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We consider the problem of optimal partisan gerrymandering: a legislator in charge of redrawing the boundaries of equal-sized congressional districts wants to ensure the best electoral outcome for his own party. The so-called gerrymanderer faces two issues: the number of districts is finite and there is uncertainty at the level of each district. Solutions to this problem consists in cracking favorable voters in as many districts as possible to get tight majorities, and in packing unfavorable voters in the remaining districts. The optimal payoff of the gerrymanderer tends to increase as the uncertainty decreases and the number of districts is large. With an infinite number of districts, this problem boils down to concavifying a function, similarly to the optimal Bayesian persuasion problem. We introduce a measure of fairness and show that optimal gerrymandering is accordingly closer to uniform districting (full cracking), which is most unfair, than to community districting (full packing), which is very fair.

As reported in 1756 by Johann Gottlob Leidenfrost, volatile liquids on hot solids form “gleaming drops resembling quicksilver”, a consequence of their levitation on a vapour cushion1,2. This makes the drops spectacularly mobile, moving away as soon as they are deposited—an observation commonly attributed to gravity or surrounding airflows. This mobility has been exploited to manipulate drops, because tiny forces such as those generated on asymmetric substrates can move them in well-defined directions3–5, a situation that also provides heat evacuation6. Here we report that Leidenfrost droplets initially at rest on horizontal substrates self-rotate and self-propel in the direction they are rolling, in the absence of any source of asymmetry or external force. Their rapid internal flow is found to be accompanied by a tilting of their base, which creates a permanent ratchet-like mechanism, entraining the rolling liquid despite the fact that it is not in contact with its substrate.

Many differential equations involved in natural sciences show singular behaviors; i.e., quantities in the model diverge as the solution goes to zero. Nonetheless, the evolution of the singularity can be captured with self-similar solutions, several of which may exist for a given system. How to characterize the transition from one self-similar regime to another remains an open question. By studying the classic example of the pinch-off of a viscous liquid thread, we show experimentally that the geometry of the system and external perturbations play an essential role in the transition from a symmetric to an asymmetric solution. Moreover, this transient regime undergoes unexpected log-scale oscillations that delay dramatically the onset of the final self-similar solution. This result sheds light on the strong impact external constraints can have on predictions established to explain the formation of satellite droplets or on the rheological tests applied on a fluid, for example.

In the version of this Letter originally published, the Supplementary Videos were incorrectly labelled; the descriptions of 1–4 should have gone with the videos of 6–9, and the descriptions of 5–9 should have gone with the videos of 1–5. This has now been corrected.

Colloids coupled to a bath of swimming cells generically display enhanced diffusion. This transport dynamics stems from a subtle interplay between the active and passive particles that still resists our understanding despite decades of intense research. Here, we tackle the root of the problem by providing a quantitative characterisation of the single scattering events between a colloid and a bacterium. Based on our experiments, we build a minimal model that quantitatively predicts the geometry of the scattering trajectories, and enhanced colloidal diffusion at long times. This quantitative confrontation between theory and experiments elucidates the microscopic origin of enhanced transport. Collisions are solely ruled by stochastic contact interactions responsible both for genuine anomalous diffusion at short times and enhanced diffusion at long times with no ballistic regime at any scale.

In the last decade, the Kepler and CoRoT space-photometry missions have demonstrated the potential of asteroseismology as a novel, versatile and powerful tool to perform exquisite tests of stellar physics, and to enable precise and accurate characterisations of stellar properties, with impact on both exoplanetary and Galactic astrophysics. Based on our improved understanding of the strengths and limitations of such a tool, we argue for a new small/medium space mission dedicated to gathering high-precision, high-cadence, long photometric series in dense stellar fields. Such a mission will lead to breakthroughs in stellar astrophysics, especially in the metal poor regime, will elucidate the evolution and formation of open and globular clusters, and aid our understanding of the assembly history and chemodynamics of the Milky Way’s bulge and a few nearby dwarf galaxies.

Microduplications of the 17q21.31 chromosomal region encompassing the MAPT gene, which encodes the Tau protein, were identified in patients with a progressive disorder initially characterized by severe memory impairment with or without behavioral changes that can clinically mimic Alzheimer disease. The unique neuropathological report showed a primary tauopathy, which could not be unanimously classified in a given known subtype, showing both 4R- and 3R-tau inclusions, mainly within temporal cortical subregions and basal ganglia, without amyloid deposits. Recently, two subjects harboring the same duplication were reported with an atypical extrapyramidal syndrome and gait disorder. To decipher the phenotypic spectrum associated with MAPT duplications, we studied ten carriers from nine families, including two novel unrelated probands, gathering clinical (n = 10), cerebrospinal fluid (n = 6), MRI (n = 8), dopamine transporter scan (n = 4), functional (n = 5), amyloid (n = 3) and Tau-tracer (n = 2) PET imaging data as well as neuropathological examination (n = 4). Ages at onset ranged from 37 to 57 years, with prominent episodic memory impairment in 8/10 patients, associated with behavioral changes in four, while two patients showed atypical extrapyramidal syndrome with gait disorder at presentation, including one with associated cognitive deficits. Amyloid imaging was negative but Tau imaging showed significant deposits mainly in both mesiotemporal cortex. Dopaminergic denervation was found in 4/4 patients, including three without extrapyramidal symptoms. Neuropathological examination exclusively showed Tau-immunoreactive lesions. Distribution, aspect and 4R/3R tau aggregates composition suggested a spectrum from predominantly 3R, mainly cortical deposits well correlating with cognitive and behavioral changes, to predominantly 4R deposits, mainly in the basal ganglia and midbrain, in patients with prominent extrapyramidal syndrome. Finally, we performed in vitro seeding experiments in HEK-biosensor cells. Morphological features of aggregates induced by homogenates of three MAPT duplication carriers showed dense/granular ratios graduating between those induced by homogenates of a Pick disease and a progressive supranuclear palsy cases. These results suggest that MAPT duplication causes a primary tauopathy associated with diverse clinical and neuropathological features.

PurposePrimary Aldosteronism (PA) is increasingly considered as a common disease affecting up to 10% of the hypertensive population. Standard of care comprises laparoscopic total adrenalectomy but innovative treatment such as RadioFrequency Ablation (RFA) constitutes an emerging promising alternative to surgery. The main aim of this study is to analyse the cost of RFA versus surgery on aldosterone-producing adenoma patient from the French National Health Insurance (FNHI) perspective.MethodsThe ADERADHTA study was a prospective pilot study aiming to evaluate both safety and efficacy of the novel use of adrenal RFA on the patients with PA. This study conducted on two French sites and enrolled adult patients, between 2016 and 2018, presenting hypertension and underwent the RFA procedure. Direct medical (inpatient and outpatient) and non-medical (transportation, daily allowance) costs were calculated over a 6-month follow-up period. Moreover, the procedure costs for the RFA were calculated from the hospital perspective. Descriptive statistics were implemented.ResultsAnalysis was done on 21 patients in RFA groups and 27 patients in the surgery group.The difference in hospital costs between the RFA and surgery groups was €3774 (RFA: €1923; Surgery: €5697 p < 0.001) in favour of RFA. Inpatient and outpatient costs over the 6-month follow-up period were estimated at €3,48 for patients who underwent RFA. The production cost of implementing the RFA procedure was estimated at €1539 from the hospital perspective.ConclusionOur study was the first to show that RFA is 2 to 3 times less costly than surgery.The trial is registered at ClinicalTrials.gov under the number NCT02756754.

Half of fatal injuries among bicyclists are head injuries. While helmet use is likely to provide protection, their use often remains rare. We assessed the influence of strategies for promotion of helmet use with direct observation of behaviour by a semi-automatic video system. We performed a single-centre randomised controlled study, with 4 balanced randomisation groups. Participants were non-helmet users, aged 18-75 years, recruited at a loan facility in the city of Bordeaux, France. After completing a questionnaire investigating their attitudes towards road safety and helmet use, participants were randomly assigned to three groups with the provision of \"helmet only\", \"helmet and information\" or \"information only\", and to a fourth control group. Bikes were labelled with a colour code designed to enable observation of helmet use by participants while cycling, using a 7-spot semi-automatic video system located in the city. A total of 1557 participants were included in the study. Between October 15th 2009 and September 28th 2010, 2621 cyclists' movements, made by 587 participants, were captured by the video system. Participants seen at least once with a helmet amounted to 6.6% of all observed participants, with higher rates in the two groups that received a helmet at baseline. The likelihood of observed helmet use was significantly increased among participants of the \"helmet only\" group (OR = 7.73 [2.09-28.5]) and this impact faded within six months following the intervention. No effect of information delivery was found. Providing a helmet may be of value, but will not be sufficient to achieve high rates of helmet wearing among adult cyclists. Integrated and repeated prevention programmes will be needed, including free provision of helmets, but also information on the protective effect of helmets and strategies to increase peer and parental pressure.

Health measurement guides policies and health care decisions are necessary to describe and attain the quintuple aim of improving patient experience, population health, care team well-being, health care costs, and equity. In the primary care setting, patient-reported outcome measurement allows outcome comparisons within and across settings and helps improve the clinical management of patients. However, these digital patient-reported outcome measures (PROMs) are still not adapted to the clinical context of primary health care, which is an indication of the complexity of integrating these tools in this context. We must then gather evidence of their impact on chronic disease management in primary health care and understand the characteristics of effective implementation. We will conduct a systematic review to identify and assess the impact of electronic PROMs (ePROMs) implementation in primary health care for chronic disease management. Our specific objectives are to (1) determine the impact of ePROMs in primary health care for chronic disease management and (2) compare and contrast characteristics of effective ePROMs' implementation strategies. We will conduct a systematic review of the literature in accordance with the guidelines of the Cochrane Methods Group and in compliance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines for its reporting. A specific search strategy was developed for relevant databases to identify studies. Two reviewers will independently apply the inclusion criteria using full texts and will extract the data. We will use a 2-phase sequential mixed methods synthesis design by conducting a qualitative synthesis first, and use its results to perform a quantitative synthesis. This study was initiated in June 2022 by assembling the research team and the knowledge transfer committee. The preliminary search strategy will be developed and completed in September 2022. The main search strategy, data collection, study selection, and application of inclusion criteria were completed between October and December 2022. Results from this review will help support implementation efforts to accelerate innovations and digital adoption for primary health care and will be relevant for improving clinical management of chronic diseases and health care services and policies. PROSPERO International Prospective Register of Systematic Reviews CRD42022333513; https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=333513. DERR1-10.2196/48155.