Flows on Simplicial Complexes

Given a graph $G$, the number of nowhere-zero \ZZ_q-flows $\phi_G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero \ZZ_q-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes.Comment: 10 pages, to appear in Discrete Mathematics and Theoretical Computer Science (proceedings of FPSAC'12

hh-vectors of small matroid complexes

Stanley conjectured in 1977 that the $h$-vector of a matroid simplicial complex is a pure $O$-sequence. We give simple constructive proofs that the conjecture is true for matroids of rank less than or equal to 3, and corank 2. We used computers to verify that Stanley's conjecture holds for all matroids on at most nine elements.Comment: 11 pages, 1 figur

Flows on Simplicial Complexes

Given a graph $G$, the number of nowhere-zero $\mathbb{Z}_q$-flows $\phi _G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\mathbb{Z} _q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes

SEASTAR: a mission to study ocean submesoscale dynamics and small-scale atmosphere-ocean processes in coastal, shelf and polar seas

High-resolution satellite images of ocean color and sea surface temperature reveal an abundance of ocean fronts, vortices and filaments at scales below 10 km but measurements of ocean surface dynamics at these scales are rare. There is increasing recognition of the role played by small scale ocean processes in ocean-atmosphere coupling, upper-ocean mixing and ocean vertical transports, with advanced numerical models and in situ observations highlighting fundamental changes in dynamics when scales reach 1 km. Numerous scientific publications highlight the global impact of small oceanic scales on marine ecosystems, operational forecasts and long-term climate projections through strong ageostrophic circulations, large vertical ocean velocities and mixed layer re-stratification. Small-scale processes particularly dominate in coastal, shelf and polar seas where they mediate important exchanges between land, ocean, atmosphere and the cryosphere, e.g., freshwater, pollutants. As numerical models continue to evolve toward finer spatial resolution and increasingly complex coupled atmosphere-wave-ice-ocean systems, modern observing capability lags behind, unable to deliver the high-resolution synoptic measurements of total currents, wind vectors and waves needed to advance understanding, develop better parameterizations and improve model validations, forecasts and projections. SEASTAR is a satellite mission concept that proposes to directly address this critical observational gap with synoptic two-dimensional imaging of total ocean surface current vectors and wind vectors at 1 km resolution and coincident directional wave spectra. Based on major recent advances in squinted along-track Synthetic Aperture Radar interferometry, SEASTAR is an innovative, mature concept with unique demonstrated capabilities, seeking to proceed toward spaceborne implementation within Europe and beyond

PDRs4All IV. An embarrassment of riches: Aromatic infrared bands in the Orion Bar

(Abridged) Mid-infrared observations of photodissociation regions (PDRs) are dominated by strong emission features called aromatic infrared bands (AIBs). The most prominent AIBs are found at 3.3, 6.2, 7.7, 8.6, and 11.2 $\mu$m. The most sensitive, highest-resolution infrared spectral imaging data ever taken of the prototypical PDR, the Orion Bar, have been captured by JWST. We provide an inventory of the AIBs found in the Orion Bar, along with mid-IR template spectra from five distinct regions in the Bar: the molecular PDR, the atomic PDR, and the HII region. We use JWST NIRSpec IFU and MIRI MRS observations of the Orion Bar from the JWST Early Release Science Program, PDRs4All (ID: 1288). We extract five template spectra to represent the morphology and environment of the Orion Bar PDR. The superb sensitivity and the spectral and spatial resolution of these JWST observations reveal many details of the AIB emission and enable an improved characterization of their detailed profile shapes and sub-components. While the spectra are dominated by the well-known AIBs at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 $\mu$m, a wealth of weaker features and sub-components are present. We report trends in the widths and relative strengths of AIBs across the five template spectra. These trends yield valuable insight into the photochemical evolution of PAHs, such as the evolution responsible for the shift of 11.2 $\mu$m AIB emission from class B$_{11.2}$ in the molecular PDR to class A$_{11.2}$ in the PDR surface layers. This photochemical evolution is driven by the increased importance of FUV processing in the PDR surface layers, resulting in a "weeding out" of the weakest links of the PAH family in these layers. For now, these JWST observations are consistent with a model in which the underlying PAH family is composed of a few species: the so-called 'grandPAHs'.Comment: 25 pages, 10 figures, to appear in A&

PDRs4All II: JWST's NIR and MIR imaging view of the Orion Nebula

The JWST has captured the most detailed and sharpest infrared images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR). We investigate the fundamental interaction of far-ultraviolet photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of 0.1-1" (0.0002-0.002 pc or 40-400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. A complex, structured, and folded DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate

Contributions of mean and shape of blood pressure distribution to worldwide trends and variations in raised blood pressure: A pooled analysis of 1018 population-based measurement studies with 88.6 million participants

© The Author(s) 2018. Background: Change in the prevalence of raised blood pressure could be due to both shifts in the entire distribution of blood pressure (representing the combined effects of public health interventions and secular trends) and changes in its high-blood-pressure tail (representing successful clinical interventions to control blood pressure in the hypertensive population). Our aim was to quantify the contributions of these two phenomena to the worldwide trends in the prevalence of raised blood pressure. Methods: We pooled 1018 population-based studies with blood pressure measurements on 88.6 million participants from 1985 to 2016. We first calculated mean systolic blood pressure (SBP), mean diastolic blood pressure (DBP) and prevalence of raised blood pressure by sex and 10-year age group from 20-29 years to 70-79 years in each study, taking into account complex survey design and survey sample weights, where relevant. We used a linear mixed effect model to quantify the association between (probittransformed) prevalence of raised blood pressure and age-group- and sex-specific mean blood pressure. We calculated the contributions of change in mean SBP and DBP, and of change in the prevalence-mean association, to the change in prevalence of raised blood pressure. Results: In 2005-16, at the same level of population mean SBP and DBP, men and women in South Asia and in Central Asia, the Middle East and North Africa would have the highest prevalence of raised blood pressure, and men and women in the highincome Asia Pacific and high-income Western regions would have the lowest. In most region-sex-age groups where the prevalence of raised blood pressure declined, one half or more of the decline was due to the decline in mean blood pressure. Where prevalence of raised blood pressure has increased, the change was entirely driven by increasing mean blood pressure, offset partly by the change in the prevalence-mean association. Conclusions: Change in mean blood pressure is the main driver of the worldwide change in the prevalence of raised blood pressure, but change in the high-blood-pressure tail of the distribution has also contributed to the change in prevalence, especially in older age groups

Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants

Summary Background Comparable global data on health and nutrition of school-aged children and adolescents are scarce. We aimed to estimate age trajectories and time trends in mean height and mean body-mass index (BMI), which measures weight gain beyond what is expected from height gain, for school-aged children and adolescents. Methods For this pooled analysis, we used a database of cardiometabolic risk factors collated by the Non-Communicable Disease Risk Factor Collaboration. We applied a Bayesian hierarchical model to estimate trends from 1985 to 2019 in mean height and mean BMI in 1-year age groups for ages 5–19 years. The model allowed for non-linear changes over time in mean height and mean BMI and for non-linear changes with age of children and adolescents, including periods of rapid growth during adolescence. Findings We pooled data from 2181 population-based studies, with measurements of height and weight in 65 million participants in 200 countries and territories. In 2019, we estimated a difference of 20 cm or higher in mean height of 19-year-old adolescents between countries with the tallest populations (the Netherlands, Montenegro, Estonia, and Bosnia and Herzegovina for boys; and the Netherlands, Montenegro, Denmark, and Iceland for girls) and those with the shortest populations (Timor-Leste, Laos, Solomon Islands, and Papua New Guinea for boys; and Guatemala, Bangladesh, Nepal, and Timor-Leste for girls). In the same year, the difference between the highest mean BMI (in Pacific island countries, Kuwait, Bahrain, The Bahamas, Chile, the USA, and New Zealand for both boys and girls and in South Africa for girls) and lowest mean BMI (in India, Bangladesh, Timor-Leste, Ethiopia, and Chad for boys and girls; and in Japan and Romania for girls) was approximately 9–10 kg/m2. In some countries, children aged 5 years started with healthier height or BMI than the global median and, in some cases, as healthy as the best performing countries, but they became progressively less healthy compared with their comparators as they grew older by not growing as tall (eg, boys in Austria and Barbados, and girls in Belgium and Puerto Rico) or gaining too much weight for their height (eg, girls and boys in Kuwait, Bahrain, Fiji, Jamaica, and Mexico; and girls in South Africa and New Zealand). In other countries, growing children overtook the height of their comparators (eg, Latvia, Czech Republic, Morocco, and Iran) or curbed their weight gain (eg, Italy, France, and Croatia) in late childhood and adolescence. When changes in both height and BMI were considered, girls in South Korea, Vietnam, Saudi Arabia, Turkey, and some central Asian countries (eg, Armenia and Azerbaijan), and boys in central and western Europe (eg, Portugal, Denmark, Poland, and Montenegro) had the healthiest changes in anthropometric status over the past 3·5 decades because, compared with children and adolescents in other countries, they had a much larger gain in height than they did in BMI. The unhealthiest changes—gaining too little height, too much weight for their height compared with children in other countries, or both—occurred in many countries in sub-Saharan Africa, New Zealand, and the USA for boys and girls; in Malaysia and some Pacific island nations for boys; and in Mexico for girls. Interpretation The height and BMI trajectories over age and time of school-aged children and adolescents are highly variable across countries, which indicates heterogeneous nutritional quality and lifelong health advantages and risks

Rising rural body-mass index is the main driver of the global obesity epidemic in adults

Body-mass index (BMI) has increased steadily in most countries in parallel with a rise in the proportion of the population who live in cities(.)(1,2) This has led to a widely reported view that urbanization is one of the most important drivers of the global rise in obesity(3-6). Here we use 2,009 population-based studies, with measurements of height and weight in more than 112 million adults, to report national, regional and global trends in mean BMI segregated by place of residence (a rural or urban area) from 1985 to 2017. We show that, contrary to the dominant paradigm, more than 55% of the global rise in mean BMI from 1985 to 2017-and more than 80% in some low- and middle-income regions-was due to increases in BMI in rural areas. This large contribution stems from the fact that, with the exception of women in sub-Saharan Africa, BMI is increasing at the same rate or faster in rural areas than in cities in low- and middle-income regions. These trends have in turn resulted in a closing-and in some countries reversal-of the gap in BMI between urban and rural areas in low- and middle-income countries, especially for women. In high-income and industrialized countries, we noted a persistently higher rural BMI, especially for women. There is an urgent need for an integrated approach to rural nutrition that enhances financial and physical access to healthy foods, to avoid replacing the rural undernutrition disadvantage in poor countries with a more general malnutrition disadvantage that entails excessive consumption of low-quality calories.Peer reviewe