A decision-making Fokker-Planck model in computational neuroscience

Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.

ModelDB in Computational Neuroscience Education - A research tool as interactive educational media

ModelDB's mission is to link computational models and publications, supporting the field of computational neuroscience (CNS) by making model source code readily available. It is continually expanding, and currently contains source code for more than 300 models that cover more than 41 topics. Investigators, educators, and students can use it to obtain working models that reproduce published results and can be modified to test for new domains of applicability. Users can browse ModelDB to survey the field of computational neuroscience, or pursue more focused explorations of specific topics. Here we describe tutorials and initial experiences with ModelDB as an interactive educational tool.

Puzzling challenges in contemporary neuroscience: Insights from complexity and emergence in epileptogenic circuits

The brain is a complex system that, in the normal condition, has emergent properties like those associated with activity-dependent plasticity in learning and memory, and in pathological situations, manifests abnormal long-term phenomena like the epilepsies. Data from our laboratory and from the literature were classified qualitatively as sources of complexity and emergent properties from behavior to electrophysiological, cellular, molecular, and computational levels. We used such models as brainstem-dependent acute audiogenic seizures and forebrain-dependent kindled audiogenic seizures. Additionally we used chemical OF electrical experimental models of temporal lobe epilepsy that induce status epilepticus with behavioral, anatomical, and molecular sequelae such as spontaneous recurrent seizures and long-term plastic changes. Current Computational neuroscience tools will help the interpretation. storage, and sharing of the exponential growth of information derived from those studies. These strategies are considered solutions to deal with the complexity of brain pathologies such as the epilepsies. (C) 2008 Elsevier Inc. All rights reserved.

Computational quest for understanding the role of astrocyte signaling in synaptic transmission and plasticity.

The complexity of the signaling network that underlies astrocyte-synapse interactions may seem discouraging when tackled from a theoretical perspective. Computational modeling is challenged by the fact that many details remain hitherto unknown and conventional approaches to describe synaptic function are unsuitable to explain experimental observations when astrocytic signaling is taken into account. Supported by experimental evidence is the possibility that astrocytes perform genuine information processing by means of their calcium signaling and are players in the physiological setting of the basal tone of synaptic transmission. Here we consider the plausibility of this scenario from a theoretical perspective, focusing on the modulation of synaptic release probability by the astrocyte and its implications on synaptic plasticity. The analysis of the signaling pathways underlying such modulation refines our notion of tripartite synapse and has profound implications on our understanding of brain function.

Computational Models of Object Recognition in Cortex: A Review

Understanding how biological visual systems perform object recognition is one of the ultimate goals in computational neuroscience. Among the biological models of recognition the main distinctions are between feedforward and feedback and between object-centered and view-centered. From a computational viewpoint the different recognition tasks - for instance categorization and identification - are very similar, representing different trade-offs between specificity and invariance. Thus the different tasks do not strictly require different classes of models. The focus of the review is on feedforward, view-based models that are supported by psychophysical and physiological data.

A computational model of the anterior intraparietal area

The monkey anterior intraparietal area (AIP) encodes visual information about three-dimensional object shape that is used to shape the hand for grasping. In robotics a similar role has been played by modules that fit point cloud data to the superquadric family of shapes and its various extensions. We developed a model of shape tuning in AIP based on cosine tuning to superquadric parameters. However, the model did not fit the data well, and we also found that it was difficult to accurately reproduce these parameters using neural networks with the appropriate inputs (modelled on the caudal intraparietal area, CIP). The latter difficulty was related to the fact that there are large discontinuities in the superquadric parameters between very similar shapes. To address these limitations we adopted an alternative shape parameterization based on an Isomap nonlinear dimension reduction. The Isomap was built using gradients and curvatures of object surface depth. This alternative parameterization was low-dimensional (like superquadrics), but data-driven (similar to an alternative clustering approach that is also sometimes used in robotics) and lacked large discontinuities. Isomaps with 16 or more dimensions reproduced the AIP data fairly well. Moreover, we found that the Isomap parameters could be approximated from CIP-like input much more accurately than the superquadric parameters. We conclude that Isomaps, or perhaps alternative dimension reductions of CIP signals, provide a promising model of AIP tuning. We have now started to integrate our model with a robot hand, to explore the efficacy of Isomap shape reductions in grasp planning. Future work will consider dynamics of spike responses and integration with related visual and motor area models.

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

Communication structure of cortical networks

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in-and out-absorption as well as in-and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdos-Renyi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

Quantifying network properties in multi-electrode recordings: spatiotemporal characterization and inter-trial variation of evoked gamma oscillations in mouse somatosensory cortex in vitro.

Linking the structural connectivity of brain circuits to their cooperative dynamics and emergent functions is a central aim of neuroscience research. Graph theory has recently been applied to study the structure-function relationship of networks, where dynamical similarity of different nodes has been turned into a "static" functional connection. However, the capability of the brain to adapt, learn and process external stimuli requires a constant dynamical functional rewiring between circuitries and cell assemblies. Hence, we must capture the changes of network functional connectivity over time. Multi-electrode array data present a unique challenge within this framework. We study the dynamics of gamma oscillations in acute slices of the somatosensory cortex from juvenile mice recorded by planar multi-electrode arrays. Bursts of gamma oscillatory activity lasting a few hundred milliseconds could be initiated only by brief trains of electrical stimulations applied at the deepest cortical layers and simultaneously delivered at multiple locations. Local field potentials were used to study the spatio-temporal properties and the instantaneous synchronization profile of the gamma oscillatory activity, combined with current source density (CSD) analysis. Pair-wise differences in the oscillation phase were used to determine the presence of instantaneous synchronization between the different sites of the circuitry during the oscillatory period. Despite variation in the duration of the oscillatory response over successive trials, they showed a constant average power, suggesting that the rate of expenditure of energy during the gamma bursts is consistent across repeated stimulations. Within each gamma burst, the functional connectivity map reflected the columnar organization of the neocortex. Over successive trials, an apparently random rearrangement of the functional connectivity was observed, with a more stable columnar than horizontal organization. This work reveals new features of evoked gamma oscillations in developing cortex.

Alternative Techniques of Neural Signal Processing in Neuroengineering

Neural signal processing is a discipline within neuroengineering. This interdisciplinary approach combines principles from machine learning, signal processing theory, and computational neuroscience applied to problems in basic and clinical neuroscience. The ultimate goal of neuroengineering is a technological revolution, where machines would interact in real time with the brain. Machines and brains could interface, enabling normal function in cases of injury or disease, brain monitoring, and/or medical rehabilitation of brain disorders. Much current research in neuroengineering is focused on understanding the coding and processing of information in the sensory and motor systems, quantifying how this processing is altered in the pathological state, and how it can be manipulated through interactions with artificial devices including brain–computer interfaces and neuroprosthetics.

Alternative Time Representation in Dopamine Models

Groupe de recherche sur le système nerveux central, Département d'informatique et de recherche opérationnelle, Département de physiologie.

Modèle informatique du coapprentissage des ganglions de la base et du cortex : l'apprentissage par renforcement et le développement de représentations

Tout au long de la vie, le cerveau développe des représentations de son environnement permettant à l’individu d’en tirer meilleur profit. Comment ces représentations se développent-elles pendant la quête de récompenses demeure un mystère. Il est raisonnable de penser que le cortex est le siège de ces représentations et que les ganglions de la base jouent un rôle important dans la maximisation des récompenses. En particulier, les neurones dopaminergiques semblent coder un signal d’erreur de prédiction de récompense. Cette thèse étudie le problème en construisant, à l’aide de l’apprentissage machine, un modèle informatique intégrant de nombreuses évidences neurologiques. Après une introduction au cadre mathématique et à quelques algorithmes de l’apprentissage machine, un survol de l’apprentissage en psychologie et en neuroscience et une revue des modèles de l’apprentissage dans les ganglions de la base, la thèse comporte trois articles. Le premier montre qu’il est possible d’apprendre à maximiser ses récompenses tout en développant de meilleures représentations des entrées. Le second article porte sur l'important problème toujours non résolu de la représentation du temps. Il démontre qu’une représentation du temps peut être acquise automatiquement dans un réseau de neurones artificiels faisant office de mémoire de travail. La représentation développée par le modèle ressemble beaucoup à l’activité de neurones corticaux dans des tâches similaires. De plus, le modèle montre que l’utilisation du signal d’erreur de récompense peut accélérer la construction de ces représentations temporelles. Finalement, il montre qu’une telle représentation acquise automatiquement dans le cortex peut fournir l’information nécessaire aux ganglions de la base pour expliquer le signal dopaminergique. Enfin, le troisième article évalue le pouvoir explicatif et prédictif du modèle sur différentes situations comme la présence ou l’absence d’un stimulus (conditionnement classique ou de trace) pendant l’attente de la récompense. En plus de faire des prédictions très intéressantes en lien avec la littérature sur les intervalles de temps, l’article révèle certaines lacunes du modèle qui devront être améliorées. Bref, cette thèse étend les modèles actuels de l’apprentissage des ganglions de la base et du système dopaminergique au développement concurrent de représentations temporelles dans le cortex et aux interactions de ces deux structures.

A Note on Object Class Representation and Categorical Perception

We present a novel scheme ("Categorical Basis Functions", CBF) for object class representation in the brain and contrast it to the "Chorus of Prototypes" scheme recently proposed by Edelman. The power and flexibility of CBF is demonstrated in two examples. CBF is then applied to investigate the phenomenon of Categorical Perception, in particular the finding by Bulthoff et al. (1998) of categorization of faces by gender without corresponding Categorical Perception. Here, CBF makes predictions that can be tested in a psychophysical experiment. Finally, experiments are suggested to further test CBF.