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Magnetic resonance plays an important role in today's science, engineering, and medical diagnostics. Learning and teaching magnetic resonance is challenging since it requires advanced knowledge of condensed matter physics and quantum mechanics. Driven by the need to popularize this technologically impactful phenomenon, we develop an inexpensive table-top demonstration experiment. It unveils the magnetic resonance of a hand-held compass in the magnetic fields of a permanent magnet. The setup provides an immediate visualization of the underlying physical concepts and allows for their translation to broad student audiences.

Domain specific accelerators present new challenges and opportunities for code generation onto novel instruction sets, communication fabrics, and memory architectures. In this paper we introduce an intermediate representation (IR) which enables both deep learning computational kernels and hardware capabilities to be described in the same IR. We then formulate and apply instruction mapping to determine the possible ways a computation can be performed on a hardware system. Next, our scheduler chooses a specific mapping and determines the data movement and computation order. In order to manage the large search space of mappings and schedules, we developed a flexible framework that allows heuristics, cost models, and potentially machine learning to facilitate this search problem. With this system, we demonstrate the automated extraction of matrix multiplication kernels out of recent deep learning kernels such as depthwise-separable convolution. In addition, we demonstrate two to five times better performance on DeepBench sized GEMMs and GRU RNN execution when compared to state-of-the-art (SOTA) implementations on new hardware and up to 85% of the performance for SOTA implementations on existing hardware.

Magnetic resonance imaging is capable of producing volumetric images without ionizing radiation. Nonetheless, long acquisitions lead to prohibitively long exams. Compressed sensing (CS) can enable faster scanning via sub-sampling with reduced artifacts. However, CS requires significantly higher reconstruction computation, limiting current clinical applications to 2D/3D or limited-resolution dynamic imaging. Here we analyze the practical limitations to T2 Shuffling, a four-dimensional CS-based acquisition, which provides sharp 3D-isotropic-resolution and multi-contrast images in a single scan. Our improvements to the pipeline on a single machine provide a 3x overall reconstruction speedup, which allowed us to add algorithmic changes improving image quality. Using four machines, we achieved additional 2.1x improvement through distributed parallelization. Our solution reduced the reconstruction time in the hospital to 90 seconds on a 4-node cluster, enabling its use clinically. To understand the implications of scaling this application, we simulated running our reconstructions with a multiple scanner setup typical in hospitals.

Most STEM students experience the introductory physics sequence in large-enrollment (N $\gtrsim$ 100 students) classrooms, led by one lecturer and supported by a few teaching assistants. This work describes methods and principles we used to create an effective "flipped classroom" in large- enrollment introductory physics courses by replacing a majority of traditional lecture time with in-class student-driven activity worksheets. In this work, we compare student learning in courses taught by the authors with the flipped classroom pedagogy versus a more traditional pedagogy. By comparing identical questions on exams, we find significant learning gains for students in the student-centered flipped classroom compared to students in the lecturer-centered traditional classroom. Furthermore, we find that the gender gap typically seen in the introductory physics sequence is significantly reduced in the flipped classroom., Comment: 12 pages, 3 figures

Querying the content of images, video, and other non-textual data sources requires expensive content extraction methods. Modern extraction techniques are based on deep convolutional neural networks (CNNs) and can classify objects within images with astounding accuracy. Unfortunately, these methods are slow: processing a single image can take about 10 milliseconds on modern GPU-based hardware. As massive video libraries become ubiquitous, running a content-based query over millions of video frames is prohibitive. One promising approach to reduce the runtime cost of queries of visual content is to use a hierarchical model, such as a cascade, where simple cases are handled by an inexpensive classifier. Prior work has sought to design cascades that optimize the computational cost of inference by, for example, using smaller CNNs. However, we observe that there are critical factors besides the inference time that dramatically impact the overall query time. Notably, by treating the physical representation of the input image as part of our query optimization---that is, by including image transforms, such as resolution scaling or color-depth reduction, within the cascade---we can optimize data handling costs and enable drastically more efficient classifier cascades. In this paper, we propose Tahoma, which generates and evaluates many potential classifier cascades that jointly optimize the CNN architecture and input data representation. Our experiments on a subset of ImageNet show that Tahoma's input transformations speed up cascades by up to 35 times. We also find up to a 98x speedup over the ResNet50 classifier with no loss in accuracy, and a 280x speedup if some accuracy is sacrificed., Comment: Camera-ready version of the paper submitted to ICDE 2019, In Proceedings of the 35th IEEE International Conference on Data Engineering (ICDE 2019)

We summarize and reanalyze observations bearing upon missing galactic baryons, where we propose a consistent picture for halo gas in L >~ L* galaxies. The hot X-ray emitting halos are detected to 50-70 kpc, where typically, M_hot(<50 kpc) ~ 5E9 Msun, and with density n \propto r^-3/2. When extrapolated to R200, the gas mass is comparable to the stellar mass, but about half of the baryons are still missing from the hot phase. If extrapolated to 1.9-3 R200, the baryon to dark matter ratio approaches the cosmic value. Significantly flatter density profiles are unlikely for R < 50 kpc and they are disfavored but not ruled out for R > 50 kpc. For the Milky Way, the hot halo metallicity lies in the range 0.3-1 solar for R < 50 kpc. Planck measurements of the thermal Sunyaev-Zeldovich effect toward stacked luminous galaxies (primarily early-type) indicate that most of their baryons are hot, near the virial temperature, and extend beyond R200. This stacked SZ signal is nearly an order of magnitude larger than that inferred from the X-ray observations of individual (mostly spiral) galaxies with M_* > 10^11.3 Msun. This difference suggests that the hot halo properties are distinct for early and late type galaxies, possibly due to different evolutionary histories. For the cooler gas detected in UV absorption line studies, we argue that there are two absorption populations: extended halos; and disks extending to ~50 kpc, containing most of this gas, and with masses a few times lower than the stellar masses. Such extended disks are also seen in 21 cm HI observations and in simulations., Comment: 22 pages, 20 figures, 2 tables, submitted to ApJ

The baryon content around local galaxies is observed to be much less than is needed in Big Bang nucleosynthesis. Simulations indicate that a significant fraction of these "missing baryons" may be stored in a hot tenuous circum-galactic medium (CGM) around massive galaxies extending to or even beyond the virial radius of their dark matter halos. Previous observations in X-ray and Sunyaev-Zel'dovich (SZ) signal claimed that $\sim(1-50)\%$ of the expected baryons are stored in a hot CGM within the virial radius. The large scatter is mainly caused by the very uncertain extrapolation of the hot gas density profile based on the detection in a small radial range (typically within 10\%-20\% of the virial radius). Here we report stacking X-ray observations of six local isolated massive spiral galaxies from the CGM-MASS sample. We find that the mean density profile can be characterized by a single power law out to a galactocentric radius of $\approx 200\rm~kpc$ (or $\approx130\rm~kpc$ above the 1~$\sigma$ background uncertainty), about half the virial radius of the dark matter halo. We can now estimate that the hot CGM within the virial radius accounts for $(8\pm4)\%$ of the baryonic mass expected for the halos. Including the stars, the baryon fraction is $(27\pm16)\%$, or $(39\pm20)\%$ by assuming a flattened density profile at $r\gtrsim130\rm~kpc$. We conclude that the hot baryons within the virial radius of massive galaxy halos are insufficient to explain the "missing baryons"., Comment: 7 pages, 4 figures, 1 table, accepted for publication by ApJL

We present new HST-COS G130M spectroscopy for a sightline toward a filament projected 1.9 kpc from the nucleus of M87. The combination of the sensitivity of COS and the proximity of M87 allows us to study the structure of this filament in unparalleled detail. We propose that the filament is composed of many cold clumps, each surrounded by an FUV-emitting boundary layer, with the filament having a radius $r_c \sim 10$ pc and the clumps filling the cylinder with a low volume filling factor. The observed velocity dispersion in emission lines from the filament results from the random motions of these clumps within the filament. We measure fluxes and kinematics for emission lines of Ly$\alpha$, C II $\lambda$1335, and N V $\lambda1238$. We associate these three lines, as well as archival measurements of H$\alpha$, C IV $\lambda$1549, and He II $\lambda$1640, with a multitemperature boundary layer around clumps which are moving with supersonic random motions in the filament. This boundary layer is a significant coolant of the hot gas. We show that the [C II] $\lambda$158$\mu$m flux observed by Herschel-PACS from this region implies the existence of a massive cold ($T \sim 10^3$ K) component in the filament which contains significantly more mass than the FUV-emitting boundary layer. We also detect [Fe XXI] $\lambda$1354 in emission at $4-5\sigma$. This line is emitted from 1 keV ($T \approx 10^7$ K) plasma, and we use it to measure the bulk radial velocity and velocity dispersion of the plasma at this temperature. In contrast to the intermediate-temperature FUV lines, [\ion{Fe}{xxi}] is blueshifted relative to M87 and matches the bulk velocity of a nearby filament to the south. We hypothesize that this line arises from the approaching face of the radio bubble expanding through this sightline, while the filament lies on the receding side of the bubble. (abstract is abridged), Comment: 27 pages, 20 figures, accepted for publication in A&A

Double-lobed radio galaxies (DLRGs) often have radio lobes which subtend an angle of less than 180 degrees, and these bent DLRGs have been shown to associate preferentially with galaxy clusters and groups. In this study, we utilize a catalog of DLRGs in SDSS quasars with radio lobes visible in VLA FIRST 20 cm radio data. We cross-match this catalog against three catalogs of galaxies over the redshift range $0 < z < 0.70$, obtaining 81 tentative matches. We visually examine each match and apply a number of selection criteria, eventually obtaining a sample of 44 securely detected DLRGs which are paired to a nearby massive galaxy, galaxy group, or galaxy cluster. Most of the DLRGs identified in this manner are not central galaxies in the systems to which they are matched. Using this sample, we quantify the projected density of these matches as a function of projected separation from the central galaxy, finding a very steep decrease in matches as the impact parameter increases (for $\Sigma \propto b^{-m}$ we find $m = 2.5^{+0.4}_{-0.3}$) out to $b \sim 2$ Mpc. In addition, we show that the fraction of DLRGs with bent lobes also decreases with radius, so that if we exclude DLRGs associated with the central galaxy in the system the bent fraction is 78\% within 1 Mpc and 56\% within 2 Mpc, compared to just 29\% in the field; these differences are significant at $3.6\sigma$ and $2.8\sigma$ respectively. This behavior is consistent with ram pressure being the mechanism that causes the lobes to bend., Comment: accepted to AJ

We present the analysis of the XMM-Newton data of the Circum-Galactic Medium of MASsive Spirals (CGM-MASS) sample of six extremely massive spiral galaxies in the local Universe. All the CGM-MASS galaxies have diffuse X-ray emission from hot gas detected above the background extending $\sim(30-100)\rm~kpc$ from the galactic center. This doubles the existing detection of such extended hot CGM around massive spiral galaxies. The radial soft X-ray intensity profile of hot gas can be fitted with a $\beta$-function with the slope typically in the range of $\beta=0.35-0.55$. This range, as well as those $\beta$ values measured for other massive spiral galaxies, including the Milky Way (MW), are in general consistent with X-ray luminous elliptical galaxies of similar hot gas luminosity and temperature, and with those predicted from a hydrostatic isothermal gaseous halo. Hot gas in such massive spiral galaxy tends to have temperature comparable to its virial value, indicating the importance of gravitational heating. This is in contrast to lower mass galaxies where hot gas temperature tends to be systematically higher than the virial one. The ratio of the radiative cooling to free fall timescales of hot gas is much larger than the critical value of $\sim10$ throughout the entire halos of all the CGM-MASS galaxies, indicating the inefficiency of gas cooling and precipitation in the CGM. The hot CGM in these massive spiral galaxies is thus most likely in a hydrostatic state, with the feedback material mixed with the CGM, instead of escaping out of the halo or falling back to the disk. We also homogenize and compare the halo X-ray luminosity measured for the CGM-MASS galaxies and other galaxy samples and discuss the "missing" galactic feedback detected in these massive spiral galaxies., Comment: 25 pages, 17 figures, 8 tables, accepted for publication by ApJS

We introduce a new perspective on the classical Nirenberg problem of understanding the possible Gauss curvatures of metrics on $S^{2}$ conformal to the round metric. A key tool is to employ the smooth Cheeger-Gromov compactness theorem to obtain general and essentially sharp a priori estimates for Gauss curvatures $K$ contained in naturally defined stable regions. We prove that in such stable regions, the map $u \rightarrow K_{g}$, $g = e^{2u}g_{+1}$ is a proper Fredholm map with well-defined degree on each component. This leads to a number of new existence and non-existence results. We also present a new proof and generalization of the Moser theorem on Gauss curvatures of even conformal metrics on $S^{2}$. In contrast to previous work, the work here does not use any of the Sobolev-type inequalities of Trudinger-Moser-Aubin-Onofri., Comment: Final version, to appear in Comm. Math. Helv, 44 pages

We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in $\mathbb R^{3}$. The regularization is geometric, and has a natural variational interpretation., Comment: 9 pages

Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined by natural geometric conditions on the boundary data of $(\bar B, g)$. We prove the validity of the second statement, i.e.~such mass-minimizers, if they exist, are indeed AF solutions of the static vacuum equations. On the other hand, we prove that the first statement is not true in general; there is a rather large class of bodies $(\bar B, g)$ for which a minimal mass extension does not exist., Comment: 38 pages, 4 figures

The scale of functional magnetic resonance image data is rapidly increasing as large multi-subject datasets are becoming widely available and high-resolution scanners are adopted. The inherent low-dimensionality of the information in this data has led neuroscientists to consider factor analysis methods to extract and analyze the underlying brain activity. In this work, we consider two recent multi-subject factor analysis methods: the Shared Response Model and Hierarchical Topographic Factor Analysis. We perform analytical, algorithmic, and code optimization to enable multi-node parallel implementations to scale. Single-node improvements result in 99x and 1812x speedups on these two methods, and enables the processing of larger datasets. Our distributed implementations show strong scaling of 3.3x and 5.5x respectively with 20 nodes on real datasets. We also demonstrate weak scaling on a synthetic dataset with 1024 subjects, on up to 1024 nodes and 32,768 cores.

The Circum-Galactic Medium of MASsive Spirals (CGM-MASS) is a project studying the overall content, physical and chemical properties, and spatial distributions of the multi-phase circum-galactic medium (CGM) around a small sample of the most massive isolated spiral galaxies in the local Universe. We introduce the sample and present a detailed case study of the XMM-Newton observation of the hot gas halo of NGC5908. After data calibration, point source removal, and background analysis, we find that the diffuse soft X-ray emission of NGC5908 is significantly more extended than the stellar light in the vertical direction. The 0.5-1.25keV radial intensity profile tracing hot gas emission can be detected above the background out to about $2^\prime$, or $30\rm~kpc$ from the nucleus. The unresolved soft X-ray emission can be characterized with a $\beta$-model with a slope of $\beta\approx0.68$. The unresolved 0.5-2keV luminosity within $1^\prime$ is $6.8\times10^{39}\rm~ergs~s^{-1}$, but young stellar sources may contribute significantly to it. Assuming a metallicity of 0.2solar, an upper limit (without subtracting the very uncertain young stellar contribution) to the mass of hot gas within this radius is $2.3\times10^9\rm~M_\odot$. The cooling radius is $r_{\rm cool}\approx25\rm~kpc$ or $\approx0.06r_{\rm 200}$, within which the hot gas could cool radiatively in less than 10Gyr, and the cooling of hot gas could significantly contribute in replenishing the gas consumed in star formation. The hot gas accounts for $\approx1.9\%$ of the baryon detected within the cooling radius. By comparing NGC5908 to other galaxies, we find that its X-ray luminosity per stellar mass is consistent with lower-mass non-starburst field spiral galaxies. However, a large scatter in hot gas soft X-ray emissivity is indicated for spiral galaxies with $M_*\gtrsim2\times10^{11}\rm~M_\odot$., Comment: 14 pages, 8 figures, 2 tables, accepted for publication in the The Astrophysical Journal

Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each edge relates to that of neighboring cells. On the other hand, we can simplify data structures and algorithms if we can a priori orient coordinate systems in such a way that the coordinate systems on the edges follows uniquely from those on the cells \textit{by rule}. Such rules require that \textit{every} unstructured mesh allows assigning directions to edges that satisfy the convention in adjacent cells. We show that the convention chosen for unstructured quadrilateral meshes in the \texttt{deal.II} library always allows to orient meshes. It can therefore be used to make codes simpler, faster, and less bug prone. We present an algorithm that orients meshes in $O(N)$ operations. We then show that consistent orientations are not always possible for 3d hexahedral meshes. Thus, cells generally need to store the direction of adjacent edges, but our approach also allows the characterization of cases where this is not necessary. The 3d extension of our algorithm either orients edges consistently, or aborts, both within $O(N)$ steps.

We propose BlackOut, an approximation algorithm to efficiently train massive recurrent neural network language models (RNNLMs) with million word vocabularies. BlackOut is motivated by using a discriminative loss, and we describe a new sampling strategy which significantly reduces computation while improving stability, sample efficiency, and rate of convergence. One way to understand BlackOut is to view it as an extension of the DropOut strategy to the output layer, wherein we use a discriminative training loss and a weighted sampling scheme. We also establish close connections between BlackOut, importance sampling, and noise contrastive estimation (NCE). Our experiments, on the recently released one billion word language modeling benchmark, demonstrate scalability and accuracy of BlackOut; we outperform the state-of-the art, and achieve the lowest perplexity scores on this dataset. Moreover, unlike other established methods which typically require GPUs or CPU clusters, we show that a carefully implemented version of BlackOut requires only 1-10 days on a single machine to train a RNNLM with a million word vocabulary and billions of parameters on one billion words. Although we describe BlackOut in the context of RNNLM training, it can be used to any networks with large softmax output layers., Comment: Published as a conference paper at ICLR 2016

False discovery rate (FDR) procedures provide misleading inference when testing multiple null hypotheses with heterogeneous multinomial data. For example, in the motivating study the goal is to identify species of bacteria near the roots of wheat plants (rhizobacteria) that are associated with productivity, but standard procedures discover the most abundant species even when the association is weak or negligible, and fail to discover strong associations when species are not abundant. Consequently, a list of abundant species is produced by the multiple testing procedure even though the goal was to provide a list of producitivity-associated species. This paper provides an FDR method based on a mixture of multinomial distributions and shows that it tends to discover more non-negligible effects and fewer negligible effects when the data are heterogeneous across tests. The proposed method and competing methods are applied to the motivating data. The new method identifies more species that are strongly associated with productivity and identifies fewer species that are weakly associated with productivity.

We use weak gravitational lensing to measure mean mass profiles around Locally Brightest Galaxies (LBGs). These are selected from the SDSS/DR7 spectroscopic and photometric catalogues to be brighter than any neighbour projected within 1.0 Mpc and differing in redshift by $<1000$ km/s. Most ($> 83\%$) are expected to be the central galaxies of their dark matter halos. Previous stacking analyses have used this LBG sample to measure mean Sunyaev-Zeldovich flux and mean X-ray luminosity as a function of LBG stellar mass. In both cases, a simulation of the formation of the galaxy population was used to estimate effective halo mass for LBGs of given stellar mass, allowing the derivation of scaling relations between the gas properties of halos and their mass. By comparing results from a variety of simulations to our lensing data, we show that this procedure has significant model dependence reflecting: (i) the failure of any given simulation to reproduce observed galaxy abundances exactly; (ii) a dependence on the cosmology underlying the simulation; and (iii) a dependence on the details of how galaxies populate halos. We use our lensing results to recalibrate the scaling relations, eliminating most of this model dependence and explicitly accounting both for residual modelling uncertainties and for observational uncertainties in the lensing results. The resulting scaling relations link the mean gas properties of dark halos to their mass over an unprecedentedly wide range, $10^{12.5}

We examine 11 XMM-Newton observations of the giant spiral galaxy NGC 1961, allowing us to study the hot gaseous halo of a spiral galaxy in unprecedented detail. We perform a spatial and a spectral analysis; with the former, the hot halo is detected to at least 80 kpc and with the latter its properties can be measured in detail up to 42 kpc. We find evidence for a negative gradient in the temperature profile as is common for elliptical galaxies. We measure a rough metallicity profile, which is consistent with being flat at $Z \sim 0.2 Z_{\odot}$. Converting to this metallicity, the deprojected density profile is consistent with previous parametric fits, with no evidence for a break within 42 kpc ($\sim$0.1R$_{\text{vir}}$). Extrapolating to the virial radius, we infer a hot halo mass comparable to the stellar mass of the galaxy, and a baryon fraction from the stars and hot gas of around 30%. The cooling time of the hot gas is orders of magnitude longer than the dynamical time, making the hot halo stable against cooling instabilities, and we argue that an extended stream of neutral Hydrogen seen to the NW of this galaxy is instead likely due to accretion from the intergalactic medium. The low metallicity of the hot halo suggests it too was likely accreted. We compare the hot halo of NGC 1961 to hot halos around isolated elliptical galaxies, and show that the total mass determines the hot halo properties better than the stellar mass., Comment: accepted to MNRAS

We prove that given any smooth metric $\gamma$ and smooth positive function $H$ on $S^{2}$, there is a constant $\lambda > 0$, depending on $(\gamma, H)$, and an asymptotically flat solution $(M, g, u)$ of the static vacuum Einstein equations on $M = {\mathbb R}^{3} \setminus B^{3}$, such that the induced metric and mean curvature of $(M, g, u)$ at $\partial M$ are given by $(\gamma, \lambda H)$. This gives a partial resolution of a conjecture of Bartnik., Comment: Substantial simplification of proof of main theorem. To appear in Class. Quantum Gravity

Non-thermal pressure from turbulence and bulk flows is a fundamental ingredient in hot gaseous halos, and in the intracluster medium it will be measured through emission line kinematics with calorimeters on future X-ray spacecraft. In this paper we present a complementary method for measuring these effects, using forbidden FUV emission lines of highly ionized Iron which trace $10^7$ K gas. The brightest of these is [Fe XXI] $\lambda$1354.1. We search for these lines in archival HST-COS spectra from the well-known elliptical galaxies M87 and NGC4696, which harbor large reservoirs of $10^7$ K gas. We report a 2.2$\sigma$ feature which we attribute to [Fe XXI] from a filament in M87, and positive residuals in the nuclei of M87 and NGC4696, for which the 90\% upper limits on the line flux are close to the predicted fluxes based on X-ray observations. In a newer reduction of the data from the Hubble Spectroscopic Legacy Archive, these limits become tighter and the [Fe XXI] feature reaches a formal significance of 5.3$\sigma$, neglecting uncertainty in fitting the continuum. Using our constraints, we perform emission measure analysis, constraining the characteristic path length and column density of the $\sim10^7$ K gas. We also examine several sightlines towards filaments or cooling flows in other galaxy clusters, for which the fraction of gas at $10^7$ K is unknown, and place upper limits on its emission measure in each case. A medium-resolution HST-COS observation of the M87 filament for $\sim$10 orbits would confirm our detection of [Fe XXI] and measure its width., Comment: accepted to MNRAS

We examine a sample of $\sim 250 000$ "locally brightest galaxies" selected from the Sloan Digital Sky Survey to be central galaxies within their dark matter halos. These were previously stacked by the Planck Collaboration to measure the Sunyaev-Zel'dovich signal as a function of central galaxy stellar mass. Here, we stack the X-ray emission from these halos using data from the ROSAT All-Sky Survey. We detect emission across almost our entire sample, including emission which we attribute to hot gas around galaxies spanning a range of 1.2 dex in stellar mass (corresponding to nearly two orders of magnitude in halo mass) down to $M* = 10^{10.8} M_{\odot}$ ($M_{500} \approx 10^{12.6} M_{\odot}$). Over this range, the X-ray luminosity can be fit by a power-law, either of stellar mass or of halo mass. A single unified scaling relation between mass and $L_X$ applies for galaxies, groups, and clusters. This relation has a steeper slope than expected for self-similarity, in contrast to the $Y_{SZ}$-$M_{500}$ relation, showing the importance of non-gravitational heating. If this heating is predominantly due to AGN feedback, the lack of a break in our relation suggests that AGN feedback is tightly self-regulated and fairly gentle, in agreement with recent high-resolution simulations. Our results are consistent with earlier measurements of the $L_X$-$L_K$ relation for elliptical galaxies and of the $L_X$-$M_{500}$ relation for optically-selected galaxy clusters. However, our $L_X$-$M_{500}$ relation lies more than a factor of two below most previous relations based on X-ray-selected cluster samples. We argue that optical selection offers a less biased view of the $L_X$-$M_{500}$ relation., Comment: 23 pages, 11 figures, accepted to MNRAS

We conduct a comprehensive search for X-ray emission lines from sterile neutrino dark matter, motivated by recent claims of unidentified emission lines in the stacked X-ray spectra of galaxy clusters and the centers of the Milky Way and M31. Since the claimed emission lines lie around 3.5 keV, we focus on galaxies and galaxy groups (masking the central regions), since these objects emit very little radiation above $\sim 2$ keV and offer a clean background against which to detect emission lines. We develop a formalism for maximizing the signal-to-noise of decaying dark matter emission lines by weighing each X-ray event according to the expected dark matter profile. In total, we examine 81 and 89 galaxies with Chandra and XMM-Newton respectively, totaling 15.0 and 14.6 Ms of integration time. We find no significant evidence of any emission lines, placing strong constraints on the mixing angle of sterile neutrinos with masses between 4.8-12.4 keV. In particular, if the 3.57 keV feature from Bulbul et al. (2014) were due to 7.1 keV sterile neutrino emission, we would have detected it at $4.4\sigma$ and $11.8\sigma$ in our two samples. The most conservative estimates of the systematic uncertainties reduce these constraints to $4.4\sigma$ and 7.8$\sigma$, or letting the line energy vary between 3.50 and 3.60 keV reduces these constraints to $2.7\sigma$ and $11.0\sigma$ respectively. Unlike previous constraints, our measurements do not depend on the model of the X-ray background or on the assumed logarithmic slope of the center of the dark matter profile., Comment: accepted to MNRAS

We prove that compact 3-manifolds $M$ of constant curvature +1 with boundary a minimal surface are locally naturally parametrized by the conformal class of the boundary metric $\gamma$ in the Teichmuller space of $\partial M$, when $genus(\partial M) \geq 2$. Stronger results are obtained in the case of genus 1 boundary, giving in particular a new proof of Brendle's solution of the Lawson conjecture. The results generalize to constant mean curvature surfaces, and surfaces in flat and hyperbolic 3-manifolds., Comment: withdrawn for reconstruction. Error in the "stability argument" on p.22