Le projet européen ANGELS a pour but de construire un robot anguille capable de naviguer par le sens électrique et de se scinder en plusieurs mono-agents pour des besoins d’exploration. Dans le cadre de ce projet, mon travail a consisté à élaborer un modèle de perception inspiré du poisson électrique, le challenge étant de faire de ce modèle un modèle de perception rapide et embarquable pour une détection en ligne par un engin sous-marin robotisé équipé du modèle. Deux modèles de perception ont été construits, s’appuyant tous deux sur une géométrie simple mais réaliste de capteur. Les deux modèles baptisés «modèle poly-sphérique » et « modèle des réflexions » provenant respectivement d’une intuition physique et d’une méthode mathématique appropriée se calibrent une fois pour toute avec un simulateur électrique, pourrevêtir in fine une forme analytique. Couplés aux modèles existant de réponses électriques d’objets, les modèles de perception ont permis de faire effectuer à un robot capteur des tâches basiques d’évitement et de détection, ce qui est à ce jour une première dans l’histoire. En parallèle, nous avons développé un formalisme générique de réponse d’objet permettant d’étendre le champ d’applicabilité des modèles de perception. Enfin, nous avons commencé à estimerl’impact d’une géométrie complexe de capteur présentant de larges surfaces isolantes sur la mesure pour envisager la modélisation du sens électrique par un capteur de forme arbitraire. / The goal of the European project ANGELS is to build an eel-like robot capable to navigate by the electric sense and to divide itself in several mono-agents for exploration purposes. In the context of this project my work consisted in creating a perception model inspired from the electric fish with the virtue of being fast and so, to be usable in-line. Two models of perception were built and were based on a simple but realistic geometry of sensor. The two models named after the « poly-spherical model » and the « reflexions model » which come respectively from a physical intuition and an appropriate mathematical model are calibrated once for all with an electrical simulator in order to have analytical forms. Coupled with models of the electrical response of objects, the two models of perception permit the robot to achieve some basic tasks like detection and obstacles’ avoidance, which is a novelty in the history. In addition we have built a generic formalism of theelectrical response that extents the application of the models of perception. Finally we have begun to estimate the influence of a complex geometry of sensor, that exhibs large insulating surfaces, on the measurement in order to open the way for the rapid modelling of a sensor of arbitrary shape.

Weakly electric fish use of a self-generated electric field to probe their environment, this behaviour is known as electrolocation. This study investigated two aspects of electrolocation in two species of knifefish (Apteronotus leptorhynchus and Eigenmannia virescens). First, we characterized the ability to track moving objects and found that tracking performance did not differ among speeds tested in either species. Second, we characterized a motion-related cue for distance perception, similar to visual parallax, for which rapidly moving objects would be perceived as closer than slowly moving objects. During tracking experiments, the fish remained centered between the moving objects. We hypothesized that the fish use electrosensory parallax to perform this centering behaviour. Thus, we predicted that if one object moved slightly slower than the other, the fish would perceive the slower-moving object as farther away, and would move towards the slower object to remain “centered.” Indeed, our results supported our hypothesis with E. virescens moving towards the slower object to an extent that increased with the relative decrease in speed.

Weakly electric fish use of a self-generated electric field to probe their environment, this behaviour is known as electrolocation. This study investigated two aspects of electrolocation in two species of knifefish (Apteronotus leptorhynchus and Eigenmannia virescens). First, we characterized the ability to track moving objects and found that tracking performance did not differ among speeds tested in either species. Second, we characterized a motion-related cue for distance perception, similar to visual parallax, for which rapidly moving objects would be perceived as closer than slowly moving objects. During tracking experiments, the fish remained centered between the moving objects. We hypothesized that the fish use electrosensory parallax to perform this centering behaviour. Thus, we predicted that if one object moved slightly slower than the other, the fish would perceive the slower-moving object as farther away, and would move towards the slower object to remain “centered.” Indeed, our results supported our hypothesis with E. virescens moving towards the slower object to an extent that increased with the relative decrease in speed.

Le projet européen ANGELS a pour but de construire un robot anguille capable de naviguer par le sens électrique et de se scinder en plusieurs mono-agents pour des besoins d'exploration. Dans le cadre de ce projet, mon travail a consisté à élaborer un modèle de perception inspiré du poisson électrique, le challenge étant de faire de ce modèle un modèle de perception rapide et embarquable pour une détection en ligne par un engin sous-marin robotisé équipé du modèle. Deux modèles de perception ont été construits, s'appuyant tous deux sur une géométrie simple mais réaliste de capteur. Les deux modèles baptisés "modèle poly-sphérique " et " modèle des réflexions " provenant respectivement d'une intuition physique et d'une méthode mathématique appropriée se calibrent une fois pour toute avec un simulateur électrique, pourrevêtir in fine une forme analytique. Couplés aux modèles existant de réponses électriques d'objets, les modèles de perception ont permis de faire effectuer à un robot capteur des tâches basiques d'évitement et de détection, ce qui est à ce jour une première dans l'histoire. En parallèle, nous avons développé un formalisme générique de réponse d'objet permettant d'étendre le champ d'applicabilité des modèles de perception. Enfin, nous avons commencé à estimerl'impact d'une géométrie complexe de capteur présentant de larges surfaces isolantes sur la mesure pour envisager la modélisation du sens électrique par un capteur de forme arbitraire.

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Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

We rely so much on vision that it is hard to imagine sensing the world differently. But most organisms primarily use other sensory information, even something as detached from our senses as electricity. Some fish, called weakly electric fish, generate electric pulses to sense their environment. Objects in their environment distort the electric pulses, and the fish use special receptors in their skin to process these distortions and identify the nearby objects. They detect the location, size, shape, and electric properties of nearby objects, enabling them to find preferred food. These fish use their discharges not only for sensing and foraging as described, but also for communication. Investigating this sensory system can provide insights into neural computations for sensory processing more broadly, and can expand our understanding of the complex stimuli present in our environment that we do not perceive.In the first half of this work, we investigated how the weakly electric fish Gnathonemus petersii processes the electric sensory information to interact with its environment. We also used the tools developed in this work to study social behavior in groups of freely swimming fish. Chapter 1 provides an in-depth introduction to this model organism and its prominent active electrolocation behavior. This introductory chapter is focused on the parts of the behavior that are relevant to the computational models developed in this work. We investigated the active electrolocation behavior using a comprehensive end-to-end model that contains multiple components, which will be detailed in the following chapters. Chapter 2 describes the physics model that simulates the fish and its environment to collect data. The physics model builds on previous work and extends it to a more general framework that can be used to simulate the fish in different environments. We developed and adequately documented an open code base that can be used to simulate various fish species and their interactions with nearby objects or electrical boundaries. Chapter 3, specifically Section 3.3, presents a data-based model of the electroreceptors that process the sensory input. We used machine learning techniques to develop a model that can predict the response of the receptors to distortions due to different objects. The model is based on local field potential data collected from the afferent layers of the electrosensory lobe, the first brain area that processes the sensory input. This data was collected by Abigail Zadina in Nathaniel Sawtell’s laboratory at Columbia University. Chapter 3, specifically Section 3.4, describes the neural network models that identify computations that help solve the behavior. We used data generated from the physics model as sensory input, we used our electroreceptor model to parse this data serving as first-stage input to down- stream brain areas, and we used neural network models to characterize the nearby objects’ spatial and electric properties based on the sensory input. Based on results from our neural network models, we set two hypotheses for how weakly electric fish sense their environment and motivate experiments on less studied brain areas to test these hypotheses. First, we suggest that decoding all spatial and electric properties of a nearby object distorting the electric discharge is very challenging due to interactions between these properties, but first decoding the spatial properties and then using the spatial properties as internal feedback to decode the electric properties helps solve the task by disentangling the interactions. Second, we suggest that the specialized Schnauzenorgan organ of the weakly electric G. petersii, previously described as an electric fovea due to the very high density of electroreceptors and believed to serve a primary role in close-range characterization, may also play a role in long-range detection of objects surrounding the fish. Chapter 4 explores social interactions in groups of freely swimming fish and starts to investigate how they use their electric discharges to navigate, interact and communicate. Here, we used our physics-based framework to accurately identify the fish that emitted each electric discharge in a group of fish. This work is currently in progress and we performed various preliminary analyses to investigate the social behavior and social rank of these fish, which we present here. Data for this project was collected by Federico Pedraja in Nathaniel Sawtell’s laboratory at Columbia University. The second half of this work addresses a variety of different research questions with loose connections in between them and in relation to the first half. The common factor present in all these projects can be generally described as investigating how computations may be used in neural circuits to produce successful behavior. We used a variety of computational models and tools to investigate these questions, and we present the results of these investigations in the following chapters. Chapter 5 provides a biologically plausible architecture alternative for the classical binary classification task. Typically, feed-forward models have been used to solve this task. However, neocortical circuits likely involved in decision making are recurrent and sparse. We used a recurrent neural network model with sparsity constraints to solve the binary classification task. We demonstrated that the sparse recurrent networks solve the task well, make use of dynamic computation similar to evidence accumulation, and distribute the information throughout the network despite the sparsity constraints. Chapter 6 explores syntactic differences of world languages and offers a potential neural computation mechanism that could account for those differences. We focused on differences in the basic word order of simple sentences because these have been extensively studied in the linguistic literature. These simple sentences only have three parts, subject, verb, and object, and the order of these parts varies across languages non-uniformly. We aimed to provide a possible language generation mechanism that could account for these differences. Chapter 7 investigates the computational journey from numerical cognition to arithmetic ability. This research direction was motivated by and based on experimental work that addressed whether bees (and later stingrays and cichlids) can learn simple arithmetic operations. This project was designed for introducing a Columbia SEAS undergraduate student, Katharyn Fatehi, to computational neuroscience research. I mentored Kat through the Women in Science at Columbia program, and provided detailed guidance, code base, tutorials and instructions for her to learn about computational neuroscience research and to contribute to this project. Chapter 8 represents my contribution to a large collaboration effort aimed at improving spike sorting techniques. This project quantified the impact on spike sorting quality of the geometry mis- match between typical recording probes (1D, or 2D at best) and the 3D structure of the brain. We leveraged the experimental setup, multi-electrode recording arrays with planar geometry recording the activity of 2D retinal tissue, to address this question. The work presented in this thesis is a collection of projects that investigate neural computations in different contexts. The first half of the work is focused on the weakly electric fish G. petersii and its active electrolocation behavior. The second half of the work explores a variety of different research questions related to computational mechanisms that could be implemented in neural circuits. The work presented here is a step towards understanding how computations in neural circuits can produce successful behavior in different contexts.

Cette thèse concerne principalement la résolution des problèmes d’inversion dynamiquedans le cadre des systèmes dynamiques non linéaires. Ainsi, un ensemble de techniquesbasées sur l’utilisation des trains de mesures passées et sauvegardées sur une fenêtreglissante, a été développé. En premier lieu, les mesures sont utilisées pour générerune famille de signatures graphiques, qui constituent un outil de classification permettantde discriminer les diverses valeurs des variables à estimer pour un système non linéairedonné. Cette première technique a été appliquée à la résolution de deux problèmes : leproblème d’électolocation d’un robot doté du sens électrique et le problème d’estimationd’état dans les systèmes à dynamiques non linéaires. Outre ces deux applications, destechniques d’inversion à horizon glissant spécifiques au problème de diagnostic des défautsd’éoliennes dans le cadre d’un benchmark international ont été développées. Cestechniques sont basées sur la minimisation de critères quadratiques basés sur des modèlesde connaissance. / This thesis mainly concerns the resolution of dynamic inverse problems involvingnonlinear dynamical systems. A set of techniques based on the use of trains of pastmeasurements saved on a sliding window was developed. First, the measurements areused to generate a family of graphical signatures, which is a classification tool, in orderto discriminate between different values of variables to be estimated for a given nonlinearsystem. This technique was applied to solve two problems : the electrolocationproblem of a robot with electrical sense and the problem of state estimation in nonlineardynamical systems. Besides these two applications, receding horizon inversion techniquesdedicated to the fault diagnosis problem of a wind turbine proposed as an internationalbenchmark were developed. These techniques are based on the minimization of quadraticcriteria based on knowledge-based models.

Cette thèse aborde deux thématiques différentes. On s’intéresse d’abord au développement et à l’analyse de méthodes pour le sens électrique appliqué à la robotique. On considère en particulier la méthode des réflexions permettant, à l’image de la méthode de Schwarz, de résoudre des problèmes linéaires à partir de sous-problèmes plus simples. Ces deniers sont obtenus par décomposition des frontières du problème de départ. Nous en présentons des preuves de convergence et des applications. Dans le but d’implémenter un simulateur du problème direct d’électrolocation dans un robot autonome, on s’intéresse également à une méthode de bases réduites pour obtenir des algorithmes peu coûteux en temps et en place mémoire. La seconde thématique traite d’un problème inverse dans le domaine de la chimie quantique. Nous cherchons ici à déterminer les caractéristiques d’un système quantique. Celui-ci est éclairé par un champ laser connu et fixé. Dans ce cadre, les données du problème inverse sont les états avant et après éclairage. Un résultat d’existence locale est présenté, ainsi que des méthodes de résolution numériques. / This thesis tackle two different topics.We first design and analyze algorithms related to the electrical sense for applications in robotics. We consider in particular the method of reflections, which allows, like the Schwartz method, to solve linear problems using simpler sub-problems. These ones are obtained by decomposing the boundaries of the original problem. We give proofs of convergence and applications. In order to implement an electrolocation simulator of the direct problem in an autonomous robot, we build a reduced basis method devoted to electrolocation problems. In this way, we obtain algorithms which satisfy the constraints of limited memory and time resources. The second topic is an inverse problem in quantum chemistry. Here, we want to determine some features of a quantum system. To this aim, the system is ligthed by a known and fixed Laser field. In this framework, the data of the inverse problem are the states before and after the Laser lighting. A local existence result is given, together with numerical methods for the solving.