Topological exploration of artificial neuronal network dynamics

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and statistical mechanics to describe the spatiotemporal structure of such network dynamics. Our novel approach employs tools from algebraic topology to characterize the global properties of network structure and dynamics. We propose a method based on persistent homology to automatically classify network dynamics using topological features of spaces built from various spike-train distances. We investigate the efficacy of our method by simulating activity in three small artificial neural networks with different sets of parameters, giving rise to dynamics that can be classified into four regimes. We then compute three measures of spike train similarity and use persistent homology to extract topological features that are fundamentally different from those used in traditional methods. Our results show that a machine learning classifier trained on these features can accurately predict the regime of the network it was trained on and also generalize to other networks that were not presented during training. Moreover, we demonstrate that using features extracted from multiple spike-train distances systematically improves the performance of our method

Interaction of cortical networks mediating object motion detection by moving observers

Published in final edited form as: Exp Brain Res. 2012 August ; 221(2): 177–189. doi:10.1007/s00221-012-3159-8.The task of parceling perceived visual motion into self- and object motion components is critical to safe and accurate visually guided navigation. In this paper, we used functional magnetic resonance imaging to determine the cortical areas functionally active in this task and the pattern connectivity among them to investigate the cortical regions of interest and networks that allow subjects to detect object motion separately from induced self-motion. Subjects were presented with nine textured objects during simulated forward self-motion and were asked to identify the target object, which had an additional, independent motion component toward or away from the observer. Cortical activation was distributed among occipital, intra-parietal and fronto-parietal areas. We performed a network analysis of connectivity data derived from partial correlation and multivariate Granger causality analyses among functionally active areas. This revealed four coarsely separated network clusters: bilateral V1 and V2; visually responsive occipito-temporal areas, including bilateral LO, V3A, KO (V3B) and hMT; bilateral VIP, DIPSM and right precuneus; and a cluster of higher, primarily left hemispheric regions, including the central sulcus, post-, pre- and sub-central sulci, pre-central gyrus, and FEF. We suggest that the visually responsive networks are involved in forming the representation of the visual stimulus, while the higher, left hemisphere cluster is involved in mediating the interpretation of the stimulus for action. Our main focus was on the relationships of activations during our task among the visually responsive areas. To determine the properties of the mechanism corresponding to the visual processing networks, we compared subjects’ psychophysical performance to a model of object motion detection based solely on relative motion among objects and found that it was inconsistent with observer performance. Our results support the use of scene context (e.g., eccentricity, depth) in the detection of object motion. We suggest that the cortical activation and visually responsive networks provide a potential substrate for this computation.This work was supported by NIH grant RO1NS064100 to L.M.V. We thank Victor Solo for discussions regarding models of functional connectivity and our subjects for participating in the psychophysical and fMRI experiments. This research was carried out in part at the Athinoula A. Martinos Center for Biomedical Imaging at the Massachusetts General Hospital, using resources provided by the Center for Functional Neuroimaging Technologies, P41RR14075, a P41 Regional Resource supported by the Biomedical Technology Program of the National Center for Research Resources (NCRR), National Institutes of Health. This work also involved the use of instrumentation supported by the NCRR Shared Instrumentation Grant Program and/or High-End Instrumentation Grant Program; specifically, grant number S10RR021110. (RO1NS064100 - NIH; National Center for Research Resources (NCRR), National Institutes of Health; S10RR021110 - NCRR)Accepted manuscrip

Discrete modes of social information processing predict individual behavior of fish in a group

Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an active mode in which they are sensitive to the swimming patterns of conspecifics, and a passive mode where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors behavior. At the group level, switching between active and passive modes is uncorrelated among fish, yet correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates, as well as to other species