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

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

Apoptosis Induced by Cytoskeletal Disruption Requires Distinct Domains of MEKK1

MEKK1 is a mitogen-activated protein kinase kinase kinase (MAP3K) that activates the MAPK JNK and is required for microtubule inhibitor-induced apoptosis in B cells. Here, we find that apoptosis induced by actin disruption via cytochalasin D and by the protein phosphatase 1/2A inhibitor okadaic acid also requires MEKK1 activation. To elucidate the functional requirements for activation of the MEKK1-dependent apoptotic pathway, we created mutations within MEKK1. MEKK1-deficient cells were complemented with MEKK1 containing mutations in either the ubiquitin interacting motif (UIM), plant homeodomain (PHD), caspase cleavage site or the kinase domain at near endogenous levels of expression and tested for their sensitivity to each drug. We found that both the kinase activity and the PHD domain of MEKK1 are required for JNK activation and efficient induction of apoptosis by drugs causing cytoskeletal disruption. Furthermore, we discovered that modification of MEKK1 and its localization depends on the integrity of the PHD

Development of estimates of dietary nitrates, nitrites, and nitrosamines for use with the short willet food frequency questionnaire

<p>Abstract</p> <p>Background</p> <p>Studies have suggested that nitrates, nitrites, and nitrosamines have an etiologic role in adverse pregnancy outcomes and chronic diseases such as cancer. Although an extensive body of literature exists on estimates of these compounds in foods, the extant data varies in quality, quantified estimates, and relevance.</p> <p>Methods</p> <p>We developed estimates of nitrates, nitrites, and nitrosamines for food items listed in the Short Willet Food Frequency Questionnaire (WFFQ) as adapted for use in the National Birth Defects Prevention Study. Multiple reference databases were searched for published literature reflecting nitrate, nitrite, and nitrosamine values in foods. Relevant published literature was reviewed; only publications reporting results for items listed on the WFFQ were selected for inclusion. The references selected were prioritized according to relevance to the U.S. population.</p> <p>Results</p> <p>Based on our estimates, vegetable products contain the highest levels of nitrate, contributing as much as 189 mg/serving. Meat and bean products contain the highest levels of nitrites with values up to 1.84 mg/serving. Alcohol, meat and dairy products contain the highest values of nitrosamines with a maximum value of 0.531 μg/serving. The estimates of dietary nitrates, nitrites, and nitrosamines generated in this study are based on the published values currently available.</p> <p>Conclusion</p> <p>To our knowledge, these are the only estimates specifically designed for use with the adapted WFFQ and generated to represent food items available to the U.S. population. The estimates provided may be useful in other research studies, specifically in those exploring the relation between exposure to these compounds in foods and adverse health outcomes.</p

Maternal characteristics associated with the dietary intake of nitrates, nitrites, and nitrosamines in women of child-bearing age: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Multiple <it>N</it>-nitroso compounds have been observed in animal studies to be both mutagenic and teratogenic. Human exposure to <it>N</it>-nitroso compounds and their precursors, nitrates and nitrites, can occur through exogenous sources, such as diet, drinking water, occupation, or environmental exposures, and through endogenous exposures resulting from the formation of <it>N</it>-nitroso compounds in the body. Very little information is available on intake of nitrates, nitrites, and nitrosamines and factors related to increased consumption of these compounds.</p> <p>Methods</p> <p>Using survey and dietary intake information from control women (with deliveries of live births without major congenital malformations during 1997-2004) who participated in the National Birth Defects Prevention Study (NBDPS), we examined the relation between various maternal characteristics and intake of nitrates, nitrites, and nitrosamines from dietary sources. Estimated intake of these compounds was obtained from the Willet Food Frequency Questionnaire as adapted for the NBDPS. Multinomial logistic regression models were used to estimate odds ratios and 95% confidence intervals for the consumption of these compounds by self-reported race/ethnicity and other maternal characteristics.</p> <p>Results</p> <p>Median intake per day for nitrates, nitrites, total nitrites (nitrites + 5% nitrates), and nitrosamines was estimated at 40.48 mg, 1.53 mg, 3.69 mg, and 0.472 μg respectively. With the lowest quartile of intake as the referent category and controlling for daily caloric intake, factors predicting intake of these compounds included maternal race/ethnicity, education, body mass index, household income, area of residence, folate intake, and percent of daily calories from dietary fat. Non-Hispanic White participants were less likely to consume nitrates, nitrites, and total nitrites per day, but more likely to consume dietary nitrosamines than other participants that participated in the NBDPS. Primary food sources of these compounds also varied by maternal race/ethnicity.</p> <p>Conclusions</p> <p>Results of this study indicate that intake of nitrates, nitrites, and nitrosamines vary considerably by race/ethnicity, education, body mass index, and other characteristics. Further research is needed regarding how consumption of foods high in nitrosamines and <it>N</it>-nitroso precursors might relate to risk of adverse pregnancy outcomes and chronic diseases.</p

Scientific assessment of the use of sugars as cigarette tobacco ingredients: A review of published and other publicly available studies

Sugars, such as sucrose or invert sugar, have been used as tobacco ingredients in American-blend cigarettes to replenish the sugars lost during curing of the Burley component of the blended tobacco in order to maintain a balanced flavor. Chemical-analytical studies of the mainstream smoke of research cigarettes with various sugar application levels revealed that most of the smoke constituents determined did not show any sugar-related changes in yields (per mg nicotine), while ten constituents were found to either increase (formaldehyde, acrolein, 2-butanone, isoprene, benzene, toluene, benzo[k]fluoranthene) or decrease (4-aminobiphenyl, N-nitrosodimethylamine, N-nitrosonornicotine) in a statistically significant manner with increasing sugar application levels. Such constituent yields were modeled into constituent uptake distributions using simulations of nicotine uptake distributions generated on the basis of published nicotine biomonitoring data, which were multiplied by the constituent/nicotine ratios determined in the current analysis. These simulations revealed extensive overlaps for the constituent uptake distributions with and without sugar application. Moreover, the differences in smoke composition did not lead to relevant changes in the activity in in vitro or in vivo assays. The potential impact of using sugars as tobacco ingredients was further assessed in an indirect manner by comparing published data from markets with predominantly American-blend or Virginia-type (no added sugars) cigarettes. No relevant difference was found between these markets for smoking prevalence, intensity, some markers of dependence, nicotine uptake, or mortality from smoking-related lung cancer and chronic obstructive pulmonary disease. In conclusion, thorough examination of the data available suggests that the use of sugars as ingredients in cigarette tobacco does not increase the inherent risk and harm of cigarette smoking

Transitions at CpG Dinucleotides, Geographic Clustering of TP53 Mutations and Food Availability Patterns in Colorectal Cancer

Colorectal cancer is mainly attributed to diet, but the role exerted by foods remains unclear because involved factors are extremely complex. Geography substantially impacts on foods. Correlations between international variation in colorectal cancer-associated mutation patterns and food availabilities could highlight the influence of foods on colorectal mutagenesis. mutations from 12 countries/geographic areas. For food availabilities, we relied on data extracted from the Food Balance Sheets of the Food and Agriculture Organization of the United Nations. Dendrograms for mutation sites, mutation types and food patterns were constructed through Ward's hierarchical clustering algorithm and their stability was assessed evaluating silhouette values. Feature selection used entropy-based measures for similarity between clusterings, combined with principal component analysis by exhaustive and heuristic approaches. hotspots. Pearson's correlation scores, computed between the principal components of the datamatrices for mutation types, food availability and mutation sites, demonstrated statistically significant correlations between transitions at CpGs and both mutation sites and availabilities of meat, milk, sweeteners and animal fats, the energy-dense foods at the basis of “Western” diets. This is best explainable by differential exposure to nitrosative DNA damage due to foods that promote metabolic stress and chronic inflammation

Prostate-specific antigen velocity in a prospective prostate cancer screening study of men with genetic predisposition.

This corrects the article DOI: 10.1038/bjc.2017.429