The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

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

Sublinear time algorithms for earth mover's distance

We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions when given access only to samples of the distributions. We give closeness testers and additive-error estimators over domains in [0, 1][superscript d], with sample complexities independent of domain size – permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other parameters, such as the diameter of the domain space, which may be significantly smaller. We also prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual l 1 metric, and give tight upper and lower bounds

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

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

Is decreased bone mineral density associated with development of scoliosis? A bipedal osteopenic rat model

<p>Abstract</p> <p>Background</p> <p>An association between adolescent idiopathic scoliosis and osteopenia has been proposed to exist. It is still not clear whether there is such an association and if so, whether osteopenia is a causative factor or a consequence. Our previous pilot studies have suggested the presence of osteopenia in scoliotic animals. The aim of this study was to investigate the development of scoliosis in an unpinealectomized bipedal osteopenic rat model, implementing osteoporosis as a causative factor.</p> <p>Methods</p> <p>Fifty Sprague-Dawley rats were rendered bipedal at the 3^rdpostnatal week and separated into control (25 rats) and heparin (25 rats receiving 1 IU/gr body weight/day) groups. DEXA scans after 4 weeks of heparin administration showed low bone mass in the heparin group. Anteroposterior and lateral x-rays of the surviving 42 animals (19 in heparin and 23 in control groups) were taken under anesthesia at the 40^thweek to evaluate for spinal deformity. Additional histomorphometric analysis was done on spine specimens to confirm the low bone mass in heparin receiving animals. Results of the DEXA scans, histomorphometric analysis and radiological data were compared between the groups.</p> <p>Results</p> <p>Bone mineral densities of rats in the heparin group were significantly lower than the control group as evidenced by both the DEXA scans and histomorphometric analyses. However, the incidence of scoliosis (82% in heparin and 65% in control; p > 0.05) as well as the curve magnitudes (12.1 ± 3.8 in heparin versus 10.1 ± 4.3 degrees in control; p > 0.05) were not significantly different. Osteopenic rats were significantly less kyphotic compared to control specimens (p = 0.001).</p> <p>Conclusions</p> <p>This study has revealed two important findings. One is that bipedality (in the absence of pinealectomy) by itself may be a cause of scoliosis in this animal model. Further studies on animal models need to consider bipedality as an independent factor. Secondly, relative hypokyphosis in osteopenic animals may have important implications. The absence of sagittal plane analyses in previous studies makes comparison impossible, but nonetheless these findings suggest that osteopenia may be important in the development of 3D deformity in adolescent idiopathic scoliosis.</p

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