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

Plasmodium falciparum glutamate dehydrogenase a is dispensable and not a drug target during erythrocytic development

<p>Background: Plasmodium falciparum contains three genes encoding potential glutamate dehydrogenases. The protein encoded by gdha has previously been biochemically and structurally characterized. It was suggested that it is important for the supply of reducing equivalents during intra-erythrocytic development of Plasmodium and, therefore, a suitable drug target.</p> <p>Methods: The gene encoding the NADP(H)-dependent GDHa has been disrupted by reverse genetics in P. falciparum and the effect on the antioxidant and metabolic capacities of the resulting mutant parasites was investigated.</p> <p>Results: No growth defect under low and elevated oxygen tension, no up-or down-regulation of a number of antioxidant and NADP(H)-generating proteins or mRNAs and no increased levels of GSH were detected in the D10(Delta gdha) parasite lines. Further, the fate of the carbon skeleton of [(13)C] labelled glutamine was assessed by metabolomic studies, revealing no differences in the labelling of a-ketoglutarate and other TCA pathway intermediates between wild type and mutant parasites.</p> <p>Conclusions: First, the data support the conclusion that D10(Delta gdha) parasites are not experiencing enhanced oxidative stress and that GDHa function may not be the provision of NADP(H) for reductive reactions. Second, the results imply that the cytosolic, NADP(H)-dependent GDHa protein is not involved in the oxidative deamination of glutamate but that the protein may play a role in ammonia assimilation as has been described for other NADP(H)dependent GDH from plants and fungi. The lack of an obvious phenotype in the absence of GDHa may point to a regulatory role of the protein providing glutamate (as nitrogen storage molecule) in situations where the parasites experience a limiting supply of carbon sources and, therefore, under in vitro conditions the enzyme is unlikely to be of significant importance. The data imply that the protein is not a suitable target for future drug development against intra-erythrocytic parasite development.</p&gt

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