Harmonic sets and the harmonic prime number theorem

We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2

The Best and Brightest Metal-Poor Stars

The chemical abundances of large samples of extremely metal-poor (EMP) stars can be used to investigate metal-free stellar populations, supernovae, and nucleosynthesis as well as the formation and galactic chemical evolution of the Milky Way and its progenitor halos. However, current progress on the study of EMP stars is being limited by their faint apparent magnitudes. The acquisition of high signal-to-noise spectra for faint EMP stars requires a major telescope time commitment, making the construction of large samples of EMP star abundances prohibitively expensive. We have developed a new, efficient selection that uses only public, all-sky APASS optical, 2MASS near-infrared, and WISE mid-infrared photometry to identify bright metal-poor star candidates through their lack of molecular absorption near 4.6 microns. We have used our selection to identify 11,916 metal-poor star candidates with V < 14, increasing the number of publicly-available candidates by more than a factor of five in this magnitude range. Their bright apparent magnitudes have greatly eased high-resolution follow-up observations that have identified seven previously unknown stars with [Fe/H] <~ -3.0. Our follow-up campaign has revealed that 3.8^{+1.3}_{-1.1}% of our candidates have [Fe/H] <~ -3.0 and 32.5^{+3.0}_{-2.9}% have -3.0 <~ [Fe/H] <~ -2.0. The bulge is the most likely location of any existing Galactic Population III stars, and an infrared-only variant of our selection is well suited to the identification of metal-poor stars in the bulge. Indeed, two of our confirmed metal-poor stars with [Fe/H] <~ -2.7 are within about 2 kpc of the Galactic Center. They are among the most metal-poor stars known in the bulge.Comment: 28 pages, 6 figures, and 4 tables in emulateapj format; accepted for publication in Ap

Chemistry of the Most Metal-poor Stars in the Bulge and the z > 10 Universe

Metal-poor stars in the Milky Way are local relics of the epoch of the first stars and the first galaxies. However, a low metallicity does not prove that a star formed in this ancient era, as metal-poor stars form over a range of redshift in different environments. Theoretical models of Milky Way formation have shown that at constant metallicity, the oldest stars are those closest to the center of the Galaxy on the most tightly-bound orbits. For that reason, the most metal-poor stars in the bulge of the Milky Way provide excellent tracers of the chemistry of the high-redshift universe. We report the dynamics and detailed chemical abundances of three stars in the bulge with [Fe/H] $\lesssim-2.7$, two of which are the most metal-poor stars in the bulge in the literature. We find that with the exception of scandium, all three stars follow the abundance trends identified previously for metal-poor halo stars. These three stars have the lowest [Sc II/Fe] abundances yet seen in $\alpha$-enhanced giant stars in the Galaxy. Moreover, all three stars are outliers in the otherwise tight [Sc II/Fe]-[Ti II/Fe] relation observed among metal-poor halo stars. Theoretical models predict that there is a 30% chance that at least one of these stars formed at $z\gtrsim15$, while there is a 70% chance that at least one formed at $10 \lesssim z \lesssim 15$. These observations imply that by $z\sim10$, the progenitor galaxies of the Milky Way had both reached [Fe/H] $\sim-3.0$ and established the abundance pattern observed in extremely metal-poor stars.Comment: Submitted to ApJ on 2014 December 23, accepted 2015 May 4th after minor revisions. ArXiv tarball includes referee report and respons

Political Competitiveness

Political competitiveness – which many interpret as the degree of democracy – can be modeled as a monopolistic competition. All regimes are constrained by the threat of "entry," and thereby seek some combination of popular support and political entry barriers. This simple model predicts that many public policies are unrelated to political competitiveness, and that even unchallenged nondemocratic regimes should tax far short of their Laffer curve maximum. Economic sanctions, odious debt repudiation, and other policies designed to punish dictators can have the unintended consequences of increasing oppression and discouraging competition. Since entry barriers are a form of increasing returns, democratic countries (defined according to low entry barriers) are more likely to subdivide and nondemocratic countries are more likely to merge. These and other predictions are consistent with previous empirical findings on comparative public finance, election contests, international conflict, the size of nations, and the Lipset hypothesis. As in the private sector, the number of competitors is not necessarily a good indicator of public sector competitiveness.

Teaching children with special needs: a Western Australian perspective

The education of children with special needs in Australia gained considerable impetus from the report of the Interim Committee for the Australian Schools Commission under the chairmanship of Professor Karmel when, in 1973, it made strong recommendations for a substantial increase in the government expenditure on special education. It highlighted inadequacies in the existing services in special education both in terms of facilities and manpower and suggested greater responsibilities for the education of handicapped children be taken by the State Education Departments. The upgrading of qualifications of teachers in Special Education and the necessary establishment of suitable courses in Australian tertiary institutions were notable consequences of the recommendations

The V Metric, Menopausal Hormone Therapy, And Breast Cancer Risk

Background and Aims. Long-term use of menopausal hormone therapy, typically in the form of estrogen or estrogen + progesterone, can increase the amount of dense breast tissue in women, which is associated with breast cancer. These changes are commonly measured using mammograms to calculate percent density; higher percent density is also associated with breast cancer. Newer methods of mammogram analysis look at spatial texture feature variation; these approaches are more sensitive than percent density, however the association between texture features and hormone therapy use is not well-documented. This study aims to analyze a specific texture feature, the V metric, which is a measure of the standard deviation of greyscale pixel intensity values from a mammogram image. We evaluated the V metric and its associations with both estrogen and estrogen + progesterone menopausal hormone therapy for durations of less than or equal to 5 years as well as more than 5 years. Our goal was to further establish V as a sensitive predictive measure of breast cancer. Methods. This was a retrospective cohort study that used participant data from the Nurses’ Health Study I and II. The study included 1,986 postmenopausal women that had available mammograms and menopausal hormone therapy use data. From both low and high-resolution mammograms, the V metric is computed. To evaluate the outcome variable V, linear mixed models were fit, adjusting for age, BMI, race, menopause, family history of breast cancer, personal history of benign breast disease, total breastfeeding, age at first birth, parity, age at menarche, age at menopause, physical activity, and alcohol intake. Models were then stratified by menopause type and percent mammogram density. Sensitivity analyses were conducted with the subset of mammograms that were high-resolution. Results. Adjusting for covariates, participants that used estrogen + progesterone for more than 5 years had significantly higher mean V measures than those that used estrogen or never used menopausal hormone therapy. Participants using any form of menopausal hormone therapy for any duration had significantly higher mean V measures than never users. Conclusions. Menopausal hormone therapy is significantly associated with higher mean V measures. Various durations of therapy can affect breast tissue physiology, leading to increases in dense tissue. This can increase risk of breast cancer. Notably, the V metric may quantify some changes that percent mammogram density does not register. Particularly in women that used estrogen + progesterone therapy for longer durations, the V metric may be a more accurate predictor of breast cancer risk. Additional evaluation of related physiological factors and their associations with the V metric will help increase its validity

No Pulsar Left Behind. I. Timing, Pulse-sequence Polarimetry, and Emission Morphology for 12 pulsars

In this paper we study a set of twelve pulsars that previously had not been characterized. Our timing shows that eleven of them are "normal" isolated pulsars, with rotation periods between 0.22 and 2.65 s, characteristic ages between 0.25 Myr and 0.63 Gyr, and estimated magnetic fields ranging from 0.05 to 3.8x 10^{12} G. The youngest pulsar in our sample, PSR~J0627+0706, is located near the Monoceros supernova remnant (SNR G205.5+0.5), but it is not the pulsar most likely to be associated with it. We also confirmed the existence of a candidate from an early Arecibo survey, PSR~J2053+1718, its subsequent timing and polarimetry are also presented here. It is an isolated pulsar with a spin period of 119 ms, a relatively small magnetic field of 5.8x10^9 G and a characteristic age of 6.7 Gyr; this suggests the pulsar was mildly recycled by accretion from a companion star which became unbound when that companion became a supernova. We report the results of single-pulse and average Arecibo polarimetry at both 327 and 1400 MHz aimed at understanding the basic emission properties and beaming geometry of these pulsars. Three of them (PSRs~J0943+2253, J1935+1159 and J2050+1259) have strong nulls and sporadic radio emission, several others exhibit interpulses (PSRs J0627+0706 and J0927+2345) and one shows regular drifting subpulses (J1404+1159).Comment: 17 pages, 14 figure

A modal/WKB inversion method for determining sound speed profiles in the ocean and ocean bottom

Submitted in partial fulfillment of the requirements for the degree of Ocean Engineer at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 1988Two approaches to determining the ocean sound speed profile using measured acoustic modal eigenvalues are examined. Both methods use measured eigenvalues and mode dependent assumed values of the WKB phase integral as input data and use the WKB phase integral as a starting point for relating the index of refraction to depth. Inversion method one is restricted to monotonic or symmetric sound speed profiles and requires a measurement of the sound speed at one depth to convert the index of refraction profile to a sound speed profile. Inversion method two assumes that the sound speed at the surface and the minimum sound speed in the profile are known and is applicable to monotonic profiles and to general single duct sound speed profiles. For asymmetric profiles, inversion method two gives the depth difference between two points of equal sound speed in the portion of the profile having two turning points, and in the remainder of the profile it gives sound speed versus depth directly. A numerical implementation of the methods is demonstrated using idealized ocean sound speed profiles numerical experiments used to test the performance of the inversions using noisy data. The two methods are used to determine the sediment sound speed profiles in two shallow water waveguide models, and inversion method one is used to find the sediment sound speed profile using data from an experiment performed in the Gulf of Mexico.Funding through the Office of Naval Research Fellowship Program