Estimating the weight of metric minimum spanning trees in sublinear time

In this paper we present a sublinear-time $(1+\varepsilon)$-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an $n$-point metric space. The running time of the algorithm is $\widetilde{\mathcal{O}}(n/\varepsilon^{\mathcal{O}(1)})$. Since the full description of an $n$-point metric space is of size $\Theta(n^2)$, the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in $o(n)$ time the weight of the minimum spanning tree to within any factor. We also show that no deterministic algorithm can achieve a $B$-approximation in $o(n^2/B^3)$ time. Furthermore, it has been previously shown that no $o(n^2)$ algorithm exists that returns a spanning tree whose weight is within a constant times the optimum

Structure of particle-hole nuclei around 100Sn

We have performed shell-model calculations for the three odd-odd nuclei 100In, 102In, and 98Ag, with neutron particles and proton holes around 100Sn. We have used a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential, the neutron-proton channel being explicitly treated in the particle-hole formalism. Particular attention has been focused on the particle-hole multiplets, which are a direct source of information on the neutron-proton effective interaction. We present our predictions for the two lowest lying multiplets in 100In, for which no spectroscopic data are yet available. For 98Ag and 102In comparison shows that our results are in very good agreement with the available experimental data.Comment: 5 pages, published in Physical review

Socioeconomic status as an independent predictor of physiological biomarkers of cardiovascular disease: Evidence from NHANES

Background C-reactive protein, homocysteine, cholesterol, and fibrinogen are known to vary by socioeconomic status (SES). Using a nationally representative study, we examined whether these factors vary independently of all other known risk factors, such as diet, exercise, and genetic predisposition. Methods We analyzed the 1999–2002 National Health Examination and Nutrition Survey using logistic regression models. Results We found that high-density lipoprotein cholesterol blood levels increase with income and educational attainment after controlling all known risk factors for elevated cholesterol (e.g., diet, exercise, and family history). Blood levels of C-reactive protein are inversely associated with income and education. Homocysteine blood levels are inversely associated with income even after controlling for blood folate level. A non-significant inverse relationship between homocysteine levels and educational attainment was also observed. Blood levels of low-density lipoprotein cholesterol and fibrinogen were not significantly associated with income or education. Conclusions Levels of “good” (high density lipoprotein) cholesterol increase with income and education even after controlling for factors known to place people at risk of high cholesterol. Stress differences by social class may play a role

Testable properties in general graphs and random order streaming

We present a novel framework closely linking the areas of property testing and data streaming algorithms in the setting of general graphs. It has been recently shown (Monemizadeh et al. 2017) that for bounded-degree graphs, any constant-query tester can be emulated in the random order streaming model by a streaming algorithm that uses only space required to store a constant number of words. However, in a more natural setting of general graphs, with no restriction on the maximum degree, no such results were known because of our lack of understanding of constant-query testers in general graphs and lack of techniques to appropriately emulate in the streaming setting off-line algorithms allowing many high-degree vertices. In this work we advance our understanding on both of these challenges. First, we provide canonical testers for all constant-query testers for general graphs, both, for one-sided and two-sided errors. Such canonizations were only known before (in the adjacency matrix model) for dense graphs (Goldreich and Trevisan 2003) and (in the adjacency list model) for bounded degree (di-)graphs (Goldreich and Ron 2011, Czumaj et al. 2016). Using the concept of canonical testers, we then prove that every property of general graphs that is constant-query testable with one-sided error can also be tested in constant-space with one-sided error in the random order streaming model. Our results imply, among others, that properties like (s,t) disconnectivity, k-path-freeness, etc. are constant-space testable in random order streams

High-quality polarization entanglement state preparation and manipulation in standard telecommunication channels

We report a novel and simple approach for generating near-perfect quality polarization entanglement in a fully guided-wave fashion. Both deterministic pair separation into two adjacent telecommunication channels and the paired photons' temporal walk-off compensation are achieved using standard fiber components. Two-photon interference experiments are performed, both for quantitatively demonstrating the relevance of our approach, and for manipulating the produced state between bosonic and fermionic symmetries. The compactness, versatility, and reliability of this configuration makes it a potential candidate for quantum communication applications.Comment: 6 figure

Waveguide-based OPO source of entangled photon pairs

In this paper we present a compact source of narrow-band energy-time entangled photon pairs in the telecom regime based on a Ti-indiffused Periodically Poled Lithium Niobate (PPLN) waveguide resonator, i.e. a waveguide with end-face dielectric multi-layer mirrors. This is a monolithic doubly resonant Optical Parametric Oscillator (OPO) far below threshold, which generates photon pairs by Spontaneous Parametric Down Conversion (SPDC) at around 1560nm with a 117MHz (0.91 pm)- bandwidth. A coherence time of 2.7 ns is estimated by a time correlation measurement and a high quality of the entangled states is confirmed by a Bell-type experiment. Since highly coherent energy-time entangled photon pairs in the telecom regime are suitable for long distance transmission and manipulation, this source is well suited to the requirements of quantum communication.Comment: 13 page

Purification of Single-photon Entanglement

Single-photon entanglement is a simple form of entanglement that exists between two spatial modes sharing a single photon. Despite its elementary form, it provides a resource as useful as polarization-entangled photons and it can be used for quantum teleportation and entanglement swapping operations. Here, we report the first experiment where single-photon entanglement is purified with a simple linear-optics based protocol. Besides its conceptual interest, this result might find applications in long distance quantum communication based on quantum repeaters.Comment: Main article: 5 pages, 4 figure