Concurrence of arbitrary dimensional bipartite quantum states

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.Comment: 4 pages, published versio

Probing QCD critical fluctuations from light nuclei production in relativistic heavy-ion collisions

Based on the coalescence model for light nuclei production, we show that the yield ratio $\mathcal{O}_\text{p-d-t} = N_{^3\text{H}} N_p / N_\text{d}^2$ of $p$, d, and $^3$H in heavy-ion collisions is sensitive to the neutron relative density fluctuation $\Delta n= \langle (\delta n)^2\rangle/\langle n\rangle^2$ at kinetic freeze-out. From recent experimental data in central Pb+Pb collisions at $\sqrt{s_{NN}}=6.3$~GeV, $7.6$~GeV, $8.8$~GeV, $12.3$~GeV and $17.3$~GeV measured by the NA49 Collaboration at the CERN Super Proton Synchrotron (SPS), we find a possible non-monotonic behavior of $\Delta n$ as a function of the collision energy with a peak at $\sqrt{s_{NN}}=8.8$~GeV, indicating that the density fluctuations become the largest in collisions at this energy. With the known chemical freeze-out conditions determined from the statistical model fit to experimental data, we obtain a chemical freeze-out temperature of $\sim 144~$MeV and baryon chemical potential of $\sim 385~$MeV at this collision energy, which are close to the critical endpoint in the QCD phase diagram predicted by various theoretical studies. Our results thus suggest the potential usefulness of the yield ratio of light nuclei in relativistic heavy-ion collisions as a direct probe of the large density fluctuations associated with the QCD critical phenomena.Comment: 6 pages, 1 figure, 2 tables. Correlations between neutron and proton density fluctuations considered and presentation improved. Accepted version to appear in PL

Entanglement of Formation of Bipartite Quantum States

We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.Comment: 4 page

Estimating Trust Strength For Supporting Effective Recommendation Services

In the age of information explosion, Internet facilitates product searching and collecting much more convenient for users. However, it is time-consuming and exhausting for users to deal with large amounts of product information. In response, various recommendation approaches have been developed to recommend products that match users’ preferences and requirements. In addition to the well-known collaborative filtering recommendation approach, the trust-based recommendation approach is the emerging one. The reason is that most of online communities allow users to express their trust on other users. Based on the analysis of trust relationships, the trust-based recommendation approach finds out and consults the opinions of more reliable users and therefore makes better recommendations. Existing trust-based recommendation techniques consider all trust relationships in a given trust network equally important and give them the same trust strength. However, in a real-world setting, trust relationships may be of various strengths. In response, in this study, we propose a mechanism for trust strength estimation on the basis of the machine learning approach and estimate the trust strength for each existing trust relationship in a given trust network. To overcome the sparsity of the trust network, we also develop a modified trust propagation method to expand the original trust network. Finally, we perform a series of experiments to demonstrate the performance of our trust-based recommendation approach based on the trust strength estimation mechanism. Our empirical evaluation results show that our proposed approach outperforms our benchmark techniques, i.e., the traditional collaborative filtering approach and the original trust-based one

A Pilot Study of the Short Term Effectiveness and Safety of Amniotic Fluid in Severe Dry Eye Disease

The aim of this study was to evaluate if amniotic fluid (AF) mixed with artificial tears or soaked with a soft contact lens (SCL) as a treatment for severe dry eye disease (DED) would improve its signs or symptoms. In this retrospective pilot study 22 consecutive eyes of 11 patients with level 3 DED classified by DEWS 1 (Dry Eye WorkShop 1 2007), were included in the study between June 1 and September 30 in 2017. The study was conducted before DEWS II (Dry Eye WorkShop II 2017), which was published in October 2017. Therefore, DEWS II was not adopted for this study. Soft Contact Lens Acuvue Oasys of Plano with 8.8 base curve and 14 mm diameters by Johnson and Johnson were used to soak in FloGraft, which is an AF, for 30 minutes before placing in 12 eyes in Group 1. The contact lenses were placed in the left eye for 1 week. In Group 2, 10 eyes used 6 mL of artificial tears mixed with 0.25 mL of AF, which were applied to the eye four times a day for 1 week. No other eye medications were used. The eyes that were included had diffuse punctate staining and fast tear breaking times of <5 seconds with severe ocular symptoms (DEWS 1 level 3-4). Photos of fluorescein stain corneas before the treatment and 1 week after the treatment were used to compare the distribution of punctate staining as the objective outcomes for signs. Several questions adopted from the Ocular Surface disease Index (OSDI) about subjective symptoms before and after the treatment were asked, and documented on the chart. Improvement either in symptoms or signs or both of DED after 1 week at follow-up examination was recorded. Group 1, with SCL 46% had improvement after 1 week and Group 2, with artificial tears 50% had improvement after 1 week. Improvement means either symptom relief or comparatively decreased distribution of punctate staining on the cornea or both. No cases had inflammation, infection, irritation or blurred vision. We concluded that FloGraft as an AF can safely improve the symptoms or the signs of severe DED either as a mix with artificial tears or soaked with SCL by about 50% in this case series without evidence of irritation, inflammation or blurred vision in the short term