Optimality properties and performance analysis of co-operative time-reversal communication in wireless sensor networks

The properties and performance of a technique, called time reversal, for co-operative communication on power-constrained wireless sensor networks are studied. A brief discussion of the optimality properties of this approach is presented, and performance is studied experimentally via a simulated indoor environment containing multiple wireless sensors. Using numerical simulation, the behaviour of the peak power received at a target sensor as a function of the number of co-operating transmitting sensors as well as the level of transmitted signal distortion and timing synchronisation errors, is studied. The simulation results demonstrate that, subject to some rather stringent synchronisation requirements, time reversal is an effective generalisation of beamforming that provides an efficient basis for co-operative communication on broadband multipath channels     

Mutually connected phase-locked loop networks: dynamical models and design parameters

Distribution of timing signals is an essential factor for the development of digital systems for telecommunication networks, integrated circuits and manufacturing automation. Originally, this distribution was implemented by using the master?slave architecture with a precise master clock generator sending signals to phaselocked loops (PLL) working as slave oscillators. Nowadays, wireless networks with dynamical connectivity and the increase in size and operation frequency of the integrated circuits suggest that the distribution of clock signals could be more efficient if mutually connected architectures were used. Here, mutually connected PLL networks are studied and conditions for synchronous states existence are analytically derived, depending on individual node parameters and network connectivity, considering that the nodes are nonlinear oscillators with nonlinear coupling conditions. An expression for the network synchronisation frequency is obtained. The lock-in range and the transmission error bounds are analysed providing hints to the design of this kind of clock distribution system.     

First-train timing synchronisation using multi-objective optimisation in urban transit networks

Missed transfers affect urban transportation by increasing the travel times and decreasing the travel possibility, especially in the case of longer headways. A synchronised timetable can improve the transport efficiency of urban mobility and become an important consideration in the operation of urban transit networks (UTN). A mixed integer programming model is proposed to generate an optimal train timetable and minimise the total connection time, which includes smooth synchronisations for rail first-trains and the seamless synchronisation from rail first-trains to the bus service. Meanwhile, to characterise the characteristics of first-trains, binary variables are used to denote key transfer directions. Subsequently, the Sub-network Connection Method in conjunction with Genetic Algorithm is designed to obtain near-optimal solutions in an efficient way. Finally, a real-world case study, 16 rail lines and 41 transfer stations, based on the Beijing metro network and travel demand is conducted to validate the proposed timetabling model. Preliminary numerical results show that our approach improves the synchronisation substantially compared with the currently operated timetable.     

地震激励邻接高层建筑的随机最优控制

采用控制设备联接相邻的高层建筑以降低其地震响应是一个切实有效的方法。基于随机动态规划原理与随机平均法,提出耦合相邻高层建筑的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型,再运用随机平均法导出关于模态能量的oIt随机微分方程,应用随机动态规划原理建立动态规划方程,由此可确定最优控制律。将结构的响应控制化为模态能量控制,缩减控制系统的维数。用高斯随机过程模拟地震激励,可计及其功率谱特性。数值结果表明该耦合结构随机最优控制方法的有效性。     

Periodic dynamics of coupled cell networks II: cyclic symmetry

A coupled cell network is a directed graph whose nodes represent dynamical systems and whose directed edges specify how those systems are coupled to each other. The typical dynamic behaviour of a network is strongly constrained by its topology. Especially important constraints arise from global (group) symmetries and local (groupoid) symmetries. The H/K theorem of Buono and Golubitsky characterises the possible spatio-temporal symmetries of time-periodic states of group-equivariant dynamical systems. A version of this theorem for group-symmetric networks has been proved by Josi? and Török. In networks, spatial symmetries correspond to synchrony of cells, and spatio-temporal symmetries correspond to phase relations between cells. Associated with any coupled cell network is a canonical class of admissible ODEs that respect the network topology. A pattern of synchrony or phase relations in a hyperbolic time-periodic state of such an ODE is rigid if the pattern persists under small admissible perturbations. We characterise rigid patterns of synchrony and rigid phase patterns in coupled cell networks, on the assumption that the periodic state is fully oscillatory (no cell is in equilibrium) and the network has a basic property, the rigid phase property. We conjecture that all networks have the rigid phase property, and that in any path-connected network an admissible ODE with a hyperbolic periodic state can always be perturbed to make the perturbed periodic state fully oscillatory. Our main result states that in any path-connected network with the rigid phase property, every rigid pattern of phase relations can be characterised in two stages. First, sets of cells form synchronous clumps according to a balanced equivalence relation. Second, the corresponding quotient network has a cyclic group of automorphisms, and the phase relations are induced by associating a fixed phase shift with a generator of this group. Thus the clumps of synchronous cells form a discrete rotating wave. As a corollary, we prove an analogue of the H/K theorem for any path-connected network. We also discuss the non-path-connected case.     

Towards an approach of synthesis,validation and implementation of distributed control for AMS by using events ordering relations

We study distributed control synthesis and validation for automated manufacturing systems (AMS) in the framework of supervisory control theory. To reduce the size of the control problem, we view an AMS as comprised of asynchronous subsystems which are coupled through imposed logical Boolean specifications. The principle of the distributed control approach is the decomposition of the global monolithic control action into local coordinated control strategies for the individual subsystems. Owing to its importance in a distributed scheme, the order in which events occur arouses interest. By extending our previous results, we develop a set of rules of events precedence ordering, under which the control strategy via decomposition promises the subsystems synchronisation and coordination. We show how these rules contribute to reduce the size of the controller models used in the verification/validation and implementation steps. The effectiveness of the proposed approach is demonstrated by means of an industrial AMS example.     

Cascaded synchronisation of multiple timedelay electro-optical semiconductor lasers

The authors report on cascaded synchronisation in coupled chaotic multiple time-delay electro-optical semiconductor lasers. The authors derive the existence and sufficient stability conditions for the synchronisation regimes. Analytical results are fully supported by numerical simulations. The results are important for chaosbased long-haul communication systems.     

Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit

Complex regulatory dynamics is ubiquitous in molecular networks composed of genes and proteins. Recent progress in computational biology and its application to molecular data generate a growing number of complex networks. Yet, it has been difficult to understand the governing principles of these networks beyond graphical analysis or extensive numerical simulations. Here the authors exploit several simplifying biological circumstances which thereby enable to directly detect the underlying dynamical regularities driving periodic oscillations in a dynamical nonlinear computational model of a protein?protein network. System analysis is performed using the cell cycle, a mathematically well-described complex regulatory circuit driven by external signals. By introducing an explicit time delay and using a `tearing-and-zooming? approach the authors reduce the system to a piecewise linear system with two variables that capture the dynamics of this complex network. A key step in the analysis is the identification of functional subsystems by identifying the relations between statevariables within the model. These functional subsystems are referred to as dynamical modules operating as sensitive switches in the original complex model. By using reduced mathematical representations of the subsystems the authors derive explicit conditions on how the cell cycle dynamics depends on system parameters, and can, for the first time, analyse and prove global conditions for system stability. The approach which includes utilising biological simplifying conditions, identification of dynamical modules and mathematical reduction of the model complexity may be applicable to other well-characterised biological regulatory circuits.     

Effective connectivity determines the critical dynamics of biochemical networks

Living systems comprise interacting biochemical components in very large networks. Given their high connectivity, biochemical dynamics are surprisingly not chaotic but quite robust to perturbations—a feature C.H. Waddington named canalization. Because organisms are also flexible enough to evolve, they arguably operate in a critical dynamical regime between order and chaos. The established theory of criticality is based on networks of interacting automata where Boolean truth values model presence/absence of biochemical molecules. The dynamical regime is predicted using network connectivity and node bias (to be on/off) as tuning parameters. Revising this to account for canalization leads to a significant improvement in dynamical regime prediction. The revision is based on effective connectivity, a measure of dynamical redundancy that buffers automata response to some inputs. In both random and experimentally validated systems biology networks, reducing effective connectivity makes living systems operate in stable or critical regimes even though the structure of their biochemical interaction networks predicts them to be chaotic. This suggests that dynamical redundancy may be naturally selected to maintain living systems near critical dynamics, providing both robustness and evolvability. By identifying how dynamics propagates preferably via effective pathways, our approach helps to identify precise ways to design and control network models of biochemical regulation and signalling.     

Bifurcations in dynamical systems with interior symmetry

We propose a definition of interior symmetry in the context of general dynamical systems. This concept appeared originally in the theory of coupled cell networks, as a generalization of the idea of symmetry of a network. The notion of interior symmetry introduced here can be seen as a special form of forced symmetry breaking of an equivariant system of differential equations. Indeed, we show that a dynamical system with interior symmetry can be written as the sum of an equivariant system and a ‘perturbation term’ which completely breaks the symmetry. Nonetheless, the resulting dynamical system still retains an important feature common to systems with symmetry, namely, the existence of flow-invariant subspaces. We define interior symmetry breaking bifurcations in analogy with the definition of symmetry breaking bifurcation from equivariant bifurcation theory and study the codimension one steady-state and Hopf bifurcations. Our main result is the full analogues of the well-known Equivariant Branching Lemma and the Equivariant Hopf Theorem from the bifurcation theory of equivariant dynamical systems in the context of interior symmetry breaking bifurcations.     

Graph theory and networks in Biology

A survey of the use of graph theoretical techniques in Biology is presented. In particular, recent work on identifying and modelling the structure of bio-molecular networks is discussed, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronisation and disease propagation.     

作大范围平动弹性梁的动力学性质

本文利用初始构形，中间构形和现时构形三种构形，给出了作大范围平动弹性结构的运动学描述方法，建立了作大范围平动弹性梁的刚－柔耦合动力学控制方程。利用Melnikov方法和数值仿真技术，讨论了作大范围平动弹性梁的全局分岔和混沌性质，通过分析表明，当大范围平动超过某一临界速度时，它对弹性结构动力学性质的影响有着决定性的作用。本文的研究将有利于柔性多体系统的刚－柔耦合动力学建模理论的发展。     

An entropic characterization of protein interaction networks and cellular robustness.

The structure of molecular networks is believed to determine important aspects of their cellular function, such as the organismal resilience against random perturbations. Ultimately, however, cellular behaviour is determined by the dynamical processes, which are constrained by network topology. The present work is based on a fundamental relation from dynamical systems theory, which states that the macroscopic resilience of a steady state is correlated with the uncertainty in the underlying microscopic processes, a property that can be measured by entropy. Here, we use recent network data from large-scale protein interaction screens to characterize the diversity of possible pathways in terms of network entropy. This measure has its origin in statistical mechanics and amounts to a global characterization of both structural and dynamical resilience in terms of microscopic elements. We demonstrate how this approach can be used to rank network elements according to their contribution to network entropy and also investigate how this suggested ranking reflects on the functional data provided by gene knockouts and RNAi experiments in yeast and Caenorhabditis elegans. Our analysis shows that knockouts of proteins with large contribution to network entropy are preferentially lethal. This observation is robust with respect to several possible errors and biases in the experimental data. It underscores the significance of entropy as a fundamental invariant of the dynamical system, and as a measure of structural and dynamical properties of networks. Our analytical approach goes beyond the phenomenological studies of cellular robustness based on local network observables, such as connectivity. One of its principal achievements is to provide a rationale to study proxies of cellular resilience and rank proteins according to their importance within the global network context.     

Combinatorial dynamics

Recently Stewart, Golubitsky and co-workers have formulated a general theory of networks of coupled cells. Their approach depends on groupoids, graphs, balanced equivalence relations and 'quotient networks'. We present a combinatorial approach to coupled cell systems. While largely equivalent to that of Stewart et al., our approach is motivated by ideas coming from analogue computers and avoids abstract algebraic formalism.     

邻接高耸结构的随机最优控制

文基于随机动态规划原理与随机平均法，提出耦合相邻高耸结构的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型，再运用随机平均法导出关于模态能量的It6随机微分方程，应用随机动态规划原理建立动态规划方程，由此可确定最优控制律。将结构的响应控制化为模态能量控制，缩减控制系统的维数。用高斯随机过程模拟地震激励，可计及其功率谱特性。数值结果表明该耦合结构控制方法的有效性。     

Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators

Systems of coupled oscillators may exhibit spontaneous dynamical formation of attracting synchronized clusters with broken symmetry; this can be helpful in modelling various physical processes. Analytical computation of the stability of synchronized cluster states is usually impossible for arbitrary nonlinear oscillators. In this paper we examine a particular class of strongly nonlinear oscillators that are analytically tractable. We examine the effect of isochronicity (a turning point in the dependence of period on energy) of periodic oscillators on clustered states of globally coupled oscillator networks. We extend previous work on networks of weakly dissipative globally coupled nonlinear Hamiltonian oscillators to give conditions for the existence and stability of certain clustered periodic states under the assumption that dissipation and coupling are small and of similar order. This is verified by numerical simulations on an example system of oscillators that are weakly dissipative perturbations of a planar Hamiltonian oscillator with a quartic potential. Finally we use the reduced phase-energy model derived from the weakly dissipative case to motivate a new class of phase-energy models that can be usefully employed for understanding effects such as clustering and torus breakup in more general coupled oscillator systems. We see that the property of isochronicity usefully generalizes to such systems, and we examine some examples of their attracting dynamics.     

Influencing factors of synchronization in manufacturing systems

Manufacturing systems exhibit two types of synchronisation phenomena: logistics and physics. Previous research has established synchronisation measures for both types and has shown that they are related to the due date performance. However, there is a lack of knowledge about the factors triggering synchronisation emergence as well as a holistic understanding of synchronisation effects on logistics performance. Thus, this research aims to further explore the relation between synchronisation, its influencing factors and its effect on logistics performance. Based on a profound literature review, we derive first hypotheses on the cause-and-effect-relationships between structural and dynamic properties of a manufacturing system and the emergence of logistics and physics synchronisation as well as logistics performance. By conducting a discrete-event simulation study on diverse manufacturing system types (line, flow shop and job shop production), we are able to test these hypotheses. We conclude that manufacturing network architecture as a structural property as well as processing time variability and system workload as dynamic properties may be exploited for an advanced and synchronisation-oriented manufacturing system design.     

Modelling hierarchical structure in functional brain networks

In this work, we focus on a complex-network approach for the study of the brain. In particular, we consider functional brain networks, where the vertices represent different anatomical regions and the links their functional connectivity. First, we build these networks using data obtained with functional magnetic resonance imaging. Then, we analyse the main characteristics of these complex networks, including degree distribution, the presence of modules and hierarchical structure. Finally, we present a network model with dynamical nodes and adaptive links. We show that the model allows for the emergence of complex networks with characteristics similar to those observed in functional brain networks.