We show that if an open set in $\mathbb{R}^d$ can be fibered by unit n-spheres, then $d \geq 2n+1$, and if $d = 2n+1$, then the spheres must be pairwise linked, and $n \in \left\{0, 1, 3, 7 \right\}$. For these values of n, we construct unit n-sphere fibrations in $\mathbb{R}^{2n+1}$.

While grain farming has seen a major shift toward organic production in recent years, the USA continues to lag behind with domestic demand continuing to outpace domestic supply, making the USA an all-around net importer. The Midwestern USA is poised to help remedy this imbalance; however, farmers continue to slowly transition to organic production systems. Existing literature has identified three prevalent narratives that farmers use to frame their organic transition: environmentalism, farm-family legacy and economic factors, in addition to a four and untested religiosity narrative. This study sought to better understand how these different narratives frame grain farmers’ thought processes for transitioning from conventional production systems to certified organic production systems. We co-created narratives around organic production with farmers, which resulted in four passages aligned with the literature: farm-family legacy, economic values, environmental values and Christianity and stewarding Eden. Then, we mailed a paper survey to conventional, in transition and certified organic Indiana grain farmers in order to test how these different narratives motivated organic production. We found that the most prevalent narrative around organic production is the farm-family legacy, which specifically resonated with midsize farmers. We also found that the religious stewardship narrative resonated with a substantial number of organic and mixed practice farmers, which is likely due to Amish farmers within the sample. These results shed light on the role that narratives and associated values play in organic practice use and can inform the organic efforts of agricultural professionals.

Narrow-windrow burning (NWB) is a form of harvest weed seed control in which crop residues and weed seeds collected by the combine are concentrated into windrows and subsequently burned. The objectives of this study were to determine how NWB will 1) affect seed survival of Italian ryegrass in wheat and Palmer amaranth in soybean and 2) determine whether a relationship exists between NWB heat index (HI; the sum of temperatures above ambient) or effective burn time (EBT; the cumulative number of seconds temperatures exceed 200 C) and the post-NWB seed survival of both species. Average soybean and wheat windrow HI totaled 140,725 ± 14,370 and 66,196 ± 6224 C, and 259 ± 27 and 116 ± 12 s of EBT, respectively. Pre-NWB versus post-NWB germinability testing revealed an estimated seed kill rate of 79.7% for Italian ryegrass, and 86.3% for Palmer amaranth. Non-linear two-parameter exponential regressions between seed kill and HI or EBT indicated NWB at an HI of 146,000 C and 277 s of EBT potentially kills 99% of Palmer amaranth seed. Seventy-six percent of soybean windrow burning events resulted in estimated Palmer amaranth seed kill rates greater than 85%. Predicted Italian ryegrass seed kill was greater than 97% in all but two wheat NWB events; therefore, relationships were not calculated. These results validate the effectiveness of the ability of NWB to reduce seed survival, thereby improving weed management and combating herbicide resistance.

Early in the COVID-19 pandemic, the World Health Organization stressed the importance of daily clinical assessments of infected patients, yet current approaches frequently consider cross-sectional timepoints, cumulative summary measures, or time-to-event analyses. Statistical methods are available that make use of the rich information content of longitudinal assessments. We demonstrate the use of a multistate transition model to assess the dynamic nature of COVID-19-associated critical illness using daily evaluations of COVID-19 patients from 9 academic hospitals. We describe the accessibility and utility of methods that consider the clinical trajectory of critically ill COVID-19 patients.

Seed retention, and ultimately seed shatter, are extremely important for the efficacy of harvest weed seed control (HWSC) and are likely influenced by various agroecological and environmental factors. Field studies investigated seed-shattering phenology of 22 weed species across three soybean [Glycine max (L.) Merr.]-producing regions in the United States. We further evaluated the potential drivers of seed shatter in terms of weather conditions, growing degree days, and plant biomass. Based on the results, weather conditions had no consistent impact on weed seed shatter. However, there was a positive correlation between individual weed plant biomass and delayed weed seed–shattering rates during harvest. This work demonstrates that HWSC can potentially reduce weed seedbank inputs of plants that have escaped early-season management practices and retained seed through harvest. However, smaller individuals of plants within the same population that shatter seed before harvest pose a risk of escaping early-season management and HWSC.

Yield losses due to weeds are a major threat to wheat production and economic well-being of farmers in the United States and Canada. The objective of this Weed Science Society of America (WSSA) Weed Loss Committee report is to provide estimates of wheat yield and economic losses due to weeds. Weed scientists provided both weedy (best management practices but no weed control practices) and weed-free (best management practices providing >90% weed control) average yield from replicated research trials in both winter and spring wheat from 2007 to 2017. Winter wheat yield loss estimates ranged from 2.9% to 34.4%, with a weighted average (by production) of 25.6% for the United States, 2.9% for Canada, and 23.4% combined. Based on these yield loss estimates and total production, the potential winter wheat loss due to weeds is 10.5, 0.09, and 10.5 billion kg with a potential loss in value of US$2.19, US$0.19, and US$2.19 billion for the United States, Canada, and combined, respectively. Spring wheat yield loss estimates ranged from 7.9% to 47.0%, with a weighted average (by production) of 33.2% for the United States, 8.0% for Canada, and 19.5% combined. Based on this yield loss estimate and total production, the potential spring wheat loss is 4.8, 1.6, and 6.6 billion kg with a potential loss in value of US$1.14, US$0.37, and US$1.39 billion for the United States, Canada, and combined, respectively. Yield loss in this analysis is greater than some previous estimates, likely indicating an increasing threat from weeds. Climate is affecting yield loss in winter wheat in the Pacific Northwest, with percent yield loss being highest in wheat-fallow systems that receive less than 30 cm of annual precipitation. Continued investment in weed science research for wheat is critical for continued yield protection.

The direct carbonate procedure for accelerator mass spectrometry radiocarbon (AMS 14C) dating of submilligram samples of biogenic carbonate without graphitization is becoming widely used in a variety of studies. We compare the results of 153 paired direct carbonate and standard graphite 14C determinations on single specimens of an assortment of biogenic carbonates. A reduced major axis regression shows a strong relationship between direct carbonate and graphite percent Modern Carbon (pMC) values (m = 0.996; 95% CI [0.991–1.001]). An analysis of differences and a 95% confidence interval on pMC values reveals that there is no significant difference between direct carbonate and graphite pMC values for 76% of analyzed specimens, although variation in direct carbonate pMC is underestimated. The difference between the two methods is typically within 2 pMC, with 61% of direct carbonate pMC measurements being higher than their paired graphite counterpart. Of the 36 specimens that did yield significant differences, all but three missed the 95% significance threshold by 1.2 pMC or less. These results show that direct carbonate 14C dating of biogenic carbonates is a cost-effective and efficient complement to standard graphite 14C dating.

Hairy buttercup and cutleaf evening primrose are winter annual weeds that have become more problematic for winter wheat growers in the southern Great Plains and the midsouthern United States in recent years. Little research exists on which to base recommendations for controlling hairy buttercup in wheat, and little research has been published on cutleaf evening primrose control in recent years. With growing concerns of increased herbicide resistance among winter annual weeds, incorporating new herbicide sites of action has become necessary. The objective of this study was to assess halauxifen-methyl as a novel herbicide to control these two problematic winter annual broadleaf weeds in winter wheat in Mississippi and Oklahoma. Studies were conducted across four site-years in Mississippi and one site-year in Oklahoma comparing 15 herbicide programs with and without halauxifen-methyl. Hairy buttercup and cutleaf evening-primrose control was the greatest when a synthetic auxin was combined with an acetolactate synthase–inhibiting herbicide. Treatments including halauxifen-methyl resulted in the greatest control of hairy buttercup, whereas a synthetic auxin herbicide plus chlorsulfuron and metsulfuron resulted in the greatest control of cutleaf evening primrose. Halauxifen-methyl is an effective addition for control of winter annual broadleaf weeds like hairy buttercup and cutleaf evening primrose in winter wheat.

Potential effectiveness of harvest weed seed control (HWSC) systems depends upon seed shatter of the target weed species at crop maturity, enabling its collection and processing at crop harvest. However, seed retention likely is influenced by agroecological and environmental factors. In 2016 and 2017, we assessed seed-shatter phenology in 13 economically important broadleaf weed species in soybean [Glycine max (L.) Merr.] from crop physiological maturity to 4 wk after physiological maturity at multiple sites spread across 14 states in the southern, northern, and mid-Atlantic United States. Greater proportions of seeds were retained by weeds in southern latitudes and shatter rate increased at northern latitudes. Amaranthus spp. seed shatter was low (0% to 2%), whereas shatter varied widely in common ragweed (Ambrosia artemisiifolia L.) (2% to 90%) over the weeks following soybean physiological maturity. Overall, the broadleaf species studied shattered less than 10% of their seeds by soybean harvest. Our results suggest that some of the broadleaf species with greater seed retention rates in the weeks following soybean physiological maturity may be good candidates for HWSC.

Seed shatter is an important weediness trait on which the efficacy of harvest weed seed control (HWSC) depends. The level of seed shatter in a species is likely influenced by agroecological and environmental factors. In 2016 and 2017, we assessed seed shatter of eight economically important grass weed species in soybean [Glycine max (L.) Merr.] from crop physiological maturity to 4 wk after maturity at multiple sites spread across 11 states in the southern, northern, and mid-Atlantic United States. From soybean maturity to 4 wk after maturity, cumulative percent seed shatter was lowest in the southern U.S. regions and increased moving north through the states. At soybean maturity, the percent of seed shatter ranged from 1% to 70%. That range had shifted to 5% to 100% (mean: 42%) by 25 d after soybean maturity. There were considerable differences in seed-shatter onset and rate of progression between sites and years in some species that could impact their susceptibility to HWSC. Our results suggest that many summer annual grass species are likely not ideal candidates for HWSC, although HWSC could substantially reduce their seed output during certain years.

Let $\unicode[STIX]{x1D707}(m,n)$ (respectively, $\unicode[STIX]{x1D702}(m,n)$) denote the number of odd-balanced unimodal sequences of size $2n$ and rank $m$ with even parts congruent to $2\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$ (respectively, $0\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$) and odd parts at most half the peak. We prove that two-variable generating functions for $\unicode[STIX]{x1D707}(m,n)$ and $\unicode[STIX]{x1D702}(m,n)$ are simultaneously quantum Jacobi forms and mock Jacobi forms. These odd-balanced unimodal rank generating functions are also duals to partial theta functions originally studied by Ramanujan. Our results also show that there is a single $C^{\infty }$ function in $\mathbb{R}\times \mathbb{R}$ to which the errors to modularity of these two different functions extend. We also exploit the quantum Jacobi properties of these generating functions to show, when viewed as functions of the two variables $w$ and $q$, how they can be expressed as the same simple Laurent polynomial when evaluated at pairs of roots of unity. Finally, we make a conjecture which fully characterizes the parity of the number of odd-balanced unimodal sequences of size $2n$ with even parts congruent to $0\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$ and odd parts at most half the peak.

Astrophysics Telescope for Large Area Spectroscopy Probe is a concept for a National Aeronautics and Space Administration probe-class space mission that will achieve ground-breaking science in the fields of galaxy evolution, cosmology, Milky Way, and the Solar System. It is the follow-up space mission to Wide Field Infrared Survey Telescope (WFIRST), boosting its scientific return by obtaining deep 1–4 μm slit spectroscopy for ∼70% of all galaxies imaged by the ∼2 000 deg2 WFIRST High Latitude Survey at z > 0.5. Astrophysics Telescope for Large Area Spectroscopy will measure accurate and precise redshifts for ∼200 M galaxies out to z < 7, and deliver spectra that enable a wide range of diagnostic studies of the physical properties of galaxies over most of cosmic history. Astrophysics Telescope for Large Area Spectroscopy Probe and WFIRST together will produce a 3D map of the Universe over 2 000 deg2, the definitive data sets for studying galaxy evolution, probing dark matter, dark energy and modifications of General Relativity, and quantifying the 3D structure and stellar content of the Milky Way. Astrophysics Telescope for Large Area Spectroscopy Probe science spans four broad categories: (1) Revolutionising galaxy evolution studies by tracing the relation between galaxies and dark matter from galaxy groups to cosmic voids and filaments, from the epoch of reionisation through the peak era of galaxy assembly; (2) Opening a new window into the dark Universe by weighing the dark matter filaments using 3D weak lensing with spectroscopic redshifts, and obtaining definitive measurements of dark energy and modification of General Relativity using galaxy clustering; (3) Probing the Milky Way’s dust-enshrouded regions, reaching the far side of our Galaxy; and (4) Exploring the formation history of the outer Solar System by characterising Kuiper Belt Objects. Astrophysics Telescope for Large Area Spectroscopy Probe is a 1.5 m telescope with a field of view of 0.4 deg2, and uses digital micro-mirror devices as slit selectors. It has a spectroscopic resolution of R = 1 000, and a wavelength range of 1–4 μm. The lack of slit spectroscopy from space over a wide field of view is the obvious gap in current and planned future space missions; Astrophysics Telescope for Large Area Spectroscopy fills this big gap with an unprecedented spectroscopic capability based on digital micro-mirror devices (with an estimated spectroscopic multiplex factor greater than 5 000). Astrophysics Telescope for Large Area Spectroscopy is designed to fit within the National Aeronautics and Space Administration probe-class space mission cost envelope; it has a single instrument, a telescope aperture that allows for a lighter launch vehicle, and mature technology (we have identified a path for digital micro-mirror devices to reach Technology Readiness Level 6 within 2 yr). Astrophysics Telescope for Large Area Spectroscopy Probe will lead to transformative science over the entire range of astrophysics: from galaxy evolution to the dark Universe, from Solar System objects to the dusty regions of the Milky Way.