Derivation of the Exponential Distribution through an Infinite Sine Series

This communication provides a derivation of the often-used oneparameter exponential family of distributions based on an infinite sine series. The main results associated with this derivation are the finite approximations of the probability density function (pdf) and the cumulative distribution function (cdf) of the exact one-parameter exponential family of distributions. The limit of these finite functions are the exact pdf and cdf. Numerical examples are provided to compare and contrast the finite approximations of distributions in terms of error using the finite-based cdf and the exact standard exponential cdf. We would also note that the finite approximations of the pdf and cdf vary in terms of both shape and percentage points. In view of this, the finite pdf and cdf offer a user the flexibility to potentially provide more accurate approximations in the context of fitting distributions to data rather than approximations that are based solely on the exact exponential pdf or cdf – most notably when distributions are heavy-(right)tailed

Shear-driven size segregation of granular materials: modeling and experiment

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then re-segregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we locally map the measured height of the experimental sample (which indicates the degree of segregation) to the local packing density. We observe that the model successfully captures the presence of a fast mixing process and relatively slower re-segregation process, but the model predicts a finite re-segregation time, while in the experiment re-segregation occurs only exponentially in time

Herbicide-Resistant Soybeans in Arkansas: Lessons Learned and Future Direction

In Arkansas Delta soybean production, glyphosate resistant (GR) Palmer amaranth has significantly impacted weed management. The incidence of herbicide resistant (HR) weeds has farreaching crop science, economic, and communications implications, which have been explored by the corresponding expertise of our research team members to form a comprehensive literature review. The review was used to develop policy recommendations to address current and future HR genetically modified (GM) crop use and the associated issues. The review of crop science research indicated an overall increase in herbicide application, as well as an increase in weed management programs focused around glyphosate rather than the application of multiple herbicides. The review also revealed some management methods have potential to resolve the problem, including alternating herbicide application, avoiding sub-lethal rates, using “burn down” herbicides prior to planting, crop rotation, tillage, and zero tolerance weed policies. The use of fewer herbicides rather than multiple types creates a monopolistic edge for the companies producing those few herbicides, allowing greater market control. Crisis communication methods, including developing internal readiness, conducting needs assessments, developing a relevant message, and conveying the message through appropriate channels, can be used to develop a response to the issue that will best communicate necessary information to the target audience. The team used these findings to formulate policy recommendations, which include management, economic, and communication plans that may provide a starting point to address the issue

Mutations in the E2 glycoprotein and the 3\u27 untranslated region enhance chikungunya virus virulence in mice

Chikungunya virus (CHIKV) is a mosquito-transmitted alphavirus that causes debilitating musculoskeletal pain and inflammation and can persist for months to years after acute infection. Although studies of humans and experimentally infected animals suggest that CHIKV infection persists in musculoskeletal tissues, the mechanisms for this remain poorly understood. To evaluate this further, we isolated CHIKV from the serum of persistently infected Rag1 -/- mice at day 28. When inoculated into naive wild-type (WT) mice, this persistently circulating CHIKV strain displayed a capacity for earlier dissemination and greater pathogenicity than the parental virus. Sequence analysis revealed a nonsynonymous mutation in the E2 glycoprotein (E2 K200R) and a deletion within the 3' untranslated region (3'-UTR). The introduction of these changes into the parental virus conferred enhanced virulence in mice, although primary tropism for musculoskeletal tissues was maintained. The E2 K200R mutation was largely responsible for enhanced viral dissemination and pathogenicity, although these effects were augmented by the 3'- UTR deletion. Finally, studies with Irf3/Irf7 -/- and Ifnar1 -/- mice suggest that the E2 K200R mutation enhances viral dissemination from the site of inoculation independently of interferon regulatory factor 3 (IRF3)-, IRF7-, and IFNAR1-mediated responses. As our findings reveal viral determinants of CHIKV dissemination and pathogenicity, their further study should help to elucidate host-virus interactions that determine acute and chronic CHIKV infection

While shoot herbivores reduce, root herbivores increase nutrient enrichment’s impact on diversity in a grassland model

Nutrient enrichment is widespread throughout grassland systems and expected to increase during the Anthropocene. Trophic interactions, like aboveground herbivory, have been shown to mitigate its effect on plant diversity. Belowground herbivory may also impact these habitats’ response to nutrient enrichment, but its influence is much less understood, and likely to depend on factors such as the herbivores’ preference for dominant species and the symmetry of belowground competition. If preferential toward the dominant, fastest growing species, root herbivores may reduce these species’ relative fitness and support diversity during nutrient enrichment. However, as plant competition belowground is commonly considered to be symmetric, root herbivores may be less impactful than shoot herbivores because they do not reduce any competitive asymmetry between the dominant and subordinate plants. To better understand this system, we used an established, two-layer, grassland community model to run a full-factorially designed simulation experiment, crossing the complete removal of aboveground herbivores and belowground herbivores with nutrient enrichment. After 100 yr of simulation, we analyzed communities' diversity, competition on the individual level, as well as their resistance and recovery. The model reproduced both observed general effects of nutrient enrichment in grasslands and the short-term trends of specific experiments. We found that belowground herbivores exacerbate the negative influence of nutrient enrichment on Shannon diversity within our model grasslands, while aboveground herbivores mitigate its effect. Indeed, data on individuals’ above- and belowground resource uptake reveals that root herbivory reduces resource limitation belowground. As with nutrient enrichment, this shifts competition aboveground. Since shoot competition is asymmetric, with larger, taller individuals gathering disproportionate resources compared to their smaller, shorter counterparts, this shift promotes the exclusion of the smallest species. While increasing the root herbivores’ preferences toward dominant species lessens their negative impact, at best they are only mildly advantageous, and they do very little reduce the negative consequences of nutrient enrichment. Because our model’s belowground competition is symmetric, we hypothesize that root herbivores may be beneficial when root competition is asymmetric. Future research into belowground herbivory should account for the nature of competition belowground to better understand the herbivores’ true influence

Effects of ruxolitinib cream on pruritus and quality of life in atopic dermatitis: Results from a phase 2, randomized, dose-ranging, vehicle- and active-controlled study

BACKGROUND: Atopic dermatitis (AD), a chronic, highly pruritic skin disorder, impairs quality of life (QoL). Janus kinase inhibitors suppress inflammatory and pruritus-associated cytokine signaling in AD. OBJECTIVE: To report the effects of ruxolitinib (RUX) cream on itch and QoL in AD. METHODS: A total of 307 adult patients with an Investigator\u27s Global Assessment (score of 2 or 3) and 3% to 20% affected body surface area were randomly assigned for 8 weeks to receive double-blind treatment with RUX (1.5% twice daily, 1.5% once daily, 0.5% once daily, or 0.15% once daily), vehicle twice daily, or triamcinolone cream (0.1% twice daily for 4 weeks then vehicle for 4 weeks). Itch was measured by using the numerical rating scale, and patient QoL was assessed with Skindex-16. RESULTS: Improvements in itch numerical rating scale and Skindex-16 were observed with RUX cream. Overall, 42.5% of patients who applied 1.5% RUX twice daily experienced minimal clinically important difference in itch within 36 hours of treatment (vehicle, 13.6%; P \u3c .01); near-maximal improvement was observed by week 4. Itch reduction was associated with improved QoL burden (Pearson correlation, 0.67; P \u3c .001). Significant improvements in Skindex-16 overall scores were noted at week 2. LIMITATIONS: Facial AD lesions were not treated. CONCLUSION: RUX cream provides a clinically meaningful reduction in itch and QoL burden

Abundances in Stars from the Red Giant Branch Tip to the Near Main Sequence in M71: II. Iron Abundance

We present [Ffe/H] abundance results that involve a sample of stars with a wide range in luminosity from luminous giants to stars near the turnoff in a globular cluster. Our sample of 25 stars in M71 includes 10 giant stars more luminous than the RHB, 3 horizontal branch stars, 9 giant stars less luminous than the RHB, and 3 stars near the turnoff. We analyzed both Fe I and Fe II lines in high dispersion spectra observed with HIRES at the W. M. Keck Observatory. We find that the [Fe/H] abundances from both Fe I and Fe II lines agree with each other and with earlier determinations. Also the [Fe/H] obtained from Fe I and Fe II lines is constant within the rather small uncertainties for this group of stars over the full range in Teff and luminosity, suggesting that NLTE effects are negligible in our iron abundance determination. In this globular cluster, there is no difference among the mean [Fe/H] of giant stars located at or above the RHB, RHB stars, giant stars located below the RHB and stars near the turnoff.Comment: Minor changes to conform to version accepted for publication, with several new figures (Paper 2 of a pair

Lessons Learned from OSIRIS-Rex Autonomous Navigation Using Natural Feature Tracking

The Origins, Spectral Interpretation, Resource Identification, Security-Regolith Explorer (Osiris-REx) spacecraft is scheduled to launch in September, 2016 to embark on an asteroid sample return mission. It is expected to rendezvous with the asteroid, Bennu, navigate to the surface, collect a sample (July 20), and return the sample to Earth (September 23). The original mission design called for using one of two Flash Lidar units to provide autonomous navigation to the surface. Following Preliminary design and initial development of the Lidars, reliability issues with the hardware and test program prompted the project to begin development of an alternative navigation technique to be used as a backup to the Lidar. At the critical design review, Natural Feature Tracking (NFT) was added to the mission. NFT is an onboard optical navigation system that compares observed images to a set of asteroid terrain models which are rendered in real-time from a catalog stored in memory on the flight computer. Onboard knowledge of the spacecraft state is then updated by a Kalman filter using the measured residuals between the rendered reference images and the actual observed images. The asteroid terrain models used by NFT are built from a shape model generated from observations collected during earlier phases of the mission and include both terrain shape and albedo information about the asteroid surface. As a result, the success of NFT is highly dependent on selecting a set of topographic features that can be both identified during descent as well as reliably rendered using the shape model data available. During development, the OSIRIS-REx team faced significant challenges in developing a process conducive to robust operation. This was especially true for terrain models to be used as the spacecraft gets close to the asteroid and higher fidelity models are required for reliable image correlation. This paper will present some of the challenges and lessons learned from the development of the NFT system which includes not just the flight hardware and software but the development of the terrain models used to generate the onboard rendered images

Simple guide to starting a research group

Conducting cutting-edge research and scholarship becomes more complicated with each passing year; forming a collaborative research group offers a way to navigate this increasing complexity. Yet many individuals whose work might benefit from the formation of a collaborative team may feel overwhelmed by the prospect of attempting to build and maintain a research group. We propose this simple guide for starting and maintaining such an enterprise