51 research outputs found
Macroscopic equations governing noisy spiking neuronal populations with linear synapses.
No full textInternational audienceDeriving tractable reduced equations of biological neural networks capturing the macroscopic dynamics of sub-populations of neurons has been a longstanding problem in computational neuroscience. In this paper, we propose a reduction of large-scale multi-population stochastic networks based on the mean-field theory. We derive, for a wide class of spiking neuron models, a system of differential equations of the type of the usual Wilson-Cowan systems describing the macroscopic activity of populations, under the assumption that synaptic integration is linear with random coefficients. Our reduction involves one unknown function, the effective non-linearity of the network of populations, which can be analytically determined in simple cases, and numerically computed in general. This function depends on the underlying properties of the cells, and in particular the noise level. Appropriate parameters and functions involved in the reduction are given for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley models. Simulations of the reduced model show a precise agreement with the macroscopic dynamics of the networks for the first two models
Domain adaptation with optimal transport improves EEG sleep stage classifiers
No full textInternational audience—Low sample size and the absence of labels on certain data limits the performances of predictive algorithms. To overcome this problem, it is sometimes possible to learn a model on a large labeled auxiliary dataset. Yet, this assumes that the two datasets exhibit similar statistical properties which is rarely the case in practice: there is a discrepancy between the large dataset, called the source, and the dataset of interest, called the target. Improving the prediction performance on the target domain by reducing the distribution discrepancy, between the source and the target domains, is known as Domain Adaptation (DA). Presently, Optimal transport DA (OTDA) methods yield state-of-the-art performances on several DA problems. In this paper, we consider the problem of sleep stage classification, and use OTDA to improve the performances of a convolutional neural network. We use features learnt from the electroencephalogram (EEG) and the electrooculogram (EOG) signals. Our results demonstrate that the method significantly improves the network predictions on the target data
Anisotropy of Alfvénic Turbulence in the Solar Wind and Numerical Simulations
No full text10.12.13 KB. Ok to add published version to spiral, RAS/OUP polic
Effective non-linearities surfaces in the McKean, Fitzhugh-Nagumo and Hodgkin-Huxley model.
No full text<p>Observe that noise tends to have a smoothing effect on the sigmoids.For the Hodgkin-Huxley model, we have empirically chosen a noise threshold under which the neuron was considered regime II and above which it is regime I. There are thus 2 branches below the threshold and only one above.</p
Comparison between the network simulations and computation of the averaged macroscopic variables (plain lines) and simulations of the macroscopic equations (dashed lines).
No full text<p>Averaged macroscopic variables are in plain lines and simulations of the macroscopic equations are in dashed lines. The variable related to the distinct populations (see text) are depicted in different colors. The inputs to the McKean and Fitzhugh-Nagumo networks are shown in (a), and for Hodgkin-Huxley networks we took an affine transform of these curves: . Transient phases in which the averaged microscopic system is imprecise due to the convolution with the symmetric window are not plotted. Initial mismatch is due to different initial conditions for both systems. We can observe it quickly disappear, showing the robustness of the reduction to variations of the initial conditions. The simulations where done using a stochastic Euler algorithm with (resp. ) time steps of size (resp. ) for McKean and FitzHugh-Nagumo (resp. Hodgkin-Huxley) networks.</p
Domain adaptation with optimal transport improves EEG sleep stage classifiers
No full textInternational audience—Low sample size and the absence of labels on certain data limits the performances of predictive algorithms. To overcome this problem, it is sometimes possible to learn a model on a large labeled auxiliary dataset. Yet, this assumes that the two datasets exhibit similar statistical properties which is rarely the case in practice: there is a discrepancy between the large dataset, called the source, and the dataset of interest, called the target. Improving the prediction performance on the target domain by reducing the distribution discrepancy, between the source and the target domains, is known as Domain Adaptation (DA). Presently, Optimal transport DA (OTDA) methods yield state-of-the-art performances on several DA problems. In this paper, we consider the problem of sleep stage classification, and use OTDA to improve the performances of a convolutional neural network. We use features learnt from the electroencephalogram (EEG) and the electrooculogram (EOG) signals. Our results demonstrate that the method significantly improves the network predictions on the target data
Domain adaptation with optimal transport improves EEG sleep stage classifiers
No full textInternational audience—Low sample size and the absence of labels on certain data limits the performances of predictive algorithms. To overcome this problem, it is sometimes possible to learn a model on a large labeled auxiliary dataset. Yet, this assumes that the two datasets exhibit similar statistical properties which is rarely the case in practice: there is a discrepancy between the large dataset, called the source, and the dataset of interest, called the target. Improving the prediction performance on the target domain by reducing the distribution discrepancy, between the source and the target domains, is known as Domain Adaptation (DA). Presently, Optimal transport DA (OTDA) methods yield state-of-the-art performances on several DA problems. In this paper, we consider the problem of sleep stage classification, and use OTDA to improve the performances of a convolutional neural network. We use features learnt from the electroencephalogram (EEG) and the electrooculogram (EOG) signals. Our results demonstrate that the method significantly improves the network predictions on the target data
Bifurcation diagrams of single neurons as a function of the input .
No full text<p>The upper row shows the temporal average of the solutions (i.e. the fixed points and average value in the case of periodic orbits) and the lower row shows the frequency of the regular spiking regime, in the McKean model (left), Fitzhugh-Nagumo model (center) and Hodgkin-Huxley model (right).</p
Function for the deterministic McKean model given in equation 10.
No full text<p>Function for the deterministic McKean model given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078917#pone.0078917.e148" target="_blank">equation 10</a>.</p
Linear part <i>L</i> for the different models.
No full text<p> is the Dirac function centered at and for the first two models (where is the Heaviside function).</p
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