On spectral minimal partitions II, the case of the rectangle

In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-\frac a2,\frac a2[\times ] -\frac b2,\frac b2[$, with $0< a\leq b$. It has been observed in \cite{HHOT} that when $0<\frac ab < \sqrt{\frac 38}$ the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles $]-\frac a2,\frac a2[\times ] -\frac b2,-\frac b6[$, $]-\frac a2,\frac a2[\times ] -\frac b6,\frac b6[$ and $]-\frac a2,\frac a2[\times ] \frac b6, \frac b2[$. We will describe a possible mechanism of transition for increasing $\frac ab$ between these nodal minimal 3-partitions and non nodal minimal 3-partitions at the value $\sqrt{\frac 38}$ and discuss the existence of symmetric candidates for giving minimal 3-partitions when $\sqrt{\frac 38}<\frac ab \leq 1$. Numerical analysis leads very naturally to nice questions of isospectrality which are solved by introducing Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle

Ranking the Risks: The 10 Pathogen-Food Combinations With the Greatest Burden on Public Health

Examines food-borne pathogens with the highest disease burdens and the top ten foods most commonly contaminated by them, such as salmonella in poultry, toxoplasma in pork, and listeria in deli meats. Makes policy recommendations for improving prevention

The electron density is smooth away from the nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.Comment: 16 page

Crosstalk Correction in Atomic Force Microscopy

Commercial atomic force microscopes usually use a four-segmented photodiode to detect the motion of the cantilever via laser beam deflection. This read-out technique enables to measure bending and torsion of the cantilever separately. A slight angle between the orientation of the photodiode and the plane of the readout beam, however, causes false signals in both readout channels, so-called crosstalk, that may lead to misinterpretation of the acquired data. We demonstrate this fault with images recorded in contact mode on ferroelectric crystals and present an electronic circuit to compensate for it, thereby enabling crosstalk-free imaging

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781

Educational interventions to improve people's understanding of key concepts in assessing the effects of health interventions: a systematic review

Abstract Background Health information is readily accessible but is of variable quality. General knowledge about how to assess whether claims about health interventions are trustworthy is not common, so people’s health decisions can be ill-informed, unnecessarily costly and even unsafe. This review aims to identify and evaluate studies of educational interventions designed to improve people’s understanding of key concepts for evaluating claims about the effects of health interventions. Methods/Design We searched multiple electronic databases and sources of grey literature. Inclusion criteria included all study types that included a comparison, any participants (except health professionals or health professional students) and educational interventions aimed at improving people’s understanding of one or more of the key concepts considered necessary for assessing health intervention claims. Knowledge and/or understanding of concepts or skills relevant to evaluating health information were our primary outcome measures. Secondary outcomes included behaviour, confidence, attitude and satisfaction with the educational interventions. Two authors independently screened search results, assessed study eligibility and risk of bias and extracted data. Results were summarised using descriptive synthesis. Results Among 24 eligible studies, 14 were randomised trials and 10 used other study designs. There was heterogeneity across study participants, settings and educational intervention type, content and delivery. The risk of bias was high in at least one domain for all randomised studies. Most studies measured outcomes immediately after the educational intervention, with few measuring later. In most of the comparisons, measures of knowledge and skills were better among those who had received educational interventions than among controls, and some of these differences were statistically significant. The effects on secondary outcomes were inconsistent. Conclusions Educational interventions to improve people’s understanding of key concepts for evaluating health intervention claims can improve people’s knowledge and skills, at least in the short term. Effects on confidence, attitude and behaviour are uncertain. Many of the studies were at moderate or greater risk of bias. Improvements in study quality, consistency of outcome measures and measures of longer-term effects are needed to improve confidence in estimates of the effects of educational interventions to improve people’s understanding of key concepts for evaluating health intervention claims. Systematic review registration PROSPERO CRD4201603310