ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 20 Sep 2024 14:23:32 GMT2024-09-20T14:23:32Z501291- Resonance effect of direction-phase clusters in a scale-free networkhttps://scholarbank.nus.edu.sg/handle/10635/115266Title: Resonance effect of direction-phase clusters in a scale-free network
Authors: Zhou, Y.; Zhou, J.; Wang, X.; Guan, S.; Lai, C.H.; Liu, Z.
Abstract: It is known that for chaotic flows, a weak coupling does not always make the coupled systems approach synchronization but sometimes makes them become more complicated (Phys. Rev. E, 67 (2003) 045203(R)). We here report that a similar situation also occurs in the coupled chaotic maps, where a weak coupling will make the number of direction-phase clusters Nc increase. We find a double-resonance effect on the coupling strength ε, where the first resonance comes from the coupling-induced periodic behaviors and the second one is due to the disappearance of the disorder phase. The mechanism of the second resonance is revealed through the out-of-phase links. Moreover, we show that the critical coupling εc of the maximum Nc will increase rapidly with the bifurcation parameter μ but slowly with the range of the distribution of non-identical oscillators. Copyright © EPLA, 2010.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152662010-01-01T00:00:00Z
- Spontaneous formation of dynamical groups in an adaptive networked systemhttps://scholarbank.nus.edu.sg/handle/10635/115294Title: Spontaneous formation of dynamical groups in an adaptive networked system
Authors: Li, M.; Guan, S.; Lai, C.-H.
Abstract: In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into two dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure that is characterized by strong intra-connections and weak inter-connections. Furthermore, the connection strengths follow a power-law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter-connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Tue, 19 Oct 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152942010-10-19T00:00:00Z
- Strange Nonchaotic Attractors in Random Dynamical Systemshttps://scholarbank.nus.edu.sg/handle/10635/115296Title: Strange Nonchaotic Attractors in Random Dynamical Systems
Authors: Wang, X.; Zhan, M.; Lai, C.-H.; Lai, Y.-C.
Abstract: The occurrence of strange nonchaotic attractors (SNA) in autonomous discrete-time maps and in periodically driven continuous-time systems was investigated. SNAs were shown to be induced by small noise in the systems. Results show that there exist open sets of finite areas in the two-dimensional parameter space for which the asymptotic attractor is strange. The physical relevance of SNAs was also discussed.
Fri, 20 Feb 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152962004-02-20T00:00:00Z
- Transition to global synchronization in clustered networkshttps://scholarbank.nus.edu.sg/handle/10635/116009Title: Transition to global synchronization in clustered networks
Authors: Guan, S.; Wang, X.; Lai, Y.-C.; Lai, C.-H.
Abstract: A clustered network is characterized by a number of distinct sparsely linked subnetworks (clusters), each with dense internal connections. Such networks are relevant to biological, social, and certain technological networked systems. For a clustered network the occurrence of global synchronization, in which nodes from different clusters are synchronized, is of interest. We consider Kuramoto-type dynamics and obtain an analytic formula relating the critical coupling strength required for global synchronization to the probabilities of intracluster and intercluster connections, and provide numerical verification. Our work also provides direct support for a previous spectral-analysis-based result concerning the role of random intercluster links in enhancing the synchronizability of a clustered network. © 2008 The American Physical Society.
Tue, 15 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1160092008-04-15T00:00:00Z
- The development of generalized synchronization on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/115980Title: The development of generalized synchronization on complex networks
Authors: Guan, S.; Wang, X.; Gong, X.; Li, K.; Lai, C.-H.
Abstract: In this paper, we numerically investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks. By adopting the auxiliary-system approach to networks, we observe that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical. We show that several factors, such as the network topology, the local dynamics, and the specific coupling strategies, can affect the development of GS on complex networks. © 2009 American Institute of Physics.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159802009-01-01T00:00:00Z
- Spurious synchronization in non-diagonally coupled identical Lorenz oscillatorshttps://scholarbank.nus.edu.sg/handle/10635/115943Title: Spurious synchronization in non-diagonally coupled identical Lorenz oscillators
Authors: He, D.; Zhan, M.; Lai, C.-H.
Abstract: It was reported in this Letter that spurious synchronization with positive transverse Lyapunov exponent (LE) can be realized between two non-diagonally coupled identical Lorenz oscillators. The possible reason for this rare phenomenon was revealed. Detection techniques of spurious synchronization region based on the distribution change of local transverse Lyapunov exponent were given. © 2004 Published by Elsevier B.V.
Mon, 14 Jun 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159432004-06-14T00:00:00Z
- Stability of the steady state of delay-coupled chaotic maps on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/115946Title: Stability of the steady state of delay-coupled chaotic maps on complex networks
Authors: Gong, X.; Guan, S.; Wang, X.; Lai, C.-H.
Abstract: We study the stability of the steady state of coupled chaotic maps with randomly distributed time delays evolving on a random network. An analysis method is developed based on the peculiar mathematical structure of the Jacobian of the steady state due to time-delayed coupling, which enables us to relate the stability of the steady state to the locations of the roots of a set of lower-order bound equations. For δ -distributed time delays (or fixed time delay), we find that the stability of the steady state is determined by the maximum modulus of the roots of a set of algebraic equations, where the only nontrivial coefficient in each equation is one of the eigenvalues of the normalized adjacency matrix of the underlying network. For general distributed time delays, we find a necessary condition for the stable steady state based on the maximum modulus of the roots of a bound equation. When the number of links is large, the nontrivial coefficients of the bound equation are just the probabilities of different time delays. Our study thus establishes the relationship between the stability of the steady state and the probability distribution of time delays, and provides a better way to investigate the influence of the distributed time delays in coupling on the global behavior of the systems. © 2008 The American Physical Society.
Tue, 20 May 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159462008-05-20T00:00:00Z
- Synchronization stability of general complex dynamical networks with time-varying delayshttps://scholarbank.nus.edu.sg/handle/10635/115963Title: Synchronization stability of general complex dynamical networks with time-varying delays
Authors: Li, K.; Guan, S.; Gong, X.; Lai, C.-H.
Abstract: The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2008 Elsevier B.V. All rights reserved.
Mon, 08 Dec 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159632008-12-08T00:00:00Z
- Synchronizability of network ensembles with prescribed statistical propertieshttps://scholarbank.nus.edu.sg/handle/10635/115962Title: Synchronizability of network ensembles with prescribed statistical properties
Authors: Guan, S.; Wang, X.; Li, K.; Wang, B.-H.; Lai, C.-H.
Abstract: It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature. © 2008 American Institute of Physics.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159622008-01-01T00:00:00Z
- The many faces of synchronization of networkshttps://scholarbank.nus.edu.sg/handle/10635/115990Title: The many faces of synchronization of networks
Authors: Guan, S.; Wang, X.; Li, K.; Lai, C.-H.
Abstract: Currently, synchronizability of networks is mainly studied in terms of the eigen ratio of the coupling matrix, which is a pure property of network topology. In this work, we clarify that although the eigen ratio is relevant to the possible range of coupling strength for achieving synchronization, it cannot fully determine the latter. The magnitude of the eigenvalues also plays a decisive role. We emphasize that synchronizability of networks is inherently related to the local dynamics on networks. It is not appropriate to discuss synchronizability of networks without considering the specific dynamics on them. For three typical types of local dynamics, we discuss the implication of synchronizability of networks. © 2009 World Scientific Publishing Company.
Tue, 30 Jun 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159902009-06-30T00:00:00Z
- Transition to amplitude death in scale-free networkshttps://scholarbank.nus.edu.sg/handle/10635/115336Title: Transition to amplitude death in scale-free networks
Authors: Liu, W.; Wang, X.; Guan, S.; Lai, C.-H.
Abstract: Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated both numerically and analytically. It is found that, as the coupling strength increases, the network will undergo three different stages in approaching the state of complete amplitude death (CAD). In the first stage of the transition, the amplitudes of the oscillators present a 'stair-like' arrangement, i.e. the squared amplitude of an oscillator linearly decreases with the number of links that the oscillator receives (node degree). In this stage, as the coupling strength increases, the amplitude stairs are eliminated hierarchically by descending order of the node degree. At the end of the first stage, except for a few synchronized oscillators, all other oscillators in the network have small amplitudes. Then, in the second stage of the transition, the synchronous clusters formed in the first stage gradually disappear and, as a consequence, the number of small-amplitude oscillators is increased. At the end of the second stage, almost all oscillators in the network have small but finite amplitudes. Finally, in the third stage of the transition, without the support of the synchronous clusters, the amplitudes of the oscillators are quickly decreased, eventually leading to the state of CAD. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Tue, 15 Sep 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1153362009-09-15T00:00:00Z
- A simple method to determine bond lengths and excited state surfaces from electronic-vibrational spectrahttps://scholarbank.nus.edu.sg/handle/10635/75486Title: A simple method to determine bond lengths and excited state surfaces from electronic-vibrational spectra
Authors: Lee, S.-Y.; Lai, C.-H.
Abstract: A fast and efficient method using the spectral moments of an electronic-vibrational spectrum is described to determine the harmonic and Morse potential fits to the excited state potential in the Franck-Condon region. Some of the drawbacks of the Franck-Condon least-squares fitting procedure are overcome by the moment method. The method is applied to some diatomics of current interest, spanning a wide range of bond length change in the electronic transition. The accuracy of the results suggests that the spectral moment method can be a replacement for the traditional and still popular Franck-Condon analysis. © 1990.
Fri, 23 Mar 1990 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/754861990-03-23T00:00:00Z
- Analysis of traffic flow on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/114996Title: Analysis of traffic flow on complex networks
Authors: Li, K.; Gong, X.; Guan, S.; Lai, C.-H.
Abstract: We propose a new routing strategy for controlling packet routing on complex networks. The delivery capability of each node is adopted as a piece of local information to be integrated with the load traffic dynamics to weight the next route. The efficiency of transport on complex network is measured by the network capacity, which is enhanced by distributing the traffic load over the whole network while nodes with high handling ability bear relative heavier traffic burden. By avoiding the packets through hubs and selecting next routes optimally, most travel times become shorter. The simulation results show that the new strategy is not only effective for scale-free networks but also for mixed networks in realistic networks. © 2011 World Scientific Publishing Company.
Wed, 20 Apr 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1149962011-04-20T00:00:00Z
- Onset of synchronization in weighted complex networks: The effect of weight-degree correlationhttps://scholarbank.nus.edu.sg/handle/10635/115215Title: Onset of synchronization in weighted complex networks: The effect of weight-degree correlation
Authors: Li, M.; Wang, X.; Fan, Y.; Di, Z.; Lai, C.
Abstract: By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and the node degree is also important to the network dynamics. © 2011 American Institute of Physics.
Fri, 01 Apr 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152152011-04-01T00:00:00Z
- Origin of chaotic transients in excitatory pulse-coupled networkshttps://scholarbank.nus.edu.sg/handle/10635/115219Title: Origin of chaotic transients in excitatory pulse-coupled networks
Authors: Zou, H.-L.; Li, M.; Lai, C.-H.; Lai, Y.-C.
Abstract: We develop an approach to understanding long chaotic transients in networks of excitatory pulse-coupled oscillators. Our idea is to identify a class of attractors, sequentially active firing (SAF) attractors, in terms of the temporal event structure of firing and receipt of pulses. Then all attractors can be classified into two groups: SAF attractors and non-SAF attractors. We establish that long transients typically arise in the transitional region of the parameter space where the SAF attractors are collectively destabilized. Bifurcation behavior of the SAF attractors is analyzed to provide a detailed understanding of the long irregular transients. Although demonstrated using pulse-coupled oscillator networks, our general methodology may be useful in understanding the origin of transient chaos in other types of networked systems, an extremely challenging problem in nonlinear dynamics and complex systems. © 2012 American Physical Society.
Fri, 21 Dec 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152192012-12-21T00:00:00Z
- Phase synchronization between two essentially different chaotic systemshttps://scholarbank.nus.edu.sg/handle/10635/115230Title: Phase synchronization between two essentially different chaotic systems
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: In this paper, we numerically investigate phase synchronization between two coupled essentially different chaotic oscillators in drive-response configuration. It is shown that phase synchronization can be observed between two coupled systems despite the difference and the large frequency detuning between them. Moreover, the relation between phase synchronization and generalized synchronization is compared with that in coupled parametrically different systems. In the systems studied, it is found that phase synchronization occurs after generalized synchronization in coupled essentially different chaotic systems. © 2005 The American Physical Society.
Fri, 01 Jul 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152302005-07-01T00:00:00Z
- Geometric phase induced by quantum nonlocalityhttps://scholarbank.nus.edu.sg/handle/10635/115124Title: Geometric phase induced by quantum nonlocality
Authors: Wang, Z.S.; Wu, C.; Feng, X.-L.; Kwek, L.C.; Lai, C.H.; Oh, C.H.; Vedral, V.
Abstract: By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior. © 2007 Elsevier B.V. All rights reserved.
Mon, 04 Feb 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151242008-02-04T00:00:00Z
- Formation of modularity in a model of evolving networkshttps://scholarbank.nus.edu.sg/handle/10635/115117Title: Formation of modularity in a model of evolving networks
Authors: Li, M.H.; Guan, S.G.; Lai, C.-H.
Abstract: Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of real social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks. © 2011 EPLA.
Thu, 01 Sep 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151172011-09-01T00:00:00Z
- Frequency locking by external force from a dynamical system with strange nonchaotic attractorhttps://scholarbank.nus.edu.sg/handle/10635/115118Title: Frequency locking by external force from a dynamical system with strange nonchaotic attractor
Authors: Guan, S.; Wang, X.; Lai, C.-H.
Abstract: Usually, phase synchronization is studied in chaotic systems driven by either periodic force or chaotic force. In the present work, we consider frequency locking in chaotic Rössler oscillator by a special driving force from a dynamical system with a strange nonchaotic attractor. In this case, a transition from generalized marginal synchronization to frequency locking is observed. We investigate the bifurcation of the dynamical system and explain why generalized marginal synchronization can occur in this model. © 2006 Elsevier B.V. All rights reserved.
Mon, 05 Jun 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151182006-06-05T00:00:00Z
- Public-key encryption based on generalized synchronization of coupled map latticeshttps://scholarbank.nus.edu.sg/handle/10635/53117Title: Public-key encryption based on generalized synchronization of coupled map lattices
Authors: Wang, X.; Gong, X.; Zhan, M.; Lai, C.H.
Abstract: Currently used public-key cryptosystems are based on difficulties in solving certain numeric theoretic problems, in which the way to predict the private key from the knowledge of the public key is computationally infeasible. Here we propose a method of constructing public-key cryptosystems by generalized synchronization of coupled map lattices, in which the difficulty in predicting the synchronous function is used as the trap-door function to deduce the private key from the public key. In specific, we implement this idea on the method of "Merkle's puzzles," and find that, incorporated with the chaotic dynamics, this traditional method is equipped with some new features and can be practical in certain situations. © 2005 American Institute of Physics.
Wed, 01 Jun 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531172005-06-01T00:00:00Z
- Spatially periodic and temporally chaotic pattern in coupled nonidentical chaotic systemshttps://scholarbank.nus.edu.sg/handle/10635/53183Title: Spatially periodic and temporally chaotic pattern in coupled nonidentical chaotic systems
Authors: Zhan, M.; Wang, X.; Gong, X.; Lai, C.-H.
Abstract: A particular spatio-temporal pattern, the spatially periodic and temporally chaotic pattern (SPTCP), can be observed in coupled one-way ring and linear array systems. This is a state chaotic in time while periodic in space in a strict sense. In this work, a driven system, of coupled nonidentical chaotic elements, which supports this structure is studied. We find that the appearance of the pattern is closely connected with the cascade of generalized synchronization in the ring. In particular, the establishment of the spatial periodicity of the SPTCP is determined by the condition that all of the coupled sites in the ring stay in the generalized synchronous state. © 2004 Elsevier Ltd. All rights reserved.
Sun, 01 May 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531832005-05-01T00:00:00Z
- Spread-spectrum communication using binary spatiotemporal chaotic codeshttps://scholarbank.nus.edu.sg/handle/10635/53187Title: Spread-spectrum communication using binary spatiotemporal chaotic codes
Authors: Wang, X.; Zhan, M.; Gong, X.; Lai, C.H.; Lai, Y.-C.
Abstract: We propose a scheme to generate binary code for baseband spread-spectrum communication by using a chain of coupled chaotic maps. We compare the performances of this type of spatiotemporal chaotic code with those of a conventional code used frequently in digital communication, the Gold code, and demonstrate that our code is comparable or even superior to the Gold code in several key aspects: security, bit error rate, code generation speed, and the number of possible code sequences. As the field of communicating with chaos faces doubts in terms of performance comparison with conventional digital communication schemes, our work gives a clear message that communicating with chaos can be advantageous and it deserves further attention from the nonlinear science community. © 2004 Elsevier B.V. All rights reserved.
Mon, 03 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531872005-01-03T00:00:00Z
- A spectral algorithm of community identificationhttps://scholarbank.nus.edu.sg/handle/10635/52763Title: A spectral algorithm of community identification
Authors: Gong, X.; Li, K.; Li, M.; Lai, C.-H.
Abstract: A novel spectral algorithm utilizing multiple eigenvectors is proposed to identify the communities in networks based on the modularity Q. We investigate the reduced modularity on low-rank approximations of the original modularity matrix consisting of leading eigenvectors. By exploiting the rotational invariance of the reduced modularity, near-optimal partitions of the network can be found. This approach generalizes the conventional spectral network partitioning algorithms which usually use only one eigenvector, and promises better results because more spectral information is used. The algorithm shows excellent performance on various real-world and computer-generated benchmark networks, and outperforms the most known community detection methods. Copyright © EPLA, 2013.
Fri, 01 Feb 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/527632013-02-01T00:00:00Z
- Chaotic digital communication by encoding initial conditionshttps://scholarbank.nus.edu.sg/handle/10635/52820Title: Chaotic digital communication by encoding initial conditions
Authors: Xiaofeng, G.; Xingang, W.; Meng, Z.; Lai, C.H.
Abstract: We investigate the possibility to improve the noise performance of a chaotic digital communication scheme by utilizing further dynamical information. We show that by encoding the initial information of the chaotic carrier according to the transmitting bits, extra redundance can be introduced into the segments of chaotic signals corresponding to the consecutive bits. Such redundant information can be exploited effectively at the receiver end to improve the noise performance of the system. Compared to other methods (e.g., differential chaos shift keying), straightforward application of the proposed modulation/demodulation scheme already provides significant performance gain in the low signal-to-noise ratio (SNR) region. Furthermore, maximum likelihood precleaning procedure based on the Viterbi algorithm can be applied before the demodulation step to overcome the performance degradation in the high SNR region. The study indicates that it is possible to improve the noise performance of the chaotic digital communication scheme if further dynamics information is added to the system. © 2004 American Institute of Physics.
Tue, 01 Jun 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/528202004-06-01T00:00:00Z
- Mechanistic modelling of viral spreading on empirical social network and popularity predictionhttps://scholarbank.nus.edu.sg/handle/10635/152067Title: Mechanistic modelling of viral spreading on empirical social network and popularity prediction
Authors: Ma S.; Feng L.; Lai C.-H.
Abstract: Online social networks are becoming major platforms for people to exchange opinions and information. While spreading models have been used to study the dynamics of spreading on social networks, the actual spreading mechanism on social networks may be different from these previous models due to users� limited attention and heterogeneous interests. The tractability of the spreading process in social networks allows us to develop a detailed and realistic model accounting for these factors. In addition, the empirical social networks have higher order correlations among node degrees, especially for directed networks like Twitter, that could affect the dynamics of spreading. Based on the analysis of the retweet process in the empirical Twitter network, we find both non-trivial correlations in network structures and non-standard spreading mechanisms for viral tweets. In particular, there is a strong evidence of information overload for retweeting behaviors that is not in line with the standard spreading model like the SIR (Susceptible, Infectious and Recovered) model, and can be described by a sublinear function. From these empirical findings, we introduce an intrinsic variable 揳ttractiveness� to the message, describing the overall propensity for any node to retweet the message, and present the analytical equations to solve such an empirical process, validated through numerical simulations. The results from our model is consistent with findings from the empirical Twitter data. Our analysis also indicates a close relationship between the spreading sub-network structure and the final popularity of the information, leading to a method to predict the popularity of tweets more accurately than existing models. � 2018, The Author(s).
Sat, 01 Dec 2018 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1520672018-12-01T00:00:00Z
- A coevolving model based on preferential triadic closure for social media networkshttps://scholarbank.nus.edu.sg/handle/10635/52745Title: A coevolving model based on preferential triadic closure for social media networks
Authors: Li, M.; Zou, H.; Guan, S.; Gong, X.; Li, K.; Di, Z.; Lai, C.-H.
Abstract: The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions-two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks. We thus proposed a coevolving dynamical model for such networks, in which the evolution is only driven by the local dynamics-the preferential triadic closure. Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/527452013-01-01T00:00:00Z
- Complete synchronization and generalized synchronization of one-way coupled time-delay systemshttps://scholarbank.nus.edu.sg/handle/10635/52836Title: Complete synchronization and generalized synchronization of one-way coupled time-delay systems
Authors: Zhan, M.; Wang, X.; Gong, X.; Wei, G.W.; Lai, C.-H.
Abstract: A study was conducted on complete synchronization (CS) and generalized synchronization (GS) of one-way coupled time delay systems. The synchronization of GS threshold for different delay times showed parameter resonance effect. It was found that desynchronization for both CS and GS identified with periodic bursts.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/528362003-09-01T00:00:00Z
- Phase synchronization of a pair of spiral waveshttps://scholarbank.nus.edu.sg/handle/10635/53089Title: Phase synchronization of a pair of spiral waves
Authors: Zhan, M.; Wang, X.; Gong, X.; Lai, C.-H.
Abstract: The interaction of a pair of spiral waves with different independent rotation frequencies is studied. In a very large frequency mismatch searching region, we observe three different pattern formation phenomena: (a) phase-synchronization-induced invasion under a relatively small frequency mismatch, i.e., the spiral wave with slower frequency (longer period) is swept away by a traveling wave, which is induced and phase synchronized by the faster spiral wave; (b) the coexistence of two spiral waves at sufficiently large parameter mismatch; and (c) an intermediate state, a non-phase-synchronous invasion, that is, similarly the slower spiral wave is swept by an approximate planar wave, whose frequency, however, is intermediate between those of the faster and slower waves. A point-source model is studied to analyze all these phenomena in a unified way. ©2005 The American Physical Society.
Tue, 01 Mar 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/530892005-03-01T00:00:00Z
- Optimal resource allocation for efficient transport on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/53072Title: Optimal resource allocation for efficient transport on complex networks
Authors: Gong, X.; Kun, L.; Lai, C.-H.
Abstract: The problem of efficient transport on a complex network is studied in this paper. We find that there exists an optimal way to allocate resources for information processing on each node to achieve the best transport capacity of the network, or the largest input information rate which does not cause jamming in network traffic, provided that the network structure and routing strategy are given. More interestingly, this achievable network capacity limit is closely related to the topological structure of the network, and is actually inversely proportional to the average distance of the network, measured according to the same routing rule. © Europhysics Letters Association.
Tue, 01 Jul 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/530722008-07-01T00:00:00Z
- Effects of a squeezed-vacuum reservoir on geometric phasehttps://scholarbank.nus.edu.sg/handle/10635/52894Title: Effects of a squeezed-vacuum reservoir on geometric phase
Authors: Wang, Z.S.; Wu, C.; Feng, X.-L.; Kwek, L.C.; Lai, C.H.; Oh, C.H.
Abstract: Geometric phase, for a two-level atom in an electromagnetic field interacting with a squeezed-vacuum reservoir, is calculated by establishing connecting density matrices, describing an evolution of a quantum open system, with a nonunit vector ray in a complex projective Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. The results show that the geometric phase for the squeezed-vacuum reservoir has fully different behavior in comparison with one for the normal vacuum reservoir. © 2007 The American Physical Society.
Thu, 15 Feb 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/528942007-02-15T00:00:00Z
- Evolution of functional subnetworks in complex systemshttps://scholarbank.nus.edu.sg/handle/10635/52922Title: Evolution of functional subnetworks in complex systems
Authors: Li, M.; Wang, X.; Lai, C.-H.
Abstract: Links in a realistic network may have different functions, which makes the network virtually a combination of some small-size functional subnetworks. Here, by a model of coupled phase oscillators, we investigate how such functional subnetworks are evolved and developed according to the network structure and dynamics. In particular, we study the case of evolutionary clustered networks in which the function type of each link (attractive or repulsive coupling) is adaptively updated according to the local network dynamics. It is found that during the process of system evolution, the network is gradually stabilized into a particular form in which the attractive (repulsive) subnetwork consists only of the intralinks (interlinks). Based on the observed properties of subnetwork evolution, we also propose a new algorithm for network partition which, compared with the conventional algorithms, is distinguished by its convenient operation and fast computing speed. © 2010 American Institute of Physics.
Thu, 30 Dec 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/529222010-12-30T00:00:00Z
- Simple driven maps as sensitive deviceshttps://scholarbank.nus.edu.sg/handle/10635/97924Title: Simple driven maps as sensitive devices
Authors: Zhou, C.; Lai, C.-H.
Abstract: Sensitive dependence of nonlinear systems on initial conditions or parameters can be useful in applications. We propose in this paper that bubbling behavior in simple driven symmetrical maps may be used as a working principle of sensitive devices. The system is stable when there is no input and displays bursting behavior when there is small input. The symmetrical property of the bursting pattern is very sensitive to the bias of the noisy inputs, which makes the system promising for detecting weak signals among noisy environment. ©1999 The American Physical Society.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979241999-01-01T00:00:00Z
- Some global properties and invariance of bundle metrics in the Kaluza-Klein schemehttps://scholarbank.nus.edu.sg/handle/10635/97971Title: Some global properties and invariance of bundle metrics in the Kaluza-Klein scheme
Authors: Oh, C.H.; Singh, K.; Lai, C.H.
Abstract: It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a "spliced" bundle with G × N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle. © 1988 American Institute of Physics.
Fri, 01 Jan 1988 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979711988-01-01T00:00:00Z
- Synchronization optimal networks obtained using local structure informationhttps://scholarbank.nus.edu.sg/handle/10635/98164Title: Synchronization optimal networks obtained using local structure information
Authors: Liang, F.-J.; Zhao, M.; Lai, C.H.
Abstract: In this paper, the networks with optimal synchronizability are obtained using the local structure information. In scale-free networks, a node will be coupled by its neighbors with maximal degree among the neighbors if and only if the maximal degree is larger than its own degree. If the obtained coupled networks are connected, they are synchronization optimal networks. The connection probability of coupled networks is greatly affected by the average degree which usually increases with the average degree. This method could be further generalized by taking into account the degree of next-nearest neighbors, which will sharply increase the connection probability. Compared to the other proposed methods that obtain synchronization optimal networks, our method uses only local structure information and can hold the structure properties of the original scale-free networks to some extent. Our method may present a useful way to manipulate the synchronizability of real-world scale-free networks. © 2012 Elsevier B.V. All rights reserved.
Thu, 01 Nov 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/981642012-11-01T00:00:00Z
- Synchronization of chaos via optimal parameter perturbation using short time series datahttps://scholarbank.nus.edu.sg/handle/10635/98162Title: Synchronization of chaos via optimal parameter perturbation using short time series data
Authors: Zhou, C.; Hou, Z.; Lai, C.-H.
Abstract: Some OGY based methods for synchronization of chaotic trajectories using small parameter perturbations rely heavily on the dynamical equations of systems. We present an alternative method for the synchronization of chaos via parameter perturbation using only time series data. Employing a very simple local model constructed from time series data, parameter perturbations necessary to achieve synchronization are easily obtained. Synchronization can be achieved even though the local model is very crude when using very short time series data.
Thu, 01 Jul 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/981621999-07-01T00:00:00Z
- Synchronization of chaotic maps by symmetric common noisehttps://scholarbank.nus.edu.sg/handle/10635/98163Title: Synchronization of chaotic maps by symmetric common noise
Authors: Lai, C.-H.; Zhou, C.
Abstract: Synchronization of identical chaotic systems subjected to common noise has been the subject of recent research. Studies on several chaotic systems have shown that the synchronization is actually induced by the nonzero mean of the noise, and symmetric noise with zero-mean cannot lead to synchronization. Here it is shown that synchronization can be achieved by zero-mean noise in some chaotic maps with large convergence regions.
Sat, 15 Aug 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/981631998-08-15T00:00:00Z
- Synchronization with positive conditional Lyapunov exponentshttps://scholarbank.nus.edu.sg/handle/10635/98165Title: Synchronization with positive conditional Lyapunov exponents
Authors: Zhou, C.; Lai, C.-H.
Abstract: Synchronization of chaotic systems may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov exponents reported in a recent paper [Phys. Rev. E 56, 2272 (1997)] is a combined result of the contracting region of the system and the finite precision in computer simulations.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/981651998-01-01T00:00:00Z
- Universal quantum computation with trapped ions in thermal motion by adiabatic passagehttps://scholarbank.nus.edu.sg/handle/10635/98529Title: Universal quantum computation with trapped ions in thermal motion by adiabatic passage
Authors: Feng, X.-L.; Wu, C.; Lai, C.H.; Oh, C.H.
Abstract: We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value. © 2008 The American Physical Society.
Thu, 26 Jun 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/985292008-06-26T00:00:00Z
- A wavelet method for the characterization of spatiotemporal patternshttps://scholarbank.nus.edu.sg/handle/10635/95703Title: A wavelet method for the characterization of spatiotemporal patterns
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: This paper introduces a wavelet-based method for the characterization of spatiotemporal patterns. Based on the wavelet multiresolution analysis, two wavelet indices, multiscale accumulative density (MAD) and multiscale accumulative change (MAC), are proposed for the characterization of the dynamics of the spatiotemporal patterns. Both indices are constructed by using orthogonal wavelet projection operators. The MAD is a measure of the spatial complexity of a pattern at a given time, whereas the MAC characterizes the spatial complexity of instantaneous change of the spatiotemporal patterns at a given time. The ratio of the MAD indices between the lowest and the highest scales reflects the order of coherence in a pattern. The time series of both MAD and MAC provide the dynamical information of morphological pattern evolutions. Numerical experiments based on the Cahn-Hilliard equation indicate that the proposed method is efficient for quantitatively characterizing the dynamics of the spatiotemporal patterns. © 2002 Published by Elsevier Science B.V.
Fri, 01 Mar 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/957032002-03-01T00:00:00Z
- Spinning braid-group representation and the fractional quantum Hall effecthttps://scholarbank.nus.edu.sg/handle/10635/97996Title: Spinning braid-group representation and the fractional quantum Hall effect
Authors: Ting, C.; Lai, C.H.
Abstract: The path-integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding number in the super-plane, we represent the braid-group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the hamiltonian, suggesting the possibility of spinning nonabelian anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as exact ground-state solutions to the respective hamiltonians associated to the braid-group representations. The energy gap of the quasi-excitation is also obtainable from this approach.
Fri, 01 Jan 1993 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979961993-01-01T00:00:00Z
- Spectral analysis on explosive percolationhttps://scholarbank.nus.edu.sg/handle/10635/97979Title: Spectral analysis on explosive percolation
Authors: Chung, N.N.; Chew, L.Y.; Lai, C.H.
Abstract: We study the spectral properties of the process of explosive percolation. In particular, we explore how the maximum eigenvalue of the adjacency matrix of a network which governs the spreading efficiency evolves as the density of connection increases. Interestingly, for networks with connectivity that grow in an explosive way, information spreading and mass transport are found to be carried out inefficiently. In the conventional explosive percolation models that we studied, the sudden emergences of large-scale connectivity are found to come with relatively lowered efficiency of spreading. Nevertheless, the spreading efficiency of the explosive model can be increased by introducing heterogeneous structures into the networks. © Copyright EPLA, 2013.
Fri, 01 Mar 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979792013-03-01T00:00:00Z
- The bifurcation characteristics of the generalized Lorenz equationshttps://scholarbank.nus.edu.sg/handle/10635/98247Title: The bifurcation characteristics of the generalized Lorenz equations
Authors: Yu, M.Y.; Zhou, C.T.; Lai, C.H.
Abstract: A graphical overview of the bifurcation characteristics of the generalized Lorenz equations obtained by Stenflo [Physica Scripta 53, 83 (1996)] for nonlinear acoustic gravity waves in a rotational system is presented.
Tue, 01 Oct 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/982471996-10-01T00:00:00Z
- Tailoring wavelets for chaos controlhttps://scholarbank.nus.edu.sg/handle/10635/98212Title: Tailoring wavelets for chaos control
Authors: Wei, G.W.; Zhan, M.; Lai, C.-H.
Abstract: A novel wavelet subspace approach to the control of chaotic dynamical systems is presented. Wavelets are used as a new efficient strategy for controlling nonlinear dynamics. The approach has potential applications to the control of other discrete and continuous dynamical systems, such as coupled map lattices, cellular automata, turbulence, and pattern formation.
Tue, 31 Dec 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/982122002-12-31T00:00:00Z
- Transition from interntittency to periodicity in lag synchronization in coupled Rössler oscillatorshttps://scholarbank.nus.edu.sg/handle/10635/98435Title: Transition from interntittency to periodicity in lag synchronization in coupled Rössler oscillators
Authors: Zhan, M.; Wei, G.W.; Lai, C.-H.
Abstract: The dynamical and statistical behavior of lag synchronization in two coupled self-sustained chaotic Rössler oscillators is reexamined. The lack of uniqueness in the conventional characterization of lag synchronization based on the similarity function has caused much skepticism about the existence of lag synchronization. We provide an evidence that the emergence of lag synchronization is associated with the transition from on-off intermittency to a periodic structure in the laminar phase distribution. © 2002 The American Physical Society.
Fri, 01 Mar 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/984352002-03-01T00:00:00Z
- Bifurcation structure and periodic orbits of the Lorenz equations in the Prandtl number spacehttps://scholarbank.nus.edu.sg/handle/10635/95870Title: Bifurcation structure and periodic orbits of the Lorenz equations in the Prandtl number space
Authors: Lai, C.H.; Zhou, C.T.; Yu, M.Y.
Abstract: The bifurcation structure and periodic orbits of the Lorenz system with the Prandtl number as the control parameter are investigated. It is shown that new bifurcation phenomena, both positive (forward) and inverse (backward) bifurcations, which do not appear together in the Rayleigh number space, can appear. The orbit characteristics in typical periodic windows are also studied. © World Scientific Publishing Company.
Fri, 20 Dec 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/958701996-12-20T00:00:00Z
- Controlling flow turbulencehttps://scholarbank.nus.edu.sg/handle/10635/96097Title: Controlling flow turbulence
Authors: Guan, S.; Zhou, Y.C.; Wei, G.W.; Lai, C.-H.
Abstract: This paper investigates the viability and effectiveness of using a technique developed for low-dimensional chaotic systems to control flow turbulence governed by the Navier-Stokes equations. By using a global pinning coupling strategy, we show that turbulence can be controlled to desirable time-varying target states, including a spatially extended periodic state and a turbulent one. Exponential convergence to the target state is found and the exponential rate scales linearly to the coupling strength. The linear scaling law breaks down when localized pinning control is applied. A wavelet multiscale technique is utilized for the characterization of both the effectiveness of the present control strategy and the inverse energy transfer in two-dimensional turbulence. © 2003 American Institute of Physics.
Sat, 01 Mar 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960972003-03-01T00:00:00Z
- Controlling complex networks: How much energy is needed?https://scholarbank.nus.edu.sg/handle/10635/96096Title: Controlling complex networks: How much energy is needed?
Authors: Yan, G.; Ren, J.; Lai, Y.-C.; Lai, C.-H.; Li, B.
Abstract: The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems. © 2012 American Physical Society.
Wed, 23 May 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960962012-05-23T00:00:00Z
- Improvement of the local prediction of chaotic time serieshttps://scholarbank.nus.edu.sg/handle/10635/96887Title: Improvement of the local prediction of chaotic time series
Authors: Xiaofeng, G.; Lai, C.H.
Abstract: In this paper we explore the effect of pseudofalse neighbor points, which are true neighbor points in the reconstructed attractor, but which are considered not suitable to be used when local methods are adopted to predict the chaotic time series. In our approach, the εp neighbor points are used to reduce the influence of the pseudofalse neighbor points, thereby improving the performance of the local prediction of the chaotic time series.
Mon, 01 Nov 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/968871999-11-01T00:00:00Z
- Network extreme eigenvalue: From mutimodal to scale-free networkshttps://scholarbank.nus.edu.sg/handle/10635/97312Title: Network extreme eigenvalue: From mutimodal to scale-free networks
Authors: Chung, N.N.; Chew, L.Y.; Lai, C.H.
Abstract: The extreme eigenvalues of adjacency matrices are important indicators on the influence of topological structures to the collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme eigenvalue have further authenticated its applicability to the study of network dynamics. However, the ensemble average of extreme eigenvalue has only been solved analytically up to the second order correction. Here, we determine the ensemble average of the extreme eigenvalue and characterize its deviation across the ensemble through the discrete form of random scale-free network. Remarkably, the analytical approximation derived from the discrete form shows significant improvement over previous results, which implies a more accurate prediction of the epidemic threshold. In addition, we show that bimodal networks, which are more robust against both random and targeted removal of nodes, are more vulnerable to the spreading of diseases. © 2012 American Institute of Physics.
Tue, 03 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973122012-01-03T00:00:00Z
- All entangled pure states violate a single Bell's inequalityhttps://scholarbank.nus.edu.sg/handle/10635/116214Title: All entangled pure states violate a single Bell's inequality
Authors: Yu, S.; Chen, Q.; Zhang, C.; Lai, C.H.; Oh, C.H.
Abstract: We show that a single Bell's inequality with two dichotomic observables for each observer, which originates from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin's theorem is proved in its most general form from which it follows that for pure states Bell's nonlocality and quantum entanglement are equivalent. © 2012 American Physical Society.
Wed, 19 Sep 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1162142012-09-19T00:00:00Z