We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O...

Experimenters often use post-stratification to adjust estimates. Post-stratification is akin to blocking, except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment. We analyze both post-stratification and blocking under the Neyman-Rubin model and compare the efficiency of these designs. We derive the variances for a pos...

The turbulent energy equation, together with a modified mixing length, is adopted to close the governing equations in the turbulent planetary boundary layer under stratification conditions. The system of governing equations is decoupled by introducing a stratification parameter, Q. Numerical integration of the system, in general, is outlined and should be easily implemented. Results for the mom...

Since Partin introduced the analysis of prostate-specific antigen, clinical T-stage and Gleason scores to estimate the risk of progression in men with localised prostate cancer, our understanding of factors that modify this risk has changed drastically. There are now multiple risk stratification tools available, including look-up tables, risk stratification/classification analyses, regression-t...

Experimenters often use post-stratification to adjust estimates. Post-stratification is akin to blocking, except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment. We analyse both post-stratification and blocking under the Neyman–Rubin model and compare the efficiency of these designs. We derive the variances for a pos...

For a complex reductive group G acting linearly on a complex affine space V with respect to a characterρ, we show two stratifications ofV associated to this action (and a choice of invariant inner product on the Lie algebra of the maximal compact subgroup ofG) coincide. The first is Hesselink’s stratification by adapted 1-parameter subgroups and the second is the Morse theoretic stratification ...

Epithelia are classified as either simple, a single cell layer thick, or stratified (multilayered). Stratified epithelia arise from simple epithelia during development, and transcription factor p63 functions as a key positive regulator of epidermal stratification. Here we show that deletion of integrin beta 1 (Itgb1) in the developing mouse airway epithelium abrogates airway branching and conve...