On invariants of elliptic curves on average

We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides $A$ and $B$. As an example, let $E$ be an elliptic curve defined over $\mathbb{Q}$ and $p$ be a prime of good reduction for $E$. Let $e_{E}(p)$ be the exponent of the group of rational points of the reduction modulo $p$ of $E$ over the finite field $\mathbb{F}_p$. Let $\mathcal{C}$ be the family of elliptic curves $$E_{a,b}:~y^2=x^3+ax+b,$$ where $|a|\leq A$ and $|b|\leq B$. We prove that, for any $c>1$ and $k\in \mathbb{N}$, $$\frac{1}{|\mathcal{C}|} \sum_{E\in \mathcal{C}} \sum_{p\leq x} e_E^k(p) = C_k {\rm li}(x^{k+1})+O\left(\frac{x^{k+1}}{(\log{x})^c} \right),$$ as $x\rightarrow \infty$, as long as $A, B>\exp\left(c_{1} (\log{x})^{1/2} \right)$ and $AB>x(\log{x})^{4+2c}$, where $c_1$ is a suitable positive constant. Here $C_k$ is an explicit constant given in the paper which depends only on $k$, and ${\rm li}(x)=\int_{2}^x dt/\log{t}$. We prove several similar results as corollaries to a general theorem. The method of the proof is capable of improving some of the known results with $A, B>x^\epsilon$ and $AB>x(\log{x})^\delta$ to $A, B>\exp\left(c_1 (\log{x})^{1/2} \right)$ and $AB>x(\log{x})^\delta$

How do coral reef fishes develop into athletes?

Adam Downie studied the development of swimming abilities of coral reef fishes during their larval phase. He found that reef fish larvae require high oxygen uptake rates to support development and swimming, mediated by genetic, cellular, and muscle-tissue changes. These physiological mechanisms are important for understanding how reef fish larvae swim toward and transition to life on the reef

Taking clinical judgment out of the equation : a call for the standardization of MCI diagnostic criteria and construction of a model to predict conversion to dementia.

Although the diagnostic criteria for mild cognitive impairment have evolved considerably since their inception, they remain varied and able to be interpreted and implemented in different ways depending on the judgment of the clinician. Because of this issue, a wide range of incidence, prevalence, and conversion rates are found in the research literature. Using data collected from 400 patients with amnestic mild cognitive impairment, limitations inherent in current mild cognitive impairment diagnostic criteria were addressed. First, using Alzheimer’s Disease Neuroimaging Initiative diagnostic criteria, an equation was constructed to predict conversion from mild cognitive impairment to dementia by analyzing the predictive ability of variables representative of a number of categories (i.e., demographic, psychiatric, functional, biomarker, imaging, and cognitive). This model accounted for over 60% of variance in conversion and exhibited an area under the curve of 0.93. Then, separate models were constructed using different applications of the current diagnostic criteria for mild cognitive impairment. As expected, criteria utilizing a one standard deviation clinical cutoff on a measure of delayed verbal recall in combination with the allowance for some functional change (i.e., scores =5 on the Functional Activities Questionnaire) exhibited the greatest utility of any combination of diagnostic criteria. Taken together, these results indicate that statistical equations can be constructed to predict conversion from mild cognitive impairment to dementia and be tailored for widespread clinical use. Moreover, these results show that the standardization of current diagnostic criteria for mild cognitive impairment is clearly needed

REMEDYING UNDERPERFORMING SOLAR PV ASSETS WITH ELECTROLYZER RETROFITS

This study explores and quantifies the value of retrofitting utility-scale solar PV-only assets with PEM electrolyzers to produce green hydrogen. Momentum for global hydrogen demand as well as pathways towards decarbonization, are discussed. The study then highlights ways in which green hydrogen electrolyzers could benefit solar PV assets’ financial performance. Hypothetical assets within California’s CAISO jurisdiction are examined and good candidates for retrofits are identified. Aspects unique to the CAISO market are fleshed-out like The Duck Curve and the high proportion of renewable energy sources. The study uses a Monte Carlo simulation to demonstrate probabilistic combinations of solar PV and green hydrogen lifecycle costs. Use of this framework as a guide would enable project developers and/or investors to facilitate necessary transitions to a reliable, affordable, and clean economy

Moral distress and moral residue among nurses working in the surgical intensive care unit: a descriptive qualitative approach.

Introduction: Approximately one in five Americans will die in the intensive care unit (ICU). Nurses spend more time with chronically ill and end-of-life patients than any other healthcare professional, and may perceive some actions in the ICU as immoral. Moral distress is defined as knowing the right course of action to take but being hindered by institutional constraints. Development of the Moral Distress Scale-Revised revealed that 31% of ICU nurses left a prior position or considered leaving their current nursing job because of moral distress. The purpose of this descriptive qualitative study is to explore surgical ICU (SICU) nurses’ perceptions and experiences of moral distress and moral residue, coping, and perceived quality of care. Methods: A descriptive qualitative approach used in-depth, semi-structured individual interviews with SICU nurses. Purposive sampling methods of maximum likelihood variation and snowball sampling recruited a heterogeneous sample of 21 SICU nurses from two SICUs in a university hospital until theoretical saturation occurred. Essential themes were identified through reflective writing, rewriting, memoing, and content and thematic analysis. Verbatim transcription of interviews and an audit trail ensured rigor and trustworthiness of the data in order to highlight descriptions, patterns, uniqueness, and interpretations of firsthand accounts. Conclusion: Moral issues were highlighted to explore root causes of moral distress at the individual-level for SICU nurses with a deeper understanding of moral distress and moral residue, particularly how nurses cope with the stress involved and their perceptions of the influence of moral distress on quality patient care. Understanding nurses’ experiences is essential to addressing ethical issues of moral distress and moral residue before they negatively impact patient outcomes

Two-dimensional electron gas in a modulation-doped SrTiO3/Sr(Ti,Zr)O3 heterostructure

A two-dimensional electron gas (2DEG) in SrTiO3 is created via modulation doping by interfacing undoped SrTiO3 with a wider-band-gap material, SrTi1-xZrxO3, that is doped n-type with La. All layers are grown using hybrid molecular beam epitaxy. Using magnetoresistance measurements, we show that electrons are transferred into the SrTiO3, and a 2DEG is formed. In particular, Shubnikov-de Haas oscillations are shown to depend only on the perpendicular magnetic field. Experimental Shubnikov-de Haas oscillations are compared with calculations that assume multiple occupied subbands.Comment: Submitted to Applied Physics Letter

Localization and Expression Level of Vascular Endothelial Growth Factor after Partial Hepatectomy of WKY Rats

Inflammation and fibrosis are indicative of liver regeneration following injury and chronic liver diseases, such as cirrhosis and hepatocellular carcinoma. The formation of new vasculature via the process of angiogenesis is vital to the pathological progression of liver regeneration and these diseases. Thus, inhibiting the process of angiogenesis could have the potential to stop or slow the progression of chronic liver diseases. Vascular endothelial growth factor (VEGF) is the most potent and specific growth factor for initiating the process of angiogenesis, making it a prime target to inhibit angiogenesis. Bevacizumab is an antibody that binds to VEGF, inhibiting it from initiating angiogenesis. To investigate the effect that bevacizumab had on VEGF, we determined the localization and expression levels of VEGF after partial hepatectomy in Wistar-Kyoto rats using quantitative immunofluorescence. The tissue samples (n=5) consisted of four groups. Group 1 received no treatment and served as the negative control. Group 2 received bevacizumab treatment without hepatectomy and group 3 had a hepatectomy without bevacizumab treatment. Groups 2 and 3 served as controls to bevacizumab treatment and hepatectomy, respectfully. Group 4, the experimental group, had both hepatectomy and bevacizumab treatment. Western Blot analysis confirmed a significant increase in the level of VEGF in rats receiving partial hepatectomy treatment only. To determine the expression level of VEGF in cells/tissues, we prepared cryosections and probed with a fluorescently labelled anti-VEGF. Digitized images were captured using Simple PCI and localization pattern and expression level determined. Our results have broadened our understanding of chronic liver diseases