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This paper considers a satellite inspection mission where the deputy satellite is required to remain a fixed distance away from the chief satellite. This constraint on the deputy’s state is modeled as the surface of a sphere. Finding minimum energy solutions to travel from one point to another point on the sphere requires solving a nonconvex optimal control problem. Various novel suboptimal algorithms are proposed that can guarantee a feasible solution. These algorithms are benchmarked by optimal values obtained via a global continuation method, and their computational performance is analyzed in a statistical setting.

Nitrogen heterocycles are a class of organic compounds with extremely versatile functionality. Imidines, HN[C(NH)R]2, are a rare class of heterocycles related to imides, HN[C(O)R]2, in which the O atoms of the carbonyl groups are replaced by N—H groups. The useful synthesis of the imidine compounds succinimidine and glutarimidine, as well as their partially hydrolyzed imino–imide congeners, was first described in the mid-1950s, though structural characterization is presented for the first time in this article. In the solid state, these structures are different from the proposed imidine form: succinimidine crystallizes as an imino–amine, 2-imino-3,4-dihydro-2H-pyrrol-5-amine, C4H7N2 (1), glutarimidine as 6-imino-3,4,5,6-tetrahydropyridin-2-amine methanol monosolvate, C5H9N3·CH3OH (2), and the corresponding hydrolyzed imino–imide compounds as amino–amides 5-amino-3,4-dihydro-2H-pyrrol-2-one, C4H6N2O (3), and 6-amino-4,5-dihydropyridin-2(3H)-one, C5H8N2O (4). Imidine 1 was also determined as the hydrochloride salt solvate 5-amino-3,4-dihydro-2H-pyrrol-2-iminium chloride–2-imino-3,4-dihydro-2H-pyrrol-5-amine–water (1/1/1), C4H8N3 +·Cl−·C4H7N3·H2O (1·HCl). As such, 1 and 2 show alternating short and long C—N bonds across the molecule, revealing distinct imino (C=NH) and amine (C—NH2) groups throughout the C—N backbone. These structures provide definitive evidence for the predominant imino–amine tautomer in the solid state, which serves to enrich the previously proposed imidine-focused structures that have appeared in organic chemistry textbooks since the discovery of this class of compounds in 1883.

Given the long-term human habitation and prolific land use change trajectories in the eastern United States, few remnants of the pre-European settlement Mid-Atlantic forest remain on the Atlantic Coastal Plain. This study utilized metes and bounds witness tree locations and descriptions produced during colonial land subdivision to understand the relationships between tree types and biogeographic environments for an area on Maryland's Eastern Shore. Using correspondence analysis, we reveal habitat partitioning among witness tree species based on soil drainage characteristics, that enable the visualization of a pre-European settlement reconstructed forest. Our research finds that oak ( Quercus), most often white oak ( Quercus alba), was the dominant genus for most of the study area underlain by well-drained soils. To a much smaller extent, gums were also associated with these well-drained soils. Areas of poor drainage most often contained pine ( Pinus) and an assemblage of different oaks ( Quercus spp.). Hickory ( Carya), also noted in the witness tree record in small numbers, was found across all soil drainages.

Characterizing compositional heterogeneity in Earth’s lower mantle is critical to understanding its dynamics. Three low-nitrogen diamonds from Koffiefontein (South Africa), containing inclusion assemblages of ferropericlase ± orthopyroxene ± magnesite, constrain diamond formation in an Mg-rich lower-mantle environment. Ferropericlase inclusions have Mg# 82.7–88.5 and orthopyroxene inclusions (retrogressed bridgmanite) have Mg# 95.0–95.1 and mantle-like δ18O of +5.6‰ ± 0.2‰. Magnesite included in one diamond implicates carbonated fluids in diamond formation. High Mg# and low Ca, Al, and Na of the assemblage indicate a melt-depleted meta-harzburgitic environment, in contrast to more fertile compositions expected for primitive lower mantle. Extremely low Ca in orthopyroxene inclusions may reflect a combination of melt depletion and low equilibration temperatures at the time of trapping. Inclusion compositions implicate subducted oceanic slab meta-harzburgite as the host for diamond growth. Mantle-like δ18O of the orthopyroxene inclusions indicates unaltered oceanic lithosphere. Similar melt-depleted characteristics in lower-mantle inclusion assemblages worldwide support that meta-harzburgite is the dominant host of lower-mantle diamonds.

Spontaneous animal behaviour is built from action modules that are concatenated by the brain into sequences1,2. However, the neural mechanisms that guide the composition of naturalistic, self-motivated behaviour remain unknown. Here we show that dopamine systematically fluctuates in the dorsolateral striatum (DLS) as mice spontaneously express sub-second behavioural modules, despite the absence of task structure, sensory cues or exogenous reward. Photometric recordings and calibrated closed-loop optogenetic manipulations during open field behaviour demonstrate that DLS dopamine fluctuations increase sequence variation over seconds, reinforce the use of associated behavioural modules over minutes, and modulate the vigour with which modules are expressed, without directly influencing movement initiation or moment-to-moment kinematics. Although the reinforcing effects of optogenetic DLS dopamine manipulations vary across behavioural modules and individual mice, these differences are well predicted by observed variation in the relationships between endogenous dopamine and module use. Consistent with the possibility that DLS dopamine fluctuations act as a teaching signal, mice build sequences during exploration as if to maximize dopamine. Together, these findings suggest a model in which the same circuits and computations that govern action choices in structured tasks have a key role in sculpting the content of unconstrained, high-dimensional, spontaneous behaviour.

The introduction of volatile-rich subducting slabs to the mantle may locally generate large redox gradients, affecting phase stability, element partitioning and volatile speciation

Full-thickness rotator cuff tears (FTRCTs) represent a common shoulder injury that, if untreated, can progress in size, become increasingly painful, and inhibit function. These lesions are often surgically repaired, with double-row arthroscopic repair often preferred for larger tears. Biological augmentation technologies have been developed to improve rates of postoperative radiographic retear and enhance patient-reported outcomes after surgical FTRCT repair. This study sought to confirm that augmented repair with a bioinductive bovine collagen implant results in favorable retear rates and patient outcomes with follow-up to 2 years.A prospective multicenter cohort study was undertaken to determine the efficacy and safety of augmenting single- or double-row arthroscopic repair of FTRCTs with a bioinductive bovine collagen implant. Of 115 adult patients participating, 66 (57.4%) had medium (1-3-cm) tears and 49 (42.6%) had large (3-5-cm) tears. Magnetic resonance imaging and patient-reported outcomes (American Shoulder and Elbow Surgeons Standardized Shoulder Assessment Form [ASES] and Constant-Murley Score [CMS]) were performed and recorded at baseline, 3 months, 1 year, and 2 years.Mean duration of follow-up was 2.1 years (range, 1.5-2.9 years). Between baseline and 2-year follow-up, mean total thickness of the supraspinatus tendon increased by 12.5% for medium tears and by 17.1% for large tears. Radiographic retear was noted in 7 of 61 available patients (11.5%) with medium tears, and in 14 of 40 patients (35.0%) with large tears. In both groups, these tears primarily occurred before the 3-month follow-up visit (13 of 21 [61.9%]). Radiographic retear with the supplemented double-row (DR) repair technique was 13.2% overall (12 of 91 DR patients; 11.3% for medium tears and 15.8% for large tears). The minimal clinically important difference was achieved by90% of patients with both medium and large tears for both ASES and CMS. There were 2 serious adverse events classified by the treating surgeon as being possibly related to the device and/or procedure (1 case of swelling/drainage and 1 case of intermittent pain). Nine patients (7.8%; 4 medium tears and 5 large tears) required reoperation of the index rotator cuff surgery.Final 2-year data from this study confirm that using this implant in augmentation of arthroscopic double-row repair of FTRCTs provides favorable rates of radiographic retear and substantial functional recovery. The relative safety of the device is also further supported.

Task-sharing is the pragmatic sharing of tasks between providers with different levels of training. To our knowledge, no study has examined the cost-effectiveness of surgical task-sharing of hernia repair in a low-resource setting. This study has aimed to evaluate and compare the cost-effectiveness of mesh repair performed by Ghanaian surgeons and medical doctors (MDs) following a standardized training program.This cost-effectiveness analysis included data for 223 operations on adult men with primary reducible inguinal hernia. Cost per surgery was calculated from the healthcare system perspective. Disability weights were calculated using pre- and postoperative pain scores and benchmarks from the Global Burden of Disease Study 2017.The mean cost/disability-adjusted life-year (DALY) averted in the surgeon group was 444.9 United States dollars (USD) (95% confidence interval [CI] 221.2-668.5) and 278.9 USD (95% CI 199.3-358.5) in the MD group (P = .168), indicating that the operation is very cost-effective when performed by both providers. The incremental cost/DALY averted showed that task-sharing with MDs is also very cost-effective (95% bootstrap CI -436.7 to 454.9). The analysis found that increasing provider salaries is cost-effective if productivity remains high. When only symptomatic cases were analyzed, the mean cost/DALY averted reduced to 232.0 USD (95% CI 17.1-446.8) for the surgeon group and 129.7 USD (95% CI 79.6-179.8) for the MD group (P = .348), and the incremental cost/DALY averted increased by 45% but remained robust.Elective inguinal hernia repair with mesh performed by Ghanaian surgeons and MDs is a low-cost procedure and very cost-effective in the context of the study. To maximize cost-effectiveness, symptomatic patients should be prioritized over asymptomatic patients and a high level of productivity should be maintained.