Long time behavior of a mean-field model of interacting neurons

We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymptotic dynamic of the membrane potential of a spiking neuron in a large network. We prove that for a small enough interaction parameter, any solution converges to the unique (in this case) invariant measure. To this aim, we first obtain global bounds on the jump rate and derive a Volterra type integral equation satisfied by this rate. We then replace temporary the interaction part of the equation by a deterministic external quantity (we call it the external current). For constant current, we obtain the convergence to the invariant measure. Using a perturbation method, we extend this result to more general external currents. Finally, we prove the result for the non-linear McKean-Vlasov equation

Causal frequency-specific contributions of frontal spatiotemporal patterns induced by non-invasive neurostimulation to human visual performance

Neural oscillatory activity is known to play a crucial role in brain function. In the particular domain of visual perception, specific frequency bands in different brain regions and networks, from sensory areas to large-scale frontoparietal systems, have been associated with distinct aspects of visual behavior. Nonetheless, their contributions to human visual cognition remain to be causally demonstrated. We hereby used non-uniform (and thus non-frequency-specific) and uniform (frequency-specific) high-beta and gamma patterns of noninvasive neurostimulation over the right frontal eye field (FEF) to isolate the behavioral effects of oscillation frequency and provide causal evidence that distinct visual behavioral outcomes could be modulated by frequency-specific activity emerging from a single cortical region. In a visual detection task using near-threshold targets, high-beta frequency enhanced perceptual sensitivity (d ) without changing response criterion (beta), whereas gamma frequency shifted response criterion but showed no effects on perceptual sensitivity. The lack of behavioral modulations by non-frequency-specific patterns demonstrates that these behavioral effects were specifically driven by burstfrequency. We hypothesizethat suchfrequency-coded behavioral impact of oscillatory activity may reflect a general brain mechanism to multiplex functions within the same neural substrate. Furthermore, pathological conditions involving impaired cerebral oscillations could potentially benefit in the near future from the use of neurostimulation to restore the characteristic oscillatory patterns of healthy systems

Time CNN and Graph Convolution Network for Epileptic Spike Detection in MEG Data

Magnetoencephalography (MEG) recordings of patients with epilepsy exhibit spikes, a typical biomarker of the pathology. Detecting those spikes allows accurate localization of brain regions triggering seizures. Spike detection is often performed manually. However, it is a burdensome and error prone task due to the complexity of MEG data. To address this problem, we propose a 1D temporal convolutional neural network (Time CNN) coupled with a graph convolutional network (GCN) to classify short time frames of MEG recording as containing a spike or not. Compared to other recent approaches, our models have fewer parameters to train and we propose to use a GCN to account for MEG sensors spatial relationships. Our models produce clinically relevant results and outperform deep learning-based state-of-the-art methods reaching a classification f1-score of 76.7% on a balanced dataset and of 25.5% on a realistic, highly imbalanced dataset, for the spike class.Comment: This work has been submitted to IEEE ISBI 2024 for possible publicatio

Spatial dependence in (origin-destination) air passenger flows

We explore the estimation of origin-destination (OD), city-pair, air passengers, in order to explicitly take into account spatial autocorrelation. To our knowledge, we are the first to test the presence of spatial autocorrelation and apply spatial econometric OD flow models to air transport. Drawing on a world sample of 279 cities, over 2010-2012, we find significant evidence of spatial autocorrelation in air passenger flows. Thus, contrary to common practice, we need to incorporate the spatial structure present in the data, when estimating OD air passengers. Importantly, failure to do it, may lead to inefficient estimated coefficients and prediction bias

Dataverse as a Single Source of Truth in a DDI-Compliant Environment

At the Center for Socio-Political Data of Sciences Po, DDI-documented data is published on several repositories. The publication workflow is not user-friendly for the data managers, as it has several entry points and duplicated processes. Additionally, there is an important risk of having platform-dependent versions. In order to preserve the system’s consistency and integrity, a Single Source of Truth (SSOT) is needed. To solve this problem, we designed a new infrastructure and workflow, coherent and interoperable by design, and compliant with both DDI and the FAIR principles. We focused on a flexible, upgradable infrastructure. After a thorough review of available solutions, we opted for a Dataverse repository as our SSOT. We are currently in the process of building a tailor-made data ecosystem, through the use of APIs querying our single repository. This presentation will focus on the processes and technologies used to set up this viable DDI-compliant platform and on the reasons for choosing this solution

Frontal eye field, where art thou? Anatomy, function, and non-invasive manipulation of frontal regions involved in eye movements and associated cognitive operations

The planning, control and execution of eye movements in 3D space relies on a distributed system of cortical and subcortical brain regions. Within this network, the Eye Fields have been described in animals as cortical regions in which electrical stimulation is able to trigger eye movements and influence their latency or accuracy. This review focuses on the Frontal Eye Field (FEF) a “hub” region located in Humans in the vicinity of the pre-central sulcus and the dorsal-most portion of the superior frontal sulcus. The straightforward localization of the FEF through electrical stimulation in animals is difficult to translate to the healthy human brain, particularly with non-invasive neuroimaging techniques. Hence, in the first part of this review, we describe attempts made to characterize the anatomical localization of this area in the human brain. The outcome of functional Magnetic Resonance Imaging (fMRI), Magneto-encephalography (MEG) and particularly, non-invasive mapping methods such a Transcranial Magnetic Stimulation (TMS) are described and the variability of FEF localization across individuals and mapping techniques are discussed. In the second part of this review, we will address the role of the FEF. We explore its involvement both in the physiology of fixation, saccade, pursuit, and vergence movements and in associated cognitive processes such as attentional orienting, visual awareness and perceptual modulation. Finally in the third part, we review recent evidence suggesting the high level of malleability and plasticity of these regions and associated networks to non-invasive stimulation. The exploratory, diagnostic, and therapeutic interest of such interventions for the modulation and improvement of perception in 3D space are discussed

Hopf bifurcation in a Mean-Field model of spiking neurons

We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons.We give sufficient conditions to have periodic solutions through a Hopf bifurcation. Our spectral conditions involve the location of the roots of an explicit holomorphic function. The proof relies on two main ingredients. First, we introduce a discrete time Markov Chain modeling the phases of the successive spikes of a neuron. The invariant measure of this Markov Chain is related to the shape of the periodic solutions. Secondly, we use the Lyapunov-Schmidt method to obtain self-consistent oscillations. We illustrate the result with a toy model for which all the spectral conditions can be analytically checked

Computing Delay-Constrained Least-Cost Paths for Segment Routing is Easier Than You Think

With the growth of demands for quasi-instantaneous communication services such as real-time video streaming, cloud gaming, and industry 4.0 applications, multi-constraint Traffic Engineering (TE) becomes increasingly important. While legacy TE management planes have proven laborious to deploy, Segment Routing (SR) drastically eases the deployment of TE paths and thus became the most appropriate technology for many operators. The flexibility of SR sparked demands in ways to compute more elaborate paths. In particular, there exists a clear need in computing and deploying Delay-Constrained Least-Cost paths (DCLC) for real-time applications requiring both low delay and high bandwidth routes. However, most current DCLC solutions are heuristics not specifically tailored for SR. In this work, we leverage both inherent limitations in the accuracy of delay measurements and an operational constraint added by SR. We include these characteristics in the design of BEST2COP, an exact but efficient ECMP-aware algorithm that natively solves DCLC in SR domains. Through an extensive performance evaluation, we first show that BEST2COP scales well even in large random networks. In real networks having up to thousands of destinations, our algorithm returns all DCLC solutions encoded as SR paths in way less than a second