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    ABSTRACT: In this technical note we compare the performance of four gradient-free MCMC samplers (random walk Metropolis sampling, slice-sampling, adaptive MCMC sampling and population-based MCMC sampling with tempering) in terms of the number of independent samples they can produce per unit computational time. For the Bayesian inversion of a single-node neural mass model, both adaptive and population-based samplers are more efficient compared with random walk Metropolis sampler or slice-sampling; yet adaptive MCMC sampling is more promising in terms of compute time. Slice-sampling yields the highest number of independent samples from the target density - albeit at almost 1000% increase in computational time, in comparison to the most efficient algorithm (i.e., the adaptive MCMC sampler). Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
    Full-text · Article · Mar 2015 · NeuroImage
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    ABSTRACT: Data assimilation is a fundamental issue that arises across many scales in neuroscience - ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fMRI. Data assimilation involves inverting a generative model that can not only explain observed data but also generate predictions. Typically, the model is inverted or fitted using conventional tools of (convex) optimization that invariably extremise some functional - norms, minimum descriptive length, variational free energy, etc. Generally, optimisation rests on evaluating the local gradients of the functional to be optimised. In this paper, we compare three different gradient estimation techniques that could be used for extremising any functional in time - (i) finite differences, (ii) forward sensitivities and a method based on (iii) the adjoint of the dynamical system. We demonstrate that the first-order gradients of a dynamical system, linear or non-linear, can be computed most efficiently using the adjoint method. This is particularly true for systems where the number of parameters is greater than the number of states. For such systems, integrating several sensitivity equations - as required with forward sensitivities - proves to be most expensive, while finite-difference approximations have an intermediate efficiency. In the context of neuroimaging, adjoint based inversion of dynamical causal models (DCMs) can, in principle, enable the study of models with large numbers of nodes and parameters.
    Full-text · Article · Apr 2014 · NeuroImage
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    ABSTRACT: Introduction In order to define the pathophysiology underlying development of peripheral neuropathies, it is important to understand the excitability effects produced by alterations in membrane potential. Sensory and motor axons display different biophysical properties which are likely to affect their responsiveness to membrane potential changes. Objective To provide a template for the effects of membrane potential changes on sensory and motor axonal excitability. Methods Sensory and motor nerve excitability studies were recorded using threshold tracking techniques and QTracS software in six participants (mean age 31 ± 2 years). The median nerve was stimulated at the wrist, with both CMAPs and CSAPs recorded. A standard axonal excitability protocol was conducted, including assessment of strength–duration properties, threshold electrotonus, recovery cycle and current-threshold relationship. DC currents set to ±50% of the baseline rheobasic current were utilised to ensure comparability between motor and sensory axons. Results As previously reported for motor axons, polarization had significant effects on axonal excitability. The overall pattern of excitability change was similar between motor and sensory axons – with depolarizing currents producing reduced threshold change in threshold electrotonus, upwards shift of the recovery cycle and reduced inward rectification in the current-threshold relationship. Effects on threshold electrotonus were more prominent in motor axons, with more significant reduction in threshold change to depolarizing and hyperpolarizing currents (TEd90ms; Depolarization: Motor: 46 ± 5%; Sensory: 23 ± 3%; P < .01; Hyperpolarization: Motor: −31 ± 2%; Sensory: −24 ± 2%; P < .05). By contrast, effects of hyperpolarization on measures associated with the hyperpolarization-activated cation conductance Ih were similar for motor and sensory axons (TEh70%peak: Motor: 18 ± 6%; Sensory 20 ± 4%; Hyperpolarizing IV drift – Motor: −4 ± 2%; Sensory: 7 ± 4%). Conclusions These findings provide a template for the differential interpretation of excitability changes associated with membrane potential change in sensory and motor neuropathies.
    No preview · Article · Apr 2014 · Clinical Neurophysiology
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