray emission from massive young stellar objects
Massive stars form in dense and massive molecular cores. The exact formation
mechanism is unclear, but it is possible that some massive stars are formed by
processes similar to those that produce the low-mass stars, with
accretion/ejection phenomena occurring at some point of the evolution of the
protostar. This picture seems to be supported by the detection of a collimated
stellar wind emanating from the massive protostar IRAS 16547-4247. A triple
radio source is associated with the protostar: a compact core and two radio
lobes. The emission of the southern lobe is clearly non-thermal. Such emission
is interpreted as synchrotron radiation produced by relativistic electrons
locally accelerated at the termination point of a thermal jet. Since the
ambient medium is determined by the properties of the molecular cloud in which
the whole system is embedded, we can expect high densities of particles and
infrared photons. Because of the confirmed presence of relativistic electrons,
inverse Compton and relativistic Bremsstrahlung interactions are unavoidable.
Proton-proton collision should also occur, producing an injection of neutral
pions. In this paper we aim at making quantitative predictions of the spectral
energy distribution of the non-thermal spots generated by massive young stellar
objects, with emphasis on the particular case of IRAS 16547-4247. We present
spectral energy distributions for the southern lobe of this source, for a
variety of conditions. We show that high-energy emission might be detectable
from this object in the gamma-ray domain (MeV to TeV). The source may also be
detectable at X-rays through long exposures with current X-ray instruments.Comment: 8 pages, 6 figures, accepted for publication in A&
Acceleration and radiation of ultra-high energy protons in galaxy clusters
Clusters of galaxies are believed to be capable to accelerate protons at
accretion shocks to energies exceeding 10^18 eV. At these energies, the losses
caused by interactions of cosmic rays with photons of the Cosmic Microwave
Background Radiation (CMBR) become effective and determine the maximum energy
of protons and the shape of the energy spectrum in the cutoff region. The aim
of this work is the study of the formation of the energy spectrum of
accelerated protons at accretion shocks of galaxy clusters and of the
characteristics of their broad band emission. The proton energy distribution is
calculated self-consistently via a time-dependent numerical treatment of the
shock acceleration process which takes into account the proton energy losses
due to interactions with the CMBR. We calculate the energy distribution of
accelerated protons, as well as the flux of broad-band emission produced by
secondary electrons and positrons via synchrotron and inverse Compton
scattering processes. We find that the downstream and upstream regions
contribute almost at the same level to the emission. For the typical parameters
characterising galaxy clusters, the synchrotron and IC peaks in the spectral
energy distributions appear at comparable flux levels. For an efficient
acceleration, the expected emission components in the X-ray and gamma-ray band
are close to the detection threshold of current generation instruments, and
will be possibly detected with the future generation of detectors.Comment: 9 pages, 13 figures, submitted to Astronomy & Astrophysic
Detection of nonthermal emission from the bow shock of a massive runaway star
The environs of massive, early-type stars have been inspected in recent years
in the search for sites where particles can be accelerated up to relativistic
energies. Wind regions of massive binaries that collide have already been
established as sources of high-energy emission; however, there is a different
scenario for massive stars where strong shocks can also be produced: the
bow-shaped region of matter piled up by the action of the stellar strong wind
of a runaway star interacting with the interstellar medium. We study the
bow-shock region produced by a very massive runaway star, BD+43 3654, to look
for nonthermal radio emission as evidence of a relativistic particle
population. We observed the field of BD+43 3654 at two frequencies, 1.42 and
4.86 GHz, with the Very Large Array (VLA), and obtained a spectral index map of
the radio emission. We have detected, for the first time, nonthermal radio
emission from the bow shock of a massive runaway star. After analyzing the
radiative mechanisms that can be at work, we conclude that the region under
study could produce enough relativistic particles whose radiation might be
detectable by forthcoming gamma-ray instruments, like CTA North.Comment: Accepted in Astronomy and Astrophysics Letter
XMM-Newton observations of the first unidentified TeV gamma-ray source TeV J2032+4130
(abridged) The first unidentified very high energy gamma ray source (TeV
J2032+4130) in the Cygnus region has been the subject of intensive search for a
counterpart source at other wavelengths. A deep ( ksec) exposure of
TeV J2032+4130 with \textit{XMM-Newton} has been obtained. The contribution of
point sources to the observed X-ray emission from TeV J2032+4130 is subtracted
from the data. The point-source subtracted X-ray data are analyzed using blank
sky exposures and regions adjacent to the position of TeV J2032+4130 in the
field of view covered by the XMM-Newton telescopes to search for diffuse X-ray
emission. An extended X-ray emission region with a full width half maximum
(FWHM) size of arc min is found. The centroid of the emission is
co-located with the position of TeV J2032+4130.The energy spectrum of the
emission coinciding with the position and extension of TeV J2032+4130 can be
modeled by a power-law model with a photon index
and an energy flux
integrated between 2 and 10 keV of ergs/(cm s) which is lower than the very high energy gamma-ray
flux observed from TeV J2032+4130. We conclude that the faint extended X-ray
emission discovered in this observation is the X-ray counterpart of TeV
J2032+4130. Formally, it can not be excluded that the extended emission is due
to an unrelated population of faint, hot ( keV) unresolved
point-sources which by chance coincides with the position and extension of TeV
J2032+4130. We discuss our findings in the frame of both hadronic and leptonic
gamma-ray production scenarios.Comment: 5 Pages, 3 Figures, accepted for publication in A&
Hypercontractivity, Sum-of-Squares Proofs, and their Applications
We study the computational complexity of approximating the 2->q norm of
linear operators (defined as ||A||_{2->q} = sup_v ||Av||_q/||v||_2), as well as
connections between this question and issues arising in quantum information
theory and the study of Khot's Unique Games Conjecture (UGC). We show the
following:
1. For any constant even integer q>=4, a graph is a "small-set expander"
if and only if the projector into the span of the top eigenvectors of G's
adjacency matrix has bounded 2->q norm. As a corollary, a good approximation to
the 2->q norm will refute the Small-Set Expansion Conjecture--a close variant
of the UGC. We also show that such a good approximation can be obtained in
exp(n^(2/q)) time, thus obtaining a different proof of the known subexponential
algorithm for Small Set Expansion.
2. Constant rounds of the "Sum of Squares" semidefinite programing hierarchy
certify an upper bound on the 2->4 norm of the projector to low-degree
polynomials over the Boolean cube, as well certify the unsatisfiability of the
"noisy cube" and "short code" based instances of Unique Games considered by
prior works. This improves on the previous upper bound of exp(poly log n)
rounds (for the "short code"), as well as separates the "Sum of
Squares"/"Lasserre" hierarchy from weaker hierarchies that were known to
require omega(1) rounds.
3. We show reductions between computing the 2->4 norm and computing the
injective tensor norm of a tensor, a problem with connections to quantum
information theory. Three corollaries are: (i) the 2->4 norm is NP-hard to
approximate to precision inverse-polynomial in the dimension, (ii) the 2->4
norm does not have a good approximation (in the sense above) unless 3-SAT can
be solved in time exp(sqrt(n) polylog(n)), and (iii) known algorithms for the
quantum separability problem imply a non-trivial additive approximation for the
2->4 norm.Comment: v1: 52 pages. v2: 53 pages, fixed small bugs in proofs of section 6
(on UG integrality gaps) and section 7 (on 2->4 norm of random matrices).
Added comments about real-vs-complex random matrices and about the
k-extendable vs k-extendable & PPT hierarchies. v3: fixed mistakes in random
matrix section. The result now holds only for matrices with random entries
instead of random column
Geant4 simulation of production and interaction of muons
A set of models for Monte Carlo simulation of production and interaction of high energy muons is developed in the framework of the Geant4 toolkit. It describes the following physics processes: ionization of high energy muons with radiative corrections, bremsstrahlung, electron-positron pair production, muon induced nuclear reactions, gamma annihilation into muon pair, positron annihilation into muon pair, and into pion pair. These processes are essential for the LHC experiments, for the understanding of the background in underground detectors, for the simulation of effects related with high-energy muons in cosmic ray experiments and for the estimation of backgrounds in future colliders. The applicability area of the models extends to 1 PeV. The major use-cases are discussed
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