A Fascinating Polynomial Sequence arising from an Electrostatics Problem on the Sphere

A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a negatively charged spherical cap to appear. The determination of the smallest distance $\rho(d)$ ($d$ is the dimension of the unit sphere) from the point charge to the sphere where still all of the sphere is positively charged is known as Gonchar's problem. Using classical potential theory for the harmonic case, we show that $1+\rho(d)$ is equal to the largest positive zero of a certain sequence of monic polynomials of degree $2d-1$ with integer coefficients which we call Gonchar polynomials. Rather surprisingly, $\rho(2)$ is the Golden ratio and $\rho(4)$ the lesser known Plastic number. But Gonchar polynomials have other interesting properties. We discuss their factorizations, investigate their zeros and present some challenging conjectures.Comment: 12 pages, 6 figures, 1 tabl

Long-term surgical outcomes of congenital supravalvular aortic stenosis:a systematic review, meta-analysis and microsimulation study

OBJECTIVES: Congenital supravalvular aortic stenosis (SVAS) is a rare form of congenital outflow tract obstruction and long-term outcomes are scarcely reported. This study aims to provide an overview of outcomes after surgical repair for congenital SVAS. METHODS: A systematic review of published literature was conducted, including observational studies reporting long-term clinical outcome (&gt;2 years) after SVAS repair in children or adults considering &gt;20 patients. Early risks, late event rates and time-to-event data were pooled and entered into a microsimulation model to estimate 30-year outcomes. Life expectancy was compared to the age-, sex- and origin-matched general population. RESULTS: Twenty-three publications were included, encompassing a total of 1472 patients (13 125 patient-years; pooled mean follow-up: 9.0 (6.2) years; median follow-up: 6.3 years). Pooled mean age at surgical repair was 4.7 (5.8) years and the most commonly used surgical technique was the single-patch repair (43.6%). Pooled early mortality was 4.2% (95% confidence interval: 3.2-5.5%) and late mortality was 0.61% (95% CI: 0.45-0.83) per patient-year. Based on microsimulation, over a 30-year time horizon, it was estimated that an average patient with SVAS repair (mean age: 4.7 years) had an observed life expectancy that was 90.7% (95% credible interval: 90.0-91.6%) of expected life expectancy in the matched general population. The microsimulation-based 30-year risk of myocardial infarction was 8.1% (95% credible interval: 7.3-9.9%) and reintervention 31.3% (95% credible interval: 29.6-33.4%), of which 27.2% (95% credible interval: 25.8-29.1) due to repair dysfunction. CONCLUSIONS: After surgical repair for SVAS, 30-year survival is lower than the matched-general-population survival and the lifetime risk of reintervention is considerable. Therefore, lifelong monitoring of the cardiovascular system and in particular residual stenosis and coronary obstruction is recommended.</p

Wholesale pricing in a small open economy

This paper addresses the empirical analysis of wholesale profit margins using data of the Dutch wholesale sector, 1986. At the heart of the analysis is the typical nature of wholesale production: wholesalers do not produce a tangible product, but offer a service capacity. This has an immediate impact on the identification, interprelation and measurement of determinants of profit variations. A model is set up to explain variations in wholesale profit margins, which is inspired by two widely applied approaches to industry pricing: the behavioural mark-up model and the marginalist price-cost model

Same data, different conclusions: Radical dispersion in empirical results when independent analysts operationalize and test the same hypothesis

In this crowdsourced initiative, independent analysts used the same dataset to test two hypotheses regarding the effects of scientists’ gender and professional status on verbosity during group meetings. Not only the analytic approach but also the operationalizations of key variables were left unconstrained and up to individual analysts. For instance, analysts could choose to operationalize status as job title, institutional ranking, citation counts, or some combination. To maximize transparency regarding the process by which analytic choices are made, the analysts used a platform we developed called DataExplained to justify both preferred and rejected analytic paths in real time. Analyses lacking sufficient detail, reproducible code, or with statistical errors were excluded, resulting in 29 analyses in the final sample. Researchers reported radically different analyses and dispersed empirical outcomes, in a number of cases obtaining significant effects in opposite directions for the same research question. A Boba multiverse analysis demonstrates that decisions about how to operationalize variables explain variability in outcomes above and beyond statistical choices (e.g., covariates). Subjective researcher decisions play a critical role in driving the reported empirical results, underscoring the need for open data, systematic robustness checks, and transparency regarding both analytic paths taken and not taken. Implications for organizations and leaders, whose decision making relies in part on scientific findings, consulting reports, and internal analyses by data scientists, are discussed

Fate of the Arterial Origin of Major Aortopulmonary Collateral Arteries After Unifocalization

Background: During unifocalization procedures for pulmonary atresia with ventricular septal defect and major aortopulmonary collateral arteries, collateral arteries are either ligated or detached. Not much is known of the fate of the remaining arterial origins in the long term. Available computed tomography (CT) or magnetic resonance (MR) imaging of the intrathoracic arteries was examined to investigate possible abnormalities at the former position of the collateral arteries as well as ascending aortic diameters. Methods: From 1989 to 2018, we performed 66 unifocalization procedures in 39 patients. One hundred and twenty-nine collateral arteries were ligated or detached. In 52% (15) of the surviving patients (with a total of 55 ligated or detached collaterals), sufficient imaging of the thoracic aorta from CT (11) and/or MR (9) was available for evaluation. Results: The median interval between unifocalization procedure and imaging was 15 years (interquartile range [IQR]: 9-19 years). In 93% (14) of the scanned patients, 18 blunt ends were detected at the location of a former collateral artery. No aneurysm formation of the descending aorta was observed. The median diameter of the ascending aorta was 35 mm (IQR: 31-40 mm). During follow-up, no aortic dissection or rupture occurred. Conclusions: Aortic imaging late after unifocalization showed abnormalities in 93% of the scanned patients. Abnormalities consisted mostly of blunt ends of the former collateral artery. We recommend to include routine imaging of the aorta during late follow-up to detect eventual future abnormalities and monitor aortic diameters. Ascending aortic diameters showed slight dilatation with no clinical implications so far

Long-term surgical outcomes of congenital supravalvular aortic stenosis:a systematic review, meta-analysis and microsimulation study

OBJECTIVES: Congenital supravalvular aortic stenosis (SVAS) is a rare form of congenital outflow tract obstruction and long-term outcomes are scarcely reported. This study aims to provide an overview of outcomes after surgical repair for congenital SVAS. METHODS: A systematic review of published literature was conducted, including observational studies reporting long-term clinical outcome (&gt;2 years) after SVAS repair in children or adults considering &gt;20 patients. Early risks, late event rates and time-to-event data were pooled and entered into a microsimulation model to estimate 30-year outcomes. Life expectancy was compared to the age-, sex- and origin-matched general population. RESULTS: Twenty-three publications were included, encompassing a total of 1472 patients (13 125 patient-years; pooled mean follow-up: 9.0 (6.2) years; median follow-up: 6.3 years). Pooled mean age at surgical repair was 4.7 (5.8) years and the most commonly used surgical technique was the single-patch repair (43.6%). Pooled early mortality was 4.2% (95% confidence interval: 3.2-5.5%) and late mortality was 0.61% (95% CI: 0.45-0.83) per patient-year. Based on microsimulation, over a 30-year time horizon, it was estimated that an average patient with SVAS repair (mean age: 4.7 years) had an observed life expectancy that was 90.7% (95% credible interval: 90.0-91.6%) of expected life expectancy in the matched general population. The microsimulation-based 30-year risk of myocardial infarction was 8.1% (95% credible interval: 7.3-9.9%) and reintervention 31.3% (95% credible interval: 29.6-33.4%), of which 27.2% (95% credible interval: 25.8-29.1) due to repair dysfunction. CONCLUSIONS: After surgical repair for SVAS, 30-year survival is lower than the matched-general-population survival and the lifetime risk of reintervention is considerable. Therefore, lifelong monitoring of the cardiovascular system and in particular residual stenosis and coronary obstruction is recommended.</p

Direct Proof of Endo-Epicardial Asynchrony of the Atrial Wall During Atrial Fibrillation in Humans

Item does not contain fulltextBACKGROUND: The presence of focal fibrillation waves during atrial fibrillation (AF) can, besides ectopic activity, also be explained by asynchronous activation of the atrial endo- and epicardial layer and transmurally propagating fibrillation waves. To provide direct proof of endo-epicardial asynchrony, we performed simultaneous high-resolution mapping of the right atrial endo- and epicardial wall during AF in humans. METHOD AND RESULTS: Intraoperative mapping of the endo- and epicardial right atrial wall was performed during (induced) AF in 10 patients with AF (paroxysmal: n=3; persistent: n=4; and longstanding persistent: n=3) and 4 patients without a history of AF. A clamp made of 2 rectangular 8x16 electrode arrays (interelectrode distance 2 mm) was inserted into the incision in the right atrial appendage. Recordings of 10 seconds of AF were analyzed to determine the incidence of asynchronous endo-epicardial activation times (>/=15 ms) of opposite electrodes. Asynchronous endo-epicardial activation ranged between 0.9 and 55.9% without preference for either side. Focal waves appeared equally frequent at endocardium and epicardium (11% versus 13%; ITALIC! P=0.18). Using strict criteria for breakthrough (presence of an opposite wave within 4 mm and </=14 ms before the origin of the focal wave), the majority (65%) of all focal fibrillation waves could be attributed to endo-epicardial excitation. CONCLUSIONS: We provided the first evidence for asynchronous activation of the endo-epicardial wall during AF in humans. Endo-epicardial asynchrony may play a major role in the pathophysiology of AF and may offer an explanation why in some patients therapy fails