Related papers: Complex active optical networks as a new laser con…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fibre laser. Ordinal analysis and the horizontal visibility graph applied to the…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
Network analysis is currently used in a myriad of contexts: from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies, and from finding friends to uncovering criminal activity.…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by…
Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems…
Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed…
When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden…
Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…