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This memoir is concerned with quantitative unique continuation estimates for equations involving a “sum of squares” operator The first result is the tunneling estimate The main result is a stability estimate for solutions to the hypoelliptic wave equation We then prove the approximate controllability of the hypoelliptic heat equation We also explain how the analyticity assumption can be relaxed, and a boundary Most results turn out to be optimal on a family of Grushin-type operators. The main proof relies on the general strategy to produce quantitative unique continuation estimates, developed by the authors in Laurent-Léautaud (2019).

The prognostic value of electrocardiograms (ECGs) has been reported in predialysis patients but not in incident hemodialysis patients with overhydration and electrolyte disturbances, both of which potentially affect ECG results. We performed a retrospective multicenter cohort study involving incident hemodialysis patients and examined whether ECG parameters immediately before hemodialysis initiation can predict subsequent cardiovascular disease (CVD) using Cox proportional hazards models. We explored potential effect modifications by several electrolytes on the predictive power of ECG abnormalities. Among the 618 enrolled patients, 16%, 10%, 46%, and 22% showed a PR interval ≥ 200 ms, QRS interval ≥120 ms, QTc interval ≥ 450/460 ms (male/female), and left ventricular hypertrophy (LVH) by voltage criteria, respectively. Over a median 3-year follow-up, 19% and 16% of the patients developed atherosclerotic and nonatherosclerotic CVD, respectively. The Cox regression model results revealed that the sum of the number of abnormalities in PR, QRS, and QT intervals was a significant risk factor for nonatherosclerotic CVD (hazard ratios (HRs) [95% confidence interval (CI)]: 1.58 [1.24-2.01] per number of abnormalities). The predictive value of LVH for atherosclerotic CVD was attenuated over time. At up to 36 months, although the proportional hazards assumption was met, LVH was significantly associated with atherosclerotic CVD (HR [95% CI]: 1.89 [1.15-3.11]). The adjusted HR was particularly high (HR [95% CI]: 4.02 [1.68-9.60]) among patients who were in the lowest tertile of serum magnesium levels (P for interaction = 0.04). PR, QRS, and QT prolongation additively predicted nonatherosclerotic CVD, while LVH predicted atherosclerotic CVD in the short term.

One of the most important physical characteristics driving lifecycle events in lakes is stratification. Already subtle variations in the timing of stratification onset and break-up (phenology) are known to have major ecological effects, mainly by determining the availability of light, nutrients, carbon and oxygen to organisms. Despite its ecological importance, historic and future global changes in stratification phenology are unknown. Here, we used a lake-climate model ensemble and long-term observational data, to investigate changes in lake stratification phenology across the Northern Hemisphere from 1901 to 2099. Under the high-greenhouse-gas-emission scenario, stratification will begin 22.0 ± 7.0 days earlier and end 11.3 ± 4.7 days later by the end of this century. It is very likely that this 33.3 ± 11.7 day prolongation in stratification will accelerate lake deoxygenation with subsequent effects on nutrient mineralization and phosphorus release from lake sediments. Further misalignment of lifecycle events, with possible irreversible changes for lake ecosystems, is also likely. Stratification has a considerable influence on lake ecology, but there is little understanding of past or future changes in its seasonality. Here, the authors use modelling and empirical data to determine that between 1901–2099, climate change causes stratification to start earlier and end later.

Schizophrenia is one of the most common, burdensome, and costly psychiatric disorders in adults worldwide. Antipsychotic drugs are its treatment of choice, but there is controversy about which agent should be used. We aimed to compare and rank antipsychotics by quantifying information from randomised controlled trials. We did a network meta-analysis of placebo-controlled and head-to-head randomised controlled trials and compared 32 antipsychotics. We searched Embase, MEDLINE, PsycINFO, PubMed, BIOSIS, Cochrane Central Register of Controlled Trials (CENTRAL), WHO International Clinical Trials Registry Platform, and ClinicalTrials.gov from database inception to Jan 8, 2019. Two authors independently selected studies and extracted data. We included randomised controlled trials in adults with acute symptoms of schizophrenia or related disorders. We excluded studies in patients with treatment resistance, first episode, predominant negative or depressive symptoms, concomitant medical illnesses, and relapse-prevention studies. Our primary outcome was change in overall symptoms measured with standardised rating scales. We also extracted data for eight efficacy and eight safety outcomes. Differences in the findings of the studies were explored in metaregressions and sensitivity analyses. Effect size measures were standardised mean differences, mean differences, or risk ratios with 95% credible intervals (CrIs). Confidence in the evidence was assessed using CINeMA (Confidence in Network Meta-Analysis). The study protocol is registered with PROSPERO, number CRD42014014919. We identified 54 417 citations and included 402 studies with data for 53 463 participants. Effect size estimates suggested all antipsychotics reduced overall symptoms more than placebo (although not statistically significant for six drugs), with standardised mean differences ranging from −0·89 (95% CrI −1·08 to −0·71) for clozapine to −0·03 (−0·59 to 0·52) for levomepromazine (40 815 participants). Standardised mean differences compared with placebo for reduction of positive symptoms (31 179 participants) varied from −0·69 (95% CrI −0·86 to −0·52) for amisulpride to −0·17 (−0·31 to −0·04) for brexpiprazole, for negative symptoms (32 015 participants) from −0·62 (−0·84 to −0·39; clozapine) to −0·10 (−0·45 to 0·25; flupentixol), for depressive symptoms (19 683 participants) from −0·90 (−1·36 to −0·44; sulpiride) to 0·04 (−0·39 to 0·47; flupentixol). Risk ratios compared with placebo for all-cause discontinuation (42 672 participants) ranged from 0·52 (0·12 to 0·95; clopenthixol) to 1·15 (0·36 to 1·47; pimozide), for sedation (30 770 participants) from 0·92 (0·17 to 2·03; pimozide) to 10·20 (4·72 to 29·41; zuclopenthixol), for use of antiparkinson medication (24 911 participants) from 0·46 (0·19 to 0·88; clozapine) to 6·14 (4·81 to 6·55; pimozide). Mean differences compared to placebo for weight gain (28 317 participants) ranged from −0·16 kg (−0·73 to 0·40; ziprasidone) to 3·21 kg (2·10 to 4·31; zotepine), for prolactin elevation (21 569 participants) from −77·05 ng/mL (−120·23 to −33·54; clozapine) to 48·51 ng/mL (43·52 to 53·51; paliperidone) and for QTc prolongation (15 467 participants) from −2·21 ms (−4·54 to 0·15; lurasidone) to 23·90 ms (20·56 to 27·33; sertindole). Conclusions for the primary outcome did not substantially change after adjusting for possible effect moderators or in sensitivity analyses (eg, when excluding placebo-controlled studies). The confidence in evidence was often low or very low. There are some efficacy differences between antipsychotics, but most of them are gradual rather than discrete. Differences in side-effects are more marked. These findings will aid clinicians in balancing risks versus benefits of those drugs available in their countries. They should consider the importance of each outcome, the patients' medical problems, and preferences. German Ministry of Education and Research and National Institute for Health Research

Hippocampal sharp wave ripples (SPW-Rs) have been hypothesized as a mechanism for memory consolidation and action planning. The duration of ripples shows a skewed distribution with a minority of long-duration events. We discovered that long-duration ripples are increased in situations demanding memory in rats. Prolongation of spontaneously occurring ripples by optogenetic stimulation, but not randomly induced ripples, increased memory during maze learning. The neuronal content of randomly induced ripples was similar to short-duration spontaneous ripples and contained little spatial information. The spike content of the optogenetically prolonged ripples was biased by the ongoing, naturally initiated neuronal sequences. Prolonged ripples recruited new neurons that represented either arm of the maze. Long-duration hippocampal SPW-Rs replaying large parts of planned routes are critical for memory.

The incidence and mortality rates of acute pulmonary embolism (APE) are high in clinical emergencies, making early diagnosis and risk stratification crucial. Electrocardiogram (ECG) plays a significant role in guiding the diagnosis and differential diagnosis of pulmonary embolism. Acute pulmonary embolism can present with various ECG manifestations. The presence of pulmonary hypertension and increased right ventricular load in pulmonary embolism can lead to T wave inversion in the right cardiac lead. Additionally, some patients may exhibit a prolonged QT interval, which is associated with the pathophysiological processes resulting from both pulmonary hypertension and myocardial ischemia. Background: Acute pulmonary embolism (APE) is characterized by high incidence, high mortality, and high misdiagnosis rate. Most symptomatic patients with APE have corresponding changes in electrocardiogram, which should be carefully observed and combined with clinical conditions is helpful for diagnosis. Case summary: A 70‐year‐old patient with chest pain and syncope for 1 day presented to the emergency department. The electrocardiogram suggested prolonged QT interval and inversion of prethoracic lead T‐wave. After improving the relevant imaging examination, it was acute pulmonary embolism, and anticoagulant treatment was given for several days, and the QT interval returned to normal. Discussion: Sometimes, it is hard to distinguish acute pulmonary embolism from acute coronary syndrome and aortic dissection because of similar manifestations. Various imaging tests can confirm the diagnosis. These diseases often lead to the appearance of T‐wave inversion and prolonged QT interval in the electrocardiogram. However, a careful analysis of the electrocardiogram can further clarify the corresponding diagnosis.

Cutaneous melanoma causes 55 500 deaths annually. The incidence and mortality rates of the disease differ widely across the globe depending on access to early detection and primary care. Once melanoma has spread, this type of cancer rapidly becomes life-threatening. For more than 40 years, few treatment options were available, and clinical trials during that time were all unsuccessful. Over the past 10 years, increased biological understanding and access to innovative therapeutic substances have transformed advanced melanoma into a new oncological model for treating solid cancers. Treatments that target B-Raf proto-oncogene serine/threonine-kinase (BRAF)V600 (Val600) mutations using selected BRAF inhibitors combined with mitogen-activated protein kinase inhibitors have significantly improved response and overall survival. Furthermore, advanced cutaneous melanoma has developed into a prototype for testing checkpoint-modulating agents, which has increased hope for long-term tumour containment and a potential cure. These expectations have been sustained by clinical success with targeted agents and antibodies that block programmed cell-death protein 1 in locoregional disease, which induces prolongation of relapse-free, distant-metastasis-free, and overall survival times.

Post-traumatic stress disorder (PTSD) presents a major public health problem for which currently available treatments are modestly effective. We report the findings of a randomized, double-blind, placebo-controlled, multi-site phase 3 clinical trial (NCT03537014) to test the efficacy and safety of 3,4-methylenedioxymethamphetamine (MDMA)-assisted therapy for the treatment of patients with severe PTSD, including those with common comorbidities such as dissociation, depression, a history of alcohol and substance use disorders, and childhood trauma. After psychiatric medication washout, participants ( n  = 90) were randomized 1:1 to receive manualized therapy with MDMA or with placebo, combined with three preparatory and nine integrative therapy sessions. PTSD symptoms, measured with the Clinician-Administered PTSD Scale for DSM-5 (CAPS-5, the primary endpoint), and functional impairment, measured with the Sheehan Disability Scale (SDS, the secondary endpoint) were assessed at baseline and at 2 months after the last experimental session. Adverse events and suicidality were tracked throughout the study. MDMA was found to induce significant and robust attenuation in CAPS-5 score compared with placebo ( P  < 0.0001, d  = 0.91) and to significantly decrease the SDS total score ( P  = 0.0116, d  = 0.43). The mean change in CAPS-5 scores in participants completing treatment was −24.4 (s.d. 11.6) in the MDMA group and −13.9 (s.d. 11.5) in the placebo group. MDMA did not induce adverse events of abuse potential, suicidality or QT prolongation. These data indicate that, compared with manualized therapy with inactive placebo, MDMA-assisted therapy is highly efficacious in individuals with severe PTSD, and treatment is safe and well-tolerated, even in those with comorbidities. We conclude that MDMA-assisted therapy represents a potential breakthrough treatment that merits expedited clinical evaluation. Results from a phase 3, double-blind, randomized, placebo-controlled trial demonstrate that MDMA-assisted therapy is safe and effective in treating severe post-traumatic stress disorder.

The Rayleigh collapse time is the time it would take to shrink an empty spherical bubble in an infinite liquid domain to zero size, which is a function of ambient pressure and initial bubble radius. If a solid boundary is located in the vicinity of the shrinking or collapsing bubble, then liquid flow is hindered, such that the collapse time is prolonged. This can be quantified with the Rayleigh prolongation factor $k$. Here, we provide $k$ for intermediate to smallest bubble to wall stand-off distances. It is measured with single laser-induced cavitation bubbles in water close to a solid boundary. Maximum bubble radii are determined from microscopic high-speed imaging at one million frames per second. Collapse times are measured acoustically via the acoustic transients emitted during bubble seeding and collapse. The experimental findings are compared, with good agreement, to numerical simulations based on a volume of fluid method. As a result, a polynomial fit of $k$ versus stand-off distance is given for the near-wall bubble collapse in water. Then the influence of the viscosity on $k$ is studied numerically in the near-wall regime.