Emulating cellular automata in chemical reaction–diffusion networks

Chemical reactions and diffusion can produce a wide variety of static or transient spatial patterns in the concentrations of chemical species. Little is known, however, about what dynamical patterns of concentrations can be reliably programmed into such reaction–diffusion systems. Here we show that given simple, periodic inputs, chemical reactions and diffusion can reliably emulate the dynamics of a deterministic cellular automaton, and can therefore be programmed to produce a wide range of complex, discrete dynamics. We describe a modular reaction–diffusion program that orchestrates each of the fundamental operations of a cellular automaton: storage of cell state, communication between neighboring cells, and calculation of cells’ subsequent states. Starting from a pattern that encodes an automaton’s initial state, the concentration of a “state” species evolves in space and time according to the automaton’s specified rules. To show that the reaction–diffusion program we describe produces the target dynamics, we simulate the reaction–diffusion network for two simple one-dimensional cellular automata using coupled partial differential equations. Reaction–diffusion based cellular automata could potentially be built in vitro using networks of DNA molecules that interact via branch migration processes and could in principle perform universal computation, storing their state as a pattern of molecular concentrations, or deliver spatiotemporal instructions encoded in concentrations to direct the behavior of intelligent materials.     

Global exponential stability of delayed reaction–diffusion neural networks with time-varying coefficients

In the current paper, a class of general neural networks with time-varying coefficients, reaction–diffusion terms, and general time delays is studied. Several sufficient conditions guaranteeing its global exponential stability and the existence of periodic solutions are obtained through analytic methods such as Lyapunov functional and Poincaré mapping. The obtained results assume no boundedness, monotonicity or differentiability of activation functions and can be applied within a broader range of neural networks. Among the presented conditions, some are independent of time delay and expressed in terms of system parameters, so easy to verify and of leading significance in applications. For illustration, an example is given.     

A novel approach to calculate diffusion matrix in ternary systems: Application to Ag–Mg–Mn and Cu–Ni–Sn systems

Diffusion behavior is of fundamental importance in material science and engineering. As a result, extensive attention has been paid to develop methodologies for obtaining the composition-dependent interdiffusivities. The present work proposed a novel approach with two steps to extract the interdiffusion coefficients from a single ternary diffusion couple. The concept of basis function is introduced, and this novel method is based on the utilization of both finite element method and optimization algorithm. Utilizing eight groups of diffusion couples together with electron probe microanalysis technique, the composition-dependent interdiffusion coefficients in fcc Ag–Mg–Mn alloys at 973 and 1073 K were determined via both the present method and Matano-Kirkaldy method. A home-made code is written to implement the novel numerical approach. The obtained interdiffusion coefficients based on the present method agree with the reliable ones from the Matano-Kirkaldy method better than previous methods for fcc Ag–Mg–Mn alloys in the present work as well as fcc Cu–Ni–Sn alloys from the literature, especially for the main interdiffusivities. In most cases, the presently computed main interdiffusivities by means of the composition-dependent diffusivities agree with the reliable ones from the Matano-Kirkaldy method within 50%. Besides, the sign of cross interdiffusivities using this novel method is usually the same as that from the Matano-Kirkaldy method. Such a high calculation precision and efficiency cannot be obtained using previous methods.     

Global exponential robust stability of reaction–diffusion interval neural networks with continuously distributed delays

This paper considers the existence of the equilibrium point and its global exponential robust stability for reaction-diffusion interval neural networks with variable coefficients and distributed delays by means of the topological degree theory and Lyapunov-functional method. The sufficient conditions on global exponential robust stability established in this paper are easily verifiable. An example is presented to demonstrate the effectiveness and efficiency of our results.     

Hamiltonian perspective on compartmental reaction–diffusion networks

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction–diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for computer-based design, we offer a spatially consistent discretization of the PDE system and, in a systematic manner, recover a compartmental ODE model on a simplicial triangulation of the spatial domain. Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points. The paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction–diffusion networks.     

Synchronisation in an array of spatial diffusion coupled reaction–diffusion neural networks via pinning control

The authors investigate pinning synchronisation for two spatial diffusion coupled reaction–diffusion neural networks under undirected and directed topologies. Combined with stability theory, some inequalities and Lyapunov functional method, several sufficient conditions are derived to assure the synchronisation of the considered networks by designing appropriate pinning controllers. It should be pointed out that a new type of spatial diffusion feedback pinning controller is designed in this paper. The correctness of the obtained results is confirmed by two simulation examples.     

Dynamic protein–protein interaction networks construction using firefly algorithm

Protein–protein interaction (PPI) networks are dynamic in the real world. That is, at different times and under different conditions, the interaction among proteins may or may not be active. In different dataset, PPI networks might be gathered as static or dynamic networks. For the conversion of static PPI networks to time graphs, i.e., dynamic PPI networks, additional information like gene expression and gene co-expression profiles is used. One of the challenges in system biology is to determine appropriate thresholds for converting static PPI networks to dynamic PPI networks based on active proteins. In the available methods, fixed thresholds are used for all genes. However, the purpose of this study is to determine an adaptive unique threshold for each gene. In this study, the available additional information at different times and conditions and gold-standard protein complexes was employed to determine fitting thresholds. By so doing, the problem is converted into an optimization problem. Thereafter, the problem is solved using the firefly meta-heuristic optimization algorithm. One of the most remarkable aspects of this study is determining the attractiveness function in the firefly algorithm. In this study, attraction is defined as a combination of standard complexes and gene co-expressions. Then, active proteins are specified utilizing the created thresholds. The MCL, ClusterOne, MCODE and Coach algorithms are used for final evaluation. The experimental results about BioGRID dataset and CYC2008 gold-standard protein complexes indicated that the produced dynamic PPI networks by the proposed method have better results than the earlier methods.     

Passivity and synchronization of switched coupled reaction–diffusion neural networks with non-delayed and delayed couplings

ABSTRACT

This paper presents a general array model of switched coupled reaction–diffusion neural networks (CRDNNs) with non-delayed and delayed couplings. By utilizing some inequality techniques, we derive several sufficient conditions ensuring the input strict passivity and output strict passivity of the proposed network model. In addition, by constructing an appropriate Lyapunov functional, a sufficient condition is established in the form of linear matrix inequations to guarantee synchronization of CRDNNs with switched topology. Numerical examples with simulation results are provided to demonstrate the effectiveness and correctness of the obtained results.     

Hierarchical system identification of states and parameters in interconnected power systems†

This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input—output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.     

Exponential stability of impulsive high-order Hopfield-type neural networks with delays and reaction–diffusion

The problem of global exponential stability analysis of Impulsive high-order Hopfield-type neural networks with time-varying delays and reaction–diffusion terms has been investigated in this paper. Using the Lyapunov function method and M-matrix theory, we establish the global exponential stability of the neural networks with its estimated exponential convergence rate. As an illustration, a numerical example is given using the results.     

Computational networks and systems – homogenization of variational problems on micro-architectured networks and devices

Networked materials and micro-architectured systems gain increasingly importance in multi-scale physics and engineering sciences. Typically, computational intractable microscopic models have to be applied to capture the physical processes and numerous transmission conditions at singularities, interfaces and borders. The topology of the periodic microstructure governs the effective behaviour of such networked systems. A mathematical concept for the analysis of microscopic models on extremely large periodic networks is developed. We consider microscopic models for diffusion–advection–reaction systems in variational form on periodic manifolds. The global characteristics are identified by a homogenization approach for singularly perturbed networks with a periodic topology. We prove that the solutions of the variational models on varying networks converge to a two-scale limit function. In addition, the corresponding tangential gradients converge to a two-scale limit function for vanishing lengths of branches. We identify the variational homogenized model. Complex network models, previously considered as completely intractable, can now be solved by standard PDE-solvers in nearly no time. Furthermore, the homogenized coefficients provide an effective characterization of the global behaviour of the variational system.     

Input–output identification of controlled discrete manufacturing systems

The automated construction of discrete event models from observations of external system's behaviour is addressed. This problem, often referred to as system identification, allows obtaining models of ill-known (or even unknown) systems. In this article, an identification method for discrete event systems (DESs) controlled by a programmable logic controller is presented. The method allows processing a large quantity of observed long sequences of input/output signals generated by the controller and yields an interpreted Petri net model describing the closed-loop behaviour of the automated DESs. The proposed technique allows the identification of actual complex systems because it is sufficiently efficient and well adapted to cope with both the technological characteristics of industrial controllers and data collection requirements. Based on polynomial-time algorithms, the method is implemented as an efficient software tool which constructs and draws the model automatically; an overview of this tool is given through a case study dealing with an automated manufacturing system.     

Emerging production systems and industrial relations: Confusion,diffusion, and exclusion?

Although there is debate about emerging production systems, there is little analysis of their direct impact on traditional industrial relations. In this article the authors begin with an exploration of the literature on production systems and argue that there is confusion between the characteristics of, and distinctions between, emerging production systems. As companies diffuse their own production systems, there arises not only a great variety of models, but also a convergence of the principle characteristics of these production models. These are identified as teams, multiskilled workers, and management-initiated employee participation programs. These “new” production models might best be generically termed “lean team” systems, and the consequences for labor and unions are potentially significant. Drawing on research in Colgate-Palmolive, a multinational manufacturing company operating in Australia, one such production model is examined. It would appear that the consequences of the new production system for the union are complex and potentially responsible for their exclusion. © 1998 John Wiley & Sons, Inc.     

Study on diffusion and Kirkendall effect in diffusion triples for fcc Ni–Al–Ta alloys

In the present work based on two diffusion triples, the composition-dependent interdiffusivity matrices in the fcc Ni–Al–Ta alloys at 1373K and 1473K were efficiently deduced by using our newly developed two-dimensional (2D) inverse scheme. This scheme determines interdiffusivities from point and one-dimensional (1D) diffusion path to 2D composition region, yet requires much less experimental efforts, with the measured 2D composition profiles being well reproduced. Further, the interdiffusivities deduced from the inverse scheme were directly compared with those extracted by the traditional Sauer-Freise method and Whittle-Green method based on nine diffusion couples designed for verification. The interdiffusivities inferred from two distinct ways are fairly consistent, either at the binary boundaries or at the intersection points within the ternary composition range. Besides, the interdiffusion flux and the shift of the Kirkendall plane over the whole diffusion zone were simulated by applying the present 2D inverse scheme. The resulting 2D mapping presents a non-uniform but curved Kirkendall plane, which is in contrast to the flat shape generated in 1D diffusion couples and well explained by the calculated diffusion variables.     

Pinning dynamic systems of networks with Markovian switching couplings and controller–node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller–node set. Here, the coupling matrices and the controller–node sets change with time, induced by a continuous-time Markov chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponential stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller–node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable subsystems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.     

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

1 Introduction Presenting new identification methods and performance analysis of identification algorithms under weak conditions are everlasting themes and melodies of identification studies and are also my everlasting pursuits in life [1～4]. Multirate systems with different input and output sampling periods are very active in process industries [5～7], e.g. fermenta- tion processes [8], and petroleum production [9]. The stud- ies of multirate systems involve various areas of control, in- clu…     

Experimental measurement of diffusion coefficients and assessment of diffusion mobilities in HCP Mg–Li–Al alloys

An atomic mobility database was established for the ternary HCP Mg–Li–Al system as a part of an ongoing effort to enable rapid development of novel lightweight Mg alloys. Three sets of three diffusion couples were assembled and annealed at temperatures ranging from 400 to 500 °C. Li concentration profiles were measured using a combination of Auger electron spectroscopy (AES) and inductively coupled plasma optical emission spectrometry (ICP-OES), while Al composition profiles were acquired using electron probe microanalysis (EPMA). The forward-simulation analysis (FSA) was employed to extract both interdiffusion and impurity diffusion coefficients from the collected experimental composition profiles. These measured diffusivity data were used to assess and iteratively optimize mobility parameters for the Mg–Li–Al system using the diffusion module within the Thermo-Calc Software package (DICTRA). The reliability of the assessed mobility parameters was further confirmed by two validation diffusion couples that were annealed at 425 and 475 °C for 96 and 48 h, respectively. It was observed that additions of Li increased the diffusivity of Al in HCP Mg, whereas additions of Al decreased the diffusivity of Li in HCP Mg.     

Some computer-aided estimators in stochastic control systems identification†

A unified exposition of certain computer-aided statistical estimators for control systems identification is presented, together with some numerical results which show and compare the effectiveness of them     

Pinning exponential synchronisation and passivity of coupled delayed reaction–diffusion neural networks with and without parametric uncertainties

In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples.