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. For multiple inputs, a hierarchy of capacities characterizes the interference of signals from each source. For an individual input, the time-resolved capacities form a profile of the reservoir's nonlinear fading memory. We illustrate this methodology for a range of echo state networks.

Compared with traditional models, semi-random epidemic network models may be more reasonable to describe the real dynamics of many epidemics. In this paper, we first investigate the optimal control problem (OCP) of semi-random epidemic networks. By using the Pontryagin's minimum principle, we obtain the optimal control strategy aimed to minimize the total epidemic incidence and control cost. We then define a centrality index which can measure average control strength of the optimal control. Based on this index, the OCP is converted into a static OCP (SOCP), whose solution is utilized to design a nonidentical constant control (NCC). NCC is suboptimal as it is optimal on a subset of the whole control set, and is determined by only the network's clustering coefficient and initial condition. We finally propose an effective targeted constant quarantine control by using this centrality index. The results uncover the relationship between the optimal control and the network's topological structure, provide a convenient method to determine suboptimal control, and present a strategy for targeted constant control. This paper can help to design effective control strategies for more general epidemic networks in the real world.

We investigate the capacity of reservoir computers to reconstruct the dynamics of a network of chaotic oscillators via the observation of its multivariate time series. The reservoir is itself a structured echo-state network which receives the current observations as inputs, and is trained to produce the next observations as outputs. We study the performance of this scheme and its dependence on the separation of the inputs, modularity of the reservoir network, and observability of the system. We observe optimal performance with a segregated input structure and extremely modular network.

Engineered transport networks occur in many domains: road networks, power grids, the internet and utility distribution. Such networks present a generic problem — how does one model and predict failure of components within them? In this paper we will use the example of a metropolitan water distribution network to model and predict failure based on topology, topological network distance, and spatial-temporal geographical distance. We show that certain topologies are either more or less likely to fail than chance, and that co-occurrence of failure within certain geographical distances can be reliably modelled and predicted in certain specific circumstances.

The ordinal network construction method was proposed at ISCAS2013. Since then a great deal of theoretical and experimental work has developed these methods to the point where they can be applied as a diagnostic tool to understand changing system behaviour from observed time series. We now also have a solid theoretical understanding of what these methods measure and why this is useful. This talk will review the method and demonstrate its application to computation and experimental systems with the aim of detecting changes or bifurcations in the underlying system. We will conclude with applications to biosignal processing for cardiac interbeat interval time series and electroencephalograms.

This paper proposes a load-oriented control parameter optimization strategy for static synchronous compensator (STATCOM) to enhance low-frequency oscillation damping (LFOD) and improve stability of overall complex power systems. Frequency deviations of generators of interest are employed as the input signals of the designed supplementary damping controller of STATCOM. In order to obtain the optimal load-oriented control parameters, a day-ahead load-forecasting scheme is devised, using artificial neural network (ANN) learning techniques. The ANN is trained by a set of data over a 4-year period, and then the control parameters are optimized using Particle Swarm Optimization technique by minimizing the critical damping index. The proposed control strategy is implemented in the IEEE standard complex power system, and the numerical results demonstrate that the low-frequency oscillations (LFOs) of the power system can be effectively mitigated using the proposed controller. Compared to conventional robust controller with universal parameters, this novel load-oriented optimal control strategy shows its superiority in alleviating LFOs and enhancing the overall stability of the power system. Since the proposed control scheme aims to adaptively adjust the controller parameters in correspondence to load variations, this study is envisaged to have practical utilizations in industrial applications.

Many real world complex systems naturally map to network data structures instead of geometric spaces because the only available information is the presence or absence of a link between two entities in the system. To enable data mining techniques to solve problems in the network domain, the nodes need to be mapped to a geometric space. We propose this mapping by representing each network node with its geodesic distances from all other nodes. The space spanned by the geodesic distance vectors is the geodesic space of that network. The position of different nodes in the geodesic space encode the network structure. In this space, considering a continuous density field induced by each node, density at a specific point is the summation of density fields induced by all nodes. We drift each node in the direction of positive density gradient using an iterative algorithm till each node reaches a local maximum. Due to the network structure captured by this space, the nodes that drift to the same region of space belong to the same communities in the original network. We use the direction of movement and final position of each node as important clues for community membership assignment. The proposed algorithm is compared with more than 10 state-of-the-art community detection techniques on two benchmark networks with known communities using Normalized Mutual Information criterion. The proposed algorithm outperformed these methods by a significant margin. Moreover, the proposed algorithm has also shown excellent performance on many real-world networks.

Information mining from networks by identifying communities is an important problem across a number of research fields including social science, biology, physics, and medicine. Most existing community detection algorithms are graph theoretic and lack the ability to detect accurate community boundaries if the ratio of intra-community to inter-community links is low. Also, algorithms based on modularity maximization may fail to resolve communities smaller than a specific size if the community size varies significantly. We propose a fundamentally different community detection algorithm based on the fact that each network community spans a different subspace in the geodesic space. Therefore, each node can only be efficiently represented as a linear combination of nodes spanning the same subspace (Fig. 1). To make the process of community detection more robust, we use sparse linear coding with ł1 norm constraint. In order to find a community label for each node, sparse spectral clustering algorithm is used. The proposed community detection technique is compared with more than ten state of the art methods on two benchmark networks (with known clusters) using normalized mutual information criterion. Our proposed algorithm outperformed existing methods with a significant margin on both benchmark networks.

Information mining from networks by identifying communities is an important problem across a number of research fields including social science, biology, physics, and medicine. Most existing community detection algorithms are graph theoretic and lack the ability to detect accurate community boundaries if the ratio of intra-community to inter-community links is low. Also, algorithms based on modularity maximization may fail to resolve communities smaller than a specific size if the community size varies significantly. In this paper, we present a fundamentally different community detection algorithm based on the fact that each network community spans a different subspace in the geodesic space. Therefore, each node can only be efficiently represented as a linear combination of nodes spanning the same subspace. To make the process of community detection more robust, we use sparse linear coding with l1norm constraint. In order to find a community label for each node, sparse spectral clustering algorithm is used. The proposed community detection technique is compared with more than 10 state of the art methods on two benchmark networks (with known clusters) using normalized mutual information criterion. Our proposed algorithm outperformed existing algorithms with a significant margin on both benchmark networks. The proposed algorithm has also shown excellent performance on three real-world networks.

Evidence of complex networks in real world settings abounds. Many data sets for physical and social systems display characteristics consistent with various models of complex networks - the most typical examples being scale-free and small-world networks. However, theory does not always match reality. While we see a wide range of real complex networks, simulated data most usually comes from a limited range of generative models (the Barabási-Albert model for scale-free networks, Watt-Strogatz's model for small world networks, and Erdos-Renyi's model of a random graph are the three usual archetypes). We argue that there is much to be learnt by examining what real world data does that these algorithms do not. To do this we propose a variety of new network generation algorithms. These algorithms allow us to sample, in a statistically unbiased manner, from the family of all networks (of a given size N) consistent with a given degree distribution. Using this technique we are able to determine which distributions really are likely origins for various observed data and (equally importantly) observe when particular real world networks are atypical. Examples include the observation that many collaboration networks are not consistent with the Barabási-Albert (BA) model but are typical of the family of graphs that exhibit a power-law degree distribution, Biological networks (protein-protein interaction and cellular metabolic processes) are scale-free (but not BA) networks with atypically large diameter.

Although it is believed that many animals tend to move together as group motion has greater benefit, until now we know only a little on how individuals interact with their neighbors. In this study, we build a directed social network for large herbivores motion based on a complex network analysis framework. By calculating the basic statistics of the two networks (for two interacting species), such as reciprocity coefficient, average path length, clustering coefficient and assortativity coefficient, we find that the induced complex interaction networks (for large herbivores) have the famous “small-world” property. Moreover, our results indicate that large herbivores (deer and sheep) have a surprising long term memory of interaction relationships and their interaction preference is stable. While we focus our attention on interacting herbivores, the methods we introduce here are expected to be applicable to multi-agent systems more generally, and also to inform the development of theoretical multi-agent models - popular in engineering applications.

There are now several algorithms with which one can generate a complex network representation of a time series. The basic motivation of these methods is that by performing such a transformation one can then apply a range of techniques from complex network science to the analysis and quantification of features of the time series. We will review our favorites among these techniques and then focus on what the current techniques do not do well - capture deterministic dynamical information directly. We will propose an alternative technique, the ordinal partition network transform, to do precisely this. By constructing networks from connectivity patterns among ordinal partitions of the time series we provide a parameter-free approach to study the dynamical evolution of the system directly. We show that the ordinal networks generated in this way from experimental time series data have statistical properties which provide a useful (and novel) characterisation of the underlying system.

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred.

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.

Topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology. Different from recent similar works in which the evolution of all the nodes in a complex network need to be received, this brief presents a novel criterion to identify the topology of a coupled FitzHugh-Nagumo (FHN) neurobiological network by receiving the membrane potentials of only a fraction of the neurons. Meanwhile, although incomplete information is received, the evolution of all the neurons including membrane potentials and recovery variables are traced. Based on Schur complement and Lyapunov stability theory, the exact weight configuration matrix can be estimated by a simple adaptive feedback control. The effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies.

Feeling the pulse on the wrist is the regular diagnostic method in traditional Chinese medicine. However it is natural to ask whether there is any difference between feeling the pulse on the wrist or at any other part of the body: such as the fingertips at which it is easily measured by electronic devices. We employ a series of neural networks to model blood pressure propagation from the wrist to the fingertip. In order to avoid the problem of over-fitting we apply information theoretic criterion to determine the optimal model in these networks and then apply surrogate data method to the residuals in this model. We demonstrate the application of this method to recordings of human pulse in six subjects. Our result indicates that there is no significant difference between pulse waveform measure on the lateral arterial artery (wrist) and at the fingertip.

Intra-day measurements of three time series (DJIA, gold fixings and USD-JPY exchange rates) are examined for evidence of deterministic nonlinear dynamics. Standard linear surrogate techniques and estimation of dynamic invariants demonstrate that linear noise models are insufficient to explain dynamic variability in intra-day returns. Therefore, the data may not be modeled as a monotonic nonlinear transformation of linearly filtered noise. Furthermore, a new nonlinear surrogate technique is employed to demonstrate that conditional heteroskedastic models are also insufficient to model this data. We conclude that the most likely model of the data is a nonlinear dynamical system driven by high dimensional dynamics (noise).