Development of proneurogenic, neuroprotective small molecules

Degeneration of the hippocampus is associated with Alzheimer's disease and occurs very early in the progression of the disease. Current options for treating the cognitive symptoms associated with Alzheimer's are inadequate, giving urgency to the search for novel therapeutic strategies. Pharmacologic agents that safely enhance hippocampal neurogenesis may provide new therapeutic approaches. We discovered the first synthetic molecule, named P7C3, which protects newborn neurons from apoptotic cell death, and thus promotes neurogenesis in mice and rats in the subgranular zone of the hippocampal dentate gyrus, the site of normal neurogenesis in adult mammals. We describe the results of a medicinal chemistry campaign to optimize the potency, toxicity profile, and stability of P7C3. Systematic variation of nearly every position of the lead compound revealed elements conducive toward increases in activity and regions subject to modification. We have discovered compounds that are orally available, nontoxic, stable in mice, rats, and cell culture, and capable of penetrating the blood-brain barrier. The most potent compounds are active at nanomolar concentrations. Finally, we have identified derivatives that may facilitate mode-of-action studies through affinity chromatography or photo-cross-linking.     

A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of $G$ is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, $k$-cycle resonant graphs, Discrete Math. 135 (1994) 113–20] that a hexagonal system is 1-cycle resonant if and only if it is catacondensed.     

Vizing's conjecture: a survey and recent results

Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this paper we survey the approaches to this central conjecture from domination theory and give some new results along the way. For instance, several new properties of a minimal counterexample to the conjecture are obtained and a lower bound for the domination number is proved for products of claw‐free graphs with arbitrary graphs. Open problems, questions and related conjectures are discussed throughout the paper. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 46–76, 2012     

Engineering process as a focus: STEM professional development with elementary STEM‐focused professional development schools

Young children are capable of engaging in STEM investigations when they are guided by skilled and knowledgeable teachers. However, many elementary teachers may lack sufficient STEM content knowledge and report feeling unprepared to teach STEM content. Two university faculty members in mathematics and science education, worked to cultivate and advance two designated Elementary STEM‐Focused professional development schools through a two year series of an after‐school STEM professional development (PD) Program. As the STEM PD Program progressed, it became evident that teachers were interested in and needed more experiences with the elements of the engineering process for young learners. With this in mind, several of the PD sessions were designed to highlight the engineering process and allow teachers to experience various activities that would engage young learners. To examine how this focus on the engineering process impacted the teachers in this STEM PD Program, a research study was organized during year two of the STEM PD Program. The results of this study provide evidence that this program had a positive influence on the teacher participants’ engineering teacher efficacy and implementation of engineering lessons and activities within their classrooms.     

Two-ended regular median graphs

We show that regular median graphs of linear growth are the Cartesian product of finite hypercubes with the two-way infinite path. Such graphs are Cayley graphs and have only two ends.For cubic median graphs G the condition of linear growth can be weakened to the condition that G has two ends. For higher degree the relaxation to two-ended graphs is not possible, which we demonstrate by an example of a median graph of degree four that has two ends, but nonlinear growth.     

The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.     

Edge-transitive products

This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edge-transitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a strong product is edge-transitive if and only if all factors are complete graphs. In addition, a connected, infinite non-trivial Cartesian product graph G is edge-transitive if and only if it is vertex-transitive and if G is a finite weak Cartesian power of a connected, edge- and vertex-transitive graph H, or if G is the weak Cartesian power of a connected, bipartite, edge-transitive graph H that is not vertex-transitive.