Global Optimization of Econometric Functions

Estimating the values of the parameter estimates of econometric functions (maximum likelihood functions or nonlinear least squares functions) are often challenging global optimization problems. Determining the global optimum for these functions is necessary to understand economic behavior and to develop effective economic policies. These functions often have flat surfaces or surfaces characterized by many local optima. Classical deterministic optimization methods often do not yield successful results. For that reason, stochastic optimization methods are becoming widely used in econometrics. Selected stochastic methods are applied to two difficult econometric functions to determine if they might be useful in estimating the parameters of these functions.     

Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.     

Characterizing STEM Teacher Education: Affordances and Constraints of Explicit STEM Preparation for Elementary Teachers

Although science, technology, engineering, and mathematics (STEM) education sits at the center of a national conversation, comparatively little attention has been given to growing need for STEM teacher preparation, particularly at the elementary level. This study analyzes the outcomes of a novel, preservice STEM teacher education model. Building on both general and STEM‐specific teacher preparation principles, this program combined two traditional mathematics and science methods courses into one STEM block. Analysis compared preservice teachers in the traditional courses with those enrolled in the STEM block, investigating STEM teaching efficacy, reported and exhibited pedagogical practices, and STEM literacies using a pre‐post survey as well as analysis of lesson planning products. Linear regression models indicated that substantial growth was seen in both approaches but STEM block preservice teachers reported significantly greater gains in STEM teaching efficacy as compared with traditional‐route teachers. Lesson planning artifacts also demonstrated increased facilitation of STEM literacies, with specific attention to content integration, engineering and design, and arts inclusion. Technology and computational thinking emerged as areas for further growth and clarification in STEM teacher education models. Findings contribute to a growing research base on developing the STEM teacher workforce.     

Photoprotective Effect of Black Tea Extracts Against UVB-induced Phototoxicity in Skin

In previous studies, we showed that green tea and black tea extracts and their major polyphenolic constituents protect against UVB light-induced carcinogenesis in murine skin. All of these studies required chronic administration of tea extracts or specific constituents either topically or orally. However, it is not known whether acute or subchronic administration of black tea extracts or constituents can ameliorate UVB-induced early effects in skin. In the present study, cultured keratinocytes and mouse and human skin were employed to assess the effect of both oral and topical administration of standardized black tea extract (SBTE) and its two major polyphenolic subfractions namely BTF1 and BTF2 against UVB-induced photodamage. In SKH-1 hairless mice, topical application of SBTE (0.2 mg/cm2) prior to UVB exposure (180 mJ/cm2) resulted in 40% reduced incidence and 64% reduced severity of erythema and 50% reduction in skinfold thickness by day 6 when compared to nontreated UVB-exposed animals. The SBTE was also effective in protecting against UVB-induced erythema in human volunteers. Administration of SBTE 5 min after UVB irradiation was similarly effective in reducing UVB-induced inflammation in both murine and human skin. The major polyphenolic subfractions, BTF1 and BTF2, were also effective in protecting in mouse skin. The SBTE subfractions inhibited UVB-induced tyrosine phosphorylation of epidermal growth factor receptor (EGFR). The UVB irradiation of human epidermoid carcinoma cells resulted in 3.3-fold induction of tyrosine phosphorylation of EGFR. Pretreatment with BTF1 and BTF2 reduced tyrosine phosphorylation of EGFR by 53% and 31%, respectively. The UVB-mediated enhanced expression of the early response genes, c-fos and c-jun in human epidermal keratinocytes was reduced in a dose-dependent manner by SBTE. Topical application of SBTE was also effective in reducing accumulation of c-fos and p53 proteins by 82% and 78%, respectively, in UVB-exposed mouse skin. These data provide evidence that constituents of black tea can abrogate UVB-induced erythema and associated early events in murine and human skin.