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

Alzheimer's disease pathology and the unfolded protein response : Prospective pathways and therapeutic targets

The authors would like to thank Alzheimer's Research UK (Grant refs: ARUK-PPG2014A-21 and ARUK-NSG2015-1 to BP and DK) who have provided support for relevant projects leading to this review.Peer reviewedPostprin

Zeroes of partial sums of the zeta-function

This article considers the positive integers $N$ for which $\zeta_{N}(s) = \sum_{n=1}^{N} n^{-s}$ has zeroes in the half-plane $\Re(s)>1$. Building on earlier results, we show that there are no zeroes for $1\leq N\leq 18$ and for $N=20, 21, 28$. For all other $N$ there are infinitely many zeroes.Comment: 5 Pages - Final Version will appear in LMS JC

Estimating the Creation and Removal Date of Fracking Ponds Using Trend Analysis of Landsat Imagery

Hydraulic fracturing, or fracking, is a process of introducing liquid at high pressure to create fractures in shale rock formations, thus releasing natural gas. Flowback and produced water from fracking operations is typically stored in temporary open-air earthen impoundments, or frack ponds. Unfortunately, in the United States there is no public record of the location of impoundments, or the dates that impoundments are created or removed. In this study we use a dataset of drilling-related impoundments in Pennsylvania identified through the FrackFinder project led by SkyTruth, an environmental non-profit. For each impoundment location, we compiled all low cloud Landsat imagery from 2000 to 2016 and created a monthly time series for three bands: red, near-infrared (NIR), and the Normalized Difference Vegetation Index (NDVI). We identified the approximate date of creation and removal of impoundments from sudden breaks in the time series. To verify our method, we compared the results to date ranges derived from photointerpretation of all available historical imagery on Google Earth for a subset of impoundments. Based on our analysis, we found that the number of impoundments built annually increased rapidly from 2006 to 2010, and then slowed from 2010 to 2013. Since newer impoundments tend to be larger, however, the total impoundment area has continued to increase. The methods described in this study would be appropriate for finding the creation and removal date of a variety of industrial land use changes at known locations

How pharmacoepidemiology networks can manage distributed analyses to improve replicability and transparency and minimize bias

Several pharmacoepidemiology networks have been developed over the past decade that use a distributed approach, implementing the same analysis at multiple data sites, to preserve privacy and minimize data sharing. Distributed networks are efficient, by interrogating data on very large populations. The structure of these networks can also be leveraged to improve replicability, increase transparency, and reduce bias. We describe some features of distributed networks using, as examples, the Canadian Network for Observational Drug Effect Studies, the Sentinel System in the USA, and the European Research Network of Pharmacovigilance and Pharmacoepidemiology. Common protocols, analysis plans, and data models, with policies on amendments and protocol violations, are key features. These tools ensure that studies can be audited and repeated as necessary. Blinding and strict conflict of interest policies reduce the potential for bias in analyses and interpretation. These developments should improve the timeliness and accuracy of information used to support both clinical and regulatory decisions

Effects Of Marine Lipid Fraction PCSO-524™ Supplementation On Biochemical And Functional Measures Of Muscle Damage And Soreness In Untrained Men

Effects of marine lipid fraction PCSO-524™ supplementation on biochemical and functional measures of muscle damage and soreness in untrained men INTRODUCTION: Intensive or unaccustomed eccentric exercise is known to cause exercise-induced muscle damage (EIMD) commonly resulting in delayed onset muscle soreness (DOMS). EIMD/DOMS can result in decrements in endurance and resistance exercise performance. Although many treatments have been investigated for the prevention and alleviation of EIMD/DOMS, success has been limited. PCSO-524™ has been found to attenuate symptoms of inflammatory diseases such as arthritis and asthma, and thus may be a viable treatment for EIMD/DOMS and may attenuate related exercise performance decrements. PURPOSE: The purpose of this study was to examine whether or not PCSO-524™ supplementation could attenuate loss of range of motion, force loss, swelling, perceived pain through algometry and biochemical markers of inflammation, intracellular muscle proteins and oxidative stress after eccentric muscle damage. METHODS: Subjects were thirty-two healthy, untrained males aged 18–26 who had not participated in a resistance training program in the past sixty days and did not exercise for more than three times per week for 30 minutes each session. Subjects supplemented for four weeks with either PCSO-524™ (400 mg/day) or placebo, after which time participated in a 20- minute downhill run (DHR) at -16% grade. Functional measures of DOMS were measured by algometry, midline thigh girth, and maximal voluntary contraction, following supplementation and 24, 48, 72 and 96 hours following eccentric exercise. Biochemical indicators of muscle damage such as Creatine Kinase-MM, Myoglobin, Slow skeletal troponin I, Fatty Acid Binding Protein 3, Interleukin-6, Tumor Necrosis Factor Alpha, 8-hydroxy-2' -deoxyguanosine (8-OHdG), and Cardiac Troponin I was measured pre-supplementation, post-supplementation and following DHR at 0, 2, 24, 48, 72 and 96 hours. RESULTS: PCSO-524™ attenuated maximal voluntary contraction force loss significantly at 96 hours (F = 8.140 p < .001). PCSO-524™ attenuated loss of range of motion at 96 hours compared to baseline (F = 8.236 p < .05) for the PCSO-524™ group but did not change 5 for the placebo group. There was no significant change in muscle swelling from baseline as measured by thigh girth for either PCSO-524™ or placebo. There was no significant change in perceived muscle soreness as measured by algometry for either PCSO-524™ or placebo. There was significant attenuation of creatine kinase MM in the blood following EMD immediately (t = 4.467, p < .001; 95% CI = 63.0 – 169.2), 2 (t = 5.076, p < .001; 95% CI = 76.1 – 178.6), 24 (t = 12.829, p < .001; 95% CI = 562.5 – 775.6), 48 (t = 11.477, p < .001; 95% CI = 493.2 – 706.7), 72 (t =9.118, p < .001; 95% CI = 359.8 – 567.5), and 96 hours (t = 11.935, p < .001; 95% CI = 574.4 – 811.6). Significant attenuation of myoglobin occurred 24 (t = 4.334, p < .001; 95% CI = 22.9 – 63.7), 48 (t = 6.402, p < .001; 95% CI = 67.7 – 131.1), 72 (t = 5.340, p < .001; 95% CI = 119.0 – 266.3), and 96 hours (t = 3.272, p < .01; 95% CI = 49.0 – 212.3) compared to placebo. Significant attenuation of skeletal muscle troponin I occurred in the PCSO-524™ group compared to placebo 2 (t = 2.562, p < .05; 95% CI = 0.9 – 8.0), 24 (t = 3.561, p < .01; 95% CI = 4.4 – 15.4), 48 (t = 4.095, p < .001; 95% CI = 4.7 – 14.0), 72 (T = 3.222, p < .01; 95% CI = 2.5 – 11.2), and 96 hours (T = 2.177, p < .05; 95% CI = 0.3 – 10.4) post EIMD. No significant effect of supplementation status on fatty acid binding protein appearance in the blood (F = .418 p = .523) post EMID. Significant attenuation of Interleukin-6 was observed 24 (t = 3.619, p < .01; 95% CI = 3.7 – 13.3), 48 (t = 3.993, p < .001; 95% CI = 5.8 – 17.8), 72 (t = 3.621, p < .01; 95% CI = 5.0 – 17.9), and 96 hours (t = 3.076, p < .01; 95% CI = 3.1 – 15.35) post EMID compared to placebo. A significant effect of time on TNF alpha concentration in the blood (F = 132.012 p < .001) was observed 24 (t = 4.633, p < .001; 95% CI = 11.1 – 28.5), 48 (t = 4.942, p < .001; 95% CI = 10.6 – 25.7), 72 (t = 4.747, p < .001; 95% CI = 11.3 – 28.5), and 96 hours (t = 6.349, p < .001; 95% CI = 16.8 – 32.8) post EIMD. No significant effect of time on 8-OHdG concentration in the blood (F = 1.018 p .419) was observed in either the PCSO-524™ group or placebo after EIMD. No significant effect of time was observed on cTn1 concentration in the blood (F = .420 p = .889) in either PCSO-524™ or placebo after EIMD. CONCLUSIONS: Four weeks of PCSO-524™ supplementation does not improve swelling as determined by thigh girth; perceived pain by the use of algometry; appearance of Fatty Acid Binding Protein, 8-hydroxy-2' -deoxyguanosine (8-OHdG), and Cardiac Troponin I in the blood in 6 untrained males after downhill running compared to placebo. Four weeks of PCSO-524™ supplementation is effective at attenuating maximal voluntary contraction force loss; loss of range of motion; and reducing the appearance of creatine kinase-MM; skeletal muscle troponin I; interleukin-6; and Tumor Necrosis Factor- alpha in the blood in untrained males after downhill running.Submitted to the faculty of the University Graduate School in partial fulfillment of the requirements for the degree Master of Science in the Department of Kinesiology, School of Public Health Indiana University, Bloomington, Indian