Late Points and Cover Times of Projections of Planar Symmetric Random Walks on the Lattice Torus

We examine the sets of late points of a symmetric random walk on $Z^2$ projected onto the torus $Z^2_K$, culminating in a limit theorem for the cover time of the toral random walk. This extends the work done for the simple random walk in Dembo, et al. (2006) to a large class of random walks projected onto the lattice torus. The approach uses comparisons between planar and toral hitting times and distributions on annuli, and uses only random walk methods.Comment: arXiv admin note: substantial text overlap with arXiv:1209.238

On Upper Bounds for Toroidal Mosaic Numbers

In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection, and present a tool to measure this reduction. We show that the order of edge identification in construction of the torus sometimes yields different resultant knots from a given mosaic when reversed. Additionally, in the Appendix we give the catalog of all 2 by 2 torus mosaics.Comment: 10 pages, 111 figure

Nitrate reductase 15N discrimination in Arabidopsis thaliana, Zea mays, Aspergillus niger, Pichea angusta, and Escherichia coli

Stable 15N isotopes have been used to examine movement of nitrogen (N) through various pools of the global N cycle. A central reaction in the cycle involves nitrate (NO3–) reduction to nitrite (NO2–) catalyzed via nitrate reductase (NR). Discrimination against 15N by NR is a major determinant of isotopic differences among N pools. Here, we measured in vitro 15N discrimination by several NRs purified from plants, fungi, and a bacterium to determine the intrinsic 15N discrimination by the enzyme and to evaluate the validity of measurements made using 15N-enriched NO3–. Observed NR isotope discrimination ranged from 22‰ to 32‰ (kinetic isotope effects of 1.022 to 1.032) among the different isozymes at natural abundance 15N (0.37%). As the fractional 15N content of substrate NO3– increased from natural abundance, the product 15N fraction deviated significantly from that expected based on substrate enrichment and 15N discrimination measured at natural abundance. Additionally, isotopic discrimination by denitrifying bacteria used to reduce NO3– and NO2– in some protocols became a greater source of error as 15N enrichment increased. We briefly discuss potential causes of artifactual results with enriched 15N and recommend against the use of highly enriched 15N tracers to study N discrimination in plants or soils

Pennsylvania Folklife Vol. 25, No. 3

• The Pennsylvania Germans and the American Revolution • The Blooming Grove Colony • The Salebill • The Schlegel Family and the Rosicrucian Movement • A Log Settler\u27s Fort/Home • Pennsylvania Dutch Studies at Ursinus College, 1976 • The Country Sale: Folk-Cultural Questionnaire No. 43https://digitalcommons.ursinus.edu/pafolklifemag/1067/thumbnail.jp