Uniform bounds on growth in o-minimal structures

We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in a paper of Friedman and Miller. Moreover, this remains true if the argument is taken to approach any element of the structure (or plus/minus infinity), and the function has limit any element of the structure (or plus/minus infinity).Comment: 3 pages. To appear in Mathematical Logic Quarterl

A mass-dependent slope of the galaxy size-mass relation out to z~3: further evidence for a direct relation between median galaxy size and median halo mass

We reassess the galaxy size-mass relation out to z~3 using a new definition of size and a sample of >29,000 galaxies from the 3D-HST, CANDELS, and COSMOS-DASH surveys. Instead of the half-light radius r_50 we use r_80, the radius containing 80% of the stellar light. We find that the r_80 -- M_star relation has the form of a broken power law, with a clear change of slope at a pivot mass M_p. Below the pivot mass the relation is shallow (r_80 \propto M_star^0.15) and above it it is steep (r_80\propto M_star^0.6). The pivot mass increases with redshift, from log(M_p/M_sun)~ 10.2 at z=0.4 to log(M_p/M_sun)~ 10.9 at z=1.7-3. We compare these r_80-M_star relations to the M_halo-M_star relations derived from galaxy-galaxy lensing, clustering analyses, and abundance matching techniques. Remarkably, the pivot stellar masses of both relations are consistent with each other at all redshifts, and the slopes are very similar both above and below the pivot when assuming M_halo \propto r_80^3. The implied scaling factor to relate galaxy size to halo size is r_80 / R_vir = 0.047, independent of stellar mass and redshift.From redshift 0 to 1.5, the pivot mass also coincides with the mass where the fraction of star-forming galaxies is 50%, suggesting that the pivot mass reflects a transition from dissipational to dissipationless galaxy growth. Finally, our results imply that the scatter in the stellar-to-halo mass ratio is relatively small for massive halos (~0.2 dex for M_halo>10^12.5 M_sun).Comment: Accepted in ApJL. Please also see complementary paper Miller et al. 201

Strategies to Help Low-Wage Workers Advance: Implementation and Early Impacts of the Work Advancement and Support Center (WASC) Demonstration

Work Advancement and Support Center (WASC) is an innovative strategy to help low-wage workers increase their incomes by stabilizing employment, improving skills, increasing earnings, and easing access to work supports. In its first year, WASC connected more workers to food stamps and publicly funded health care coverage and, in one site, substantially increased training activities

Charge Independence and Charge Symmetry

Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.Comment: 41 pages, report # DOE/ER/40427-17-N94, Chapter for a book titled "Symmetries and Fundamental Interactions in Nuclei" eds. E.M. Henley and W. Haxton, to be published by World Scientifi

On the null-controllability of the heat equation in unbounded domains

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator.Comment: References [CdMZ01, dTZ00] added, abstract modifie

A New View of the Size-Mass Distribution of Galaxies: Using r20r_{20} and r80r_{80} instead of r50r_{50}

When investigating the sizes of galaxies it is standard practice to use the half-light radius, $r_{50}$. Here we explore the effects of the size definition on the distribution of galaxies in the size -- stellar mass plane. Specifically, we consider $r_{20}$ and $r_{80}$, the radii that contain 20% and 80% of a galaxy's total luminosity, as determined from a Sersic profile fit, for galaxies in the 3D-HST/CANDELS and COSMOS-DASH surveys. These radii are calculated from size catalogs based on a simple calculation assuming a Sersic profile. We find that the size-mass distributions for $r_{20}$ and $r_{80}$ are markedly different from each other and also from the canonical $r_{50}$ distribution. The most striking difference is in the relative sizes of star forming and quiescent galaxies at fixed stellar mass. Whereas quiescent galaxies are smaller than star forming galaxies in $r_{50}$, this difference nearly vanishes for $r_{80}$. By contrast, the distance between the two populations increases for $r_{20}$. Considering all galaxies in a given stellar mass and redshift bin we detect a significant bimodality in the distribution of $r_{20}$, with one peak corresponding to star forming galaxies and the other to quiescent galaxies. We suggest that different measures of the size are tracing different physical processes within galaxies; $r_{20}$ is closely related to processes controlling the star formation rate of galaxies and $r_{80}$ may be sensitive to accretion processes and the relation of galaxies with their halos.Comment: Resubmitted to ApJL after responding to referee's comments. Please also see Mowla et al. submitted today as wel

A mass-dependent slope of the galaxy size-mass relation out to z ∼ 3 : further evidence for a direct relation between median galaxy size and median halo mass

We reassess the galaxy size-mass relation out to z similar to 3 using a new definition of size and a sample of >29,000 galaxies from the 3D-HST, CANDELS, and COSMOS-DASH surveys. Instead of the half-light radius r(50) we use r(80), the radius containing 80% of the stellar light. We find that the r(80)M(*) relation has the form of a broken power law, with a clear change of slope at a pivot mass M-p. Below the pivot mass the relation is shallow (r(80) proportional to M-*(0.)15); above it, it is steep (r(80) proportional to M-*(0.)6). The pivot mass increases with redshift, from log(M-p/M-circle dot) approximate to 10.2 at z = 0.4 to log(M-p/M-circle dot) approximate to 10.9 at z = 1.7-3. We compare these r(80)-M-* relations to the M-helo-M-* relations derived from galaxy-galaxy lensing, clustering analyses, and abundance matching techniques. Remarkably, the pivot stellar masses of both relations are consistent with each other at all redshifts, and the slopes are very similar both above and below the pivot when assuming M-halo proportional to r(8)(0)(3). The implied scaling factor to relate galaxy size to halo size is r(80)/R-vir = 0.047, independent of stellar mass and redshift. From redshift 0 to 1.5, the pivot mass also coincides with the mass where the fraction of star-forming galaxies is 50%, suggesting that the pivot mass reflects a transition from dissipational to dissipationless galaxy growth. Finally, our results imply that the scatter in the stellar-to-halo mass is relatively small for massive halos (similar to 0.2 dex for M-halo > 10(1)(2.)(5) M-circle dot)