On the Complexity of Local Distributed Graph Problems

This paper is centered on the complexity of graph problems in the well-studied LOCAL model of distributed computing, introduced by Linial [FOCS '87]. It is widely known that for many of the classic distributed graph problems (including maximal independent set (MIS) and $(\Delta+1)$-vertex coloring), the randomized complexity is at most polylogarithmic in the size $n$ of the network, while the best deterministic complexity is typically $2^{O(\sqrt{\log n})}$. Understanding and narrowing down this exponential gap is considered to be one of the central long-standing open questions in the area of distributed graph algorithms. We investigate the problem by introducing a complexity-theoretic framework that allows us to shed some light on the role of randomness in the LOCAL model. We define the SLOCAL model as a sequential version of the LOCAL model. Our framework allows us to prove completeness results with respect to the class of problems which can be solved efficiently in the SLOCAL model, implying that if any of the complete problems can be solved deterministically in $\log^{O(1)} n$ rounds in the LOCAL model, we can deterministically solve all efficient SLOCAL-problems (including MIS and $(\Delta+1)$-coloring) in $\log^{O(1)} n$ rounds in the LOCAL model. We show that a rather rudimentary looking graph coloring problem is complete in the above sense: Color the nodes of a graph with colors red and blue such that each node of sufficiently large polylogarithmic degree has at least one neighbor of each color. The problem admits a trivial zero-round randomized solution. The result can be viewed as showing that the only obstacle to getting efficient determinstic algorithms in the LOCAL model is an efficient algorithm to approximately round fractional values into integer values

Nonlinear optics and light localization in periodic photonic lattices

We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals pointing towards practical applications in optical communications and computing, beam shaping, and bio-sensing.Comment: to appear in Journal of Nonlinear Optical Physics & Materials (JNOPM

Anomalous spectral scaling of light emission rates in low dimensional metallic nanostructures

The strength of light emission near metallic nanostructures can scale anomalously with frequency and dimensionality. We find that light-matter interactions in plasmonic systems confined in two dimensions (e.g., near metal nanowires) strengthen with decreasing frequency owing to strong mode confinement away from the surface plasmon frequency. The anomalous scaling also applies to the modulation speed of plasmonic light sources, including lasers, with modulation bandwidths growing at lower carrier frequencies. This allows developing optical devices that exhibit simultaneously femto-second response times at the nano-meter scale, even at longer wavelengths into the mid IR, limited only by non-local effects and reversible light-matter coupling

Observation of 2nd band vortex solitons in 2D photonic lattices

We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly-localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes

Laser generated neutron source for neutron resonance spectroscopy

Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Plasmas, 17(10), 100701, 2010 and may be found at http://dx.doi.org/10.1063/1.348421

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Aerosolized amikacin for treatment of pulmonary Mycobacterium avium infections: an observational case series

BACKGROUND: Current systemic therapy for nontuberculous mycobacterial pulmonary infection is limited by poor clinical response rates, drug toxicities and side effects. The addition of aerosolized amikacin to standard oral therapy for nontuberculous mycobacterial pulmonary infection may improve treatment efficacy without producing systemic toxicity. This study was undertaken to assess the safety, tolerability and preliminary clinical benefits of the addition of aerosolized amikacin to a standard macrolide-based oral treatment regimen. CASE PRESENTATIONS: Six HIV-negative patients with Mycobacterium avium intracellulare pulmonary infections who had failed standard therapy were administered aerosolized amikacin at 15 mg/kg daily in addition to standard multi-drug macrolide-based oral therapy. Patients were monitored clinically and serial sputum cultures were obtained to assess response to therapy. Symptomatic improvement with radiographic stabilization and eradication of mycobacterium from sputum were considered markers of success. Of the six patients treated with daily aerosolized amikacin, five responded to therapy. All of the responders achieved symptomatic improvement and four were sputum culture negative after 6 months of therapy. Two patients became re-infected with Mycobacterium avium intracellulare after 7 and 21 months of treatment. One of the responders who was initially diagnosed with Mycobacterium avium intracellulare became sputum culture positive for Mycobacterium chelonae resistant to amikacin after being on intermittent therapy for 4 years. One patient had progressive respiratory failure and died despite additional therapy. There was no evidence of nephrotoxicity or ototoxicity associated with therapy. CONCLUSION: Aerosolized delivery of amikacin is a promising adjunct to standard therapy for pulmonary nontuberculous mycobacterial infections. Larger prospective trials are needed to define its optimal role in therapy of this disease

Local algorithms : Self-stabilization on speed

Non peer reviewe

Fast Electron Generation in Cones with Ultra-Intense Laser Pulses

Experimental results from copper cones irradiated with ultra-intense laser light are presented. Spatial images and total yields of Cu K{sub {alpha}} fluorescence were measured as a function of the laser focusing properties. The fluorescence emission extends into the cone approximately 300 {micro}m from the cone tip and cannot be explained by ray tracing including cone wall absorption. In addition the total fluorescence yield from cones is an order of magnitude higher than for equivalent mass foil targets. Indications are that the physics of the laser cone interaction is dominated by preplasma created from the long duration, low energy pre-pulse from the laser

Altered Arterial Stiffness and Subendocardial Viability Ratio in Young Healthy Light Smokers after Acute Exercise

Studies showed that long-standing smokers have stiffer arteries at rest. However, the effect of smoking on the ability of the vascular system to respond to increased demands (physical stress) has not been studied. The purpose of this study was to estimate the effect of smoking on arterial stiffness and subendocardial viability ratio, at rest and after acute exercise in young healthy individuals.Healthy light smokers (n = 24, pack-years = 2.9) and non-smokers (n = 53) underwent pulse wave analysis and carotid-femoral pulse wave velocity measurements at rest, and 2, 5, 10, and 15 minutes following an exercise test to exhaustion. Smokers were tested, 1) after 12h abstinence from smoking (chronic condition) and 2) immediately after smoking one cigarette (acute condition). At rest, chronic smokers had higher augmentation index and lower aortic pulse pressure than non-smokers, while subendocardial viability ratio was not significantly different. Acute smoking increased resting augmentation index and decreased subendocardial viability ratio compared with non-smokers, and decreased subendocardial viability ratio compared with the chronic condition. After exercise, subendocardial viability ratio was lower, and augmentation index and aortic pulse pressure were higher in non-smokers than smokers in the chronic and acute conditions. cfPWV rate of recovery of was greater in non-smokers than chronic smokers after exercise. Non-smokers were also able to achieve higher workloads than smokers in both conditions.Chronic and acute smoking appears to diminish the vascular response to physical stress. This can be seen as an impaired 'vascular reserve' or a blunted ability of the blood vessels to accommodate the changes required to achieve higher workloads. These changes were noted before changes in arterial stiffness or subendocardial viability ratio occurred at rest. Even light smoking in young healthy individuals appears to have harmful effects on vascular function, affecting the ability of the vascular bed to respond to increased demands