Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the $k$-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

Red green blue emissive lead sulfide quantum dots: heterogeneous synthesis and applications.

Visible emission colloidal quantum dots (QDs) have shown promise in optical and optoelectronic applications. These QDs are typically composed of relatively expensive elements in the form of indium, cadmium, and gallium since alternative candidate materials exhibiting similar properties are yet to be realized. Herein, for the first time, we report red green blue (RGB) photoluminescences with quantum yields of 18% from earth-abundant lead sulfide (PbS) QDs. The visible emissive property is mainly attributed to a high degree of crystallinity even for the extremely small QD sizes (1-3 nm), which is realized by employing a heterogeneous reaction methodology at high growth temperatures (>170 °C). We demonstrate that the proposed heterogeneous synthetic method can be extended to the synthesis of other metal chalcogenide QDs, such as zinc sulfide and zinc selenide, which are promising for future industrial applications. More importantly, benefiting from the enlarged band gaps, the as-prepared PbS solar cells show an impressive open circuit voltage (∼0.8 V) beyond that reported to date

A Novel Role of Three Dimensional Graphene Foam to Prevent Heater Failure during Boiling

We report a novel boiling heat transfer (NBHT) in reduced graphene oxide (RGO) suspended in water (RGO colloid) near critical heat flux (CHF), which is traditionally the dangerous limitation of nucleate boiling heat transfer because of heater failure. When the heat flux reaches the maximum value (CHF) in RGO colloid pool boiling, the wall temperature increases gradually and slowly with an almost constant heat flux, contrary to the rapid wall temperature increase found during water pool boiling. The gained time by NBHT would provide the safer margin of the heat transfer and the amazing impact on the thermal system as the first report of graphene application. In addition, the CHF and boiling heat transfer performance also increase. This novel boiling phenomenon can effectively prevent heater failure because of the role played by the self-assembled three-dimensional foam-like graphene network (SFG).open2

Determination of Pericardial Adipose Tissue Increases the Prognostic Accuracy of Coronary Artery Calcification for Future Cardiovascular Events

Objectives: Pericardial adipose tissue (PAT) is associated with coronary artery plaque accumulation and the incidence of coronary heart disease. We evaluated the possible incremental prognostic value of PAT for future cardiovascular events. Methods: 145 patients (94 males, age 60 10 years) with stable coronary artery disease underwent coronary artery calcification (CAC) scanning in a multislice CT scanner, and the volume of pericardial fat was measured. Mean observation time was 5.4 years. Results: 34 patients experienced a severe cardiac event. They had a significantly higher CAC score (1,708 +/- 2,269 vs. 538 +/- 1,150, p 400, 3.5 (1.9-5.4; p = 0.007) for scores > 800 and 5.9 (3.7-7.8; p = 0.005) for scores > 1,600. When additionally a PAT volume > 200 cm(3) was determined, there was a significant increase in the event rate and relative risk. We calculated a relative risk of 2.9 (1.9-4.2; p = 0.01) for scores > 400, 4.0 (2.1-5.0; p = 0.006) for scores > 800 and 7.1 (4.1-10.2; p = 0.005) for scores > 1,600. Conclusions:The additional determination of PAT increases the predictive power of CAC for future cardiovascular events. PAT might therefore be used as a further parameter for risk stratification. Copyright (C) 2012 S. Karger AG, Base

Combination of surgical excision and custom designed silicon pressure splint therapy for keloids on the helical rim

Keloids are defined as dermal fibrotic lesions which are considered an aberration of the wound healing process. Their etiology and pathogenesis are poorly understood. Different treatment modalities are described in the literature depending on the morphology and size of the keloid. We report a case of a large ear keloid on the helical rim which was successfully treated with surgery and a custom designed silicon pressure clip

The mu - e Conversion in Nuclei, mu --> e gamma, mu --> 3e Decays and TeV Scale See-Saw Scenarios of Neutrino Mass Generation

We perform a detailed analysis of lepton flavour violation (LFV) within minimal see-saw type extensions of the Standard Model (SM), which give a viable mechanism of neutrino mass generation and provide new particle content at the electroweak scale. We focus, mainly, on predictions and constraints set on each scenario from mu --> e gamma, mu --> 3e and mu - e conversion in the nuclei. In this class of models, the flavour structure of the Yukawa couplings between the additional scalar and fermion representations and the SM leptons is highly constrained by neutrino oscillation measurements. In particular, we show that in some regions of the parameters space of type I and type II see-saw models, the Dirac and Majorana phases of the neutrino mixing matrix, the ordering and hierarchy of the active neutrino mass spectrum as well as the value of the reactor mixing angle theta_{13} may considerably affect the size of the LFV observables. The interplay of the latter clearly allows to discriminate among the different low energy see-saw possibilities.Comment: Expressions for the factors |C_{me}|^2 and |C_{mu3e}|^2 in the mu-e conversion and mu-->3e decay rates, eqs. (36) and (49), respectively, corrected; results in subsections 2.2 and 2.3 quantitatively changed, qualitatively remain the same; figures 2, 3, 4 and 5 replace

Constraints from muon g-2 and LFV processes in the Higgs Triplet Model

Constraints from the muon anomalous magnetic dipole moment and lepton flavor violating processes are translated into lower bounds on v_Delta*m_H++ in the Higgs Triplet Model by considering correlations through the neutrino mass matrix. The discrepancy of the sign of the contribution to the muon anomalous magnetic dipole moment between the measurement and the prediction in the model is clarified. It is shown that mu to e gamma, tau decays (especially, tau to mu e e), and the muonium conversion can give a more stringent bound on v_Delta*m_H++ than the bound from mu to eee which is expected naively to give the most stringent one.Comment: 18 pages, 16 figure