On commuting varieties of parabolic subalgebras

Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$, and assume that the characteristic of $k$ is zero or a pretty good prime for $G$. Let $P$ be a parabolic subgroup of $G$ and let $\mathfrak p$ be the Lie algebra of $P$. We consider the commuting variety $\mathcal C(\mathfrak p) = \{(X,Y) \in \mathfrak p \times \mathfrak p \mid [X,Y] = 0\}$. Our main theorem gives a necessary and sufficient condition for irreducibility of $\mathcal C(\mathfrak p)$ in terms of the modality of the adjoint action of $P$ on the nilpotent variety of $\mathfrak p$. As a consequence, for the case $P = B$ a Borel subgroup of $G$, we give a classification of when $\mathcal C(\mathfrak b)$ is irreducible; this builds on a partial classification given by Keeton. Further, in cases where $\mathcal C(\mathfrak p)$ is irreducible, we consider whether $\mathcal C(\mathfrak p)$ is a normal variety. In particular, this leads to a classification of when $\mathcal C(\mathfrak b)$ is normal.Comment: 19 pages; minor update

Ensemble Transport Adaptive Importance Sampling

Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods increases. In this paper, we present a particle ensemble algorithm. At each iteration, an importance sampling proposal distribution is formed using an ensemble of particles. A stratified sample is taken from this distribution and weighted under the posterior, a state-of-the-art ensemble transport resampling method is then used to create an evenly weighted sample ready for the next iteration. We demonstrate that this ensemble transport adaptive importance sampling (ETAIS) method outperforms MCMC methods with equivalent proposal distributions for low dimensional problems, and in fact shows better than linear improvements in convergence rates with respect to the number of ensemble members. We also introduce a new resampling strategy, multinomial transformation (MT), which while not as accurate as the ensemble transport resampler, is substantially less costly for large ensemble sizes, and can then be used in conjunction with ETAIS for complex problems. We also focus on how algorithmic parameters regarding the mixture proposal can be quickly tuned to optimise performance. In particular, we demonstrate this methodology's superior sampling for multimodal problems, such as those arising from inference for mixture models, and for problems with expensive likelihoods requiring the solution of a differential equation, for which speed-ups of orders of magnitude are demonstrated. Likelihood evaluations of the ensemble could be computed in a distributed manner, suggesting that this methodology is a good candidate for parallel Bayesian computations

Desafiar el orden establecido: la necesidad de “localizar” la protección

Existe una crítica cada vez mayor a los actores de protección por ignorar las estrategias de resolución de problemas y las capacidades de los autóctonos, lo que debería impulsar que se reconsideraran radical y creativamente las actitudes y los enfoques

Reflexiones desde el terreno

Trabajar con los líderes religiosos es esencial cuando se proporciona ayuda a las comunidades autóctonas, así como comprender su vida religiosa y cómo las creencias influyen en su toma de decisiones

The Integration of Positron Emission Tomography With Magnetic Resonance Imaging

A number of laboratories and companies are currently exploring the development of integrated imaging systems for magnetic resonance imaging (MRI) and positron emission tomography (PET). Scanners for both preclinical and human research applications are being pursued. In contrast to the widely distributed and now quite mature PET/computed tomography technology, most PET/MRI designs allow for simultaneous rather than sequential acquisition of PET and MRI data. While this offers the possibility of novel imaging strategies, it also creates considerable challenges for acquiring artifact-free images from both modalities. This paper discusses the motivation for developing combined PET/MRI technology, outlines the obstacles in realizing such an integrated instrument, and presents recent progress in the development of both the instrumentation and of novel imaging agents for combined PET/MRI studies. The performance of the first-generation PET/MRI systems is described. Finally, a range of possible biomedical applications for PET/MRI are outlined

A magnetic study of the west Iberia and conjugate rifted continental margins: constraints on rift-to-/drift processes

The analysis and modelling of magnetic anomalies at the conjugate rifted continental margins of the southern Iberia Abyssal Plain (TAP) and Newfoundland Basin have revealed that the sources of magnetic anomalies are distinctly different across both each margin and between the two margins. Analyses of synthetic anomalies and gridded sea surface magnetic anomaly charts west of Iberia and east of Newfoundland were accomplished by the methods of Euler deconvolution, forward and inverse modelling of the power spectrum, reduction-to-the-pole, and forward and inverse indirect methods. In addition, three near-bottom magnetometer profiles were analysed by the same methods in addition to the application of componental magnetometry. The results have revealed that oceanic crust, transitional basement and thinned continental crust are defined by magnetic sources with different characteristics. Over oceanic crust, magnetic sources are present as lava-flow-like bodies whose depths coincide with the top of acoustic basement seen on MCS profiles. Top-basement source depths are consistent with those determined in two other regions of oceanic crust. In the southern IAP, oceanic crust, ~4 km thick with magnetizations up to +1.5 A/m, generated by organized seafloor spreading was first accreted -126 Ma at the position of a N-S oriented segmented basement peridotite ridge. To the west, seafloor spreading anomalies can be modelled at spreading rates of 10 mm/yr or more. Immediately to the east, in a zone -10-20 km in width, I identify seafloor spreading anomahes which can only be modelled assuming variable spreading rates. In the OCT, sources of magnetic anomalies are present at the top of basement and up to -6 km beneath. I interpret the uppermost source as serpentinized peridotite, and the lowermost source as intruded gabbroic bodies which were impeded, whilst rising upwards, by the lower density serpentinized peridotites. Intrusion was accompanied by tectonism and a gradual change in conditions from rifting to seafloor spreading as the North Atlantic rift propagated northwards in Early Cretaceous times. Within thinned continental crust, sources are poorly lineated, and distributed in depth. Scaling relationships of susceptibility are consistent with the sources of magnetic anomalies within continental crust. OCT-type intrusions may be present in the mantle beneath continental crust. At the conjugate Newfoundland margin, seafloor spreading anomalies can be modelled at rates of 8 and 10 mm/yr suggesting an onset age consistent with that of the IAP. In the OCT there, I propose that magnetic anomalies are sourced in near top-basement serpentinized peridotites. An absence of magmatic material and the differences in basement character (with the IAP) suggest that conjugate margin evolution may have been asymmetric

Estimating the effects of preventive and weight-management interventions on the prevalence of childhood obesity in England: a modelling study

BACKGROUND: The effects of the systematic delivery of treatments for obesity are unknown. We aimed to estimate the potential effects on the prevalence of childhood obesity of systematically offering preventive and treatment interventions to eligible children in England, based on weight or health status. METHODS: For this modelling study, we developed a cross-sectional simulation model of the child and young adult population in England using data from multiple years of the Health Survey of England conducted between Jan 1, 2010, and Dec 31, 2019. Individuals were assessed for eligibility via age, BMI, and medical complications. Weight status was defined based on clinical criteria used by the UK National Institute of Health and Care Excellence. Published systematic reviews were used to estimate effect sizes for treatments, uptake, and completion for each weight-management tier. We used all available evidence, including evidence from studies that showed an unfavourable effect. We estimated the effects of two systematic approaches: a staged approach, in which children and young people were simultaneously given the most intensive treatment for which they were eligible, and a stepped approach, in which each management tier was applied sequentially, with additive effects. The primary outcomes were estimated prevalence of clinical obesity, defined as a BMI ≥98th centile on the UK90 growth chart, and difference in comparison with the estimated baseline prevalence. FINDINGS: 18 080 children and young people were included in the analytical sample. Baseline prevalence of clinical obesity was estimated to be 11·2% (95% CI 10·5 to 11·8) for children and young people aged 2-18 years. In modelling, we estimated absolute decreases in the prevalence of obesity of 0·9% (95% CI 0·1 to 1·8) for universal, preventive interventions; 0·2% (0·1 to 0·4) for interventions within a primary-care setting; 1·0% (0·1 to 2·1) for community and lifestyle interventions; 0·2% (0·0 to 0·4) for pharmaceutical interventions; and 0·4% (0·1 to 0·7) for surgical interventions. Staged care was estimated to result in an absolute decrease in the prevalence of obesity of 1·3% (-0·3 to 2·4) and stepped care was estimated to lead to an absolute decrease of 2·4% (0·1 to 4·8). INTERPRETATION: Although individual effect sizes for prevention and treatment interventions were small, when delivered at scale across England, these interventions have the potential to meaningfully contribute to reducing the prevalence of childhood obesity. FUNDING: UK National Institute for Health and Care Research