The utility and application of mixed-effects models in second language research

Second language acquisition researchers often face particular challenges when attempting to generalize study findings to the wider learner population. For example, language learners constitute a heterogeneous group, and it is not always clear how a study’s findings may generalize to other individuals who may differ in terms of language background and proficiency, among many other factors. In this paper, we provide an overview of how mixed-effects models can be used to help overcome these and other issues in the field of second language acquisition. We provide an overview of the benefits of mixed-effects models and a practical example of how mixed-effects analyses can be conducted. Mixed-effects models provide second language researchers with a powerful statistical tool in the analysis of a variety of different types of data.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.

Moderate stake variations for risk and uncertainty, gains and losses: methodological implications for comparative studies

Risk attitudes are known to be sensitive to large stake variations. However, little is known on the sensitivity to moderate variations in stakes. This is important for studies that want to compare risk attitudes between countries or over time. I find that variations of ±20% affect only utility, while larger variations may affect also probability weighting. Surprisingly, the effect on weighting functions is larger for losses than for gains. It is also more pronounced for risk than for uncertainty.

Biodiversity and resilience of ecosystem functions

Accelerating rates of environmental change and the continued loss of global biodiversity threaten functions and services delivered by ecosystems. Much ecosystem monitoring and management is focused on the provision of ecosystem functions and services under current environmental conditions, yet this could lead to inappropriate management guidance and undervaluation of the importance of biodiversity. The maintenance of ecosystem functions and services under substantial predicted future environmental change (i.e., their ‘resilience’) is crucial. Here we identify a range of mechanisms underpinning the resilience of ecosystem functions across three ecological scales. Although potentially less important in the short term, biodiversity, encompassing variation from within species to across landscapes, may be crucial for the longer-term resilience of ecosystem functions and the services that they underpin.

The utility of convection-permitting ensembles for the prediction of stationary convective bands

This study examines convection-permitting numerical simulations of four cases of terrain-locked quasi-stationary convective bands over the UK. For each case, a 2.2-km grid-length 12-member ensemble and 1.5-km grid-length deterministic forecast are analyzed, each with two different initialization times. Object-based verification is applied to determine whether the simulations capture the structure, location, timing, intensity and duration of the observed precipitation. These verification diagnostics reveal that the forecast skill varies greatly between the four cases. Although the deterministic and ensemble simulations captured some aspects of the precipitation correctly in each case, they never simultaneously captured all of them satisfactorily. In general, the models predicted banded precipitation accumulations at approximately the correct time and location, but the precipitating structures were more cellular and less persistent than the coherent quasi-stationary bands that were observed. Ensemble simulations from the two different initialization times were not significantly different, which suggests a potential benefit of time-lagging subsequent ensembles to increase ensemble size. The predictive skill of the upstream larger-scale flow conditions and the simulated precipitation on the convection-permitting grids were strongly correlated, which suggests that more accurate forecasts from the parent ensemble should improve the performance of the convection-permitting ensemble nested within it.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

Declining resilience of ecosystem functions under biodiversity loss

The composition of species communities is changing rapidly through drivers such as habitat loss and climate change, with potentially serious consequences for the resilience of ecosystem functions on which humans depend. To assess such changes in resilience, we analyse trends in the frequency of species in Great Britain that provide key ecosystem functions-specifically decomposition, carbon sequestration, pollination, pest control and cultural values. For 4,424 species over four decades, there have been significant net declines among animal species that provide pollination, pest control and cultural values. Groups providing decomposition and carbon sequestration remain relatively stable, as fewer species are in decline and these are offset by large numbers of new arrivals into Great Britain. While there is general concern about degradation of a wide range of ecosystem functions, our results suggest actions should focus on particular functions for which there is evidence of substantial erosion of their resilience.

Does modulation of the endocannabinoid system have potential therapeutic utility in cerebellar ataxia?

Cerebellar ataxias represent a spectrum of disorders which are, however, linked by common symptoms of motor incoordination and are typically associated with deficient in Purkinje cell firing activity and, often, degeneration. Cerebellar ataxias currently lack a curative agent. The endocannabinoid (eCB) system includes eCB compounds and their associated metabolic enzymes, together with cannabinoid receptors, predominantly the cannabinoid CB1 receptor (CB1R) in the cerebellum; activation of this system in the cerebellar cortex is associated with deficits in motor coordination characteristic of ataxia, effects which can be prevented by CB1R antagonists. Of further interest are various findings that CB1R deficits may also induce a progressive ataxic phenotype. Together these studies suggest that motor coordination is reliant on maintaining the correct balance in eCB system signalling. Recent work also demonstrates deficient cannabinoid signalling in the mouse ‘ducky2J’ model of ataxia. In light of these points, the potential mechanisms whereby cannabinoids may modulate the eCB system to ameliorate dysfunction associated with cerebellar ataxias are considered.

Cosmic shear requirements on the wavelength dependence of telescope point spread functions

Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational point spread function (PSF) that smears out the image. The PSF must therefore be known for each galaxy to a high accuracy. However, for several reasons, the PSF is usually wavelength dependent; therefore, the differences between the spectral energy distribution of the observed objects introduce further complexity. In this paper, we investigate the effect of the wavelength dependence of the PSF, focusing on instruments in which the PSF size is dominated by the diffraction limit of the telescope and which use broad-band filters for shape measurement. We first calculate biases on cosmological parameter estimation from cosmic shear when the stellar PSF is used uncorrected. Using realistic galaxy and star spectral energy distributions and populations and a simple three-component circular PSF, we find that the colour dependence must be taken into account for the next generation of telescopes. We then consider two different methods for removing the effect: (i) the use of stars of the same colour as the galaxies and (ii) estimation of the galaxy spectral energy distribution using multiple colours and using a telescope model for the PSF. We find that both of these methods correct the effect to levels below the tolerances required for per cent level measurements of dark energy parameters. Comparison of the two methods favours the template-fitting method because its efficiency is less dependent on galaxy redshift than the broad-band colour method and takes full advantage of deeper photometry.

Moho map of South America from receiver functions and surface waves

We estimate crustal structure and thickness of South America north of roughly 40 degrees S. To this end, we analyzed receiver functions from 20 relatively new temporary broadband seismic stations deployed across eastern Brazil. In the analysis we include teleseismic and some regional events, particularly for stations that recorded few suitable earthquakes. We first estimate crustal thickness and average Poisson`s ratio using two different stacking methods. We then combine the new crustal constraints with results from previous receiver function studies. To interpolate the crustal thickness between the station locations, we jointly invert these Moho point constraints, Rayleigh wave group velocities, and regional S and Rayleigh waveforms for a continuous map of Moho depth. The new tomographic Moho map suggests that Moho depth and Moho relief vary slightly with age within the Precambrian crust. Whether or not a positive correlation between crustal thickness and geologic age is derived from the pre-interpolation point constraints depends strongly on the selected subset of receiver functions. This implies that using only pre-interpolation point constraints (receiver functions) inadequately samples the spatial variation in geologic age. The new Moho map also reveals an anomalously deep Moho beneath the oldest core of the Amazonian Craton.

Deep crustal structure of the Parana Basin from receiver functions and Rayleigh-wave dispersion: Evidence for a fragmented cratonic root

The deep crustal structure of the Parana Basin of southern Brazil is investigated by analyzing P- and PP-wave receiver functions at 17 Brazilian Lithosphere Seismic Project stations within the basin. The study area can be described as a typical Paleozoic intracratonic basin that hosts one of the largest Large Igneous Province of the world and makes a unique setting for investigating models of basin subsidence and their interaction with mantle plumes. Our study consists of (1) an analysis of the Moho interaction phases in the receiver functions to obtain the thickness and bulk Vp/Vs ratio of the basin`s underlying crust and (2) a joint inversion with Rayleigh-wave dispersion velocities from an independent tomographic study to delineate the detailed S-wave velocity variation with depth. The results of our analysis reveal that Moho depths and bulk Vp/Vs ratios (including sediments) vary between 41 and 48 km and between 1.70 and 1.76, respectively, with the largest values roughly coinciding with the basin`s axis, and that S-wave velocities in the lower crust are generally below 3.8 km/s. Select sites within the basin, however, show lower crustal S-wave velocities slightly above 3.9 km/s suggestive of underplated mafic material. We show that these observations are consistent with a fragmented cratonic root under the Parana basin that defined a zone of weakness for the initial Paleozoic subsidence of the basin and which allowed localized mafic underplating of the crust along the suture zones by Cenozoic magmatism.