Predicting triadic closure in networks using communicability distance functions

We propose a communication-driven mechanism for predicting triadic closure in complex networks. It is mathematically formulated on the basis of communicability distance functions that account for the quality of communication between nodes in the network. We study $25$ real-world networks and show that the proposed method predicts correctly $20\%$ of triadic closures in these networks, in contrast to the $7.6\%$ predicted by a random mechanism. We also show that the communication-driven method outperforms the random mechanism in explaining the clustering coefficient, average path length, and average communicability. The new method also displays some interesting features with regards to optimizing communication in networks

Exact and approximate moment closures for non-Markovian network epidemics

Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods. We initially study two special networks, namely the open triplet and closed triangle, for which we can obtain analytical results. We then explore numerically the exactness of moment closures for a wide range of larger motifs, thus gaining understanding of the factors that introduce errors in the approximations, in particular the presence of a random duration of the infectious period and the presence of overlapping triangles in a network. We also derive a simpler and more intuitive proof than previously available concerning the known result that pair-based moment closure is exact for the Markovian SIR model on tree-like networks under pure initial conditions. We also extend such a result to all infectious models, Markovian and non-Markovian, in which susceptibles escape infection independently from each infected neighbour and for which infectives cannot regain susceptible status, provided the network is tree-like and initial conditions are pure. This works represent a valuable step in deepening understanding of the assumptions behind moment closure approximations and for putting them on a more rigorous mathematical footing.Comment: Main text (45 pages, 11 figures and 3 tables) + supplementary material (12 pages, 10 figures and 1 table). Accepted for publication in Journal of Theoretical Biology on 27th April 201

Critical Cooperation Range to Improve Spatial Network Robustness

A robust worldwide air-transportation network (WAN) is one that minimizes the number of stranded passengers under a sequence of airport closures. Building on top of this realistic example, here we address how spatial network robustness can profit from cooperation between local actors. We swap a series of links within a certain distance, a cooperation range, while following typical constraints of spatially embedded networks. We find that the network robustness is only improved above a critical cooperation range. Such improvement can be described in the framework of a continuum transition, where the critical exponents depend on the spatial correlation of connected nodes. For the WAN we show that, except for Australia, all continental networks fall into the same universality class. Practical implications of this result are also discussed

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables

In silico generation of novel, drug-like chemical matter using the LSTM neural network

The exploration of novel chemical spaces is one of the most important tasks of cheminformatics when supporting the drug discovery process. Properly designed and trained deep neural networks can provide a viable alternative to brute-force de novo approaches or various other machine-learning techniques for generating novel drug-like molecules. In this article we present a method to generate molecules using a long short-term memory (LSTM) neural network and provide an analysis of the results, including a virtual screening test. Using the network one million drug-like molecules were generated in 2 hours. The molecules are novel, diverse (contain numerous novel chemotypes), have good physicochemical properties and have good synthetic accessibility, even though these qualities were not specific constraints. Although novel, their structural features and functional groups remain closely within the drug-like space defined by the bioactive molecules from ChEMBL. Virtual screening using the profile QSAR approach confirms that the potential of these novel molecules to show bioactivity is comparable to the ChEMBL set from which they were derived. The molecule generator written in Python used in this study is available on request.Comment: in this version fixed some reference number