A mutual information statistic for assessing state space partitions of dynamical systems.

We propose a mutual information statistic to quantify the information encoded by a partition of the state space of a dynamical system. We measure the mutual information between each point's symbolic trajectory history under a coarse partition (one with few unique symbols) and its partition assignment under a fine partition (one with many unique symbols). When applied to a set of test cases, this statistic demonstrates predictable and consistent behavior.

Recent achievements in nonlinear dynamics, synchronization, and networks.

This Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data.

Misinformation spreading on activity-driven networks with heterogeneous spreading rates.

The spread of misinformation on social media is inextricably related to each user's forwarding habits. In this paper, given that users have heterogeneous forwarding probabilities to their neighbors with varied relationships when they receive misinformation, we present a novel ignorant-spreader-refractory (ISR) spreading model with heterogeneous spreading rates on activity-driven networks with various types of links that encode these differential relationships. More exactly, in this model, the same type of links has an identical spreading rate, while different types of links have distinct ones.

Focus on the disruption of networks and system dynamics.

Networks are designed to ensure proper functioning and sustained operability of the underlying systems. However, disruptions are generally unavoidable. Internal interactions and external environmental effects can lead to the removal of nodes or edges, resulting in unexpected collective behavior.

Network Spreading from Network Dimension.

Continuous-state network spreading models provide critical numerical and analytic insights into transmission processes in epidemiology, rumor propagation, knowledge dissemination, and many other areas. Most of these models reflect only local features such as adjacency, degree, and transitivity, so can exhibit substantial error in the presence of global correlations typical of empirical networks. Here, we propose mitigating this limitation via a network property ideally suited to capturing spreading.

Mobility data shows effectiveness of control strategies for COVID-19 in remote, sparse and diffuse populations.

Data that is collected at the individual-level from mobile phones is typically aggregated to the population-level for privacy reasons. If we are interested in answering questions regarding the mean, or working with groups appropriately modeled by a continuum, then this data is immediately informative. However, coupling such data regarding a population to a model that requires information at the individual-level raises a number of complexities.

Reservoir computing with higher-order interactive coupled pendulums.

The reservoir computing approach utilizes a time series of measurements as input to a high-dimensional dynamical system known as a reservoir. However, the approach relies on sampling a random matrix to define its underlying reservoir layer, which leads to numerous hyperparameters that need to be optimized. Here, we propose a nonlocally coupled pendulum model with higher-order interactions as a novel reservoir, which requires no random underlying matrices and fewer hyperparameters.

Searching for Key Cycles in a Complex Network.

Searching for key nodes and edges in a network is a long-standing problem. Recently cycle structure in a network has received more attention. Is it possible to propose a ranking algorithm for cycle importance? We address the problem of identifying the key cycles of a network.

Ordinal Poincaré sections: Reconstructing the first return map from an ordinal segmentation of time series.

We propose a robust algorithm for constructing first return maps of dynamical systems from time series without the need for embedding. A first return map is typically constructed using a convenient heuristic (maxima or zero-crossings of the time series, for example) or a computationally nuanced geometric approach (explicitly constructing a Poincaré section from a hyper-surface normal to the flow and then interpolating to determine intersections with trajectories). Our method is based on ordinal partitions of the time series, and the first return map is constructed from successive intersections with specific ordinal sequences.

Correlation dimension in empirical networks.

Network correlation dimension governs the distribution of network distance in terms of a power-law model and profoundly impacts both structural properties and dynamical processes. We develop new maximum likelihood methods which allow us robustly and objectively to identify network correlation dimension and a bounded interval of distances over which the model faithfully represents structure. We also compare the traditional practice of estimating correlation dimension by modeling as a power law the fraction of nodes within a distance to a proposed alternative of modeling as a power law the fraction of nodes at a distance.

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology.

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag.

Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics.

The ongoing COVID-19 pandemic has inflicted tremendous economic and societal losses. In the absence of pharmaceutical interventions, the population behavioral response, including situational awareness and adherence to non-pharmaceutical intervention policies, has a significant impact on contagion dynamics. Game-theoretic models have been used to reproduce the concurrent evolution of behavioral responses and disease contagion, and social networks are critical platforms on which behavior imitation between social contacts, even dispersed in distant communities, takes place.

A tighter generalization bound for reservoir computing.

While reservoir computing (RC) has demonstrated astonishing performance in many practical scenarios, the understanding of its capability for generalization on previously unseen data is limited. To address this issue, we propose a novel generalization bound for RC based on the empirical Rademacher complexity under the probably approximately correct learning framework. Note that the generalization bound for the RC is derived in terms of the model hyperparameters.

Multiple Sensors Data Integration for Traffic Incident Detection Using the Quadrant Scan.

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss in productivity, and driver frustration. Traffic incidents are one of the six causes of non-recurrent congestion. Early and accurate detection helps reduce incident duration, but it remains a challenge due to the limitation of current sensor technologies.

Reservoir time series analysis: Using the response of complex dynamical systems as a universal indicator of change.

We present the idea of reservoir time series analysis (RTSA), a method by which the state space representation generated by a reservoir computing (RC) model can be used for time series analysis. We discuss the motivation for this with reference to the characteristics of RC and present three ad hoc methods for generating representative features from the reservoir state space. We then develop and implement a hypothesis test to assess the capacity of these features to distinguish signals from systems with varying parameters.

Link prediction for long-circle-like networks.

Link prediction is the problem of predicting the uncertain relationship between a pair of nodes from observed structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observation of exemplars. Existing local and quasilocal link prediction algorithms with low computational complexity focus on regular complex networks with sufficiently many closed triangular motifs or on tree-like networks with the vast majority of open triangular motifs.

Characterisation of neonatal cardiac dynamics using ordinal partition network.

The maturation of the autonomic nervous system (ANS) starts in the gestation period and it is completed after birth in a variable time, reaching its peak in adulthood. However, the development of ANS maturation is not entirely understood in newborns. Clinically, the ANS condition is evaluated with monitoring of gestational age, Apgar score, heart rate, and by quantification of heart rate variability using linear methods.

Epidemic dynamics on higher-dimensional small world networks.

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension.

Grading your models: Assessing dynamics learning of models using persistent homology.

Assessing model accuracy for complex and chaotic systems is a non-trivial task that often relies on the calculation of dynamical invariants, such as Lyapunov exponents and correlation dimensions. Well-performing models are able to replicate the long-term dynamics and ergodic properties of the desired system. We term this phenomenon "dynamics learning.

Consistency Hierarchy of Reservoir Computers.

We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as reservoir computers. Through different combinations of repeated input signals, a multivariate correlation analysis reveals measures known as the consistency spectrum and consistency capacity. These are high-dimensional portraits of the nonlinear functional dependence between input and reservoir state.

Modelling Strong Control Measures for Epidemic Propagation With Networks-A COVID-19 Case Study.

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions. Contact between individuals in the community is characterised by a contact graph, the structure of that contact graph is selected to mimic community control measures.

Revisiting the memory capacity in reservoir computing of directed acyclic network.

Reservoir computing (RC) is an attractive area of research by virtue of its potential for hardware implementation and low training cost. An intriguing research direction in this field is to interpret the underlying dynamics of an RC model by analyzing its short-term memory property, which can be quantified by the global index: memory capacity (MC). In this paper, the global MC of the RC whose reservoir network is specified as a directed acyclic network (DAN) is examined, and first we give that its global MC is theoretically bounded by the length of the longest path of the reservoir DAN.