A Generalized Method of Undetermined Coefficients

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that are polynomial in a first order differential operator. In addition, we provide a number of constant coefficient, Cauchy-Euler, and novel examples

An Instrument to Enable Identification of Anthropogenic CO2 Emissions Using Concurrent CO Measurements

We have developed an instrument concept that will enable the measurement of CO from the top of the atmosphere to the Earth's surface with very high sensitivity and at the high spatial and temporal resolutions required by the NRC Decadal Survey mission Active Sensing of Carbon Dioxide (CO2) over Nights, Days and Seasons (ASCENDS). We are developing an innovative CO sensor that will enable the ASCENDS mission to differentiate between anthropogenic and natural sources and sinks of global carbon. The NRC Decadal Survey places particular emphasis on retrieving CO information for the planetary boundary layer. Measurement made using both the 2.3 micron and 4.7 micron channels are needed to achieve the sensitivity required in the lower atmosphere where the degree of CO - CO2 correlation is indicative of anthropogenic sources of CO2. Measurements made using only the 4.7 micron channel cannot provide sufficient sensitivity to CO in the very lowest layers of the atmosphere. The fundamental method we use is Gas Filter Correlation Radiometry (GFCR), a highly successful technique used in other airborne and space-based missions for detecting trace species in the Earth's atmosphere. Our version of GFCR overcomes many of the limitations encountered by prior and existing instruments, allowing us to measure weak signals from small targets very quickly and with extremely high specificity by employing a new dual beam radiometer concept using a focal plane array. Our design will provide a means to make the desired CO measurements for the ASCENDS mission. A simple change in gas filter cell contents would allow the same hardware to measure CH4 with high precision under the nominal ASCENDS mission spatial and temporal constraints. All critical components in the sensor design are mature, many subsystems tested, and the system has been extensively modeled, bringing it to a present Technology Readiness Level (TRL) of 3 (though some individual components are at TRLs 6-9). We are presently developing critical components for the new spectrometer and advancing our understanding of the measurement requirements for both CO and CH4. This new GFCR technique/sensor will enable measurements of trace gases with high sensitivity while maintaining the inherent robustness and simplicity of the more traditional radiometer hardware. Initial estimates of cost/risk of a spacebased 2-channel GFCR indicate that our design is extremely cost effective and will fit within existing ASCENDS mission budget constraints as determined by the NRC Decadal Survey and a NASA-sponsored mission study

Clarithromycin and endoscopic sinus surgery for adults with chronic rhinosinusitis with and without nasal polyps: study protocol for the MACRO randomised controlled trial.

BACKGROUND: Chronic rhinosinusitis (CRS) is a common source of ill health; 11% of UK adults reported CRS symptoms in a worldwide population study. Guidelines are conflicting regarding whether antibiotics should be included in primary medical management, reflecting the lack of evidence in systematic reviews. Insufficient evidence to inform the role of surgery contributes to a fivefold variation in UK intervention rates. The objective of this trial is to establish the comparative effectiveness of endoscopic sinus surgery (ESS) or a prolonged course of antibiotics (clarithromycin) in adult patients with CRS in terms of symptomatic improvement and costs to the National Health Service compared with standard medical care (intranasal medication) at 6 months. METHODS/DESIGN: A three-arm parallel-group trial will be conducted with patients who remain symptomatic after receiving appropriate medical therapy (either in primary or secondary care). They will be randomised to receive: (1) intranasal medication plus ESS, (2) intranasal medication plus clarithromycin (250 mg) or (3) intranasal medication plus a placebo. Intranasal medication (current standard medical care) is defined as a spray or drops of intranasal corticosteroids and saline irrigations. The primary outcome measure is the SNOT-22 questionnaire, which assesses disease-specific health-related quality of life. The study sample size is 600. Principal analyses will be according to the randomised groups irrespective of compliance. The trial will be conducted in at least 16 secondary or tertiary care centres with an internal pilot at six sites for 6 months. DISCUSSION: The potential cardiovascular side effects of macrolide antibiotics have been recently highlighted. The effectiveness of antibiotics will be established through this trial, which may help to reduce unnecessary usage and potential morbidity. If ESS is shown to be clinically effective and cost-effective, the trial may encourage earlier intervention. In contrast, if it is shown to be ineffective, then there should be a significant reduction in surgery rates. The trial results will feed into the other components of the MACRO research programme to establish best practice for the management of adults with CRS and design the ideal patient pathway across primary and secondary care. TRIAL REGISTRATION: ISRCTN36962030 . Registered on 17 October 2018

Association and Mutation Analyses of 16p11.2 Autism Candidate Genes

Background: Autism is a complex childhood neurodevelopmental disorder with a strong genetic basis. Microdeletion or duplication of a ∼500–700-kb genomic rearrangement on 16p11.2 that contains 24 genes represents the second most frequent chromosomal disorder associated with autism. The role of common and rare 16p11.2 sequence variants in autism etiology is unknown.Methodology/Principal Findings: To identify common 16p11.2 variants with a potential role in autism, we performed association studies using existing data generated from three microarray platforms: Affymetrix 5.0 (777 families), Illumina 550 K (943 families), and Affymetrix 500 K (60 families). No common variants were identified that were significantly associated with autism. To look for rare variants, we performed resequencing of coding and promoter regions for eight candidate genes selected based on their known expression patterns and functions. In total, we identified 26 novel variants in autism: 13 exonic (nine non-synonymous, three synonymous, and one untranslated region) and 13 promoter variants. We found a significant association between autism and a coding variant in the seizure-related gene SEZ6L2 (12/1106 autism vs. 3/1161 controls; p = 0.018). Sez6l2 expression in mouse embryos was restricted to the spinal cord and brain. SEZ6L2 expression in human fetal brain was highest in post-mitotic cortical layers, hippocampus, amygdala, and thalamus. Association analysis of SEZ6L2 in an independent sample set failed to replicate our initial findings.Conclusions/Significance: We have identified sequence variation in at least one candidate gene in 16p11.2 that may represent a novel genetic risk factor for autism. However, further studies are required to substantiate these preliminary findings.</p

Ernst Freund as Precursor of the Rational Study of Corporate Law

Gindis, David, Ernst Freund as Precursor of the Rational Study of Corporate Law (October 27, 2017). Journal of Institutional Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2905547, doi: https://dx.doi.org/10.2139/ssrn.2905547The rise of large business corporations in the late 19th century compelled many American observers to admit that the nature of the corporation had yet to be understood. Published in this context, Ernst Freund's little-known The Legal Nature of Corporations (1897) was an original attempt to come to terms with a new legal and economic reality. But it can also be described, to paraphrase Oliver Wendell Holmes, as the earliest example of the rational study of corporate law. The paper shows that Freund had the intuitions of an institutional economist, and engaged in what today would be called comparative institutional analysis. Remarkably, his argument that the corporate form secures property against insider defection and against outsiders anticipated recent work on entity shielding and capital lock-in, and can be read as an early contribution to what today would be called the theory of the firm.Peer reviewe

Density dependence of ion cyclotron emission from deuterium plasmas in the large helical device

Ion cyclotron emission (ICE) driven by perpendicular neutral beam-injected (NBI) deuterons, together with the distinctive ICE driven by tangential NBI, have been observed from heliotron–stellarator plasmas in the large helical device (LHD). Radio frequency radiation in the lower hybrid range has also been observed Saito K. et al (2018 Plasma Fusion Res. 13 3402043), with frequency dependent on plasma density. Here we focus on recent measurements of ICE from deuterium plasmas in LHD, which show substantial variation in spectral character, between otherwise similar plasmas that have different local density in the emitting region. We analyse this variation by means of first principles simulations, carried out using a particle-in-cell (PIC) kinetic approach. We show, first, that this ICE is driven by perpendicular NBI deuterons, freshly ionised near their injection point in the outer midplane edge of LHD. We find that these NBI deuterons undergo collective sub-Alfvénic relaxation, which we follow deep into the nonlinear phase of the magnetoacoustic cyclotron instability (MCI). The frequency and wavenumber dependence of the saturated amplitudes of the excited fields determine our simulated ICE spectra, and these spectra are obtained for different local densities corresponding to the different LHD ICE-emitting plasmas. The variation with density of the spectral character of the simulated ICE corresponds well with that of the observed ICE from LHD. These results from heliotron–stellarator plasmas complement recent studies of density-dependent ICE from tokamak plasmas in KSTAR Thatipamula S.G. et al (2016 Plasma Phys. Control. Fusion 58 065003); Chapman B. et al (2017 Nucl. Fusion 57 124004), where the spectra vary on sub-microsecond timescales after an ELM crash. Taken together, these results confirm the strongly spatially localised character of ICE physics, and reinforce the potential of ICE as a diagnostic of energetic ion populations and of the ambient plasma

Endomicroscopic and transcriptomic analysis of impaired barrier function and malabsorption in environmental enteropathy

Introduction: Environmental enteropathy (EE) is associated with growth failure, micronutrient malabsorption and impaired responses to oral vaccines. We set out to define cellular mechanisms of impaired barrier function in EE and explore protective mechanisms. Methods: We studied 49 adults with environmental enteropathy in Lusaka, Zambia using confocal laser endomicroscopy (CLE); histology, immunohistochemistry and mRNA sequencing of small intestinal biopsies; and correlated these with plasma lipopolysaccharide (LPS) and a zinc uptake test. Results: CLE images (median 134 for each study) showed virtually ubiquitous small intestinal damage. Epithelial defects, imaged by histology and claudin 4 immunostaining, were predominantly seen at the tips of villi and corresponded with leakage imaged in vivo by CLE. In multivariate analysis, circulating log-transformed LPS was correlated with cell shedding events (β = 0.83; P = 0.035) and with serum glucagon-like peptide-2 (β = -0.13; P = 0.007). Zinc uptake from a test dose of 25mg was attenuated in 30/47 (64%) individuals and in multivariate analysis was reduced by HIV, but positively correlated with GLP-2 (β = 2.72; P = 0.03). There was a U-shaped relationship between circulating LPS and villus surface area. Transcriptomic analysis identified 23 differentially expressed genes in severe enteropathy, including protective peptides and proteins. Conclusions: Confocal endomicroscopy, claudin 4 immunostaining and histology identify epithelial defects which are probably sites of bacterial translocation, in the presence of which increased epithelial surface area increases the burden of translocation. GLP 2 and other protective peptides may play an important role in mucosal protection in EE

Expression Quantitative Trait Loci and Receptor Pharmacology Implicate Arg1 and the GABA-A Receptor as Therapeutic Targets in Neuroblastoma

SummaryThe development of targeted therapeutics for neuroblastoma, the third most common tumor in children, has been limited by a poor understanding of growth signaling mechanisms unique to the peripheral nerve precursors from which tumors arise. In this study, we combined genetics with gene-expression analysis in the peripheral sympathetic nervous system to implicate arginase 1 and GABA signaling in tumor formation in vivo. In human neuroblastoma cells, either blockade of ARG1 or benzodiazepine-mediated activation of GABA-A receptors induced apoptosis and inhibited mitogenic signaling through AKT and MAPK. These results suggest that ARG1 and GABA influence both neural development and neuroblastoma and that benzodiazepines in clinical use may have potential applications for neuroblastoma therapy