A comparison study of extreme precipitation from six different regional climate models via spatial hierarchical modeling

We analyze output from six regional climate models (RCMs) via a spatial Bayesian hierarchical model. The primary advantage of this approach is that the statistical model naturally borrows strength across locations via a spatial model on the parameters of the generalized extreme value distribution. This is especially important in this application as the RCM output we analyze have extensive spatial coverage, but have a relatively short temporal record for characterizing extreme behavior. The hierarchical model we employ is also designed to be computationally efficient as we analyze RCM output for nearly 12000 locations. The aim of this analysis is to compare the extreme precipitation as generated by these RCMs. Our results show that, although the RCMs produce similar spatial patterns for the 100-year return level, their characterizations of extreme precipitation are quite different. Additionally, we examine the spatial behavior of the extreme value index and find differing spatial patterns for the point estimates for the RCMs. However, these differences may not be significant given the uncertainty associated with estimating this parameter.     

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling (specifically, the inner tube formula for each generator of the fractal spray is required to be polynomial). Now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators, and also by giving a proof which holds pointwise, rather than distributionally. Hence, our results for fractal sprays extend to higher dimensions the pointwise tube formula for (1-dimensional) fractal strings obtained earlier by Lapidus and van Frankenhuijsen.Our pointwise tube formulas are expressed as a sum of the residues of the “tubular zeta function” of the fractal spray in Rd. This sum ranges over the complex dimensions of the spray, that is, over the poles of the geometric zeta function of the underlying fractal string and the integers 0,1,…,d. The resulting “fractal tube formulas” are applied to the important special case of self-similar tilings, but are also illustrated in other geometrically natural situations. Our tube formulas may also be seen as fractal analogues of the classical Steiner formula.     

Development and validation of a high school STEM self-assessment inventory

The development of inclusive STEM high schools that have no academic admission requirements has been a national goal in the United States. However, there is no umbrella organization that gives guidance for structuring such schools. The purpose of this study was to develop and validate a self-assessment using critical components of successful inclusive STEM high schools for school personnel and educational researchers who wish to better understand their STEM programs and identify areas of strength. A multi-phase methodology was employed. In the first step, eight in-depth case studies were generated, and common themes were identified. In the second step, inventory items were iteratively generated and tested for reliability and validity, using a sample of 78 teachers and researchers in five schools. In the third step, the inventory was field-tested in a single school. The OSPRI inventory demonstrates strong content validity and reliability. Teachers and researchers generally responded similarly, although some differences emerged that are indicative of their respective experiences and perspectives. School stakeholders and educational researchers can use this inventory, in whole or in part, to better understand their STEM programs and establish a future agenda that best capitalizes on their strengths.