Lossy gossip and composition of metrics

We study the monoid generated by n-by-n distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and we compute the structure of this fan for n up to 5. The monoid captures gossip among n gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid, as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new.Comment: Minor textual edits, final versio

GALAXY DYNAMICS IN CLUSTERS

We use high resolution simulations to study the formation and distribution of galaxies within a cluster which forms hierarchically. We follow both dark matter and baryonic gas which is subject to thermal pressure, shocks and radiative cooling. Galaxy formation is identified with the dissipative collapse of the gas into cold, compact knots. We examine two extreme representations of galaxies during subsequent cluster evolution --- one purely gaseous and the other purely stellar. The results are quite sensitive to this choice. Gas-galaxies merge efficiently with a dominant central object while star-galaxies merge less frequently. Thus, simulations in which galaxies remain gaseous appear to suffer an ``overmerging'' problem, but this problem is much less severe if the gas is allowed to turn into stars. We compare the kinematics of the galaxy population in these two representations to that of dark halos and of the underlying dark matter distribution. Galaxies in the stellar representation are positively biased (\ie over-represented in the cluster) both by number and by mass fraction. Both representations predict the galaxies to be more centrally concentrated than the dark matter, whereas the dark halo population is more extended. A modest velocity bias also exists in both representations, with the largest effect, $\sigma_{gal}/\sigma_{DM} \simeq 0.7$, found for the more massive star-galaxies. Phase diagrams show that the galaxy population has a substantial net inflow in the gas representation, while in the stellar case it is roughly in hydrostatic equilibrium. Virial mass estimators can underestimate the true cluster mass by up to a factor of 5. The discrepancy is largest if only the most massive galaxies are used, reflecting significant mass segregation.Comment: 30 pages, self-unpacking (via uufiles) postscript file without figures. Eighteen figures (and slick color version of figure 3) and entire paper available at ftp://oahu.physics.lsa.umich.edu/groups/astro/fews Total size of paper with figures is ~9.0 Mb uncompressed. Submitted to Ap.J

Dominating Sets for Convex Functions with some Applications

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the fields of Linear Regression and Location

Dominating Sets for Convex Functions with some Applications

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity.In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems.The applicability of the results obtained is illustrated with the statement of new localization results in the fields of Linear Regression and Location.location;convexity;regression;dominating set

Endogenous glutathione levels modulate the frequency of both spontaneous and long wavelength ultraviolet induced mutations in human cells

Spontaneous and induced mutations at the hypoxanthine guanine phosphoribosyt transferase locus have been measured in cultured human lymphoblastoid (TK6) cell populations under conditions in which cellular glutathione has been severely depleted by overnight treatment with buthionine-S,R-sulfoximine. At maximum levels of glutathione depletion, the increase in spontaneous frequency is at least 5-fold, a finding consistent with the possibility that cellular redox state can modulate the levels of pre-mutagenic damage arising as a result of normal metabolism in cultured human cells. Glutathione depletion does not lead to a significant enhancement in the frequency of mutants that arise as a result of irradiation at 313 run but does lead to a 3-fold increase in mutations resulting from irradiation at 365 nm. These results indicate that glutathione may quench reactive intermediates that would otherwise lead to spontaneous mutations as well as a fraction of UVA radiation-induced premutagenic damag

The Mass Profile and Accretion History of Cold Dark Matter Halos

We use the Millennium Simulation series to study the relation between the accretion history (MAH) and mass profile of cold dark matter halos. We find that the mean density within the scale radius, r_{-2} (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the main progenitor's virial mass equals the mass enclosed within r_{-2}. Scaled to these characteristic values of mass and density, the mean MAH, expressed in terms of the critical density of the Universe, M(\rho_{crit}(z)), resembles that of the enclosed density profile, M(), at z=0. Both follow closely the NFW profile, suggesting that the similarity of halo mass profiles originates from the mass-independence of halo MAHs. Support for this interpretation is provided by outlier halos whose accretion histories deviate from the NFW shape; their mass profiles show correlated deviations from NFW and are better approximated by Einasto profiles. Fitting both M() and M(\rho_{crit}) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work linking the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only halos whose accretion histories differ greatly from the NFW shape show noticeable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter halos, which do not form hierarchically, and for fluctuation power spectra other than CDM. Our findings, however, predict a subtle but systematic dependence of mass profile shape on accretion history which, if confirmed, would provide strong support for the link between accretion history and halo structure we propose here.Comment: 12 pages, 8 figures, MNRAS 432 1103L (2013

A G1-like globular cluster in NGC 1023

The structure of a very bright (MV = -10.9) globular cluster in NGC 1023 is analyzed on two sets of images taken with the Hubble Space Telescope. From careful modeling of King profile fits to the cluster image, a core radius of 0.55+/-0.1 pc, effective radius 3.7+/-0.3 pc and a central V-band surface brightness of 12.9+/-0.5 mag / square arcsec are derived. This makes the cluster much more compact than Omega Cen, but very similar to the brightest globular cluster in M31, G1 = Mayall II. The cluster in NGC 1023 appears to be very highly flattened with an ellipticity of about 0.37, even higher than for Omega Cen and G1, and similar to the most flattened clusters in the Large Magellanic Cloud.Comment: 14 pages, 3 figures, 1 table. Accepted for AJ, Oct 200

The First Galaxies: Clues from Element Abundances

It has recently become possible to measure directly the abundances of several chemical elements in a variety of environments at redshifts up to z = 5. In this review I summarise the latest observations of Lyman break galaxies, damped Lyman alpha systems and the Lyman alpha forest with a view to uncovering any clues which these data may offer to the first episodes of star formation. The picture which is emerging is one where the universe at z = 3 already included many of the components of today's galaxies--even at these early times we see evidence for Populations I and II stars, while the `smoking gun' for Population III objects may be hidden in the chemical composition of the lowest density regions of the IGM, yet to be deciphered.Comment: 15 pages, LaTex, 8 Postscript Figures. To appear in the Philosophical Transactions of The Royal Society, Series