How do circuits in the mammalian cerebral cortex encode properties of the sensory environment in a way that can drive adaptive behavior? This question is fundamental to neuroscience, but it has been very difficult to approach directly. Various computational and theoretical models can explain a wide range of phenomena observed in the primary visual cortex (V1), including the anatomical organization of its circuits, the development of functional properties like orientation tuning, and behavioral effects like surround modulation. However, so far no model has been able to bridge these levels of description to explain how the machinery that develops directly affects behavior. Bridging these levels is important, because phenomena at any one specific level can have many possible explanations, but there are far fewer possibilities to consider once all of the available evidence is taken into account. In this thesis we integrate the information gleaned about cortical development, circuit and cell-type specific interactions, and anatomical, behavioral and electrophysiological measurements, to develop a computational model of V1 that is constrained enough to make predictions across multiple levels of description. Through a series of models incorporating increasing levels of biophysical detail and becoming increasingly better constrained, we are able to make detailed predictions for the types of mechanistic interactions required for robust development of cortical maps that have a realistic anatomical organization, and thereby gain insight into the computations performed by the primary visual cortex. The initial models focus on how existing anatomical and electrophysiological knowledge can be integrated into previously abstract models to give a well-grounded and highly constrained account of the emergence of pattern-specific tuning in the primary visual cortex. More detailed models then address the interactions between specific excitatory and inhibitory cell classes in V1, and what role each cell type may play during development and function. Finally, we demonstrate how these cell classes come together to form a circuit that gives rise not only to robust development but also the development of realistic lateral connectivity patterns. Crucially, these patterns reflect the statistics of the visual environment to which the model was exposed during development. This property allows us to explore how the model is able to capture higher-order information about the environment and use that information to optimize neural coding and aid the processing of complex visual tasks. Using this model we can make a number of very specific predictions about the mechanistic workings of the brain. Specifically, the model predicts a crucial role of parvalbumin-expressing interneurons in robust development and divisive normalization, while it implicates somatostatin immunoreactive neurons in mediating longer range and feature-selective suppression. The model also makes predictions about the role of these cell classes in efficient neural coding and under what conditions the model fails to organize. In particular, we show that a tight coupling of activity between the principal excitatory population and the parvalbumin population is central to robust and stable responses and organization, which may have implications for a variety of diseases where parvalbumin interneuron function is impaired, such as schizophrenia and autism. Further the model explains the switch from facilitatory to suppressive surround modulation effects as a simple by-product of the facilitating response function of long-range excitatory connections targeting a specialized class of inhibitory interneurons. Finally, the model allows us to make predictions about the statistics that are encoded in the extensive network of long-range intra-areal connectivity in V1, suggesting that even V1 can capture high-level statistical dependencies in the visual environment. The final model represents a comprehensive and well constrained model of the primary visual cortex, which for the first time can relate the physiological properties of individual cell classes to their role in development, learning and function. While the model is specifically tuned for V1, all mechanisms introduced are completely general, and can be used as a general cortical model, useful for studying phenomena across the visual cortex and even the cortex as a whole. This work is also highly relevant for clinical neuroscience, as the cell types studied here have been implicated in neurological disorders as wide ranging as autism, schizophrenia and Parkinson’s disease.

L'objet de cette thèse est d'étudier divers problèmes de statistique non-paramétrique dans le cadre d'un modèle d'interactions poissoniennes. De tels modèles sont, par exemple, utilisés en neurosciences pour analyser les interactions entre deux neurones au travers leur émission de potentiels d'action au cours de l'enregistrement de l'activité cérébrale ou encore en génomique pour étudier les distances favorisées ou évitées entre deux motifs le long du génome. Dans ce cadre, nous introduisons une fonction dite de reproduction qui permet de quantifier les positions préférentielles des motifs et qui peut être modélisée par l'intensité d'un processus de Poisson. Dans un premier temps, nous nous intéressons à l'estimation de cette fonction que l'on suppose très localisée. Nous proposons une procédure d'estimation adaptative par seuillage de coefficients d'ondelettes qui est optimale des points de vue oracle et minimax. Des simulations et une application en génomique sur des données réelles provenant de la bactérie E. coli nous permettent de montrer le bon comportement pratique de notre procédure. Puis, nous traitons les problèmes de test associés qui consistent à tester la nullité de la fonction de reproduction. Pour cela, nous construisons une procédure de test optimale du point de vue minimax sur des espaces de Besov faibles, qui a également montré ses performances du point de vue pratique. Enfin, nous prolongeons ces travaux par l'étude d'une version discrète en grande dimension du modèle précédent en proposant une procédure adaptative de type Lasso. / The subject of this thesis is the study of some adaptive nonparametric statistical problems in the framework of a Poisson interactions model. Such models are used, for instance, in neurosciences to analyze interactions between two neurons through their spikes emission during the recording of the brain activity or in genomics to study favored or avoided distances between two motifs along a genome. In this setting, we naturally introduce a so-called reproduction function that allows to quantify the favored positions of the motifs and which is considered as the intensity of a Poisson process. Our first interest is the estimation of this function assumed to be well localized. We propose a data-driven wavelet thresholding estimation procedure that is optimal from oracle and minimax points of view. Simulations and an application to genomic data from the bacterium E. coli allow us to show the good practical behavior of our procedure. Then, we deal with associated problems on tests which consist in testing the nullity of the reproduction function. For this purpose, we build a minimax optimal testing procedure on weak Besov spaces and we provide some simulations showing good practical performances of our procedure. Finally, we extend this work with the study of a high-dimensional discrete setting of our previous model by proposing an adaptive Lasso-type procedure.