Sequences of reflection functors and the preprojective component of a valued quiver

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix

The Auslander-Reiten Components in the Rhombic Picture

For an indecomposable module $M$ over a path algebra of a quiver of type $\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts. We describe how these invariants for $M$ and for its dual specify the position of $M$ in the Auslander-Reiten quiver of the algebra.Comment: 29 pages; 6 figures; references added to Section 1 as per the referee's suggestions; to appear in Communications in Algebr

Visualization of structures and cosmic flows in the Local Universe

A visualization of three-dimensional structures and cosmic flows is presented using information from the Extragalactic Distance Database V8k redshift catalog and peculiar velocities from the Cosmicflows-1 survey. Structures within a volume bounded at 8000 km/s on the cardinal Supergalactic axes are explored in terms of both the display of the positions of the 30124 galaxies of the catalog and its reconstructed luminosity density field, corrected to account for growing incompleteness with distance. Cosmography of the Local Universe is discussed with the intent to identify the most prominent structures, including voids, galaxy clusters, filaments and walls. The mapping also benefits from precise distance measures provided through the Cosmicflows-1 observational program. Three-dimensional visualizations of the coherent flows of galaxies in the nearby universe are presented using recent results obtained on the reconstruction of cosmic flows with the Wiener Filter approach. The three major components of the Milky Way motion, namely the expulsion from the Local Void, the infall toward the Virgo Cluster, and the bulk flow of the historic Local Supercluster toward the Great Attractor are illustrated using different visualization techniques and analyzed in the light of the cosmography derived from the V8k redshift and Cosmicflows-1 distance catalogs.Comment: Advancing the physics of cosmic distances Proceedings IAU Symposium No. 289, 2012 R. de Grijs, G. Bono 2012 International Astronomical Unio

The Meaning of Animals

This research examines the social construction of animals by a rural Allegheny culture using a linguistic approach based on estimating the set of attributes associated with the words they used to describe animals. We asked 268 respondents to free-associate with the nouns, chicken and deer when seen in a context of other words related to nature. Their responses were coded and the frequencies of of words and word groupings were tabulated for sub-samples of differing age, gender and occupation. Response words were categorized into seven typologies including two affective types. The results indicate that except for possibly the very young, the social meanings of chicken and deer did not vary with gender, age or occupation. The respondents interpretation of living chicken was indistinguishable from that of unprepared food. Their interpretation of deer was broader and primarily one of interaction with a lesser adversary

The force, power and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen et al. studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen et al. to model Bolt's velocity time-dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008

Cosmic Bulk Flow and the Local Motion from Cosmicflows-2

Full sky surveys of peculiar velocity are arguably the best way to map the large scale structure out to distances of a few times 100 Mpc/h. Using the largest and most accurate ever catalog of galaxy peculiar velocities "Cosmicflows-2", the large scale structure has been reconstructed by means of the Wiener filter and constrained realizations assuming as a Bayesian prior model the LCDM model with the WMAP inferred cosmological parameters. The present paper focuses on studying the bulk flow of the local flow field, defined as the mean velocity of top-hat spheres with radii ranging out to R=500 Mpc/h. The estimated large scale structures, in general, and the bulk flow, in particular, are determined by the tension between the observational data and the assumed prior model. A prerequisite for such an analysis is the requirement that the estimated bulk flow is consistent with the prior model. Such a consistency is found here. At R=50(150) Mpc/h the estimated bulk velocity is 250+/-21 (239+/-38) km/s. The corresponding cosmic variance at these radii is 126(60)km/s, which implies that these estimated bulk flows are dominated by the data and not by the assumed prior model. The estimated bulk velocity is dominated by the data out to R~200 Mpc/h, where the cosmic variance on the individual Supergalactic Cartesian components (of the r.m.s. values) exceeds the variance of the Constrained Realizations by at least a factor of 2. The supergalactic SGX and SGY components of the CMB dipole velocity are recovered by the Wiener filter velocity field down to a very few km/s. The SGZ component of the estimated velocity, the one that is most affected by the Zone of Avoidance, is off by 126 km/s (an almost 2 sigma discrepancy).Comment: 10 pages, accepted for MNRA

The Mid-Infrared Tully-Fisher Relation: Calibration of the SNIa Scale and Ho

This paper builds on a calibration of the SNIa absolute distance scale begun with a core of distances based on the correlation between galaxy rotation rates and optical Ic band photometry. This new work extends the calibration through the use of mid-infrared photometry acquired at 3.6 microns with Spitzer Space Telescope. The great virtue of the satellite observations is constancy of the photometry at a level better than 1% across the sky. The new calibration is based on 39 individual galaxies and 8 clusters that have been the sites of well observed SNIa. The new 3.6 micron calibration is not yet as extensively based as the Ic band calibration but is already sufficient to justify a preliminary report. Distances based on the mid-infrared photometry are 2% greater in the mean than reported at Ic band. This difference is only marginally significant. The Ic band result is confirmed with only a small adjustment. Incorporating a 1% decrease in the LMC distance, the present study indicates Ho = 75.2 +/- 3.0 km/s/Mpc.Comment: Accepted for publication in The Astrophysical Journal Letters, 6 pages, 2 figure

Goodness-of-fit analysis of the Cosmicflows-2 database of velocities

The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) database of peculiar velocities with the LCDM standard model of cosmology is presented. Standard application of the Chi^2 statistics of the full database, of its 4,838 data points, is hampered by the small scale nonlinear dynamics which is not accounted for by the (linear regime) velocity power spectrum. The bulk velocity constitutes a highly compressed representation of the data which filters out the small scales non-linear modes. Hence the statistics of the bulk flow provides an efficient tool for assessing the GoF of the data given a model. The particular approach introduced here is to use the (spherical top-hat window) bulk velocity extracted from the Wiener filter reconstruction of the 3D velocity field as a linear low pass filtered highly compressed representation of the CF2 data. An ensemble 2250 random linear realizations of the WMAP/LCDM model has been used to calculate the bulk velocity auto-covariance matrix. We find that the CF2 data is consistent with the WMAP/LCDM model to better than the 2 sigma confidence limits. This provides a further validation that the CF2 database is consistent with the standard model of cosmology.Comment: submitted to MNRAS, V2 : solved page sizing proble

The Arrowhead Mini-Supercluster of Galaxies

Superclusters of galaxies can be defined kinematically from local evaluations of the velocity shear tensor. The location where the smallest eigenvalue of the shear is positive and maximal defines the center of a basin of attraction. Velocity and density fields are reconstructed with Wiener Filter techniques. Local velocities due to the density field in a restricted region can be separated from external tidal flows, permitting the identification of boundaries separating inward flows toward a basin of attraction and outward flows. This methodology was used to define the Laniakea Supercluster that includes the Milky Way. Large adjacent structures include Perseus-Pisces, Coma, Hercules, and Shapley but current kinematic data are insufficient to capture their full domains. However there is a small region trapped between Laniakea, Perseus-Pisces, and Coma that is close enough to be reliably characterized and that satisfies the kinematic definition of a supercluster. Because of its shape, it is given the name the Arrowhead Supercluster. This entity does not contain any major clusters. A characteristic dimension is ~25 Mpc and the contained mass is only ~10^15 Msun.Comment: Accepted for publication in The Astrophysical Journal. Video can be viewed at http://irfu.cea.fr/arrowhea