The intrinsic stiffness of human trabecular meshwork cells increases with senescence.

Dysfunction of the human trabecular meshwork (HTM) plays a central role in the age-associated disease glaucoma, a leading cause of irreversible blindness. The etiology remains poorly understood but cellular senescence, increased stiffness of the tissue, and the expression of Wnt antagonists such as secreted frizzled related protein-1 (SFRP1) have been implicated. However, it is not known if senescence is causally linked to either stiffness or SFRP1 expression. In this study, we utilized in vitro HTM senescence to determine the effect on cellular stiffening and SFRP1 expression. Stiffness of cultured cells was measured using atomic force microscopy and the morphology of the cytoskeleton was determined using immunofluorescent analysis. SFRP1 expression was measured using qPCR and immunofluorescent analysis. Senescent cell stiffness increased 1.88±0.14 or 2.57±0.14 fold in the presence or absence of serum, respectively. This was accompanied by increased vimentin expression, stress fiber formation, and SFRP1 expression. In aggregate, these data demonstrate that senescence may be a causal factor in HTM stiffening and elevated SFRP1 expression, and contribute towards disease progression. These findings provide insight into the etiology of glaucoma and, more broadly, suggest a causal link between senescence and altered tissue biomechanics in aging-associated diseases

Stability Analysis of Discrete-Time Linear Complementarity Systems

A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient conditions for Lyapunov stability of a DLCS when using a quadratic Lyapunov function that depends only on the state variables and a quadratic Lyapunov function that depends both on the state and the algebraic variables. The sufficient conditions require checking the feasibility of a copositive program over nonconvex cones. Our results only assume that the LCP is solvable and do not require the solutions to be unique. We devise a novel, exact cutting plane algorithm for the verification of stability and the computation of the Lyapunov functions. To the best of our knowledge, our algorithm is the first exact approach for stability verification of DLCS. A number of numerical examples are presented to illustrate the approach. Though our main object of study in this paper is the DLCS, the proposed algorithm can be readily applied to the stability verification of LCS. In this context, we show the equivalence between the stability of a LCS and the DLCS, resulting from a time-stepping procedure applied to the LCS for all sufficiently small time steps

Mass Calibration of Optically Selected DES Clusters Using a Measurement of CMB-cluster Lensing with SPTpol Data

We use cosmic microwave background (CMB) temperature maps from the 500 deg2 SPTpol survey to measure the stacked lensing convergence of galaxy clusters from the Dark Energy Survey (DES) Year-3 redMaPPer (RM) cluster catalog. The lensing signal is extracted through a modified quadratic estimator designed to be unbiased by the thermal Sunyaev–Zel'dovich (tSZ) effect. The modified estimator uses a tSZ-free map, constructed from the SPTpol 95 and 150 GHz data sets, to estimate the background CMB gradient. For lensing reconstruction, we employ two versions of the RM catalog: a flux-limited sample containing 4003 clusters and a volume-limited sample with 1741 clusters. We detect lensing at a significance of 8.7σ(6.7σ) with the flux (volume)–limited sample. By modeling the reconstructed convergence using the Navarro–Frenk–White profile, we find the average lensing masses to be M_(200 m) = (1.62^(+0.32)_(-0.25) [stat.] ± 0.04 [sys.]) and (1.28^(+0.14)_(-0.18) [stat.] ± 0.03 [sys.] x 10^(14) M⊙ for the volume- and flux-limited samples, respectively. The systematic error budget is much smaller than the statistical uncertainty and is dominated by the uncertainties in the RM cluster centroids. We use the volume-limited sample to calibrate the normalization of the mass-richness scaling relation, and find a result consistent with the galaxy weak-lensing measurements from DES

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules

We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach accuracies on par with density functional theory reference. Locality is exploited within non-linear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9k small organic molecules. Linear scaling of computational cost in system size is demonstrated for saturated polymers with up to sub-mesoscale lengths

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that SL$(n,\mathbb{Z})$ and its congruence subgroups have the $R_\infty$-property. Further we show that any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion free non-elementary hyperbolic group, or SL$(n,\mathbb{Z})$, Sp$(2n,\mathbb{Z})$ or a principal congruence subgroup of SL$(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian manifold of constant negative curvature

Combining Information from Multiple Data Sources to Improve Sampling Efficiency

Many surveys target population subgroups that may not be readily identified in sampling frames. In the case study that motivated this study, the target population was households with children between the ages of 3 and 10 from two areas surrounding Cleveland, Ohio and Dallas, Texas. A standard approach is to sample households from these two areas and then screen for the presence of age-eligible children. Based on the estimated number of age-eligible households in these two areas, this approach would have required completing screening interviews with 5.4 to 5.7 households to find one eligible household. We developed a model-assisted sample design strategy to improve screening efficiency by attaching a measure of eligibility propensity to each household in the population. For this, we used a modeling and imputation strategy that combined information from several data sources: (1) the population of addresses for these two areas with demographic covariates from a commercial vendor, (2) external population data (from the American Community Survey and Census Planning Data) for these two areas, and (3) screening data from a large nationally representative survey. We first tested this sampling strategy in a pilot study and then implemented it in the main study. This strategy required 4.2 to 4.3 completed screeners to identify one eligible household. The proposed approach therefore improved the sampling efficiency by about 25% relative to the standard approach

Detection of CMB-Cluster Lensing using Polarization Data from SPTpol

We report the first detection of gravitational lensing due to galaxy clusters using only the polarization of the cosmic microwave background (CMB). The lensing signal is obtained using a new estimator that extracts the lensing dipole signature from stacked images formed by rotating the cluster-centered Stokes QU map cutouts along the direction of the locally measured background CMB polarization gradient. Using data from the SPTpol 500  deg² survey at the locations of roughly 18 000 clusters with richness λ ≥ 10 from the Dark Energy Survey (DES) Year-3 full galaxy cluster catalog, we detect lensing at 4.8σ. The mean stacked mass of the selected sample is found to be (1.43±0.40)×10¹⁴14M⊙ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data. This measurement is a key first step for cluster cosmology with future low-noise CMB surveys, like CMB-S4, for which CMB polarization will be the primary channel for cluster lensing measurements

Detection of CMB-Cluster Lensing using Polarization Data from SPTpol

We report the first detection of gravitational lensing due to galaxy clusters using only the polarization of the cosmic microwave background (CMB). The lensing signal is obtained using a new estimator that extracts the lensing dipole signature from stacked images formed by rotating the cluster-centered Stokes QU map cutouts along the direction of the locally measured background CMB polarization gradient. Using data from the SPTpol 500  deg² survey at the locations of roughly 18 000 clusters with richness λ ≥ 10 from the Dark Energy Survey (DES) Year-3 full galaxy cluster catalog, we detect lensing at 4.8σ. The mean stacked mass of the selected sample is found to be (1.43±0.40)×10¹⁴14M⊙ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data. This measurement is a key first step for cluster cosmology with future low-noise CMB surveys, like CMB-S4, for which CMB polarization will be the primary channel for cluster lensing measurements

Weighing neutrinos using high redshift galaxy luminosity functions

Laboratory experiments measuring neutrino oscillations, indicate small mass differences between different mass eigenstates of neutrinos. The absolute mass scale is however not determined, with at present the strongest upper limits coming from astronomical observations rather than terrestrial experiments. The presence of massive neutrinos suppresses the growth of perturbations below a characteristic mass scale, thereby leading to a decreased abundance of collapsed dark matter halos. Here we show that this effect can significantly alter the predicted luminosity function (LF) of high redshift galaxies. In particular we demonstrate that a stringent constraint on the neutrino mass can be obtained using the well measured galaxy LF and our semi-analytic structure formation models. Combining the constraints from the Wilkinson Microwave Anisotropy Probe 7 year (WMAP7) data with the LF data at z = 4, we get a limit on the sum of the masses of 3 degenerate neutrinos \Sigma m_\nu < 0.52 eV at the 95 % CL. The additional constraints using the prior on Hubble constant strengthens this limit to \Sigma m_\nu < 0.29 eV at the 95 % CL. This neutrino mass limit is a factor of order 4 improvement compared to the constraint based on the WMAP7 data alone, and as stringent as known limits based on other astronomical observations. As different astronomical measurements may suffer from different set of biases, the method presented here provides a complementary probe of \Sigma m_\nu . We suggest that repeating this exercise on well measured luminosity functions over different redshift ranges can provide independent and tighter constraints on \Sigma m_\nu .Comment: 14 pages, 7 figures, submitted to PR

Constrained semi-analytical models of Galactic outflows

We present semi-analytic models of galactic outflows, constrained by available observations on high redshift star formation and reionization. Galactic outflows are modeled in a manner akin to models of stellar wind blown bubbles. Large scale outflows can generically escape from low mass halos (M<10^9 M_sun) for a wide range of model parameters but not from high mass halos (M> 10^{11} M_sun). The gas phase metallicity of the outflow and within the galaxy are computed. Ionization states of different metal species are calculated and used to examine the detectability of metal lines from the outflows. The global influence of galactic outflows is also investigated. Models with only atomic cooled halos significantly fill the IGM at z~3 with metals (with -2.5>[Z/Z_sun]>-3.7), the actual extent depending on the efficiency of winds, the IMF, the fractional mass that goes through star formation and the reionization history of the universe. In these models, a large fraction of outflows at z~3 are supersonic, hot (T> 10^5 K) and have low density, making metal lines difficult to detect. They may also result in significant perturbations in the IGM gas on scales probed by the Lyman-alpha forest. On the contrary, models including molecular cooled halos with a normal mode of star formation can potentially volume fill the universe at z> 8 without drastic dynamic effects on the IGM, thereby setting up a possible metallicity floor (-4.0<[Z/Z_sun]<-3.6). Interestingly, molecular cooled halos with a ``top-heavy'' mode of star formation are not very successful in establishing the metallicity floor because of the additional radiative feedback, that they induce. (Abridged)Comment: 27 pages, 31 figures, 2 tables, pdflatex. Accepted for publication in MNRA