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 $\tilde{O}(n)$, 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 $\alpha$-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 $\sim$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 $10^{34-35}$ erg s$^{-1}$. 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 ($\approx 50$ 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 $\approx 12$ 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 $\Gamma=1.5\pm0.2_\mathrm{stat}\pm0.3_\mathrm{sys}$ and an energy flux integrated between 2 and 10 keV of $f_{2-10 \mathrm{keV}} \approx 7\cdot 10^{-13}$ ergs/(cm$^2$ 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 ($k_BT\approx 10$ 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 $G$ 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