Gregorio D'Agostino

Networks of Networks: The Last Frontier of Complexity

The present work is meant as a reference to provide an organic and comprehensive view of the most relevant results in the exciting new field of Networks of Networks (NetoNets). Seminal papers have recently been published posing the basis to study what happens when different networks interact, thus providing evidence for the emergence of new, unexpected behaviors and vulnerabilities. From those seminal works, the awareness on the importance understanding Networks of Networks (NetoNets) has spread to the entire community of Complexity Science. The reader will benefit from the experience of some of the most well-recognized leaders in this field. The contents have been aggregated under four headings; General Theory, Phenomenology, Applications and Risk Assessment. The reader will be impressed by the different applications of the general paradigm that span from physiology, to financial risk, to transports. We are currently making the first steps to reduce the distance between the language and the way of thinking of the two communities of experts in real infrastructures and the complexity scientists. Although this path may prove to be long, it is extremely promising, both in extending our understanding of complex systems and in finding concrete applications that can enhance the life quality of millions of people.

Assortativity decreases the robustness of interdependent networks.

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and, hence, systemwide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e., the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture and, thus, enhance the level of protection of critical infrastructures.

Effect of the interconnected network structure on the epidemic threshold.

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N×2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N×2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptible-infected-susceptible (SIS) epidemic threshold in two interconnected networks is 1/λ(1)(A+αB), where the infection rate is β within each of the two individual networks and αβ in the interconnected links between the two networks and λ(1)(A+αB) is the largest eigenvalue of the matrix A+αB. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive λ(1)(A+αB) using a perturbation approximation for small and large α, the lower and upper bound for any α as a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues and eigenvectors. We verify these approximation and boundary values for λ(1)(A+αB) using numerical simulations, and determine how component network features affect λ(1)(A+αB). We note that, given two isolated networks G(1) and G(2) with principal eigenvectors x and y, respectively, λ(1)(A+αB) tends to be higher when nodes i and j with a higher eigenvector component product x(i)y(j) are interconnected. This finding suggests essential insights into ways of designing interconnected networks to be robust against epidemics.

Robustness and assortativity for diffusion-like processes in scale-free networks

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk.

Microstructure evolution from the atomic scale up

Abstract Microstructure evolution under external forces results from the complicate interplay of competing events originating at the atomic scale. The movement and interaction of, e.g., dislocations, grain boundaries, microcracks, occurs via many elementary atomic-scale events, which can be conveniently grouped into “geometric” and “topological”: the former can modify only the size and shape of the microstructure elements, while the latter may alter their number and connectivity (e.g. turning a bunch of dislocations into a grain boundary). We present and discuss the results of atomic-level simulations of both isolated and interacting defects. Then we describe a mesoscopic simulation framework based on a variational formulation of the dissipated work rate; such a model allows to correlate the elementary, atomic-scale events into a microstructure evolution model of great richness and complexity.

Knowing power grids and understanding complexity science

Complex networks theory has been well established as a useful framework for studying and analysing structure, dynamics and evolution of many complex systems. Infrastructural and man-made systems like power grids, gas and water networks and the internet, have been also included in this network framework, albeit sometimes ignoring the huge historical body of knowledge surrounding them. Although there seems to exist clear evidence that both complexity approach in general, and complex networks in particular, can be useful, it is necessary and profitable to put forward some of the limits that this scheme is facing when dealing with not so complex but rather complicated systems like the power grid. In this introductory paper, we offer a critical revision of the usefulness of the complexity and complex networks’ approach in this later case, highlighting both its strengths and weaknesses. At the same time we emphasise the disconnection between the so called complex and the more traditional engineering communities as one of the major drawbacks in the advent of a true body of understanding, more than simply knowing the subtleties of this kind of complex systems.

Methodologies for inter-dependency assessment

We report on an recent European Project aimed at assessment of suited Methodologies to measure interdependencies between the Electric and the ICT System. Based on best practices and available data, several different metrics have been defined. Depending on the methodology involved, three main types of metrics can be identified; namely “topological”; “system theory based” and “simulation based” metrics. The selected methodologies have been applied to the Roma Area electric and communication system. Results from all the different approaches are discussed. All metrics provide quantitative measures of the inter-dependence between both the two systems and their components. In addition to the established metrics, a novel “spectral” metric has been introduced specific for cascade effects. Such an innovative methodology has also been applied to the US Power Grid and results compared with those from the Roma Area.

Copper clusters simulated by a many-body tight-binding potential

Abstract We have estimated the classical ground states of copper clusters consisting of 13–1289 atoms using a tight-binding many-body potential. Starting from perfect face-centred-cubic (f.c.c.) and icosahedral structures, each system was allowed to evolve toward its inherent structure (that is the nearest local minimum energy configuration at T = 0K). The (relaxed) icosahedra turned out to be more cohesive for all the directly simulated systems. We have also estimated the critical size at which the f.c.c. structure becomes energetically favourable performing nuclear fits of the ground-state energy for both structures. The icosahedral configuration is more stable for clusters containing less than about 1500 atoms whereas f.c.c. structures are preferred for clusters of larger size. From the simulated phonon spectra, one has that the mean square displacement of an atom depends on the shell it belongs to and that, at least in the pure harmonic approximation, atoms near the centre of the cluster perform small...

Search of Molecular Ground State Via Genetic Algorithm: Implementation on a Hybrid Simd–Mimd Platform

A genetic algorithm for the optimization of the ground-state structure of a metallic cluster has been developed and ported on a SIMD–MIMD parallel platform. The SIMD part of the parallel platform is represented by a Quadrics/APE100 consisting of 512 floating point units, while the MIMD part is formed by a cluster of workstations. The proposed algorithm is composed by a part where the genetic operators are applied to the elements of the population and a part which performs a further local relaxation and the fitness calculation via Molecular Dynamics. These parts have been implemented on the MIMD and on the SIMD part, respectively. Results have been compared to those generated by using Simulated Annealing.

Spectral analysis of a real power network

We present a spectral analysis of a significant part of the Italian bulk power system. Spectral analysis applied to graphs is not a new tool, but analyses of the real world, especially of technological networks, currently are lacking. We show the spectral pattern of a high voltage power network, calculate the ratio between the smallest and largest non-zero Laplacian eigenvalue to check its synchronisability and calculate the epidemics threshold of a real HV power grid. We indicate the trade-off between sinchronisability and epidemic threshold as a major network design problem. Moreover, following Restrepo, Ott, Hunt, we propose the usage of the maximum eigenvalue of the adjacency matrix to assess a metric for the inter-dependency in the technological networks.