The approach to equilibrium in N-body gravitational systems

The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational systems: the possibility of the existence of stable equilibrium states and the associated relaxation time would provide an ideal situation where relaxation theory can be tested. Indeed, these states are found to exist for single mass $N$-body systems, and the condition condition for this is simply that obtained from elementary thermodynamical considerations applied to self-gravitating ideal gas spheres. However, even when this condition is satisfied, some initial states may not end as isothermal spheres. It is therefore only a necessary condition. Simple considerations also predict that, for fixed total mass, energy and radius, stable isothermal spheres are unique. Therefore, statistically irreversible perturbations to the density profile caused by the accumulation of massive particles near the centre of multimass systems, destroy these equilibria if the aforementioned quantities are kept fixed. The time-scale for this to happen was found to be remarkably short (a few dynamical times when $N= 2500$) in systems undergoing violent relaxation. The time taken to achieve thermal equilibrium depended on the initial conditions and could be comparable to a dynamical time (even when the conditions for violent relaxation were not satisfied) or the two body relaxation time. The relaxation time for velocity anisotropies was intermediate between these two time-scales, being long compared to the dynamical time but much (about four times) shorter than the time-scale of energy relaxation.Comment: To appear in Physical Review

Lancet HIV

BACKGROUND: Universal antiretroviral therapy (ART), as per the 2015 WHO recommendations, might reduce population HIV incidence. We investigated the effect of universal test and treat on HIV acquisition at population level in a high prevalence rural region of South Africa. METHODS: We did a phase 4, open-label, cluster randomised trial of 22 communities in rural KwaZulu-Natal, South Africa. We included individuals residing in the communities who were aged 16 years or older. The clusters were composed of aggregated local areas (neighbourhoods) that had been identified in a previous study in the Hlabisa subdistrict. The study statisticians randomly assigned clusters (1:1) with MapInfo Pro (version 11.0) to either the control or intervention communities, stratified on the basis of antenatal HIV prevalence. We offered residents repeated rapid HIV testing during home-based visits every 6 months for about 4 years in four clusters, 3 years in six clusters, and 2 years in 12 clusters (58 cluster-years) and referred HIV-positive participants to trial clinics for ART (fixed-dose combination of tenofovir, emtricitabine, and efavirenz) regardless of CD4 cell count (intervention) or according to national guidelines (initially </=350 cells per muL and <500 cells per muL from January, 2015; control). Participants and investigators were not masked to treatment allocation. We used dried blood spots once every 6 months provided by participants who were HIV negative at baseline to estimate the primary outcome of HIV incidence with cluster-adjusted Poisson generalised estimated equations in the intention-to-treat population after 58 cluster-years of follow-up. This study is registered with ClinicalTrials.gov, number NCT01509508, and the South African National Clinical Trials Register, number DOH-27-0512-3974. FINDINGS: Between March 9, 2012, and June 30, 2016, we contacted 26 518 (93%) of 28 419 eligible individuals. Of 17 808 (67%) individuals with a first negative dried blood spot test, 14 223 (80%) had subsequent dried blood spot tests, of whom 503 seroconverted after follow-up of 22 891 person-years. Estimated HIV incidence was 2.11 per 100 person-years (95% CI 1.84-2.39) in the intervention group and 2.27 per 100 person-years (2.00-2.54) in the control group (adjusted hazard ratio 1.01, 95% CI 0.87-1.17; p=0.89). We documented one case of suicidal attempt in a woman following HIV seroconversion. 128 patients on ART had 189 life-threatening or grade 4 clinical events: 69 (4%) of 1652 in the control group and 59 (4%) of 1367 in the intervention group (p=0.83). INTERPRETATION: The absence of a lowering of HIV incidence in universal test and treat clusters most likely resulted from poor linkage to care. Policy change to HIV universal test and treat without innovation to improve health access is unlikely to reduce HIV incidence. FUNDING: ANRS, GiZ, and 3ie

Training sensory signal-to-noise resolution in children with ADHD in a global mental health setting

Children with attention deficit/hyperactivity disorder (ADHD) have impaired focus on goal-relevant signals and fail to suppress goal-irrelevant distractions. To address both these issues, we developed a novel neuroplasticity-based training program that adaptively trains the resolution of challenging sensory signals and the suppression of progressively more challenging distractions. We evaluated this sensory signal-to-noise resolution training in a small sample, global mental health study in Indian children with ADHD. The children trained for 30 h over 6 months in a double-blind, randomized controlled trial. Training completers showed steady and significant improvements in ADHD-associated behaviors from baseline to post training relative to controls, and benefits sustained in a 6-month follow-up. Post-training cognitive assessments showed significant positive results for response inhibition and Stroop interference tests in training completers vs controls, while measures of sustained attention and short-term memory showed nonsignificant improvement trends. Further, training-driven improvements in distractor suppression correlated with the improved ADHD symptoms. This initial study suggests utility of signal-to-noise resolution training for children with ADHD; it emphasizes the need for further research on this intervention and substantially informs the design of a larger trial