The number of points from a random lattice that lie inside a ball

We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices.Comment: 29 page

Analysis of Cross Complementation of Archaeal Bax1 Protein in Saccharomyces cerevisiae

DNA repair mechanisms are essential in maintaining cell life and ensuring efficient cell replication. In this experiment, we tested for cross complementation of archaeal DNA repair genes (obtained from Methanosarcina acetivorans) in Saccharomyces cerevisiae yeast cells lacking Rad 1 and Rad 2 proteins. Five different cell conditions were tested: S. cerevisiae lacking rad 1 with a Bax 1 or a vector plasmid, S. cerevisiae lacking rad 2 with a Bax 1 or vector plasmid, and a wild type S. cerevisiae and no plasmid. Each week, cells were grown in broth culture, plated, and exposed to ultra-violent light, damaging the cell and inducing cellular DNA repair. After incubation, the plates were examined and cell counts were taken to determine percent survival after UV light exposure. Early results indicate that S. cerevisiae mutant strains carrying the Bax 1 gene can substitute for the Rad 1 protein but not the Rad 2 protein. We are currently conducting more trials of this experiment to increase confidence in our results and elaborate on current findings

Aging and Weight-Ratio Estimation

Many researchers have explored the way younger people perceive weight ratios using a variety of methodologies; however, very few researchers have used a more direct ratio estimation procedure, in which participants estimate an actual ratio between two or more weights. Of the few researchers who have used a direct method, the participants who were recruited were invariably younger adults. To date, there has been no research performed to examine how older adults perceive weight-ratios, using direct estimation or any other technique. Past research has provided evidence that older adults have more difficulty than younger adults in perceiving small differences in weight (i.e., the difference threshold for older adults is higher than that of younger adults). Given this result, one might expect that older adults would demonstrate similar impairments in weight ratio estimation compared to younger adults. The current experiment compared the abilities of 17 younger and 17 older adults to estimate weight ratios, using a direct ratio estimation procedure. On any given trial, participants were presented with two weights, and were asked to provide a direct estimate of the ratio, with the heavier in relation to the lighter. The results showed that the participants’ perceived weight ratios increased as a linear function of the actual weight ratios and that compared to younger adults, the older adults overestimated the weight ratios. The age-related overestimation was especially pronounced at higher weight ratios

Surglcel ® Reinforced Resection Lines in Left-sided Hepatectomy with Linear Stapling Device. An Experimental Study on Pigs

Fourteen pigs underwent left-sided hepatectomy. The resection was performed with a linear stapling device and the pigs were randomised to either Surgicel ® reinforced resection lines or not. The median time required for resection was 25 min (range 17-30) in the Surgicel® reinforced group compared to 30 min (range 21-41) in the stapled group. This difference was, however, not statistically significant (p=0.053)

Left-Sided Hepatectomy With a Linear Stapling Device: An Experimental Study on Pigs

Thirteen pigs underwent resection of the left liver lobe. By random selection, the animals were resected either with the aid of an RLG 90R linear stapling device or by the conventional finger-fracture technique. There was one postoperative death due to anaesthetic complications. The median operative time using the stapler was 27 min (range 19–40 min) which was significantly shorter (p = 0.0065) than that required for resection by the finger-fracture technique (42.5 min; range 37–55 min)