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)

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

Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid

We present an optical mode solver for a whispering gallery resonator coupled to an adjacent arbitrary shaped nano-particle that breaks the axial symmetry of the resonator. Such a hybrid resonator-nanoparticle is similar to what was recently used for bio-detection and for field enhancement. We demonstrate our solver by parametrically studying a toroid-nanoplasmonic device and get the optimal nano-plasmonic size for maximal enhancement. We investigate cases near a plasmonic resonance as well as far from a plasmonic resonance. Unlike common plasmons that typically benefit from working near their resonance, here working far from plasmonic resonance provides comparable performance. This is because the plasmonic resonance enhancement is accompanied by cavity quality degradation through plasmonic absorption.Comment: Supplementary COMSOL script, see http://www.quantumchaos.de/Media/comsol2013/Supplement_Script_for_Fig.3_Comsol_4.3a.mp

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

Personalized Feedback on Staff Dose in Fluoroscopy-Guided Interventions: A New Era in Radiation Dose Monitoring

Radiation safety and protection are a key component of fluoroscopy-guided interventions. We hypothesize that providing weekly personal dose feedback will increase radiation awareness and ultimately will lead to optimized behavior. Therefore, we designed and implemented a personalized feedback of procedure and personal doses for medical staff involved in fluoroscopy-guided interventions. Medical staff (physicians and technicians, n = 27) involved in fluoroscopy-guided interventions were equipped with electronic personal dose meters (PDMs). Procedure dose data including the dose area product and effective doses from PDMs were prospectively monitored for each consecutive procedure over an 8-month period (n = 1082). A personalized feedback form was designed displaying for each staff individually the personal dose per procedure, as well as relative and cumulative doses. This study consisted of two phases: (1) 1-5th months: Staff did not receive feedback (n = 701) and (2) 6-8th months: Staff received weekly individual dose feedback (n = 381). An anonymous evaluation was performed on the feedback and occupational dose. Personalized feedback was scored valuable by 76% of the staff and increased radiation dose awareness for 71%. 57 and 52% reported an increased feeling of occupational safety and changing their behavior because of personalized feedback, respectively. For technicians, the normalized dose was significantly lower in the feedback phase compared to the prefeedback phase: [median (IQR) normalized dose (phase 1) 0.12 (0.04-0.50) A mu Sv/Gy cm(2) versus (phase 2) 0.08 (0.02-0.24) A mu Sv/Gy cm(2), p = 0.002]. Personalized dose feedback increases radiation awareness and safety and can be provided to staff involved in fluoroscopy-guided interventions

Local algorithms : Self-stabilization on speed

Non peer reviewe

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

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