Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

The du2J mouse model of ataxia and absence epilepsy has deficient cannabinoid CB1 receptor-mediated signalling

Key point summary • Cerebellar ataxias are progressive debilitating diseases with no known treatment and are associated with defective motor function and, in particular, abnormalities to Purkinje cells. • Mutant mice with deficits in Ca2+ channel auxiliary α2δ-2 subunits are used as models of cerebellar ataxia. • Our data in the du2J mouse model shows an association between the ataxic phenotype exhibited by homozygous du2J/du2J mice and increased irregularity of Purkinje cell firing. • We show that both heterozygous +/du2J and homozygous du2J/du2J mice completely lack the strong presynaptic modulation of neuronal firing by cannabinoid CB1 receptors which is exhibited by litter-matched control mice. • These results show that the du2J ataxia model is associated with deficits in CB1 receptor signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity due to reduced α2δ-2 subunit expression. Knowledge of such deficits may help design therapeutic agents to combat ataxias. Abstract Cerebellar ataxias are a group of progressive, debilitating diseases often associated with abnormal Purkinje cell (PC) firing and/or degeneration. Many animal models of cerebellar ataxia display abnormalities in Ca2+ channel function. The ‘ducky’ du2J mouse model of ataxia and absence epilepsy represents a clean knock-out of the auxiliary Ca2+ channel subunit, α2δ-2, and has been associated with deficient Ca2+ channel function in the cerebellar cortex. Here, we investigate effects of du2J mutation on PC layer (PCL) and granule cell (GC) layer (GCL) neuronal spiking activity and, also, inhibitory neurotransmission at interneurone-Purkinje cell(IN-PC) synapses. Increased neuronal firing irregularity was seen in the PCL and, to a less marked extent, in the GCL in du2J/du2J, but not +/du2J, mice; these data suggest that the ataxic phenotype is associated with lack of precision of PC firing, that may also impinge on GC activity and requires expression of two du2J alleles to manifest fully. du2J mutation had no clear effect on spontaneous inhibitory postsynaptic current (sIPSC) frequency at IN-PC synapses, but was associated with increased sIPSC amplitudes. du2J mutation ablated cannabinoid CB1 receptor (CB1R)-mediated modulation of spontaneous neuronal spike firing and CB1Rmediated presynaptic inhibition of synaptic transmission at IN-PC synapses in both +/du2J and du2J/du2J mutants; effects that occurred in the absence of changes in CB1R expression. These results demonstrate that the du2J ataxia model is associated with deficient CB1R signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity and the ataxic phenotype.

A digital ecosystems model of assessment feedback on student learning

The term ecosystem has been used to describe complex interactions between living organisms and the physical world. The principles underlying ecosystems can also be applied to complex human interactions in the digital world. As internet technologies make an increasing contribution to teaching and learning practice in higher education, the principles of digital ecosystems may help us understand how to maximise technology to benefit active, self-regulated learning especially among groups of learners. Here, feedback on student learning is presented within a conceptual digital ecosystems model of learning. Additionally, we have developed a Web 2.0-based system, called ASSET, which incorporates multimedia and social networking features to deliver assessment feedback within the functionality of the digital ecosystems model. Both the digital ecosystems model and the ASSET system are described and their implications for enhancing feedback on student learning are discussed.

Home, meaning and identity: learning from the English model of shared ownership

This article explores the problematic nature of the label “home ownership” through a case study of the English model of shared ownership, one of the methods used by the UK government to make home ownership affordable. Adopting a legal and socio-legal analysis, the article considers whether shared ownership is capable of fulfilling the aspirations households have for home ownership. To do so, the article considers the financial and nonfinancial meanings attached to home ownership and suggests that the core expectation lies in ownership of the value. The article demonstrates that the rights and responsibilities of shared owners are different in many respects from those of traditional home owners, including their rights as regards ownership of the value. By examining home ownership through the lens of shared ownership the article draws out lessons of broader significance to housing studies. In particular, it is argued that shared ownership shows the limitations of two dichotomies commonly used in housing discourse: that between private and social housing; and the classification of tenure between owner-occupiers and renters. The article concludes that a much more nuanced way of referring to home ownership is required, and that there is a need for a change of expectations amongst consumers as to what sharing ownership means.

A dynamic model of neurovascular coupling: Implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

A dynamic causal model of the coupling between pulse stimulation and neural activity

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers. The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1–40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different. Following Friston, Mechelli, Turner, and Price (2000), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

A three-compartment model of the hemodynamic response and oxygen delivery to brain

We describe a mathematical model linking changes in cerebral blood flow, blood volume and the blood oxygenation state in response to stimulation. The model has three compartments to take into account the fact that the cerebral blood flow and volume as measured concurrently using laser Doppler flowmetry and optical imaging spectroscopy have contributions from the arterial, capillary as well as the venous compartments of the vasculature. It is an extension to previous one-compartment hemodynamic models which assume that the measured blood volume changes are from the venous compartment only. An important assumption of the model is that the tissue oxygen concentration is a time varying state variable of the system and is driven by the changes in metabolic demand resulting from changes in neural activity. The model takes into account the pre-capillary oxygen diffusion by flexibly allowing the saturation of the arterial compartment to be less than unity. Simulations are used to explore the sensitivity of the model and to optimise the parameters for experimental data. We conclude that the three-compartment model was better than the one-compartment model at capturing the hemodynamics of the response to changes in neural activation following stimulation.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

Updated empirical model of genetically-modified maize grain production practices to achieve European Union labeling thresholds

An updated empirical approach is proposed for specifying coexistence requirements for genetically modified (GM) maize (Zea mays L.) production to ensure compliance with the 0.9% labeling threshold for food and feed in the European Union. The model improves on a previously published (Gustafson et al., 2006) empirical model by adding recent data sources to supplement the original database and including the following additional cases: (i) more than one GM maize source field adjacent to the conventional or organic field, (ii) the possibility of so-called “stacked” varieties with more than one GM trait, and (iii) lower pollen shed in the non-GM receptor field. These additional factors lead to the possibility for somewhat wider combinations of isolation distance and border rows than required in the original version of the empirical model. For instance, in the very conservative case of a 1-ha square non-GM maize field surrounded on all four sides by homozygous GM maize with 12 m isolation (the effective isolation distance for a single GM field), non-GM border rows of 12 m are required to be 95% confident of gene flow less than 0.9% in the non-GM field (with adventitious presence of 0.3%). Stacked traits of higher GM mass fraction and receptor fields of lower pollen shed would require a greater number of border rows to comply with the 0.9% threshold, and an updated extension to the model is provided to quantify these effects.

The competition–performance relation: a meta-analytic review and test of the opposing processes model of competition and performance

What is the relation between competition and performance? The present research addresses this important multidisciplinary question by conducting a meta-analysis of existing empirical work and by proposing a new conceptual model—the opposing processes model of competition and performance. This model was tested by conducting an additional meta-analysis and 3 new empirical studies. The first meta-analysis revealed that there is no noteworthy relation between competition and performance. The second meta-analysis showed, in accord with the opposing processes model, that the absence of a direct effect is the result of inconsistent mediation via achievement goals: Competition prompts performance-approach goals which, in turn, facilitate performance; and competition also prompts performance-avoidance goals which, in turn, undermine performance. These same direct and mediational findings were also observed in the 3 new empirical studies (using 3 different conceptualizations of competition and attending to numerous control variables). Our findings provide both interpretational clarity regarding past research and conceptual guidance regarding future research on the competition–performance relation.

A 27 day persistence model of near-Earth solar wind conditions: a long lead-time forecast and a benchmark for dynamical models

Geomagnetic activity has long been known to exhibit approximately 27 day periodicity, resulting from solar wind structures repeating each solar rotation. Thus a very simple near-Earth solar wind forecast is 27 day persistence, wherein the near-Earth solar wind conditions today are assumed to be identical to those 27 days previously. Effective use of such a persistence model as a forecast tool, however, requires the performance and uncertainty to be fully characterized. The first half of this study determines which solar wind parameters can be reliably forecast by persistence and how the forecast skill varies with the solar cycle. The second half of the study shows how persistence can provide a useful benchmark for more sophisticated forecast schemes, namely physics-based numerical models. Point-by-point assessment methods, such as correlation and mean-square error, find persistence skill comparable to numerical models during solar minimum, despite the 27 day lead time of persistence forecasts, versus 2–5 days for numerical schemes. At solar maximum, however, the dynamic nature of the corona means 27 day persistence is no longer a good approximation and skill scores suggest persistence is out-performed by numerical models for almost all solar wind parameters. But point-by-point assessment techniques are not always a reliable indicator of usefulness as a forecast tool. An event-based assessment method, which focusses key solar wind structures, finds persistence to be the most valuable forecast throughout the solar cycle. This reiterates the fact that the means of assessing the “best” forecast model must be specifically tailored to its intended use.

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008 – 2010: Lessons for Future Observations of Earth-Directed CMEs

We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO spacecraft up to large heliocentric distances. We compare the predictions of the Fixed-Φ and Harmonic Mean (HM) fitting methods, which only differ by the assumed geometry of the CME. It is possible to use these techniques to determine from remote-sensing observations the CME direction of propagation, arrival time and final speed which are compared to in-situ measurements. We find evidence that for large viewing angles, the HM fitting method predicts the CME direction better. However, this may be due to the fact that only wide CMEs can be successfully observed when the CME propagates more than 100∘ from the observing spacecraft. Overall eight CMEs, originating from behind the limb as seen by one of the STEREO spacecraft can be tracked and their arrival time at the other STEREO spacecraft can be successfully predicted. This includes CMEs, such as the events on 4 December 2009 and 9 April 2010, which were viewed 130∘ away from their direction of propagation. Therefore, we predict that some Earth-directed CMEs will be observed by the HIs until early 2013, when the separation between Earth and one of the STEREO spacecraft will be similar to the separation of the two STEREO spacecraft in 2009 – 2010.

Linguistic and cognitive motivations for the typological primacy model of third language (L3) transfer: considering the role of timing of acquisition and proficiency in the previous languages

This article elucidates the Typological Primacy Model (TPM; Rothman, 2010, 2011, 2013) for the initial stages of adult third language (L3) morphosyntactic transfer, addressing questions that stem from the model and its application. The TPM maintains that structural proximity between the L3 and the L1 and/or the L2 determines L3 transfer. In addition to demonstrating empirical support for the TPM, this article articulates a proposal for how the mind unconsciously determines typological (structural) proximity based on linguistic cues from the L3 input stream used by the parser early on to determine holistic transfer of one previous (the L1 or the L2) system. This articulated version of the TPM is motivated by argumentation appealing to cognitive and linguistic factors. Finally, in line with the general tenets of the TPM, I ponder if and why L3 transfer might obtain differently depending on the type of bilingual (e.g. early vs. late) and proficiency level of bilingualism involved in the L3 process.