With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application.

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Abstract : Electroencephalography (EEG) is a non-invasive neuroimaging modality that was first introduced over 80 years ago. Surface EEG does not directly measure neuronal activity, and it is often assumed that it cannot provide indications on the underlying neuronal firing. However, recent studies based on invasive measurements in monkeys have shown that the coupling between two EEG frequency bands, namely the Gamma (25-45 Hz) and Delta (2-4 Hz) bands, is a good predictor of underlying mass-spiking activity. Specifically, when the Delta signal is in its trough and Gamma power is high, the probability of mass- firing of neurons is large. Here, we investigate this property in healthy human EEG acquired during resting-state. Using the interaction between Delta phase and Gamma power, we derived a modeled spike signal (MSS) from the recorded EEG. We found the power spectrum density (PSD) pattern of the MSS to be similar to that observed in animal studies. Specifically, between 1-10 Hz that the PSD deviates from a 1/[florin] trend and exhibits a small peak at about 2-3Hz. In addition, an inter-hemispheric correlation was found between the MSS of the different pairs of electrode in opposite hemispheres. Our results open the possibility of studying underlying neuronal output with non-invasive EEG. // Résumé : L'électroencéphalographie (EEG) est une modalité de neuro-imagerie non invasive qui a été introduite il y a plus de 80 ans. L’EEG de surface ne mesure pas directement l’activité neuronale et il est généralement supposé qu’elle ne donne pas d’indications sur la décharge neuronale sous-jacente. Cependant des études récentes ont montré à l’aide de mesures invasives que le couplage entre deux bandes de fréquences EEG, soit les bandes Gamma (25-45 Hz) et Delta (2-4 Hz), est un bon indicateur de l’activité neuronale de masse sous-jacente chez les singes. Plus précisément, lorsque le signal Delta est dans un creux (phase de π) et que la puissance dans le signal Gamma est élevée, la probabilité de décharge de masse des neurones est grande. Cette propriété est ici étudiée dans les signaux EEG d’humains sains en état de repos. En se basant sur l'interaction entre la phase du signal Delta et la puissance du signal Gamma, nous avons dérivé un modèle de l’activité neuronale de masse sous-jacente (modeled spike signal-MSS) obtenu à partir du signal l'EEG enregistrée. On trouve que la densité spectrale de puissance (power spectal density-PSD) du MSS est similaire à celle observée dans les études animales. Plus spécifiquement, entre 1-10 Hz la PSD s’écarte d’une tendance en 1 / [florin] et présente un pic de faible amplitude à environ 2-3Hz. En outre, une corrélation inter-hémisphérique a été observée entre les MSS de différentes paires d'électrodes positionnées sur les hémisphères opposés. Nos résultats ouvrent la possibilité d'étudier l’activité neuronale sous-jacente par EEG non-invasive.

In order to understand how the neural system encodes and processes information, research has focused on the study of neural representations of simple stimuli, paying no particular attention to it's temporal structure, with the assumption that a deeper understanding of how the neural system processes simpli fied stimuli will lead to an understanding of how the brain functions as a whole [1]. However, time is intrinsically bound to neural processing as all sensory, motor, and cognitive processes are inherently dynamic. Despite the importance of neural and stimulus dynamics, little is known of how the neural system represents rich spatio-temporal stimulus, which ultimately link the neural system to a continuously changing environment. The purpose of this thesis is to understand whether and how temporally-structured neural activity modulates the processing of information within the brain, proposing in turn that, the precise interaction between the spatio-temporal structure of the stimulus and the neural system is particularly relevant, particularly when considering the ongoing plasticity mechanisms which allow the neural system to learn from experience. In order to answer these questions, three studies were conducted. First, we studied the impact of spiking temporal structure on a single neuron spiking response, and explored in which way the functional connections to pre-synaptic neurons are modulated through adaptation. Our results suggest that, in a generic spiking neuron, the temporal structure of pre-synaptic excitatory and inhibitory neurons modulate both the spiking response of that same neuron and, most importantly, the speed and strength of learning. In the second, we present a generic model of a spiking neural network that processes rich spatio-temporal stimuli, and explored whether the processing of stimulus within the network is modulated due to the interaction with an external dynamical system (i.e. extracellular media), as well as several plasticity mechanisms. Our results indicate that the memory capacity, that re ects a dynamic short-term memory of incoming stimuli, can be extended on the presence of plasticity and through the interaction with an external dynamical system, while maintaining the network dynamics in a regime suitable for information processing. Finally, we characterized cortical signals of human subjects (electroencephalography, EEG) associated to a visual categorization task. Among other aspects, we studied whether changes in the dynamics of the stimulus leads to a changes in the neural processing at the cortical level, and introduced the relevance of large-scale integration for cognitive processing. Our results suggest that the dynamic synchronization across distributed cortical areas is stimulus specific and specifically linked to perceptual grouping. Taken together, the results presented here suggest that the temporal structure of the stimulus modulates how the neural system encodes and processes information within single neurons, network of neurons and cortical areas. In particular, the results indicate that timing modulates single neuron connectivity structures, the memory capability of networks of neurons, and the cortical representation of a visual stimuli. While the learning of invariant representations remains as the best framework to account for a number of neural processes (e.g. long-term memory [2]), the reported studies seem to provide support the idea that, at least to some extent, the neural system functions in a non-stationary fashion, where the processing of information is modulated by the stimulus dynamics itself. Altogether, this thesis highlights the relevance of understanding adaptive processes and their interaction with the temporal structure of the stimulus, arguing that a further understanding how the neural system processes dynamic stimuli is crucial for the further understanding of neural processing itself, and any theory that aims to understand neural processing should consider the processing of dynamic signals. 1. Frankish, K., and Ramsey, W. The Cambridge Handbook of Cognitive Science. Cambridge University Press, 2012. // 2. McGaugh, J. L. Memory{a Century of Consolidation. Science 287, 5451 (Jan. 2000), 248{251.