Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks.

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Monensin and forskolin inhibit the transcription rate of sucrase-isomaltase but not the stability of its mRNA in Caco-2 cells

AbstractTreatment of Caco-2 cells with forskolin (25 μM) or monensin (1 μM) has previously been shown to cause a marked decrease in the level of sucrase-isomaltase (SI) mRNA, without any effect on the expression of dipeptidylpeptidase IV (DPP-IV). In the present work, we report that there is no significant difference in the stability of SI mRNA between control and treated cells. On the other hand, we demonstrate a decrease in the transcription rate of SI mRNA which is sufficient to account for the decrease in the steady-state level of SI mRNA both in forskolin- and monensin-treated Caco-2 cells

Number theoretic example of scale-free topology inducing self-organized criticality

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Critical behavior of a Ginzburg-Landau model with additive quenched noise

We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a self-consistent theory to calculate the phase diagram of the system, predicting the onset of an order-disorder critical transition at a critical value {\sigma}c of the quenched noise intensity \sigma, with critical exponents that follow Landau theory of thermal phase transitions. We subsequently perform a numerical integration of the system's dynamical variables in order to compare the analytical results (valid in the thermodynamic limit and associated to the ground state of the global Lyapunov potential) with the stationary state of the (finite size) system. In the region of the parameter space where metastability is absent (and therefore the stationary state coincide with the ground state of the Lyapunov potential), a finite-size scaling analysis of the order parameter fluctuations suggests that the magnetic susceptibility diverges quadratically in the vicinity of the transition, what constitutes a violation of the fluctuation-dissipation relation. We derive an effective Hamiltonian and accordingly argue that its functional form does not allow to straightforwardly relate the order parameter fluctuations to the linear response of the system, at odds with equilibrium theory. In the region of the parameter space where the system is susceptible to have a large number of metastable states (and therefore the stationary state does not necessarily correspond to the ground state of the global Lyapunov potential), we numerically find a phase diagram that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure

A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

LL’s acknowledges funding from an EPSRC Early Career Fellowship EP/P01660X/1

Emergence of collective intonation in the musical performance of crowds

To be published in EPLTo be published in EP

Sequential motif profile of natural visibility graphs

6 figures captioned6 figures captione

Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy