Complex Networks Theory

By combining graph theory and statistical physics, complex network theory provides a powerful tool to investigate the structure and function of complex systems with a large number of interacting elements. The development and characterization of complex networks makes their application suitable to analyze a wide range of systems from nature to economy, from engineering to society. Beside the well-established applications to Internet and World Wide Web, neural connections and social dynamics, complex networks have been successfully used to study many different phenomena such as, for example, human migration, cancer metastasis and earthquake occurrence.  

CLIMATE NETWORKS

The extension of complex network theory to climate sciences is a very recent area yielding climate networks, which usually rely on gridded time series of meteorological preprocessed variables. The nodes of the network are identified by geographical regions corresponding to single points of measurement on the spatial grid of the underlying climate database. Each node has a measured state variable which varies in time. A link between two nodes exists if there is a significant statistical interdependence between their time series.

The complex network theory has been used here to analyze the spatial dynamics of annual precipitation over seventy years (1941–2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only.

Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns.

 

TURBULENCE NETWORKS

Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. A new approach based on the complex network theory is presented, offering a powerful framework to explore complex systems with a huge number of interacting elements. Although interest on complex networks has been increasing in the last years, few recent studies have been applied to turbulence. We investigate starting from a two-point correlation for the kinetic energy of a forced isotropic field numerically solved. Among all the metrics analyzed, the degree centrality is the most significant, suggesting the formation of spatial patterns which coherently move with similar vorticity over the large eddy turnover time scale. Pattern size can be quantified through a newly-introduced parameter (i.e., average physical distance) and varies from small to intermediate scales. The network analysis allows a systematic identification of different spatial regions, providing new insights into the spatial characterization of turbulent flows. Based on present findings, the application to highly inhomogeneous flows seems promising and deserves additional future investigation.

 

CARDIOVASCULAR NETWORKS

The growing size of numerical data coming from multiscale simulations, highly-resolved imaging and computational fluid dynamics approaches requires refined quantitative tools to appropriately analyze biomedical signals. A network-based approach is proposed to investigate the cerebrovascular flow patterns during atrial fibrillation (AF) with respect to normal sinus rhythm (NSR). AF, the most common cardiac arrhythmia with faster and irregular beating, has been recently and independently associated with the increased risk of dementia. However, the underlying hemodynamic mechanisms relating the two pathologies remain mainly undetermined so far; thus the contribution of modeling and refined statistical tools is valuable. Pressure and flow rate temporal series in NSR and AF are here evaluated along representative cerebral sites (from carotid arteries to capillary brain circulation), exploiting reliable artificially built signals recently obtained from an in silico approach. The complex network analysis evidences, in a synthetic and original way, a dramatic signal variation towards the distal/capillary cerebral regions during AF, which has no counterpart in NSR conditions. At the large artery level, networks obtained from both AF and NSR hemodynamic signals exhibit elongated and chained features, which are typical of pseudo-periodic series. These aspects are almost completely lost towards the microcirculation during AF, where the networks are topologically more circular and present random-like characteristics. As a consequence, all the physiological phenomena at microcerebral level ruled by periodicity - such as regular perfusion, mean pressure per beat, and average nutrient supply at cellular level - can be strongly compromised, since the AF hemodynamic signals assume irregular behaviour and random-like features. Through a powerful approach which is complementary to the classical statistical tools, the present findings further strengthen the potential link between AF hemodynamic and cognitive decline.

 

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