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International audience; Given a pattern on a network, i.e. a subset of nodes, can we assess, whether they are randomly distributed on the network or have been generated in a systematic fashion following the network architecture? This question is at the core of network-based data analyses across a range of disciplines-from incidents of infection in social networks to sets of differentially expressed genes in biological networks. Here we introduce generic 'pattern generators' based on an Eden growth model. We assess the capacity of different pattern measures like connectivity, edge density or various average distances, to infer the parameters of the generator from the observed patterns. Some measures perform consistently better than others in inferring the underlying pattern generator, while the best performing measures depend on the global topology of the underlying network. Moreover, we show that pattern generator inference remains possible in case of limited visibility of the patterns.

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1 . These results allow us to obtain theoretical values of three measures: (i) the recurrence rate ( R E C ) (ii) the percent determinism ( D E T ) and (iii) RP-based estimation of the e -entropy κ ( e ) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.

How signals propagate through a network as a function of the network architecture and under the influence of noise is a fundamental question in a broad range of areas dealing with signal processing - from neuroscience to electrical engineering and communication technology. Here we use numerical simulations and a mean-field approach to analyze a minimal dynamic model for signal propagation. By labeling and tracking the excitations propagating from a single input node to remote output nodes in random networks, we show that noise (provided by spontaneous node excitations) can lead to an enhanced signal propagation, with a peak in the signal-to-noise ratio at intermediate noise intensities. This network analog of stochastic resonance is not captured by a mean-field description that incorporates topology only on the level of the average degree, indicating that the detailed network topology plays a significant role in signal propagation.

During eukaryotic transcription, RNA-polymerase activity generates torsional stress in DNA, having a negative impact on the elongation process. Using our previous studies of chromatin fiber structure and conformational transitions, we suggest that this torsional stress can be alleviated, thanks to a tradeoff between the fiber twist and nucleosome conformational transitions into an activated state named “reversome”. Our model enlightens the origin of polymerase pauses, and leads to the counterintuitive conclusion that chromatin-organized compaction might facilitate polymerase progression. Indeed, in a compact and well-structured chromatin loop, steric hindrance between nucleosomes enforces sequential transitions, thus ensuring that the polymerase always meets a permissive nucleosomal state.

The influence of the network topology on the dynamics of systems of coupled excitable units is studied numerically and demonstrates a lower dynamical variability for power-law networks than for Poisson ones. This effect which reflects a robust collective excitable behavior is however lower than that observed for diffusion processes or network robustness. Instead, the presence (and number) of triangles and larger loops in the networks appears as a parameter with strong influence on the considered dynamics.