Numerical analysis of a mechanotransduction dynamical model reveals homoclinic bifurcations of extracellular matrix mediated oscillations of the mesenchymal stem cell fate

We perform one and two-parameter numerical bifurcation analysis of a mechanotransduction model approximating the dynamics of mesenchymal stem cell differentiation into neurons, adipocytes, myocytes and osteoblasts. For our analysis, we use as bifurcation parameters the stiffness of the extracellular matrix and parameters linked with the positive feedback mechanisms that up-regulate the production of the YAP/TAZ transcriptional regulators (TRs) and the cell adhesion area. Our analysis reveals a rich nonlinear behaviour of the cell differentiation including regimes of hysteresis and multistability, stable oscillations of the effective adhesion area, the YAP/TAZ TRs and the PPAR$\gamma$ receptors associated with the adipogenic fate, as well as homoclinic bifurcations that interrupt relatively high-amplitude oscillations abruptly. The two-parameter bifurcation analysis of the Andronov-Hopf points that give birth to the oscillating patterns predicts their existence for soft extracellular substrates ($<1kPa$), a regime that favours the neurogenic and the adipogenic cell fate. Furthermore, in these regimes, the analysis reveals the presence of homoclinic bifurcations that result in the sudden loss of the stable oscillations of the cell-substrate adhesion towards weaker adhesion and high expression levels of the gene encoding Tubulin beta-3 chain, thus favouring the phase transition from the adipogenic to the neurogenic fate

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 (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. 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 lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

Reducing wildland fire hazard exploiting complex network theory. A case study analysis

We discuss a new systematic methodology to mitigate wildland fire hazard by appropriately distributing fuel breaks in space. In particular, motivated by the concept of information flow in complex networks we create a hierarchical allocation of the landscape patches that facilitate the fire propagation based on the Bonacich centrality. Reducing the fuel load in these critical patches results to lower levels of fire hazard. For illustration purposes we apply the proposed strategy to a real case of wildland fire. In particular we focus on the wildland fire that occurred in Spetses Island, Greece in 1990 and burned the one third of the forest. The efficiency of the proposed strategy is compared against the benchmark of random distribution of fuel breaks for a wide range of fuel breaks densities

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

Can social microblogging be used to forecast intraday exchange rates?

The Efficient Market Hypothesis (EMH) is widely accepted to hold true under certain assumptions. One of its implications is that the prediction of stock prices at least in the short run cannot outperform the random walk model. Yet, recently many studies stressing the psychological and social dimension of financial behavior have challenged the validity of the EMH. Towards this aim, over the last few years, internet-based communication platforms and search engines have been used to extract early indicators of social and economic trends. Here, we used Twitter's social networking platform to model and forecast the EUR/USD exchange rate in a high-frequency intradaily trading scale. Using time series and trading simulations analysis, we provide some evidence that the information provided in social microblogging platforms such as Twitter can in certain cases enhance the forecasting efficiency regarding the very short (intradaily) forex.Comment: This is a prior version of the paper published at NETNOMICS. The final publication is available at http://www.springer.com/economics/economic+theory/journal/1106

Complex network statistics to the design of fire breaks for the control of fire spreading

A computational approach for identifying efficient fuel breaks partitions for the containment of fire incidents in forests is proposed. The approach is based on the complex networks statistics, namely the centrality measures and cellular automata modeling. The efficiency of various centrality statistics, such as betweenness, closeness, Bonacich and eigenvalue centrality to select fuel breaks partitions vs. the random-based distribution is demonstrated. Two examples of increasing complexity are considered: (a) an artificial forest of randomly distributed density of vegetation, and (b) a patch from the area of Vesuvio, National Park of Campania, Italy. Both cases assume flat terrain and single type of vegetation. Simulation results over an ensemble of lattice realizations and runs show that the proposed approach appears very promising as it produces statistically significant better outcomes when compared to the random distribution approach

Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a single hidden layer with sigmoidal functions and fixed, random, internal weights and biases can be used to compute accurately a collocation solution. The choice to fix internal weights and bias leads to the so-called Extreme Learning Machine network. We discuss how to determine the range for both internal weights and biases in order to obtain a good underlining approximating space, and we explore the required number of collocation points. We demonstrate the efficiency of the proposed method with several one-dimensional diffusion-advection-reaction problems that exhibit steep behaviors, such as boundary layers. The boundary conditions are imposed directly as collocation equations. We point out that there is no need of training the network, as the proposed numerical approach results to a linear problem that can be easily solved using least-squares. Numerical results show that the proposed method achieves a good accuracy. Finally, we compare the proposed method with finite differences and point out the significant improvements in terms of computational cost, thus avoiding the time-consuming training phase

Coarse-graining the dynamics of network evolution: the rise and fall of a networked society

We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be developed. We illustrate our approach through a particular social network model: the "rise and fall" of a networked society [1]: we implement our low-dimensional description computationally using the equation-free approach and show how it can be used to (a) accelerate simulations and (b) extract system-level stability/bifurcation information from the detailed dynamic model. We discuss other system-level tasks that can be enabled through such a computer-assisted coarse graining approach.Comment: 18 pages, 11 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