Investigations in Patterns in Last Digits of Square Numbers and Higher Powers

It is interesting to see what patterns exist in the final digits of powers of integers; the goal of this work is to introduce some new problems and results, which are ideally suited for interested readers to pursue further. We start our investigation with squares and say a square is a k-square good number if its last k digits base 10 are the same non-zero number, and the last k + 1 digits are not identical. We completely analyze k-square good numbers; when k = 1 we can have final digits of 1, 4, 5, 6 and 9 (with the second to last digit different), when k = 2 we can end with 44 but not 444, when k = 3 we can end with 444 but not 4444, and there are no 4-square good numbers. We then generalize these arguments to look at k-cube and k-fourth good numbers, completely analyzing these cases. Noting that any even power 2m is the same as squaring an mth power, we can extend our results to even powers more easily than to odd, as the behavior has to be a subset of what we have seen for squares. There are complications arising from powers of 2 dividing our numbers, but using results from elementary number theory (in particular concerning the totient function and Euler’s theorem), we reduce the problem for even powers to a tractable finite computation, and completely resolve this case, and then end with a list of accessible next problems

Lantana: Current Management Status and Future Prospects

Crop Production/Industries,

A Teacher Fellowship Program: Integrating Place-Based Sustainability Education into K - 12 Classrooms

The Dow Innovation Teacher Fellowship (DITF), sponsored by Dow Chemical, aims to provide educators with more support as they become stewards of the environment. DITF is implemented through the University of Michigan’s Center for Education Design, Evaluation, and Research (CEDER). DITF supports professional development of teachers in the SaginawMidland-Bay tri-city area of Michigan on sustainability education methods, through professional development opportunities. The program integrates sustainability across school subjects, to support the execution of interdisciplinary sustainability learning units in middle and high school classrooms, using project and place-based pedagogical methods. This project leveraged a targeted qualitative research process (under IRB exemption number HUM00165059) by UM School for Environment and Sustainability (UMSEAS) graduate students to enrich the pilot year of the DITF program. We began in Spring 2019, conducting an annotated literature review about place-based and environmental education, as well as other approaches to sustainability learning. The idea being to benchmark for professional development activities on best practices with incoming fellows in addition to professionals interested in this work. As the cohort embarked on designing sustainability learning units for their respective classrooms further research was conducted to monitor their progress. Research methods included: ● Documentation of Fellows early progress on developing learning units through semi structured entry interviews ● Track challenges and collaborative successes through participant observations and touchpoint interviews ● Evaluate learning experiences for educators, civic partners, and students through concept maps and exit interviews ● Analyze all observations, interviews, and media to design a case study on one Fellows experience with the program utilizing supportive information from other cohort members. Interviews were transcribed and coded using Dedoose software. Interviews enabled us to elicit feedback, provide suggestions for future DITF growth, and recruit and train for a second cohort in Spring 2020. Interviews also allowed us to select from among the cohort a focal “case” from which other educators, school administrators and civic partners can learn about evolving best practices through the perspective of Phil Schwedler. An online case study is pertinent especially in the current time (we are currently in the global CoVid-19 pandemic) as shifts to online learning are becoming more prominent. We scoped the resultant learning case through analysis of our qualitative data and a series of case conceptualization workshops alternately held in the gala platform offices at UMSEAS and at CEDER in the UM School of Education. The case, hosted on Gala, an open access platform www.learngala.com, follows Phil, an eighth-grade teacher from Freeland Middle School in Bay City, Michigan from the summer professional development workshop through lesson creation and implementation, to mentoring others participating in similar work. Trying something new as a teacher is always risky but teaching in times of environmental crisis brings new challenges. The DITF Program offers supportive partnerships and professional development experiences for educators; the collaboration between UM SEAS and CEDER displays how support can be paid forward through agile, responsively designed, learning tools for integrating modules on emerging fields of knowledge in environmental curricula. A note to the reader: The purpose of this research was to develop an inaugural CEDER Michigan Sustainability Case Study about how teachers develop and implement place-based sustainability education. The case is set up to narrate these experiences in order to reach a broad range of audiences with specific helpful insights to aid educators and other sustainability education organizations in their future endeavors with this work. Michigan Case Studies are one library of modules showcased on learngala.com. What follows is the main content of the case study, in text form. For a more interactive experience, follow this link to see our case study on the Gala platform. Learning Questions 1. What is the importance of place-based learning in terms of sustainability education? 2. What methods and modalities can educators use for sustainability education? 3. How can we better support our educators as they help us learn more about the environments we live in? 4. How can place-based sustainability education inspire future environmental leaders?Master of ScienceSchool for Environment and SustainabilityUniversity of Michiganhttps://deepblue.lib.umich.edu/bitstream/2027.42/155015/1/A Teacher Fellowship Program.pd

The role of sand lances (Ammodytes sp.) in the Northwest Atlantic ecosystem: a synthesis of current knowledge with implications for conservation and management

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Staudinger, M. D., Goyert, H., Suca, J. J., Coleman, K., Welch, L., Llopiz, J. K., Wiley, D., Altman, I., Applegate, A., Auster, P., Baumann, H., Beaty, J., Boelke, D., Kaufman, L., Loring, P., Moxley, J., Paton, S., Powers, K., Richardson, D., Robbins, J., Runge, J., Smith, B., Spiegel, C., & Steinmetz, H. The role of sand lances (Ammodytes sp.) in the Northwest Atlantic ecosystem: a synthesis of current knowledge with implications for conservation and management. Fish and Fisheries, 00, (2020): 1-34, doi:10.1111/faf.12445.The American sand lance (Ammodytes americanus, Ammodytidae) and the Northern sand lance (A. dubius, Ammodytidae) are small forage fishes that play an important functional role in the Northwest Atlantic Ocean (NWA). The NWA is a highly dynamic ecosystem currently facing increased risks from climate change, fishing and energy development. We need a better understanding of the biology, population dynamics and ecosystem role of Ammodytes to inform relevant management, climate adaptation and conservation efforts. To meet this need, we synthesized available data on the (a) life history, behaviour and distribution; (b) trophic ecology; (c) threats and vulnerabilities; and (d) ecosystem services role of Ammodytes in the NWA. Overall, 72 regional predators including 45 species of fishes, two squids, 16 seabirds and nine marine mammals were found to consume Ammodytes. Priority research needs identified during this effort include basic information on the patterns and drivers in abundance and distribution of Ammodytes, improved assessments of reproductive biology schedules and investigations of regional sensitivity and resilience to climate change, fishing and habitat disturbance. Food web studies are also needed to evaluate trophic linkages and to assess the consequences of inconsistent zooplankton prey and predator fields on energy flow within the NWA ecosystem. Synthesis results represent the first comprehensive assessment of Ammodytes in the NWA and are intended to inform new research and support regional ecosystem‐based management approaches.This manuscript is the result of follow‐up work stemming from a working group formed at a two‐day multidisciplinary and international workshop held at the Parker River National Wildlife Refuge, Massachusetts in May 2017, which convened 55 experts scientists, natural resource managers and conservation practitioners from 15 state, federal, academic and non‐governmental organizations with interest and expertise in Ammodytes ecology. Support for this effort was provided by USFWS, NOAA Stellwagen Bank National Marine Sanctuary, U.S. Department of the Interior, U.S. Geological Survey, Northeast Climate Adaptation Science Center (Award # G16AC00237), an NSF Graduate Research Fellowship to J.J.S., a CINAR Fellow Award to J.K.L. under Cooperative Agreement NA14OAR4320158, NSF award OCE‐1325451 to J.K.L., NSF award OCE‐1459087 to J.A.R, a Regional Sea Grant award to H.B. (RNE16‐CTHCE‐l), a National Marine Sanctuary Foundation award to P.J.A. (18‐08‐B‐196) and grants from the Mudge Foundation. The contents of this paper are the responsibility of the authors and do not necessarily represent the views of the National Oceanographic and Atmospheric Administration, U.S. Fish and Wildlife Service, New England Fishery Management Council and Mid‐Atlantic Fishery Management Council. This manuscript is submitted for publication with the understanding that the United States Government is authorized to reproduce and distribute reprints for Governmental purposes. Any use of trade, firm or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government

Assessment of a Program for SARS-CoV-2 Screening and Environmental Monitoring in an Urban Public School District

Importance: Scalable programs for school-based SARS-CoV-2 testing and surveillance are needed to guide in-person learning practices and inform risk assessments in kindergarten through 12th grade settings. Objectives: To characterize SARS-CoV-2 infections in staff and students in an urban public school setting and evaluate test-based strategies to support ongoing risk assessment and mitigation for kindergarten through 12th grade in-person learning. Design, Setting, and Participants: This pilot quality improvement program engaged 3 schools in Omaha, Nebraska, for weekly saliva polymerase chain reaction testing of staff and students participating in in-person learning over a 5-week period from November 9 to December 11, 2020. Wastewater, air, and surface samples were collected weekly and tested for SARS-CoV-2 RNA to evaluate surrogacy for case detection and interrogate transmission risk of in-building activities. Main Outcomes and Measures: SARS-CoV-2 detection in saliva and environmental samples and risk factors for SARS-CoV-2 infection. Results: A total of 2885 supervised, self-collected saliva samples were tested from 458 asymptomatic staff members (mean [SD] age, 42.9 [12.4] years; 303 women [66.2%]; 25 Black or African American [5.5%], 83 Hispanic [18.1%], 312 White [68.1%], and 35 other or not provided [7.6%]) and 315 students (mean age, 14.2 [0.7] years; 151 female students [48%]; 20 Black or African American [6.3%], 201 Hispanic [63.8%], 75 White [23.8%], and 19 other race or not provided [6.0%]). A total of 46 cases of SARS-CoV-2 (22 students and 24 staff members) were detected, representing an increase in cumulative case detection rates from 1.2% (12 of 1000) to 7.0% (70 of 1000) among students and from 2.1% (21 of 1000) to 5.3% (53 of 1000) among staff compared with conventional reporting mechanisms during the pilot period. SARS-CoV-2 RNA was detected in wastewater samples from all pilot schools as well as in air samples collected from 2 choir rooms. Sequencing of 21 viral genomes in saliva specimens demonstrated minimal clustering associated with 1 school. Geographical analysis of SARS-CoV-2 cases reported district-wide demonstrated higher community risk in zip codes proximal to the pilot schools. Conclusions and Relevance: In this study of staff and students in 3 urban public schools in Omaha, Nebraska, weekly screening of asymptomatic staff and students by saliva polymerase chain reaction testing was associated with increased SARS-CoV-2 case detection, exceeding infection rates reported at the county level. Experiences differed among schools, and virus sequencing and geographical analyses suggested a dynamic interplay of school-based and community-derived transmission risk. Collectively, these findings provide insight into the performance and community value of test-based SARS-CoV-2 screening and surveillance strategies in the kindergarten through 12th grade educational setting

Presenilin 2 Is the Predominant γ-Secretase in Microglia and Modulates Cytokine Release

Presenilin 1 (PS1) and Presenilin 2 (PS2) are the enzymatic component of the γ-secretase complex that cleaves amyloid precursor protein (APP) to release amyloid beta (Aβ) peptide. PS deficiency in mice results in neuroinflammation and neurodegeneration in the absence of accumulated Aβ. We hypothesize that PS influences neuroinflammation through its γ-secretase action in CNS innate immune cells. We exposed primary murine microglia to a pharmacological γ-secretase inhibitor which resulted in exaggerated release of TNFα and IL-6 in response to lipopolysaccharide. To determine if this response was mediated by PS1, PS2 or both we used shRNA to knockdown each PS in a murine microglia cell line. Knockdown of PS1 did not lead to decreased γ-secretase activity while PS2 knockdown caused markedly decreased γ-secretase activity. Augmented proinflammatory cytokine release was observed after knockdown of PS2 but not PS1. Proinflammatory stimuli increased microglial PS2 gene transcription and protein in vitro. This is the first demonstration that PS2 regulates CNS innate immunity. Taken together, our findings suggest that PS2 is the predominant γ-secretase in microglia and modulates release of proinflammatory cytokines. We propose PS2 may participate in a negative feedback loop regulating inflammatory behavior in microglia

Efficacy of APX2039 in a Rabbit Model of Cryptococcal Meningitis

Cryptococcal Meningitis (CM) is uniformly fatal if not treated, and treatment options are limited. We previously reported on the activity of APX2096, the prodrug of the novel Gwt1 inhibitor APX2039, in a mouse model of CM. Here, we investigated the efficacy of APX2039 in mouse and rabbit models of CM. In the mouse model, the controls had a mean lung fungal burden of 5.95 log10 CFU/g, whereas those in the fluconazole-, amphotericin B-, and APX2039-treated mice were 3.56, 4.59, and 1.50 log10 CFU/g, respectively. In the brain, the control mean fungal burden was 7.97 log10 CFU/g, while the burdens were 4.64, 7.16, and 1.44 log10 CFU/g for treatment with fluconazole, amphotericin B, and APX2039, respectively. In the rabbit model of CM, the oral administration of APX2039 at 50 mg/kg of body weight twice a day (BID) resulted in a rapid decrease in the cerebrospinal fluid (CSF) fungal burden, and the burden was below the limit of detection by day 10 postinfection. The effective fungicidal activity (EFA) was -0.66 log10 CFU/mL/day, decreasing from an average of 4.75 log10 CFU/mL to 0 CFU/mL, over 8 days of therapy, comparing favorably with good clinical outcomes in humans associated with reductions of the CSF fungal burden of -0.4 log10 CFU/mL/day, and, remarkably, 2-fold the EFA of amphotericin B deoxycholate in this model (-0.33 log10 CFU/mL/day). A total drug exposure of the area under the concentration-time curve from 0 to 24 h (AUC0-24) of 25 to 50 mg · h/L of APX2039 resulted in near-maximal antifungal activity. These data support the further preclinical and clinical evaluation of APX2039 as a new oral fungicidal monotherapy for the treatment of CM. IMPORTANCE Cryptococcal meningitis (CM) is a fungal disease with significant global morbidity and mortality. The gepix Gwt1 inhibitors are a new class of antifungal drugs. Here, we demonstrated the efficacy of APX2039, the second member of the gepix class, in rabbit and mouse models of cryptococcal meningitis. We also analyzed the drug levels in the blood and cerebrospinal fluid in the highly predictive rabbit model and built a mathematical model to describe the behavior of the drug with respect to the elimination of the fungal pathogen. We demonstrated that the oral administration of APX2039 resulted in a rapid decrease in the CSF fungal burden, with an effective fungicidal activity of -0.66 log10 CFU/mL/day, comparing favorably with good clinical outcomes in humans associated with reductions of -0.4 log10 CFU/mL/day. The drug APX2039 had good penetration of the central nervous system and is an excellent candidate for future clinical testing in humans for the treatment of CM

Transmission Characteristics of Primate Vocalizations: Implications for Acoustic Analyses

Acoustic analyses have become a staple method in field studies of animal vocal communication, with nearly all investigations using computer-based approaches to extract specific features from sounds. Various algorithms can be used to extract acoustic variables that may then be related to variables such as individual identity, context or reproductive state. Habitat structure and recording conditions, however, have strong effects on the acoustic structure of sound signals. The purpose of this study was to identify which acoustic parameters reliably describe features of propagated sounds. We conducted broadcast experiments and examined the influence of habitat type, transmission height, and re-recording distance on the validity (deviation from the original sound) and reliability (variation within identical recording conditions) of acoustic features of different primate call types. Validity and reliability varied independently of each other in relation to habitat, transmission height, and re-recording distance, and depended strongly on the call type. The smallest deviations from the original sounds were obtained by a visually-controlled calculation of the fundamental frequency. Start- and end parameters of a sound were most susceptible to degradation in the environment. Because the recording conditions can have appreciable effects on acoustic parameters, it is advisable to validate the extraction method of acoustic variables from recordings over longer distances before using them in acoustic analyses

Upconversion Nanomaterials: Synthesis, Mechanism, and Applications in Sensing

Upconversion is an optical process that involves the conversion of lower-energy photons into higher-energy photons. It has been extensively studied since mid-1960s and widely applied in optical devices. Over the past decade, high-quality rare earth-doped upconversion nanoparticles have been successfully synthesized with the rapid development of nanotechnology and are becoming more prominent in biological sciences. The synthesis methods are usually phase-based processes, such as thermal decomposition, hydrothermal reaction, and ionic liquids-based synthesis. The main difference between upconversion nanoparticles and other nanomaterials is that they can emit visible light under near infrared irradiation. The near infrared irradiation leads to low autofluorescence, less scattering and absorption, and deep penetration in biological samples. In this review, the synthesis of upconversion nanoparticles and the mechanisms of upconversion process will be discussed, followed by their applications in different areas, especially in the biological field for biosensing

Using Population Genetic Theory and DNA Sequences for Species Detection and Identification in Asexual Organisms

It is widely agreed that species are fundamental units of biology, but there is little agreement on a definition of species or on an operational criterion for delimiting species that is applicable to all organisms.We focus on asexual eukaryotes as the simplest case for investigating species and speciation. We describe a model of speciation in asexual organisms based on basic principles of population and evolutionary genetics. The resulting species are independently evolving populations as described by the evolutionary species concept or the general lineage species concept. Based on this model, we describe a procedure for using gene sequences from small samples of individuals to assign them to the same or different species. Using this method of species delimitation, we demonstrate the existence of species as independent evolutionary units in seven groups of invertebrates, fungi, and protists that reproduce asexually most or all of the time.This wide evolutionary sampling establishes the general existence of species and speciation in asexual organisms. The method is well suited for measuring species diversity when phenotypic data are insufficient to distinguish species, or are not available, as in DNA barcoding and environmental sequencing. We argue that it is also widely applicable to sexual organisms