The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodynamics. For instance, for current J and magnetic field BS(J), we show that Maxwell's equations naturally hold. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. This article describes several properties of BS: we show it is self-adjoint, bounded, and extends to a compact operator on a Hilbert space. For vector fields that act like currents, we prove the curl operator is a left inverse to BS; thus the Biot-Savart operator is important in the study of curl eigenvalues, with applications to energy-minimization problems in geometry and physics. We conclude with two examples, which indicate our bounds are typically within an order of magnitude of being sharp.Comment: 24 pages (was 28 pages) Revised to include a new introduction, a detailed example, and results about helicity; other changes for readabilit

Governors and directors: Competing models of corporate governance

Why do we use the term ‘corporate governance’ rather than ‘corporate direction’? Early British joint stock companies were normally managed by a single ‘governor’. The ‘court of governors’ or ‘board of directors’ emerged slowly as the ruling body for companies. By the nineteenth century, however, companies were typically run by directors while not-for-profit entities such as hospitals, schools and charitable bodies had governors. The nineteenth century saw steady refinement of the roles of company directors, often in response to corporate scandals, with a gradual change from the notion of the director as a ‘representative shareholder’ to the directors being seen collectively as ‘representatives of the shareholders’. Governors in not-for-profit entities, however, were regarded as having broader responsibilities. The term ‘governance’ itself suggests that corporate boards should be studied as ‘political’ entities rather than merely through economic lenses such as agency theory

Cubic and hexagonal InGaAsN dilute arsenides by unintentional homogeneous incorporation of As into InGaN

Arsenic alloying is observed for epitaxial layers nominally intended to be In0.75Ga0.25N. Voids form beneath their interfaces with GaAs substrates, acting as sources of Ga + As out-diffusion into the growing epilayers. As a result, heteroepitaxial single-phase quaternary InxGa1-xAsyN1-y, films are formed with x similar to 0.55 and 0.05 menor que y menor que 0,10. While an undoped epilayer retains the wurtzite structure, a Mn-doped sample showed randomly spaced dopant segregations, which, together with a slightly higher As concentration, led to a transformation from the hexagonal to the twinned cubic phase

Unsteady turbulence in tidal bores: Effects of bed roughness

A tidal bore is a wave propagating upstream as the tidal flow turns to rising. It forms during spring tide conditions when the flood tide is confined to a narrow funneled channel. To date, theoretical and numerical studies rely upon physical experiments to validate the developments, but the experimental data are limited mostly to visual observations and sometimes free-surface measurements. Herein turbulent velocity measurements were obtained in a large-size laboratory facility with a fine spatial and temporal resolution. The instantaneous velocity measurements showed rapid flow deceleration at all vertical elevations, and large fluctuations of all velocity components were recorded beneath the bore and secondary waves. A comparison between undular (nonbreaking) and breaking bores suggested some basic differences. In an undular bore, large velocity fluctuations were recorded beneath the first wave crest and the secondary waves showing a long-lasting effect after the bore passage. In a breaking bore, some large turbulent stresses were observed next to the shear zone in a region of high velocity gradients, while some transient flow recirculation was recorded next to the bed. The effects of bed roughness were tested further. The boundary friction contributed to some wave attenuation and dispersion, and the free-surface data showed some agreement with the wave dispersion theory for intermediate gravity waves. The instantaneous velocity data showed however a significant effect of the boundary roughness on the velocity field next to the boundary (z/d(o)< 0.2) for both undular and breaking bores. Overall the findings were consistent with field observations of tidal bores and highlighted the significant impact of undular (nonbreaking) bores on natural systems

Jasmonic acid-dependent regulation of seed dormancy following maternal herbivory in Arabidopsis

Maternal experience of abiotic environmental factors such as temperature and light are well known to control seed dormancy in many plant species. Maternal biotic stress alters offspring defence phenotypes, but whether it also affects seed dormancy remains unexplored. We exposed Arabidopsis thaliana plants to herbivory and investigated plasticity in germination and defence phenotypes in their offspring, along with the roles of phytohormone signalling in regulating maternal effects. Maternal herbivory resulted in the accumulation of jasmonic acid-isoleucine and loss of dormancy in seeds of stressed plants. Dormancy was also reduced by engineering seed-specific accumulation of jasmonic acid in transgenic plants. Loss of dormancy was dependent on an intact jasmonate signalling pathway and was associated with increased gibberellin content and reduced abscisic acid sensitivity during germination. Altered dormancy was only observed in the first generation following herbivory, whereas defence priming was maintained for at least two generations. Herbivory generates a jasmonic acid-dependent reduction in seed dormancy, mediated by alteration of gibberellin and abscisic acid signalling. This is a direct maternal effect, operating independently from transgenerational herbivore resistance priming

Physical Modelling of the Flow Field in an Undular Tidal Bore

A tidal bore may form in a converging channel with a funnel shape when the tidal range exceeds 6-9 m. The advancing surge has a major impact on the estuarine ecosystem. Physical modelling of an undular bore has been conducted based upon a quasi-steady flow analogy. The experimental data highlight rapid flow redistributions between successive wave troughs and crests as well as large bottom shear stress variations. The results suggest a sediment transport process combining scour beneath wave troughs associated with upward matter dispersion between a trough and the following wave crest. The process is repeated at each trough and significant sediment transport takes place with deposition in upstream intertidal zones. The conceptual model is supported by field observations showing murky waters after the bore passage and long-lasting chaotic waves

Turbulence measurements in positive surges and bores

A positive surge results from a sudden change in flow that increases the flow depth. New experiments were conducted in a large channel. Most positive surge tests were conducted with a horizontal bed slope, a constant flow rate and uncontrolled flow conditions. The only dependant variable was the downstream gate opening after closure. Detailed turbulence measurements were performed with high-temporal resolution using side-looking acoustic Doppler velocimetry. Two types of positive surge were observed: undular surge for Froude numbers less than 1.7, and weak (breaking) surges above. Instantaneous velocity measurements beneath advancing surges showed a marked effect of the surge passage on the velocity field. Streamwise velocities showed rapid flow deceleration at all vertical elevations. Large fluctuations of longitudinal and transverse velocities were recorded beneath the surges, including some unsteady flow recirculation beneath a weak surge front. Turbulent stresses were deduced from high-pass filtered data. The results showed large normal and tangential Reynolds stresses beneath the surges. A comparison between undular and weak surges suggested some major difference. In weak surge flows, the data showed rapid flow separation beneath the surge front. In undular surges, maximum Reynolds stresses were observed beneath and just before each wave crest behind the leading wave

Urinary levels of N-nitroso compounds in relation to risk of gastric cancer: Findings from the Shanghai cohort study

Background: N-Nitroso compounds are thought to play a significant role in the development of gastric cancer. Epidemiological data, however, are sparse in examining the associations between biomarkers of exposure to N-nitroso compounds and the risk of gastric cancer. Methods: A nested case-control study within a prospective cohort of 18,244 middle-aged and older men in Shanghai, China, was conducted to examine the association between urinary level of N-nitroso compounds and risk of gastric cancer. Information on demographics, usual dietary intake, and use of alcohol and tobacco was collected through in-person interviews at enrollment. Urinary levels of nitrate, nitrite, N-nitroso-2-methylthiazolidine-4-carboxylic acid (NMTCA), N-nitrosoproline (NPRO), N-nitrososarcosine (NSAR), N-nitrosothiazolidine-4-carboxylic acid (NTCA), as well as serum H. pylori antibodies were quantified in 191 gastric cancer cases and 569 individually matched controls. Logistic regression method was used to assess the association between urinary levels of N-nitroso compounds and risk of gastric cancer. Results: Compared with controls, gastric cancer patients had overall comparable levels of urinary nitrate, nitrite, and N-nitroso compounds. Among individuals seronegative for antibodies to H. pylori, elevated levels of urinary nitrate were associated with increased risk of gastric cancer. The multivariate-adjusted odds ratios for the second and third tertiles of nitrate were 3.27 (95% confidence interval = 0.76-14.04) and 4.82 (95% confidence interval = 1.05-22.17), respectively, compared with the lowest tertile (P for trend = 0.042). There was no statistically significant association between urinary levels of nitrite or N-nitroso compounds and risk of gastric cancer. Urinary NMTCA level was significantly associated with consumption of alcohol and preserved meat and fish food items. Conclusion: The present study demonstrates that exposure to nitrate, a precursor of N-nitroso compounds, may increase the risk of gastric cancer among individuals without a history of H. pylori infection

A novel TP53 splicing mutation in a Li-Fraumeni syndrome family: a patient with Wilms' tumour is not a mutation carrier.

We report a Li-Fraumeni syndrome family in which we have detected a splice acceptor mutation in intron 3 of TP53. The mutation affects one of the invariant residues at the splice acceptor site, as a result of which two aberrant transcripts are produced. A child with Wilms' tumour aged 3 years in this family was shown not to be a mutation carrier

Electroceutical enhancement of self-compassion training using transcutaneous vagus nerve stimulation: results from a preregistered fully factorial randomized controlled trial

Background Physiological signals conveyed by the vagus nerve may generate quiescent psychological states conducive to contemplative practices. This suggests that vagal neurostimulation could interact with contemplative psychotherapies (e.g. mindfulness and compassion-based interventions) to augment their efficacy. Methods In a fully factorial experimental trial, healthy adults (n = 120) were randomized to transcutaneous vagus nerve stimulation (tVNS) plus Self-Compassion-Mental-Imagery Training (SC-MIT) or alternative factorial combinations of stimulation (tVNS or sham) plus mental imagery training (MIT: SC-MIT or Control-MIT). Primary outcomes were self-reported state self-compassion, self-criticism, and heart rate variability (HRV). Exploratory outcomes included state mindfulness and oculomotor attentional bias to compassion-expressing faces. Most outcomes were assessed acutely on session 1 at the pre-stimulation (T1), peri-stimulation (T2), and post-MIT + stimulation (T3) timepoints, and after daily stimulation+MIT sessions (eight sessions). Results During session 1, a significant Timepoint × Stimulation × MIT interaction (p = 0.025) was observed, reflecting a larger acute T1→T3 increase in state self-compassion after tVNS+SC-MIT, with similar rapid effects on state mindfulness. Additionally, significant Session × MIT and Session × Stimulation interactions (p ≤ 0.027) on state mindfulness (but not self-compassion) suggested that tVNS+SC-MIT’s effects may accumulate across sessions for some outcomes. By contrast, changes in state self-criticism and compassion-related attentional bias were only moderated by MIT (not stimulation) condition. HRV was unaffected by stimulation or MIT condition. Conclusion tVNS augmented the effects of SC-MIT and might, therefore, be a useful strategy for enhancing meditation-based psychotherapies. Our findings also highlight the value of oculomotor attentional metrics as responsive markers of self-compassion training and the continued need for sensitive indices of successful vagal stimulation