Clear and Compress: Computing Persistent Homology in Chunks

We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by G\"unther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we improve the performance through parallelized computation.Comment: This result was presented at TopoInVis 2013 (http://www.sci.utah.edu/topoinvis13.html

Polarization of X-ray lines from galaxy clusters and elliptical galaxies - a way to measure tangential component of gas velocity

We study the impact of gas motions on the polarization of bright X-ray emission lines from the hot intercluster medium (ICM). The polarization naturally arises from resonant scattering of emission lines owing to a quadrupole component in the radiation field produced by a centrally peaked gas density distribution. If differential gas motions are present then a photon emitted in one region of the cluster will be scattered in another region only if their relative velocities are small enough and the Doppler shift of the photon energy does not exceed the line width. This affects both the degree and the direction of polarization. The changes in the polarization signal are in particular sensitive to the gas motions perpendicular to the line of sight. We calculate the expected degree of polarization for several patterns of gas motions, including a slow inflow expected in a simple cooling flow model and a fast outflow in an expanding spherical shock wave. In both cases, the effect of non-zero gas velocities is found to be minor. We also calculate the polarization signal for a set of clusters, taken from large-scale structure simulations and evaluate the impact of the gas bulk motions on the polarization signal. We argue that the expected degree of polarization is within reach of the next generation of space X-ray polarimeters.Comment: 25 pages, 18 figures, accepted to MNRA

Assessment and enhancement of MERRA land surface hydrology estimates

The Modern-Era Retrospective Analysis for Research and Applications (MERRA) is a state-of-the-art reanalysis that provides, in addition to atmospheric fields, global estimates of soil moisture, latent heat flux, snow, and runoff for 1979 present. This study introduces a supplemental and improved set of land surface hydrological fields ("MERRA-Land") generated by rerunning a revised version of the land component of the MERRA system. Specifically, the MERRA-Land estimates benefit from corrections to the precipitation forcing with the Global Precipitation Climatology Project pentad product (version 2.1) and from revised parameter values in the rainfall interception model, changes that effectively correct for known limitations in the MERRA surface meteorological forcings. The skill (defined as the correlation coefficient of the anomaly time series) in land surface hydrological fields from MERRA and MERRA-Land is assessed here against observations and compared to the skill of the state-of-the-art ECMWF Re-Analysis-Interim (ERA-I). MERRA-Land and ERA-I root zone soil moisture skills (against in situ observations at 85 U.S. stations) are comparable and significantly greater than that of MERRA. Throughout the Northern Hemisphere, MERRA and MERRA-Land agree reasonably well with in situ snow depth measurements (from 583 stations) and with snow water equivalent from an independent analysis. Runoff skill (against naturalized stream flow observations from 18 U.S. basins) of MERRA and MERRA-Land is typically higher than that of ERA-I. With a few exceptions, the MERRA-Land data appear more accurate than the original MERRA estimates and are thus recommended for those interested in using MERRA output for land surface hydrological studies

From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph $G$ and the dimer model defined on a decorated version \GD of this graph \cite{Fisher}. In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain \GD_1. Our main result consists in explicitly constructing CRSFs of \GD_1 counted by the dimer characteristic polynomial, from CRSFs of $G_1$ where edges are assigned Kenyon's critical weight function \cite{Kenyon3}; thus proving a relation on the level of configurations between two well known 2-dimensional critical models.Comment: 51 pages, 24 figures. To appear, Comm. Math. Phys. Revised version: title has changed. The terminology `correspondence' has been changed to that of `explicit construction' and `mapping

The persistent cosmic web and its filamentary structure I: Theory and implementation

We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and corresponding piece of software allows a genuinely scale free and parameter free identification of the voids, walls, filaments, clusters and their configuration within the cosmic web, directly from the discrete distribution of particles in N-body simulations or galaxies in sparse observational catalogues. To achieve that goal, the method works directly over the Delaunay tessellation of the discrete sample and uses the DTFE density computed at each tracer particle; no further sampling, smoothing or processing of the density field is required. The idea is based on recent advances in distinct sub-domains of computational topology, which allows a rigorous application of topological principles to astrophysical data sets, taking into account uncertainties and Poisson noise. Practically, the user can define a given persistence level in terms of robustness with respect to noise (defined as a "number of sigmas") and the algorithm returns the structures with the corresponding significance as sets of critical points, lines, surfaces and volumes corresponding to the clusters, filaments, walls and voids; filaments, connected at cluster nodes, crawling along the edges of walls bounding the voids. The method is also interesting as it allows for a robust quantification of the topological properties of a discrete distribution in terms of Betti numbers or Euler characteristics, without having to resort to smoothing or having to define a particular scale. In this paper, we introduce the necessary mathematical background and describe the method and implementation, while we address the application to 3D simulated and observed data sets to the companion paper.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material. Submitted to MNRA

Determinant of Laplacians on Heisenberg Manifolds

We give an integral representaion of the zeta-reguralized determinant of Laplacians on three dimensional Heisenberg manifolds, and study a behaivior of the values when we deform the uniform discrete subgroups. Heiseberg manifolds are the total space of a fiber bundle with a torus as the base space and a circle as a typical fiber, then the deformation of the uniform discrete subgroups means that the "radius" of the fiber goes to zero. We explain the lines of the calculations precisely for three dimensional cases and state the corresponding results for five dimensional Heisenberg manifolds. We see that the values themselves are of the product form with a factor which is that of the flat torus. So in the last half of this paper we derive general formulas of the zeta-regularized determinant for product type manifolds of two Riemannian manifolds, discuss the formulas for flat tori and explain a relation of the formula for the two dimensional flat torus and Kronecker's second limit formula.Comment: 42 pages, no figure

The diverse hot gas content and dynamics of optically similar low-mass elliptical galaxies

The presence of hot X-ray emitting gas is ubiquitous in massive early-type galaxies. However, much less is known about the content and physical status of the hot X-ray gas in low-mass ellipticals. In the present paper we study the X-ray gas content of four low-mass elliptical galaxies using archival Chandra X-ray observations. The sample galaxies, NGC821, NGC3379, NGC4278, and NGC4697, have approximately identical K-band luminosities, and hence stellar masses, yet their X-ray appearance is strikingly different. We conclude that the unresolved emission in NGC821 and NGC3379 is built up from a multitude of faint compact objects, such as coronally active binaries and cataclysmic variables. Despite the non-detection of X-ray gas, these galaxies may host low density, and hence low luminosity, X-ray gas components, which undergo a Type Ia supernova (SN Ia) driven outflow. We detect hot X-ray gas with a temperature of kT ~ 0.35 keV in NGC4278, the component of which has a steeper surface brightness distribution than the stellar light. Within the central 50 arcsec (~3.9 kpc) the estimated gas mass is ~3 x 10^7 M_sun, implying a gas mass fraction of ~0.06%. We demonstrate that the X-ray gas exhibits a bipolar morphology in the northeast-southwest direction, indicating that it may be outflowing from the galaxy. The mass and energy budget of the outflow can be maintained by evolved stars and SNe Ia, respectively. The X-ray gas in NGC4697 has an average temperature of kT ~ 0.3 keV, and a significantly broader distribution than the stellar light. The total gas mass within 90 arcsec (~5.1 kpc) is ~2.1 x 10^8 M_sun, hence the gas mass fraction is ~0.4%. Based on the distribution and physical parameters of the X-ray gas, we conclude that it is most likely in hydrostatic equilibrium, although a subsonic outflow may be present.Comment: 14 pages, 8 figures, 3 tables, accepted for publication in Ap

Metal transport by gas sloshing in M87

We present the results of an XMM-Newton mosaic covering the central ~200 kpc of the nearby Virgo cluster. We focus on a strong surface brightness discontinuity in the outskirts of the brightest cluster galaxy, M87. Using both XMM-Newton and Suzaku, we derive accurate temperature and metallicity profiles across this feature and show that it is a cold front probably due to sloshing of the Virgo ICM. It is also associated with a discontinuity in the chemical composition. The gas in the inner, bright region of the front is ~40% more abundant in Fe than the gas outside the front, suggesting the important role of sloshing in transporting metals through the ICM. For the first time, we provide a quantitative estimate of the mass of Fe transported by a cold front. This amounts to ~6% of the total Fe mass within the radial range affected by sloshing, significantly more than the amount of metals transported by the AGN in the same cluster core. The very low Fe abundance of only ~0.2 solar immediately outside the cold front at a radius of 90 kpc suggests we are witnessing first-hand the transport of higher metallicity gas into a pristine region, whose abundance is typical of the cluster outskirts. The Mg/Fe and O/Fe abundance ratios remain approximately constant over the entire radial range between the centre of M87 and the faint side of the cold front, which requires the presence of a centrally peaked distribution not only for Fe but also for core-collapse type supernova products. This peak may stem from the star formation triggered as the BCG assembled during the protocluster phase.Comment: accepted for publication in MNRA

An Inversion Disrupting FAM134B Is Associated with Sensory Neuropathy in the Border Collie Dog Breed

Sensory neuropathy in the Border Collie is a severe neurological disorder caused by the degeneration of sensory and, to a lesser extent, motor nerve cells with clinical signs starting between 2 and 7 months of age. Using a genome-wide association study approach with three cases and 170 breed matched controls, a suggestive locus for sensory neuropathy was identified that was followed up using a genome sequencing approach. An inversion disrupting the candidate gene FAM134B was identified. Genotyping of additional cases and controls and RNAseq analysis provided strong evidence that the inversion is causal. Evidence of cryptic splicing resulting in novel exon transcription for FAM134B was identified by RNAseq experiments. This investigation demonstrates the identification of a novel sensory neuropathy associated mutation, by mapping using a minimal set of cases and subsequent genome sequencing. Through mutation screening, it should be possible to reduce the frequency of or completely eliminate this debilitating condition from the Border Collie breed population

Confined two-dimensional fermions at finite density

We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.Comment: 15 pages, LaTe