The Effect of Star Formation History on the Inferred Initial Stellar Mass Function

Peaks and lulls in the star formation rate (SFR) over the history of the Galaxy produce plateaux and declines in the present day mass function (PDMF) where the main-sequence lifetime overlaps the age and duration of the SFR variation. These PDMF features can be misinterpreted as the form of the intrinsic stellar initial mass function (IMF) if the star formation rate is assumed to be constant or slowly varying with time. This effect applies to all regions that have formed stars for longer than the age of the most massive stars, including OB associations, star complexes, and especially galactic field stars. Related problems may apply to embedded clusters. Evidence is summarized for temporal SFR variations from parsec scales to entire galaxies, all of which should contribute to inferred IMF distortions. We give examples of various star formation histories to demonstrate the types of false IMF structures that might be seen. These include short-duration bursts, stochastic histories with log-normal amplitude distributions, and oscillating histories with various periods and phases. The inferred IMF should appear steeper than the intrinsic IMF over mass ranges where the stellar lifetimes correspond to times of decreasing SFRs; shallow portions of the inferred IMF correspond to times of increasing SFRs. If field regions are populated by dispersed clusters and defined by their low current SFRs, then they should have steeper inferred IMFs than the clusters. The SFRs required to give the steep field IMFs in the LMC and SMC are determined. Structure observed in several determinations of the Milky Way field star IMF can be accounted for by a stochastic and bursty star formation history.Comment: accepted by ApJ for 1 Jan 2006, Vol 636, 12 pages + 6 figure

A Closed-Form Expression for the Gravitational Radiation Rate from Cosmic Strings

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10, (section 7 has been expanded, two figures added, and minor grammatical changes made.

THE STUDENT-LOAN FINANCIAL CRISIS: A CASE OF CREDIT-CARD USAGE AMONG AFRICAN-AMERICAN COLLEGE STUDENTS

Abstract There is current concern about a student-loan crisis, as student-loan debt, which now exceeds $1 trillion, has surpassed credit-card debt for the first time

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

Interactions of a j=1j=1 boson in the 2(2j+1)2(2j+1) component theory

The amplitudes for boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the used model is the Weinberg's $2(2j+1)$ component formalism for describing a particle of spin $j$, recently developed substantially. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the ground of the hamiltonian formulation of quantum field theory on the mass hyperboloid, $p_0^2 -{\bf p}^2=M^2$, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of $T$ matrices for the fermion and the boson cases. However, certain differences are found. Possible physical applications are discussed.Comment: REVTeX 3.0 file. 12pp. Substantially revised version of IFUNAM preprints FT-93-24, FT-93-3

Back to Business and (Re)employing Workers? Labor Market Activity During State COVID-19 Reopenings

We study the effect of state reopening policies on a large set of labor market indicators through May 2020 to: (1) understand the recent increase in employment using longitudinal as well as cross-sectional data, (2) assess the likely trajectory of reemployment going forward, and (3) investigate the strength of job matches that were disrupted by COVID-19. Estimates from event studies and difference-in-difference regressions suggest that some of the recent increases in employment activity, as measured by cellphone data on work-related mobility, internet searches related to employment, and new and continuing unemployment insurance claims, were likely related to state reopenings, often predating actual reopening dates somewhat. We provide suggestive evidence that increases in employment stem from people returning to their prior jobs: reopenings are only weakly related to job postings, and longitudinal CPS data show that large shares of the unemployed-on-layoff and employed-but-absent in April who transitioned to employment in May remain in the same industry or occupation. Longitudinal CPS estimates further show declines in reemployment probabilities with time away from work. Taken together, these estimates suggest that employment relationships are durable in the short run, but raise concerns that employment gains requiring new employment matches may not be as rapid.Weinberg gratefully acknowledges support from UL1 TR002733 and R24 HD058484

Extra Dirac Equations

This paper has rather a pedagogical meaning. Surprising symmetries in the $(j,0)\oplus (0,j)$ Lorentz group representation space are analyzed. The aim is to draw reader's attention to the possibility of describing the particle world on the ground of the Dirac "doubles". Several tune points of the variational principle for this kind of equations are briefly discussed.Comment: REVTeX 3.0, 14p

Green's function for gravitational waves in FRW spacetimes

A method for calculating the retarded Green's function for the gravitational wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of linearized Einstein gravity is developed. Hadamard's general solution to Cauchy's problem for second-order, linear partial differential equations is applied to the FRW gravitational wave equation. The retarded Green's function may be calculated for any FRW spacetime, with curved or flat spatial sections, for which the functional form of the Ricci scalar curvature $R$ is known. The retarded Green's function for gravitational waves propagating through a cosmological fluid composed of both radiation and dust is calculated analytically for the first time. It is also shown that for all FRW spacetimes in which the Ricci scalar curvatures does not vanish, $R \neq 0$, the Green's function violates Huygens' principle; the Green's function has support inside the light-cone due to the scatter of gravitational waves off the background curvature.Comment: 9 pages, FERMILAB-Pub-93/189-

Effects of a Government-Academic Partnership: Has the NSF-Census Bureau Research Network Helped Improve the U.S. Statistical System?

The National Science Foundation-Census Bureau Research Network (NCRN) was established in 2011 to create interdisciplinary research nodes on methodological questions of interest and significance to the broader research community and to the Federal Statistical System (FSS), particularly to the Census Bureau. The activities to date have covered both fundamental and applied statistical research and have focused at least in part on the training of current and future generations of researchers in skills of relevance to surveys and alternative measurement of economic units, households, and persons. This article focuses on some of the key research findings of the eight nodes, organized into six topics: (1) improving census and survey data-quality and data collection methods; (2) using alternative sources of data; (3) protecting privacy and confidentiality by improving disclosure avoidance; (4) using spatial and spatio-temporal statistical modeling to improve estimates; (5) assessing data cost and data-quality tradeoffs; and (6) combining information from multiple sources. The article concludes with an evaluation of the ability of the FSS to apply the NCRN’s research outcomes, suggests some next steps, and discusses the implications of this research-network model for future federal government research initiatives