Ground-based adaptive optics coronagraphic performance under closed-loop predictive control

The discovery of the exoplanet Proxima b highlights the potential for the coming generation of giant segmented mirror telescopes (GSMTs) to characterize terrestrial --- potentially habitable --- planets orbiting nearby stars with direct imaging. This will require continued development and implementation of optimized adaptive optics systems feeding coronagraphs on the GSMTs. Such development should proceed with an understanding of the fundamental limits imposed by atmospheric turbulence. Here we seek to address this question with a semi-analytic framework for calculating the post-coronagraph contrast in a closed-loop AO system. We do this starting with the temporal power spectra of the Fourier basis calculated assuming frozen flow turbulence, and then apply closed-loop transfer functions. We include the benefits of a simple predictive controller, which we show could provide over a factor of 1400 gain in raw PSF contrast at 1 $\lambda/D$ on bright stars, and more than a factor of 30 gain on an I = 7.5 mag star such as Proxima. More sophisticated predictive control can be expected to improve this even further. Assuming a photon noise limited observing technique such as High Dispersion Coronagraphy, these gains in raw contrast will decrease integration times by the same large factors. Predictive control of atmospheric turbulence should therefore be seen as one of the key technologies which will enable ground-based telescopes to characterize terrrestrial planets.Comment: Accepted to JATI

On tt-core and self-conjugate (2t−1)(2t-1)-core partitions in arithmetic progressions

We extend recent results of Ono and Raji, relating the number of self-conjugate $7$-core partitions to Hurwitz class numbers. Furthermore, we give a combinatorial explanation for the curious equality $2\operatorname{sc}_7(8n+1) = \operatorname{c}_4(7n+2)$. We also conjecture that an equality of this shape holds if and only if $t=4$, proving the cases $t\in\{2,3,5\}$ and giving partial results for $t>5$

Youth Health Services, Development Programs, and Teenage Birth Rates in 55 California Cities

Many advocacy groups depict sexuality education, abstinence education, health services, and development services to teenagers as pivotal factors in their birth rates. Data from California’s 55 largest cities for 1990-2002 allow regression analyses of the associations between levels of health and development services to youth, socioeconomic factors such as poverty, and environmental factors such adult birth rates on rates of and changes in births to teenage mothers. The analysis found teenage birth rates vary 30-fold from California’s richest to poorest city. Socioeconomic and environmental factors, chiefly adult birth rates and youth poverty rates, are associated with nearly 90% of the variance in teen birth rates. Contrary to assertions by many advocates, lower-income teens have greater access to health, sexuality education, and development services, and the availability of these services is not associated with lower rates of or greater reductions over time in teenage birth rates

Curricular noticing: A comprehensive framework to describe teachers’ interactions with curriculum materials

Building on the work of Professional Noticing of Children’s Mathematical Thinking, we introduce the Curricular Noticing Framework to describe how teachers recognize opportunities within curriculum materials, understand their affordances and limitations, and use strategies to act on them. This framework builds on Remillard’s (2005) notion of participation with curriculum materials, connects with and broadens existing research on the relationship between teachers and written curriculum, and highlights new are as for research. We argue that once mathematics educators better understand the strategic curricular practices that support ambitious teaching, which we refer to as professional curricular noticing, then this knowledge can lead to recommendations for how to support the curricular work of teachers, particularly novice teachers

Geography, environment, and organismal traits in the diversification of a major tropical herbaceous angiosperm radiation

The generation of plant diversity involves complex interactions between geography, environment, and organismal traits. Many macroevolutionary processes and emergent patterns have been identified in different plant groups through the study of spatial data, but rarely in the context of a large radiation of tropical herbaceous angiosperms. A powerful system for testing interrelated biogeographical hypotheses is provided by the terrestrial bromeliads, a Neotropical group of extensive ecological diversity and importance. In this investigation, distributional data for 564 species of terrestrial bromeliads were used to estimate variation in the position and width of species-level hydrological habitat occupancy and test six core hypotheses linking geography, environment, and organismal traits. Taxonomic groups and functional types differed in hydrological habitat occupancy, modulated by convergent and divergent trait evolution, and with contrasting interactions with precipitation abundance and seasonality. Plant traits in the Bromeliaceae are intimately associated with bioclimatic differentiation, which is in turn strongly associated with variation in geographical range size and species richness. These results emphasise the ecological relevance of structural-functional innovation in a major plant radiation

A note on the equidistribution of 33-colour partitions

In this short note, we prove equidistribution results regarding three families of three-colour partitions recently introduced by Schlosser and Zhou. To do so, we prove an asymptotic for the infinite product $F_{a,c}(\zeta ; q) \coloneqq \prod_{n \geq 0} \left(1- \zeta q^{a+cn}\right)$ ($a,c \in \N$ with $0<a\leq c$ and $\zeta$ a root of unity) in certain cones in the right half-plane, which may be useful in studying similar problems. As a corollary, we obtain the asymptotic behaviour of the three-colour partition families at hand.Comment: Short 7-page note detailing some asymptotics for functions introduced by Schlosser & Zhou last wee