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

Predicting the connectivity of primate cortical networks from topological and spatial node properties

The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked together, in an attempt to recover the original network structure. Inferring primate cortical connectivity from the properties of the nodes, remarkably good reconstructions of the global network organization could be obtained, with the topological features allowing slightly superior accuracy to the spatial ones. Analogous reconstruction attempts for the C. elegans neuronal network resulted in substantially poorer recovery, indicating that cortical area interconnections are relatively stronger related to the considered topological and spatial properties than neuronal projections in the nematode. The close relationship between area-based features and global connectivity may hint on developmental rules and constraints for cortical networks. Particularly, differences between the predictions from topological and spatial properties, together with the poorer recovery resulting from spatial properties, indicate that the organization of cortical networks is not entirely determined by spatial constraints

Simplest random K-satisfiability problem

We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In statistical-mechanics language, the considered model can be seen as a diluted p-spin model at zero temperature. While such problems become extraordinarily hard to solve by local search methods in a large region of the parameter space, still at least one solution may be superimposed by construction. The statistical properties of the model can be studied exactly by the replica method and each single instance can be analyzed in polynomial time by a simple global solution method. The geometrical/topological structures responsible for dynamic and static phase transitions as well as for the onset of computational complexity in local search method are thoroughly analyzed. Numerical analysis on very large samples allows for a precise characterization of the critical scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor errors and references correcte

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

EEG Resting-State Brain Topological Reorganization as a Function of Age

Resting state connectivity has been increasingly studied to investigate the effects of aging on the brain. A reduced organization in the communication between brain areas was demonstrated b y combining a variety of different imaging technologies (fMRI, EEG, and MEG) and graph theory. In this paper, we propose a methodology to get new insights into resting state connectivity and its variations with age, by combining advanced techniques of effective connectivity estimation, graph theoretical approach, and classification by SVM method. We analyzed high density EEG signal srecordedatrestfrom71healthysubjects(age:20–63years). Weighted and directed connectivity was computed by means of Partial Directed Coherence based on a General Linear Kalman filter approach. To keep the information collected by the estimator, weighted and directed graph indices were extracted from the resulting networks. A relation between brain network properties and age of the subject was found, indicating a tendency of the network to randomly organize increasing with age. This result is also confirmed dividing the whole population into two subgroups according to the age (young and middle-aged adults): significant differences exist in terms of network organization measures. Classification of the subjects by means of such indices returns an accuracy greater than 80

Flexible couplings: diffusing neuromodulators and adaptive robotics

Recent years have seen the discovery of freely diffusing gaseous neurotransmitters, such as nitric oxide (NO), in biological nervous systems. A type of artificial neural network (ANN) inspired by such gaseous signaling, the GasNet, has previously been shown to be more evolvable than traditional ANNs when used as an artificial nervous system in an evolutionary robotics setting, where evolvability means consistent speed to very good solutions¿here, appropriate sensorimotor behavior-generating systems. We present two new versions of the GasNet, which take further inspiration from the properties of neuronal gaseous signaling. The plexus model is inspired by the extraordinary NO-producing cortical plexus structure of neural fibers and the properties of the diffusing NO signal it generates. The receptor model is inspired by the mediating action of neurotransmitter receptors. Both models are shown to significantly further improve evolvability. We describe a series of analyses suggesting that the reasons for the increase in evolvability are related to the flexible loose coupling of distinct signaling mechanisms, one ¿chemical¿ and one ¿electrical.

Building flat space-time from information exchange between quantum fluctuations

We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how frequently particles interact, through an individual rate $dt\sim 1/f_t$ and spatially interconnecting rates $dl\sim c/f$. The question is if space-time can be modelled consistently in this way. The ansatz would be opposite to the standard treatment of space-time as insensitive to altered physics at event horizons (disrupted propagation of information) but by extension relate to the connection of space-time to entanglement (interactions) through the gauge/gravity duality. We make a first, rough analysis of the implications this type of quantization would have on the classical structure of flat space-time, and of what would be required of the interactions. Seeing no obvious reason for why the origin would be unrealistic, we comment on expected effects in the presence of curvature.Comment: 22 pages. v3: extended introductio