Power-grid vulnerability and its relation with network structure

Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.

Buffering variability in cell regulation motifs close to criticality

Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality.

The reliability of recurrence network analysis is influenced by the observability properties of the recorded time series

Recurrence network analysis (RNA) is a remarkable technique for the detection of dynamical transitions in experimental applications. However, in practical experiments, often only a scalar time series is recorded. This requires the state-space reconstruction from this single time series which, as established by embedding and observability theory, is shown to be hampered if the recorded variable conveys poor observability. In this work, we investigate how RNA metrics are impacted by the observability properties of the recorded time series. Following the framework of Zou et al. [Chaos 20, 043130 (2010)], we use the Rössler and Duffing-Ueda systems as benchmark models for our study. It is shown that usually RNA metrics perform badly with variables of poor observability as for recurrence quantification analysis. An exception is the clustering coefficient, which is rather robust to observability issues. Along with its efficacy to detect dynamical transitions, it is shown to be an efficient tool for RNA-especially when no prior information of the variable observability is available.

Particle filtering of dynamical networks: Highlighting observability issues

In a network of high-dimensionality, it is not feasible to measure every single node. Thus, an important goal is to define the optimal choice of sensor nodes that provides a reliable state reconstruction of the network system state-space. This is an observability problem. In this paper, we propose a particle filtering (PF) framework as a way to assess observability properties of a dynamical network, where each node is composed of an individual dynamical system. The PF framework is applied to two benchmarks, networks of Kuramoto and Rössler oscillators, to investigate how the interplay between dynamics and topology impacts the network observability. Based on the numerical results, we conjecture that, when the network nodal dynamics are heterogeneous, better observability is conveyed for sets of sensor nodes that share some dynamical affinity to its neighbourhood. Moreover, we also investigate how the choice of an internal measured variable of a multidimensional sensor node affects the PF performance. The PF framework effectiveness as an observability measure is compared with a well-consolidated nonlinear observability metric for a small network case and some chaotic system benchmarks.