Neural field models with threshold noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches

Temporal-spatial profiling of pedunculopontine galanin-cholinergic neurons in the lactacystin rat model of Parkinson’s disease

Parkinson’s disease (PD) is conventionally seen as resulting from single-system neurodegeneration affecting nigrostriatal dopaminergic neurons. However, accumulating evidence indicates a multi-system degeneration and neurotransmitter deficiencies, including cholinergic neurons which degenerate in a brainstem nucleus, the pedunculopontine nucleus (PPN), resulting in motor- and cognitive impairments. The neuropeptide galanin can inhibit cholinergic transmission, whilst being upregulated in degenerating brain regions associated with cognitive decline. Here we determined the temporal-spatial profile of progressive expression of endogenous galanin within degenerating cholinergic neurons, across the rostro-caudal axis of the PPN, by utilising the lactacystin-induced rat model of PD. First, we show progressive neuronal death affecting nigral dopaminergic and PPN cholinergic neurons, reflecting that seen in PD patients, to facilitate use of this model for assessing the therapeutic potential of bioactive peptides. Next, stereological analyses of the lesioned brain hemisphere found that the number of PPN cholinergic neurons expressing galanin increased by 11%, compared to sham-lesioned controls, increasing by a further 5% as the neurodegenerative process evolved. Galanin upregulation within cholinergic PPN neurons was most prevalent closest to the intra-nigral lesion site, suggesting that galanin upregulation in such neurons adapt intrinsically to neurodegeneration, to possibly neuroprotect. This is the first report on the extent and pattern of galanin expression in cholinergic neurons across distinct PPN subregions in both the intact rat CNS and lactacystin lesioned rats. The findings pave the way for future work to target galanin signaling in the PPN, to determine the extent to which upregulated galanin expression could offer a viable treatment strategy for ameliorating PD symptoms associated with cholinergic degeneration

Measurement of electroweak production of two jets in association with a Z boson in proton–proton collisions at √s = 8TeV

The purely electroweak (EW) cross section for the production of two jets in association with a Z boson, in proton–proton collisions at vs = 8TeV, is measured using data recorded by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 19.7 fb-1. The electroweak cross section for the lljj final state (with l=e or µ and j representing the quarks produced in the hard interaction) in the kinematic region defined by Mll>50 GeV, Mjj>120 GeV, transverse momentum pTj>25 GeV, and pseudorapidity |?j|<5, is found to be sEW(lljj)=174±15(stat)±40(syst)\,fb, in agreement with the standard model prediction. The associated jet activity of the selected events is studied, in particular in a signal-enriched region of phase space, and the measurements are found to be in agreement with QCD predictions

Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics

This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the stage for subsequent applications. These are demonstrated through detailed treatments of elementary problems, as well as in more elaborate examples involving vortex-dominated flows and compressible flows at low Mach numbers. Some recent developments are also outlined in the book, including iterative techniques (such as stochastic multigrids and Newton schemes), intrusive and non-intrusive formalisms, spectral representations using mixed and discontinuous bases, multi-resolution approximations, and adaptive techniques. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral approximation is helpful but not essential

On the sensitivity of structural turbulence uncertainty estimates to time and space resolution

International audienceThis paper presents a sensitivity analysis of structural turbulence uncertainty estimates to time and space resolution of numerical computations. Turbulence uncertainty estimates are obtained by means of the Eigenspace Perturbation Method (EPM). Results show that, in general, one can not expect the turbulence uncertainty estimates to be mesh and time-step independent based on the sole sensitivity analysis of the baseline solution. The recommendation is to carry out independent sensitivity studies, to guarantee that the confidence uncertainty estimates are well-predicted regardless of the space and time resolution