Robin's inequality for 20-free integers

In 1984, Robin showed that the Riemann Hypothesis for $\zeta$ is equivalent to demonstrating $\sigma(n) 5040$. Robin's inequality has since been proven for various infinite families of power-free integers: $5$-free integers, $7$-free integers, and $11$-free integers. We extend these results to cover $20$-free integers

LEPTIN RESISTANCE INDUCED OBESITY AND DIABETES PROMOTE NEUROPATHOLOGICAL CHANGES IN THE AGING BRAIN

The aging brain is prone to the development of pathology and dementia. With a rapidly growing elderly population diagnoses of neurodegenerative diseases, such as Alzheimer’s disease (AD), frontotemporal dementia (FTD), and Parkinson’s disease are on the rise. Additionally, diabetes and obesity are linked to an increased risk of dementia. The convergence of this increasingly aged population with the obesity and diabetes epidemic give rise to new concerns regarding the future of prevention and treatment of neurodegenerative diseases. Our lab has previously shown that leptin, an adipokine involved in signaling satiety to the hypothalamus, can modulate the generation of the amyloid beta (Aβ) peptide (a toxic peptide associated with neurologic disease) and attenuate hyperphosphorylation of the tau protein (another peptide prone to forming large insoluble structures causing neurodegeneration). From these studies we have elucidated that leptin resistant mice (which develop severe obesity and type-2 diabetes mellitus) with knock-in mutations for the amyloid precursor protein (APP) and presenilin-1 (PS1) genes develop extensive vascular pathology and cognitive impairments. Interestingly, these mice do not display increased levels of amyloid deposition in the brain. Additionally, increased tau phosphorylation occurs in these mice with leptin resistance. As a follow up to this study db mice were transduced, via adeno-associated virus, with the tau P301L mutant to induce the development of tangle pathology. These mice displayed no cognitive deficits, yet they displayed increases in both tau phosphorylation and tangle count within the hippocampus. Collectively, these studies indicate leptin resistance, obesity, and type-2 diabetes mellitus promote the development of cerebrovascular and neurofibrillary tangle pathologies associated with neurodegeneration and dementia. These observations open many previously unexplored avenues for developing novel therapeutics to treat these devastating diseases

Brief Note A Survey of the Helminth Fauna of Two Turtle Species from Northwestern Ohio

Author Institution: Department of Biology, Bowling Green State Universit

An Analysis of the Metropolitan Atlanta Residential Real Estate Market: Beyond the Housing Bubble

This thesis examines the Metropolitan Atlanta housing market after the collapse of the Atlanta housing bubble between 2007 and 2011. Time-series analyses were performed for home prices, the amount of time homes spent on the market (days on market), and the number of homes listed for sale (inventory). Simple linear regression analyses were used to determine the effects of days on market and inventory on home prices. Homes were separated into quartiles and the analyses were repeated to determine how different price ranges behaved over the four-year period. Following the collapse of the Atlanta housing bubble, home prices and inventory fell dramatically and the amount of time homes spent the market increased. The lowest price range of homes experienced the greatest decrease in price and continually suffered from the worst market conditions. Days on market and inventory both had significant effects on the reduction of home prices during the four-year period. As of January 2012, it seems unlikely that the Atlanta housing market will recover in the near future, as home prices continued to trend downward from their peak in the summer on of2007

The “ideal” spectrograph for atmospheric observations

Spectroscopy of scattered sunlight in the near-UV to near-IR spectral ranges has proven to be an extremely useful tool for the analysis of atmospheric trace gas distributions. A central parameter for the achievable sensitivity and spatial resolution of spectroscopic instruments is the étendue (product of aperture angle and entrance area) of the spectrograph, which is at the heart of the instrument. The étendue of an instrument can be enhanced by (1) upscaling all instrument dimensions or (2) by changing the instrument F number, (3) by increasing the entrance area, or (4) by operating many instruments (of identical design) in parallel. The étendue can be enhanced by (in principle) arbitrary factors by options (1) and (4); the effect of options (2) and (3) is limited

A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes

Abstract Background Individual patient data meta-analyses (IPD-MA) are often performed using a one-stage approach-- a form of generalized linear mixed model (GLMM) for binary outcomes. We compare (i) one-stage to two-stage approaches (ii) the performance of two estimation procedures (Penalized Quasi-likelihood-PQL and Adaptive Gaussian Hermite Quadrature-AGHQ) for GLMMs with binary outcomes within the one-stage approach and (iii) using stratified study-effect or random study-effects. Methods We compare the different approaches via a simulation study, in terms of bias, mean-squared error (MSE), coverage and numerical convergence, of the pooled treatment effect (β 1) and between-study heterogeneity of the treatment effect (τ 1 2 ). We varied the prevalence of the outcome, sample size, number of studies and variances and correlation of the random effects. Results The two-stage and one-stage methods produced approximately unbiased β 1 estimates. PQL performed better than AGHQ for estimating τ 1 2 with respect to MSE, but performed comparably with AGHQ in estimating the bias of β 1 and of τ 1 2 . The random study-effects model outperformed the stratified study-effects model in small size MA. Conclusion The one-stage approach is recommended over the two-stage method for small size MA. There was no meaningful difference between the PQL and AGHQ procedures. Though the random-intercept and stratified-intercept approaches can suffer from their underlining assumptions, fitting GLMM with a random-intercept are less prone to misfit and has good convergence rate