The Zeta Function of a Hypergraph

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Sol\'e. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.Comment: 24 pages, 6 figure

How Can Mathematics Students Learn to Play?

When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more

Type 1 adenylyl cyclase is essential for maintenance of remote contextual fear memory

Although molecular mechanisms for hippocampus-dependent memory have been extensively studied, much less is known about signaling events important for remote memory. Here we report that mice lacking type 1 adenylyl cyclase (AC1) are able to establish and retrieve remote contextual memory but unable to sustain it as long as wild-type mice. Interestingly, mice overexpressing AC1 show superior remote contextual memory even though they exhibit normal hippocampus-dependent contextual memory. These data illustrate that calcium coupling to cAMP contributes to the stability of remote memory and identifies AC1 as a potential drug target site to improve long-term remote memory

Promoting Active Studying: The Study Challenge

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom

A review of the literature on patient participation in transitions of the elderly

Patient participation is highlighted in healthcare policy documents as an important area to address in order to improve and secure healthcare quality. The literature on healthcare quality and safety furthermore reveals that transitional care carries a risk of adverse events. Elderly persons with co-morbidities are in need of treatment and healthcare from several care professionals and are transferred between different care levels. Patient-centered care, shared decision-making and user involvement are concepts of care that incorporate patient participation and the patients’ experiences with care. Even though these care concepts are highlighted in healthcare policy documents, limited knowledge exists about their use in transitions, and therefore points to a need for a review of the existing literature. The purpose of the paper is to give an overview of studies including patient participation as applied in transitional care of the elderly. The methodology used is a literature review searching electronic databases. Results show that participation from elderly in discharge planning and decision-making was low, although patients wanted to participate. Some tools were successfully implemented, but several did not stimulate patient participation. The paper has documented that improvements in quality of transitional care of elderly is called for, but has not been well explored in the research literature and a need for future research is revealed. Clinical practice should take into consideration implementing tools to support patient participation to improve the quality of transitional care of the elderly