Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Impact of community structure on information transfer

The observation that real complex networks have internal structure has important implication for dynamic processes occurring on such topologies. Here we investigate the impact of community structure on a model of information transfer able to deal with both search and congestion simultaneously. We show that networks with fuzzy community structure are more efficient in terms of packet delivery than those with pronounced community structure. We also propose an alternative packet routing algorithm which takes advantage of the knowledge of communities to improve information transfer and show that in the context of the model an intermediate level of community structure is optimal. Finally, we show that in a hierarchical network setting, providing knowledge of communities at the level of highest modularity will improve network capacity by the largest amount.

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.

Improved flooding of broadcast messages using extended multipoint relaying

A common operation in wireless ad hoc networks is the flooding of broadcast messages to establish network topologies and routing tables. The flooding of broadcast messages is, however, a resource consuming process. It might require the retransmission of messages by most network nodes. It is, therefore, very important to optimize this operation. In this paper, we first analyze the multipoint relaying (MPR) flooding mechanism used by the Optimized Link State Routing (OLSR) protocol to distribute topology control (TC) messages among all the system nodes. We then propose a new flooding method, based on the fusion of two key concepts: distance-enabled multipoint relaying and connected dominating set (CDS) flooding. We present experimental simulationsthat show that our approach improves the performance of previous existing proposals.