In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatio-temporal network complexity. In this paper, we propose a new hierarchical coupled-geometry analysis that implicitly takes into account the connectivity structures between neurons and the dynamic patterns at multiple time scales. Our approach gives rise to the joint organization of neurons and dynamic patterns in data-driven hierarchical data structures. These structures provide local to global data representations, from local partitioning of the data in flexible trees through a new multiscale metric to a global manifold embedding. The application of our techniques to in-vivo neuronal recordings demonstrate the capability of extracting neuronal activity patterns and identifying temporal trends, associated with particular behavioral events and manipulations introduced in the experiments.
Current network analysis approaches in neuroscience can be divided into two main classes @cite_38 @cite_46 . The first class comprises methods, which aim to determine functional connectivity, defined in terms of statistical dependencies between measured elements (e.g., neurons or networks), by constructing direct statistical models from the data (e.g., Granger causality, transfer entropy, point process modeling and graph based methods @cite_5 @cite_35 @cite_7 @cite_46 . The second class of methods is often based on Latent Dynamical Systems (LDS), which accommodates effective connectivity characterizing the causal relations between elements through an underlying hidden dynamical system @cite_38 @cite_45 @cite_11 . Non-linear and non-Gaussian extensions of the Kalman filter, contemporary sequential Monte Carlo methods and particle filters, have also been introduced in neuroscience @cite_9 @cite_28 .
@cite_38 @cite_35 @cite_7 @cite_28 @cite_9 @cite_45 @cite_5 @cite_46 @cite_11
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This review considers state-of-the-art analyses of functional integration in neuronal macrocircuits. We focus on detecting and estimating directed connectivity in neuronal networks using Granger causality (GC) and dynamic causal modelling (DCM). These approaches are considered in the context of functional segregation and integration and — within functional integration — the distinction between functional and effective connectivity. We review recent developments that have enjoyed a rapid uptake in the discovery and quantification of functional brain architectures. GC and DCM have distinct and complementary ambitions that are usefully considered in relation to the detection of functional connectivity and the identification of models of effective connectivity. We highlight the basic ideas upon which they are grounded, provide a comparative evaluation and point to some outstanding issues. This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic cyclic, directed undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results. The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes, and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales. By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms. As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attention-deficit hyperactivity disorder children, 26 autism spectrum disorder children, and 11 pediatric control subjects. r r Abstract: Characterization of large-scale brain networks using blood-oxygenation-level-dependent functional magnetic resonance imaging is typically based on the assumption of network stationarity across the duration of scan. Recent studies in humans have questioned this assumption by showing that within-network functional connectivity fluctuates on the order of seconds to minutes. Time-varying profiles of resting-state networks (RSNs) may relate to spontaneously shifting, electrophysiological network states and are thus mechanistically of particular importance. However, because these studies acquired data from awake subjects, the fluctuating connectivity could reflect various forms of conscious brain processing such as passive mind wandering, active monitoring, memory formation, or changes in attention and arousal during image acquisition. Here, we characterize RSN dynamics of anesthetized macaques that control for these accounts, and compare them to awake human subjects. We find that functional connectivity among nodes comprising the ''oculomotor (OCM) network'' strongly fluctuated over time during awake as well as anaesthetized states. For time dependent anal- ysis with short windows (<60 s), periods of positive functional correlations alternated with prominent anticor- relations that were missed when assessed with longer time windows. Similarly, the analysis identified network nodes that transiently link to the OCM network and did not emerge in average RSN analysis. Further- more, time-dependent analysis reliably revealed transient states of large-scale synchronization that spanned all seeds. The results illustrate that resting-state functional connectivity is not static and that RSNs can exhibit non- stationary, spontaneous relationships irrespective of conscious, cognitive processing. The findings imply that mechanistically important network information can be missed when using average functional connectivity as the single network measure.Hum Brain Mapp 00:000-000, 2012. V C 2012 Wiley Periodicals, Inc.