Light Spanners

A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality -- in this work we focus on the latter. Specifically, it is shown that for any parameters $k\ge 1$ and $\epsilon>0$, any weighted graph $G$ on $n$ vertices admits a $(2k-1)\cdot(1+\epsilon)$-stretch spanner of weight at most $w(MST(G))\cdot O_\epsilon(kn^{1/k}/\log k)$, where $w(MST(G))$ is the weight of a minimum spanning tree of $G$. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of $O(\log k)$.Comment: 10 pages, 1 figure, to appear in ICALP 201

Probing compact dark matter objects with microlensing in gravitationally lensed quasars

The microlensing signal in the light curves of gravitationally lensed quasars can shed light on the dark matter (DM) composition in their lensing galaxies. Here, we investigate a sample of six lensed quasars from the most recent and best COSMOGRAIL observations: HE 1104-1805, HE 0435-1223, RX J1131-1231, WFI 2033-4723, PG 1115+080, and J1206+4332, yielding a total of eight microlensing light curves, when combining independent image pairs and typically spanning ten years. We explore the microlensing signals to determine whether the standard assumptions on the stellar populations are sufficient to account for the amplitudes of the measured signals or whether additional microlenses are needed. We use the most detailed lens models to date from the H0LiCOW/TDCOSMO collaboration to derive the microlensing parameters, such as the convergence, shear, and stellar/dark matter mass fraction at the position of the quasar images. We use these parameters to generate simulated microlensing light curves. Finally, we propose a methodology based on the Kolmogorov-Smirnov test to verify whether the observed microlensing amplitudes in our data are compatible with the most standard scenario, whereby galaxies are composed of stars as compact bodies and smoothly distributed DM. Given our current sample, we show that the standard scenario cannot be rejected, in contrast with previous results by Hawkins (2020a, A&amp;A, 633, A107), claiming that a population of stellar mass primordial black holes (PBHs) is necessary to explain the observed amplitude of the microlensing signal in lensed quasar light curves. We further estimate the number of microlensing light curves needed to effectively distinguish between the standard scenario with stellar microlensing and a scenario that describes that all the DM contained in galaxies is in the form of compact objects such as PBHs, with a mean mass of 0.2 Mo. We find that about 900 microlensing curves from the Rubin Observatory will be sufficient to discriminate between the two extreme scenarios at a 95% confidence level.</p

The effects of mindfulness-based stress reduction program on the mental health of family caregivers: a randomized controlled trial

&lt;b&gt;Background&lt;/b&gt; Caregivers of people with chronic conditions are more likely than non-caregivers to have depression and emotional problems. Few studies have examined the effectiveness of mindfulness-based stress reduction (MBSR) in improving their mental well-being. &lt;p&gt;&lt;/p&gt; &lt;b&gt;Methods&lt;/b&gt; Caregivers of persons with chronic conditions who scored 7 or above in the Caregiver Strain Index were randomly assigned to the 8-week MBSR group (n = 70) or the self-help control group (n = 71). Validated instruments were used to assess the changes in depressive and anxiety symptoms, quality of life, self-efficacy, self-compassion and mindfulness. Assessments were conducted at baseline, post-intervention and at the 3-month follow-up. &lt;p&gt;&lt;/p&gt; &lt;b&gt;Results &lt;/b&gt;Compared to the participants in the control group, participants in the MBSR group had a significantly greater decrease in depressive symptoms at post-intervention and at 3 months post-intervention (p &lt; 0.01). The improvement in state anxiety symptoms was significantly greater among participants in the MBSR group than those of the control group at post-intervention (p = 0.007), although this difference was not statistically significant at 3 months post-intervention (p = 0.084). There was also a statistically significant larger increase in self-efficacy (controlling negative thoughts; p = 0.041) and mindfulness (p = 0.001) among participants in the MBSR group at the 3-month follow-up compared to the participants in the control group. No statistically significant group effects (MBSR vs. control) were found in perceived stress, quality of life or self-compassion. &lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusions &lt;/b&gt;MBSR appears to be a feasible and acceptable intervention to improve mental health among family caregivers with significant care burden, although further studies that include an active control group are needed to make the findings more conclusive

Viral Retinitis following Intraocular or Periocular Corticosteroid Administration: A Case Series and Comprehensive Review of the Literature.

Abstract Purpose: To describe viral retinitis following intravitreal and periocular corticosteroid administration. Methods: Retrospective case series and comprehensive literature review. Results: We analyzed 5 unreported and 25 previously published cases of viral retinitis following local corticosteroid administration. Causes of retinitis included 23 CMV (76.7%), 5 HSV (16.7%), and 1 each VZV and unspecified (3.3%). Two of 22 tested patients (9.1%) were HIV positive. Twenty-one of 30 (70.0%) cases followed one or more intravitreal injections of triamcinolone acetonide (TA), 4 (13.3%) after one or more posterior sub-Tenon injections of TA, 3 (10.0%) after placement of a 0.59-mg fluocinolone acetonide implant (Retisert), and 1 (3.3%) each after an anterior subconjunctival injection of TA (together with IVTA), an anterior chamber injection, and an anterior sub-Tenon injection. Mean time from most recent corticosteroid administration to development of retinitis was 4.2 months (median 3.8; range 0.25-13.0). Twelve patients (40.0%) had type II diabetes mellitus. Treatments used included systemic antiviral agents (26/30, 86.7%), intravitreal antiviral injections (20/30, 66.7%), and ganciclovir intravitreal implants (4/30, 13.3%). Conclusions: Viral retinitis may develop or reactivate following intraocular or periocular corticosteroid administration. Average time to development of retinitis was 4 months, and CMV was the most frequently observed agent. Diabetes was a frequent co-morbidity and several patients with uveitis who developed retinitis were also receiving systemic immunosuppressive therapy

On WZ-pairs which prove Ramanujan series

The known WZ-proofs for Ramanujan-type series related to $1/\pi$ gave us the insight to develop a new proof strategy based on the WZ-method. Using this approach we are able to find more generalizations and discover first WZ-proofs for certain series of this type.Comment: 12 pages (preprint) + 1 page (addendum). The addendum (A Maple program) is not in the Journal referenc

Muon spin relaxation studies of incommensurate magnetism and superconductivity in stage-4 La2_{2}CuO4.11_{4.11} and La1.88_{1.88}Sr0.12_{0.12}CuO4_{4}

This paper reports muon spin relaxation (MuSR) measurements of two single crystals of the title high-Tc cuprate systems where static incommensurate magnetism and superconductivity coexist. By zero-field MuSR measurements and subsequent analyses with simulations, we show that (1) the maximum ordered Cu moment size (0.36 Bohr magneton) and local spin structure are identical to those in prototypical stripe spin systems with the 1/8 hole concentration; (2) the static magnetism is confined to less than a half of the volume of the sample, and (3) regions with static magnetism form nano-scale islands with the size comparable to the in-plane superconducting coherence length. By transverse-field MuSR measurements, we show that Tc of these systems is related to the superfluid density, in the same way as observed in cuprate systems without static magnetism. We discuss a heuristic model involving percolation of these nanoscale islands with static magnetism as a possible picture to reconcile heterogeneity found by the present MuSR study and long-range spin correlations found by neutron scattering.Comment: 19 pages, 15 figures, submitted to Phys. Rev. B. E-mail: [email protected]

Toward an internally consistent astronomical distance scale

Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of methods, tracers, and techniques, an internally consistent astronomical distance framework has not yet been established. We review current efforts to homogenize the Local Group's distance framework, with particular emphasis on the potential of RR Lyrae stars as distance indicators, and attempt to extend this in an internally consistent manner to cosmological distances. Calibration based on Type Ia supernovae and distance determinations based on gravitational lensing represent particularly promising approaches. We provide a positive outlook to improvements to the status quo expected from future surveys, missions, and facilities. Astronomical distance determination has clearly reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press (chapter 8 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age