Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.Comment: 10 figure

Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations

We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of neurons that interact on complex networks. In particular we show how the Equation-Free approach can be exploited to perform system-level tasks such as bifurcation, stability analysis and estimation of mean appearance times of rare events, bypassing the need for obtaining analytical approximations, providing an "on-demand" model reduction. Using the detailed simulator as a black-box timestepper, we compute the coarse-grained equilibrium bifurcation diagrams, examine the stability of the solution branches and perform a rare-events analysis with respect to certain characteristics of the underlying network topology such as the connectivity degre

On the effect of the path length and transitivity of small-world networks on epidemic dynamics

We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have developed algorithms that allow the tuning of the transitivity (clustering coefficient) and the average mean-path length allowing the investigation of the "pure" impacts of the two characteristics on the emergent behavior of detailed epidemic models. The framework could be used to shed more light into the influence of weak and strong social ties on epidemic spread within small-world network structures, and ultimately to provide novel systematic computational modeling and exploration of better contagion control strategies

Construction of embedded fMRI resting-state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

We address a new numerical method based on a class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of (one-dimensional) bifurcation diagrams of nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) the one-dimensional viscous Burgers with both homogeneous (Dirichlet) and non-homogeneous boundary conditions, and, (b) the one- and two-dimensional Liouville–Bratu–Gelfand PDEs with homogeneous Dirichlet boundary conditions. For the one-dimensional Burgers and Bratu PDEs, exact analytical solutions are available and used for comparison purposes against the numerical derived solutions. Furthermore, the numerical efficiency (in terms of numerical accuracy, size of the grid and execution times) of the proposed numerical machine-learning method is compared against central finite differences (FD) and Galerkin weighted-residuals finite-element (FEM) methods. We show that the proposed numerical machine learning method outperforms in terms of numerical accuracy both FD and FEM methods for medium to large sized grids, while provides equivalent results with the FEM for low to medium sized grids; both methods (ELM and FEM) outperform the FD scheme. Furthermore, the computational times required with the proposed machine learning scheme were comparable and in particular slightly smaller than the ones required with FE

Analytical and Numerical Bifurcation Analysis of a Forest-Grassland Ecosystem Model with Human Interaction

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of forest/grassland value. The system displays multiple steady states corresponding to different forest densities as well as regimes characterized by both stable and unstable limit cycles. We derive analytically the conditions with respect to the model parameters that give rise to various types of codimension-one criticalities such as transcritical, saddle-node, and Andronov-Hopf bifurcations and codimension-two criticalities such as cusp and Bogdanov-Takens bifurcations. We also perform a numerical continuation of the branches of limit cycles. By doing so, we reveal turning points of limit cycles marking the appearance/disappearance of sustained oscillations. These far-from-equilibrium criticalities that cannot be detected analytically give rise to the abrupt loss of the sustained oscillations, thus leading to another mechanism of catastrophic shift

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