Measurable realizations of abstract systems of congruences

An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility of actions. We consider the general question of when there are realizations of abstract systems of congruences satisfying various measurability constraints. We completely characterize which abstract systems of congruences can be realized by nonmeager Baire measurable pieces of the sphere under the action of rotations on the $2$-sphere. This answers a question of Wagon. We also construct Borel realizations of abstract systems of congruences for the action of $\mathsf{PSL}_2(\mathbb{Z})$ on $\mathsf{P}^1(\mathbb{R})$. The combinatorial underpinnings of our proof are certain types of decomposition of Borel graphs into paths. We also use these decompositions to obtain some results about measurable unfriendly colorings.Comment: minor correction

Training New Instructors to Implement Discrete Trial Teaching Strategies With Children With Autism in a Community-Based Intervention Program

The effects of training and supervision on instructor knowledge and performance of discrete trial teaching (DTT) within three domains (DTT Technical Skills; Work Session Preparation/Conclusion; and Student Engagement/Management) were examined in this study. Eight undergraduate student instructors received an 8-hr training in DTT and support skills accompanied by a pre- and post-test of knowledge. The instructors then taught a variety of skills to six students with autism in a community-based preschool, where instructor competence was tracked and performance feedback provided using the Discrete Trial Teaching Competency Checklist for Instructors. Competence in all three domains improved over time with performance feedback. However, significant variability was observed within and between instructors, and performance in some areas remained below optimal levels even with regular supervision and performance feedback. Implications for training and supervising instructors to implement DTT with children with autism in community-based settings are discussed

Folner tilings for actions of amenable groups

We show that every probability-measure-preserving action of a countable amenable group G can be tiled, modulo a null set, using finitely many finite subsets of G ("shapes") with prescribed approximate invariance so that the collection of tiling centers for each shape is Borel. This is a dynamical version of the Downarowicz--Huczek--Zhang tiling theorem for countable amenable groups and strengthens the Ornstein--Weiss Rokhlin lemma. As an application we prove that, for every countably infinite amenable group G, the crossed product of a generic free minimal action of G on the Cantor set is Z-stable.Comment: Minor revisions. Final versio

Predicted and observed evolution in the mean properties of Type Ia supernovae with redshift

Recent studies indicate that Type Ia supernovae (SNe Ia) consist of two groups - a "prompt" component whose rates are proportional to the host galaxy star formation rate, whose members have broader lightcurves and are intrinsically more luminous, and a "delayed" component whose members take several Gyr to explode, have narrower lightcurves, and are intrinsically fainter. As cosmic star formation density increases with redshift, the prompt component should begin to dominate. We use a two-component model to predict that the average lightcurve width should increase by 6% from z=0-1.5. Using data from various searches we find an 8.1% +/- 2.7% increase in average lightcurve width for non-subluminous SNe Ia from z=0.03 - 1.12, corresponding to an increase in the average intrinsic luminosity of 12%. To test whether there is any bias after supernovae are corrected for lightcurve shape we use published data to mimic the effect of population evolution and find no significant difference in the measured dark energy equation of state parameter, w. However, future measurements of time-variable w will require standardization of SN Ia magnitudes to 2% up to z=1.7, and it is not yet possible to assess whether lightcurve shape correction works at this level of precision. Another concern at z=1.5 is the expected order of magnitude increase in the number of SNe Ia that cannot be calibrated by current methods.Comment: 5 pages, 3 figures, accepted to ApJ Letters, addressed referee's comments, table adde

Medical Tourism and International Healthcare Options

Medical tourism has evolved from traveling to the United States (U.S.) and a select few other countries, such as India and Thailand, to a global trend in affordable alternative healthcare. Medical tourism in the U.S. and in other countries has evolved because of cost and lengthy waiting periods. Some insurance companies are marketing kidney transplants and joint replacements through medical choice programs in order to save overall expense. As an economical approach to controlling rising health care costs in the U.S., medical tourism is becoming a valid alternative

Attribution of chemistry-climate model initiative (CCMI) ozone radiative flux bias from satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6 µm ozone band is a fundamental quantity for understanding chemistry–climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present-day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6 µm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Intercomparison Project (ACCMIP) simulations. The principal culprits are tropical middle and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mW m−2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mW m−2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mW m−2). We found that the atmospheric component (AM3) of the Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model and Canadian Middle Atmosphere Model (CMAM) have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to different processes. Overall, the multi-model ensemble mean bias is −133±98  mW m−2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation