Stochastic Block Model and Community Detection in the Sparse Graphs: A spectral algorithm with optimal rate of recovery

In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the gap between the density inside a block and the density between the blocks. As a co-product, we settle an open question posed by Abbe et. al. concerning censor block models

Bilateral abducens nerve palsy due to septic thrombophlebitis.

PurposeTo report a case of septic thrombophlebitis producing bilateral abducens nerve palsy.ObservationA 65 year-old woman with recent sinus surgery experienced the onset of horizontal diplopia during treatment for bacteremia. Computer tomography of head and a neck ultrasonography showed right internal jugular vein occlusion. Ophthalmology examination was consistent with bilateral abducens nerve palsy. She was treated with systemic antibiotics and antiplatelet therapy with resolution of the internal jugular vein occlusion. The diplopia improved over a six-months.Conclusion and importanceOur patient had Lemierre syndrome with an unusual presentation. The patient was treated for septic thrombophlebitis with a resolution of her ocular symptoms

Total Number of Alterations in Liquid Biopsies Is an Independent Predictor of Survival in Patients With Advanced Cancers.

PurposeStudies have demonstrated an association between quantity of circulating tumor DNA (ctDNA) and poorer survival. We investigated the relationship between percent ctDNA (%ctDNA), total number of ctDNA alterations, and overall survival (OS) in liquid biopsies.Materials and methodsOverall, 418 patients with blood-based next-generation sequencing (54 to 73 genes) were analyzed. Eligible patients included those who had advanced/metastatic solid tumor malignancies and never received immunotherapy treatment, which may alter the survival curve in patients with high mutational burden.ResultsPatients with a high (≥ 5%) %ctDNA had significantly shorter OS versus those with intermediate (≥ 0.4% to < 5%) or low (< 0.4%) values (median OS, 7.0 v 14.1 v not reached [NR] months, respectively; P < .0001). Patients with a high (≥ 5) total number of alterations had significantly shorter OS versus those with intermediate (≥ 1.46 to < 5), low (< 1.46), or no alterations (median OS, 4.6 v 11.7 v 21.3 v NR months, respectively; P < .0001). The total number of alterations correlated with %ctDNA (r = 0.85; 95% CI, 0.81 to 0.87; P < .0001). However, only an intermediate to high total number of alterations (≥ 1.46) was an independent predictor of worse OS (hazard ratio, 1.96; 95% CI, 1.30 to 2.96; P = .0014; multivariate analysis).ConclusionWe demonstrate that the total number of alterations and %ctDNA have prognostic value and correlate with one another, but only the total number of alterations was independently associated with survival outcomes. Our findings suggest that the total number of alterations in plasma may be an indicator of more aggressive tumor biology and therefore poorer survival

Effect of transitions in the Planck mass during inflation on primordial power spectra

We study the effect of sudden transitions in the effective Planck mass during inflation on primordial power spectra. Specifically, we consider models in which this variation results from the non-minimal coupling of a Brans-Dicke type scalar field. We find that the scalar power spectra develop features at the scales corresponding to those leaving the horizon during the transition. In addition, we observe that the tensor perturbations are largely unaffected, so long as the variation of the Planck mass is below the percent level. Otherwise, the tensor power spectra exhibit damped oscillations over the same scales. Due to significant features in the scalar power spectra, the tensor-to-scalar ratio r shows variation over the corresponding scales. Thus, by studying the spectra of both scalar and tensor perturbations, one can constrain sudden but small variations of the Planck mass during inflation. We illustrate these effects with a number of benchmark single- and two-field models. In addition, we comment on their implications and the possibility to alleviate the tension between the observations of the tensor-to-scalar ratio performed by the Planck and BICEP2 experiments.Comment: 23 pages, 13 figures; to match version accepted for publication in Phys. Rev.

Crew Launch Vehicle Mobile Launcher Solid Rocket Motor Plume Induced Environment

The plume-induced environment created by the Ares 1 first stage, five-segment reusable solid rocket motor (RSRMV) will impose high heating rates and impact pressures on Launch Complex 39. The extremes of these environments pose a potential threat to weaken or even cause structural components to fail if insufficiently designed. Therefore the ability to accurately predict these environments is critical to assist in specifying structural design requirements to insure overall structural integrity and flight safety. This paper presents the predicted thermal and pressure environments induced by the launch of the Crew Launch Vehicle (CLV) from Launch Complex (LC) 39. Once the environments are predicted, a follow-on thermal analysis is required to determine the surface temperature response and the degradation rate of the materials. An example of structures responding to the plume-induced environment will be provided