Resolving diffusion in clay minerals at different time scales: Combination of experimental and modeling approaches

Since no single experimental or modeling technique provides data that allow a description of transport processes in clays and clay minerals at all relevant scales, several complementary approaches have to be combined to understand and explain the interplay between transport relevant phenomena. In this paper molecular dynamics simulations (MD) were used to investigate the mobility of water in the interlayer of montmorillonite (Mt), and to estimate the influence of mineral surfaces and interlayer ions on the water diffusion. Random Walk (RW) simulations based on a simplified representation of pore space in Mt were used to estimate and understand the effect of the arrangement of Mt particles on the meso- to macroscopic diffusivity of water. These theoretical calculations were complemented with quasielastic neutron scattering (QENS) measurements of aqueous diffusion in Mt with two pseudo-layers of water performed at four significantly different energy resolutions (i.e. observation times). The size of the interlayer and the size of Mt particles are two characteristic dimensions which determine the time dependent behavior of water diffusion in Mt. MD simulations show that at very short time scales water dynamics has the characteristic features of an oscillatory motion in the cage formed by neighbors in the first coordination shell. At longer time scales, the interaction of water with the surface determines the water dynamics, and the effect of confinement on the overall water mobility within the interlayer becomes evident. At time scales corresponding to an average water displacement equivalent to the average size of Mt particles, the effects of tortuosity are observed in the meso- to macroscopic pore scale simulations. Consistent with the picture obtained in the simulations, the QENS data can be described using a (local) 3D diffusion at short observation times, whereas at sufficiently long observation times a 2D diffusive motion is clearly observed. The effects of tortuosity measured in macroscopic tracer diffusion experiments are in qualitative agreement with RW simulations. By using experimental data to calibrate molecular and mesoscopic theoretical models, a consistent description of water mobility in clay minerals from the molecular to the macroscopic scale can be achieved. In turn, simulations help in choosing optimal conditions for the experimental measurements and the data interpretation. (C) 2014 Elsevier B.V. All rights reserved.

Early bursts of body size and shape evolution are rare in comparative data

George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations-more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.

How do indirect measures of evaluation work? Evaluating the inference of prejudice in the Implicit Association Test

There has been significant interest in indirect measures of attitudes like the Implicit Association Test (IAT), presumably because of the possibility of uncovering implicit prejudices. The authors derived a set of qualitative predictions for people's performance in the IAT on the basis of random walk models. These were supported in 3 experiments comparing clearly positive or negative categories to nonwords. They also provided evidence that participants shift their response criterion when doing the IAT. Because of these criterion shifts, a response pattern in the IAT can have multiple causes. Thus, it is not possible to infer a single cause (such as prejudice) from IAT results. A surprising additional result was that nonwords were treated as though they were evaluated more negatively than obviously negative items like insects, suggesting that low familiarity items may generate the pattern of data previously interpreted as evidence for implicit prejudice.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.

Effectiveness of non-steroidal anti-inflammatory drugs for the treatment of pain in knee and hip osteoarthritis: a network meta-analysis.

BACKGROUND Non-steroidal anti-inflammatory drugs (NSAIDs) are the backbone of osteoarthritis pain management. We aimed to assess the effectiveness of different preparations and doses of NSAIDs on osteoarthritis pain in a network meta-analysis. METHODS For this network meta-analysis, we considered randomised trials comparing any of the following interventions: NSAIDs, paracetamol, or placebo, for the treatment of osteoarthritis pain. We searched the Cochrane Central Register of Controlled Trials (CENTRAL) and the reference lists of relevant articles for trials published between Jan 1, 1980, and Feb 24, 2015, with at least 100 patients per group. The prespecified primary and secondary outcomes were pain and physical function, and were extracted in duplicate for up to seven timepoints after the start of treatment. We used an extension of multivariable Bayesian random effects models for mixed multiple treatment comparisons with a random effect at the level of trials. For the primary analysis, a random walk of first order was used to account for multiple follow-up outcome data within a trial. Preparations that used different total daily dose were considered separately in the analysis. To assess a potential dose-response relation, we used preparation-specific covariates assuming linearity on log relative dose. FINDINGS We identified 8973 manuscripts from our search, of which 74 randomised trials with a total of 58 556 patients were included in this analysis. 23 nodes concerning seven different NSAIDs or paracetamol with specific daily dose of administration or placebo were considered. All preparations, irrespective of dose, improved point estimates of pain symptoms when compared with placebo. For six interventions (diclofenac 150 mg/day, etoricoxib 30 mg/day, 60 mg/day, and 90 mg/day, and rofecoxib 25 mg/day and 50 mg/day), the probability that the difference to placebo is at or below a prespecified minimum clinically important effect for pain reduction (effect size [ES] -0·37) was at least 95%. Among maximally approved daily doses, diclofenac 150 mg/day (ES -0·57, 95% credibility interval [CrI] -0·69 to -0·46) and etoricoxib 60 mg/day (ES -0·58, -0·73 to -0·43) had the highest probability to be the best intervention, both with 100% probability to reach the minimum clinically important difference. Treatment effects increased as drug dose increased, but corresponding tests for a linear dose effect were significant only for celecoxib (p=0·030), diclofenac (p=0·031), and naproxen (p=0·026). We found no evidence that treatment effects varied over the duration of treatment. Model fit was good, and between-trial heterogeneity and inconsistency were low in all analyses. All trials were deemed to have a low risk of bias for blinding of patients. Effect estimates did not change in sensitivity analyses with two additional statistical models and accounting for methodological quality criteria in meta-regression analysis. INTERPRETATION On the basis of the available data, we see no role for single-agent paracetamol for the treatment of patients with osteoarthritis irrespective of dose. We provide sound evidence that diclofenac 150 mg/day is the most effective NSAID available at present, in terms of improving both pain and function. Nevertheless, in view of the safety profile of these drugs, physicians need to consider our results together with all known safety information when selecting the preparation and dose for individual patients. FUNDING Swiss National Science Foundation (grant number 405340-104762) and Arco Foundation, Switzerland.

Impact of random and systematic recall errors and selection bias in case--control studies on mobile phone use and brain tumors in adolescents (CEFALO study)

Whether the use of mobile phones is a risk factor for brain tumors in adolescents is currently being studied. Case--control studies investigating this possible relationship are prone to recall error and selection bias. We assessed the potential impact of random and systematic recall error and selection bias on odds ratios (ORs) by performing simulations based on real data from an ongoing case--control study of mobile phones and brain tumor risk in children and adolescents (CEFALO study). Simulations were conducted for two mobile phone exposure categories: regular and heavy use. Our choice of levels of recall error was guided by a validation study that compared objective network operator data with the self-reported amount of mobile phone use in CEFALO. In our validation study, cases overestimated their number of calls by 9% on average and controls by 34%. Cases also overestimated their duration of calls by 52% on average and controls by 163%. The participation rates in CEFALO were 83% for cases and 71% for controls. In a variety of scenarios, the combined impact of recall error and selection bias on the estimated ORs was complex. These simulations are useful for the interpretation of previous case-control studies on brain tumor and mobile phone use in adults as well as for the interpretation of future studies on adolescents.

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.