Complex network perspective on modelling chaotic systems via machine learning

Recent advances have demonstrated that a machine learning technique known as "reservoir computing" is a significantly effective method for modelling chaotic systems. Going beyond short-term prediction, we show that long-term behaviors of an observed chaotic system are also preserved in the trained reservoir system by virtue of network measurements. Specifically, we find that a broad range of network statistics induced from the trained reservoir system is nearly identical with that of a learned chaotic system of interest. Moreover, we show that network measurements of the trained reservoir system are sensitive to distinct dynamics and can in turn detect the dynamical transitions in complex systems. Our findings further support that rather than dynamical equations, reservoir computing approach in fact provides an alternative way for modelling chaotic systems.     

Complex network analysis in inclined oil--water two-phase flow

Complex networks have established themselves in recent years as being particularly suitable and flexible for representing and modelling many complex natural and artificial systems. Oil--water two-phase flow is one of the most complex systems. In this paper, we use complex networks to study the inclined oil--water two-phase flow. Two different complex network construction methods are proposed to build two types of networks, i.e. the flow pattern complex network (FPCN) and fluid dynamic complex network (FDCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used for identifying three inclined oil--water flow patterns. To investigate the dynamic characteristics of the inclined oil--water two-phase flow, we construct 48 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of the inclined oil--water two-phase flow. In this paper, from a new perspective, we not only introduce a complex network theory into the study of the oil--water two-phase flow but also indicate that the complex network may be a powerful tool for exploring nonlinear time series in practice.     

Complex network approach for recurrence analysis of time series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.     

Properties of wealth distribution in multi-agent systems of a complex network

We present a simple model for examining the wealth distribution with agents playing evolutionary games (the Prisoners’ Dilemma and the Snowdrift Game) on complex networks. Pareto’s power law distribution of wealth (from 1897) is reproduced on a scale-free network, and the Gibbs or log-normal distribution for a low income population is reproduced on a random graph. The Pareto exponents of a scale-free network are in agreement with empirical observations. The Gini coefficient of an ER random graph shows a sudden increment with game parameters. We suggest that the social network of a high income group is scale-free, whereas it is more like a random graph for a low income group.     

Koopman analysis of nonlinear systems with a neural network representation

The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields. The intrinsic complexity of their dynamics defies many existing tools based on individual orbits, while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits, which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator. However, it is difficult to identify and represent the most relevant eigenfunctions in practice. Here, combined with the Koopman analysis, a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems. By invoking the error minimization, a fundamental set of Koopman eigenfunctions are derived, which may reproduce the input dynamics through a nonlinear transformation provided by the neural network. The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.     

Characterization of water mobility and distribution in low- and intermediate-moisture food systems

The mechanism of water uptake in low moisture cereals and cookies has been studied by NMR relaxometry and solid imaging technology implemented on a low-resolution benchtop NMR spectrometer. A comparison between classical MRI and SPRITE imaging are also presented to highlight the benefits of each technology. The spin lattice (T(1)) and spin spin (T(2)) relaxation times, the 1D and 2D SPRITE imaging, were determined on Smacks, corn flakes, chocolate chips cookies, soft caramel candies with a chocolate crème filler, and corn starch/water systems. The Smacks and corn flakes were studied based on the soaking time in milk, and the results showed that T(1) and T(2) decreased in the first 20 sec of soaking and then increased with the soaking time. For Smacks stored at different relative humidity, T(1) decreased during the first day of storage and then was relatively constant over storage time indicating that the system reached an equilibrium. 1D SPRITE profiles indicated an increase in signal intensity over storage time for cookies in 58% RH. However, the moisture uptake was insignificant indicating that the water mobility (and not the amount of water) changed due to various chemical interactions in the system (hydrogen bonding, starch retrogradation, glassy/rubbery equilibrium). The T(1) and T(2) of corn starch/water systems decreased as the concentration in starch increased and temperature increased from 30 degrees C to 60 degrees C. However, for temperatures higher than 60 degrees C, the relaxation times increased showing more mobility and flexibility of the polymer chains during gelatinization.     

Acoustic attenuation analysis of network systems by using impedance matrix method

An impedance matrix method is proposed to predict the acoustic attenuation characteristics of network systems. The system may contain several silencer modules and each module may be composed of complex components such as multiply connected tubes, portions with any-shaped cross-section and dissipative parts. The technique of substructuring is adopted and the system is divided into several substructure modules. Three strategies: boundary element method (BEM), numerical point collocation approach and numerical mode matching technique are introduced and the impedance matrix of each module may be computed by a certain appropriate methodology according to the dimensions and geometry of the substructure. Impedance matrix synthesis is employed to obtain the resultant impedance matrix and then transmission loss may be calculated. All the calculation results are verified by experimental measurements and 3-D BEM predictions.     

照明光学系统照度分布的计算机模拟分析

本文阐述了照明光学系统与传统成像光学系统的区别，提出了几种计算照明光学系统照度分布的原理和方法，并给出了一个具体的利用计算机对投影照明光学系统照度分布的模拟分析方法和运算结果。     

An exponential distribution network

A complex network with an exponential distribution p(k)\propto\e^{{-\frac{k}{k_{c}}}}with k _c =3.50±0.02 is introduced and found to have assortative correlation k _i ⁿⁿ =B+qk _i (q>0) from numerical simulation.     

Complex power distribution analysis in plates covered with passive constrained layer damping patches

The vibration of a plate partially covered with a passive constrained layer damping (PCLD) patch is studied from an energetic point of view. The damped plate is excited by an acoustic plane wave. The study is done with a numerical two-dimensional multilayer plate model. Results of the present model are compared to those obtained with three-dimensional finite element models. It is shown that the present model gives accurate results, even for the layer's inner behavior. It is less expansive in terms of computational cost; hence, it can simulate efficiently the structure for higher frequencies. Mathematical formulas for complex mechanical power are presented, and the link with strain and kinetic energies and dissipated power is detailed. Both local and global complex power balance are established, and corresponding expressions for the discretized problem are formulated. Conservative and dissipative powers are studied for the PCLD damped plate. After a global balance analysis versus frequency, a local study has been carried out in order to quantify the relative contribution of the components of strain and stress tensors to the total strain energy and dissipated power; the individual layer's contributions is also investigated. The in-plane distributions of powers are mapped, showing the location where dissipative phenomenon occurs and where strain energy is stored. Finally, three criteria based on the previous power quantities are proposed in order to quantify the mechanical damping efficiency of the patch.     

Complex stock trading network among investors

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extract detailed information of each executed order for each trading day and demonstrate that the trade size distributions for different trading days exhibit power-law tails and that most of the estimated power-law exponents are well within the Lévy stable regime. Based on the records of order matching among investors, we can construct a stock trading network for each trading day, in which the investors are mapped into nodes and each transaction is translated as a direct edge from the seller to the buyer with the trade size as its weight. We find that all the trading networks comprise a giant component and have power-law degree distributions and disassortative architectures. In particular, the degrees are correlated with order sizes by a power-law function. By regarding the size of executed order as its fitness, the fitness model can reproduce the empirical power-law degree distribution.     

Complex dynamics in gelling systems

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical-mechanics model. The model is based on percolation and bond fluctuation dynamics. The values for the critical exponents of the viscosity and elasticity agree with a part of the experimental observations and of the theoretical predictions. The obtained relaxation patterns well reproduce the behaviour observed in different gelling systems. Received 10 March 2002 and Received in final form 30 April 2002     

Complex network study of Asian Go players

Tournaments of the game of Go can be represented as a directed network in which the vertices are players and a directed link is pointing from the winner to the loser for each game. In this article, we present some interesting results for the network of Asian Go players, which is composed of 756 Go players and 9473 tournaments. It is found that the topological structure of this network displays the small-world property and a significant rich-club phenomenon where high-degree nodes are tightly interconnected. In addition, we consider the weighted version of the network, and find the weights obey power-law distributions, while the strengths follow stretched exponential distributions. The time evolution of the network structure is studied and the corresponding results discussed. The analysis of this work provides a deeper understanding for the competition network structure of Asian Go players.     

Complex network perspective on structure and function of Staphylococcus aureus metabolic network

With remarkable advances in reconstruction of genome-scale metabolic networks, uncovering complex network structure and function from these networks is becoming one of the most important topics in system biology. This work aims at studying the structure and function of Staphylococcus aureus (S. aureus) metabolic network by complex network methods. We first generated a metabolite graph from the recently reconstructed high-quality S. aureus metabolic network model. Then, based on ‘bow tie’ structure character, we explain and discuss the global structure of S. aureus metabolic network. The functional significance, global structural properties, modularity and centrality analysis of giant strong component in S. aureus metabolic networks are studied.     

Degree distribution of random birth-and-death network with network size decline

In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network(RBDN) with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 p 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.     

Complex networks and banking systems supervision

Comprehensive and thorough supervision of all banking institutions under a Central Bank’s regulatory control has become necessary as recent banking crises show. Promptly identifying bank distress and contagion issues is of great importance to the regulators. This paper proposes a methodology that can be used additionally to the standard methods of bank supervision or the new ones proposed to be implemented. By this, one can reveal the degree of banks’ connectedness and thus identify “core” instead of just “big” banks. Core banks are central in the network in the sense that they are shown to be crucial for network supervision. Core banks can be used as gauges of bank distress over a sub-network and promptly raise a red flag so that the central bank can effectively and swiftly focus on the corresponding neighborhood of financial institutions. In this paper we demonstrate the proposed scheme using as an example the asset returns variable. The method may and should be used with alternative variables as well.     

Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization

We give an overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics and dynamics of series of blackouts with approximate global models. Blackout data from several countries suggest that the frequency of large blackouts is governed by a power law. The power law makes the risk of large blackouts consequential and is consistent with the power system being a complex system designed and operated near a critical point. Power system overall loading or stress relative to operating limits is a key factor affecting the risk of cascading failure. Power system blackout models and abstract models of cascading failure show critical points with power law behavior as load is increased. To explain why the power system is operated near these critical points and inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near a critical point and confirm this idea using a power system model. The slow evolution of the power system is driven by a steady increase in electric loading, economic pressures to maximize the use of the grid, and the engineering responses to blackouts that upgrade the system. Mitigation of blackout risk should account for dynamical effects in complex self-organized critical systems. For example, some methods of suppressing small blackouts could ultimately increase the risk of large blackouts.