Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding, which is a necessary procedure to remove the secular properties of the spectrum, on different spectral statistics. We find that, while the spacing distribution of the eigenvalues shows little sensitivity to the unfolding method used, the spectral rigidity has greater sensitivity to unfolding.Comment: Complex Adaptive Systems Conference 201

Stimulus sensitivity of a spiking neural network model

Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been used to model spiking neural networks. Using mean-field approximation, the response of the network to a stimulus is computed and we provide a notion of stimulus sensitivity. It appears that the maximal sensitivity is achieved in the sub-critical regime, yet almost critical for a range of biologically relevant parameters

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kB signaling pathway

Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the state-space formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IB-NF-B signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-B oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks

Structural Changes in Data Communication in Wireless Sensor Networks

Wireless sensor networks are an important technology for making distributed autonomous measures in hostile or inaccessible environments. Among the challenges they pose, the way data travel among them is a relevant issue since their structure is quite dynamic. The operational topology of such devices can often be described by complex networks. In this work, we assess the variation of measures commonly employed in the complex networks literature applied to wireless sensor networks. Four data communication strategies were considered: geometric, random, small-world, and scale-free models, along with the shortest path length measure. The sensitivity of this measure was analyzed with respect to the following perturbations: insertion and removal of nodes in the geometric strategy; and insertion, removal and rewiring of links in the other models. The assessment was performed using the normalized Kullback-Leibler divergence and Hellinger distance quantifiers, both deriving from the Information Theory framework. The results reveal that the shortest path length is sensitive to perturbations.Comment: 12 pages, 4 figures, Central European Journal of Physic