Asynchronous and corrected-asynchronous finite difference solutions of PDEs on MIMD multiprocessors

A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent processes. Removing the synchronization constraint has the potential of speeding up the computation, while maintaining greater computation flexibility (e.g. differences in processors speed; differences in the data input to processors). We construct asynchronous (AS) finite difference schemes for the solution of PDEs by removing the synchronization constraint. We analyze the numerical properties of these schemes. Based on the analysis, we develop corrected-asynchronous (CA) finite difference schemes which are specifically constructed for an asynchronous processing. We present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although our discussion concentrates on the Euler scheme it should serve only as a sample, as it can be extended to other schemes and other PDEs.These schemes are implemented on the shared-memory multi-userSequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that synchronization penalty can be about 50% of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time-level, and with the problem dimension. The efficiency of the AS may reach 90% and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient but provides more accurate results for intermediate (non steady-state) values. The results show the potential of developing asynchronous finite deference schemes for steady-state as well as non steadystate problems.This research was partially supported by a grant from The Basic Research Foundation administrated by The Israel Academy of Sciences and Humanities.A reduced version of the paper was presented at the 4th SIAM Conference on Parallel Processing for Scientific Computing, Dec. 11–13, 1989, Chicago, USA.The work by this author was supported by research grant 337 of the Israeli National Council for Research and Development in the years 1990–1991.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NASI-18107 while the author was in residence at the Institute for Computer Applications in Sciences and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, USA.     

Inverse chaos synchronization between bidirectionally coupled variable multiple time delay systems

We make first report on inverse chaos synchronization between bidirectionally non-linearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model. The results are of certain importance in secure chaos-based communication systems.     

Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

Superluminal Signals and the Resolution of the Causal Paradox

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e₁, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e₁≠0. No standard experiment on relativity depends on e₁, but if accelerations are considered only e₁=0 remains possible. The causal paradox generated by superluminal signals (SLS) in the theory of relativity does not exist in the theory with e₁=0. The irrelevance of SLS for the Einstein, Podolsky and Rosen paradox is pointed out.     

Modulation of brain functional connectivity with manual acupuncture in healthy subjects: An electroencephalograph case studying

Manual acupuncture is widely used for pain treatment and stress control. Previous studies on acupuncture have shown its modulatory effects on functional connectivity associated with one or a few preselected brain regions. To investigate how manual acupuncture modulates the organization of functional networks at a whole-brain level, we acupuncture at ST36 of right leg to obtain electroencephalograph (EEG) signals. By coherence estimation, we determine the synchronizations between all pairwise combinations of EEG channels in three acupuncture states. The resulting synchronization matrices are converted into functional networks by applying a threshold, and clustering coefficients and path lengths are computed as a function of threshold. The results show that acupuncture can increase functional connections and synchronizations between different brain areas. For a wide range of threshold, the clustering coefficient during acupuncture and post-acupuncture period is higher than that during the pre-acupuncture control period, whereas characteristic path length is shorter. We provide further support for the presence of "small-world" network characteristics in functional networks by acupuncture. These preliminary results highlight the beneficial modulations of functional connectivity by manual acupuncture, which could contribute to the understanding of acupuncture effects on the entire brain, as well as the neurophysiological mechanisms underlying acupuncture. Moreover, the proposed method may be a useful approach to the further investigation of the complexity of patterns of interrelations between EEG channels.     

一类混沌神经网络的全局同步

研究了一类时滞混沌神经网络的全局同步问题.应用驱动-响应同步方法和线性矩阵不等式技术，给出了时滞混沌神经网络全局同步的充分条件和同步控制器设计方法，而且所得到的控制器易于实现.仿真示例验证了本文方法的有效性. 关键词： 混沌神经网络 同步 驱动-响应法 线性矩阵不等式     

注入半导体激光器混沌调制性能与内部相位键控编码方法研究

研究注入半导体激光混沌调制解调及其性能特性，提出外部光注入半导体激光器混沌内部相位编码方法. 小信号调制分析了系统混沌调制响应函数和解调响应函数以及解调因子，系统的调制解调响应函数以及解调因子在60MHz有一个峰值，系统在高频调制时，响应函数和解调因子明显下降. 理论推导出混沌调制解调方程，给出了小信号调制时的信息信号的解，数值分析出系统在低频有一个调制解调峰值，高频调制解调效果下降，但系统仍可以进行10⁹Hz频率调制解调. 数值模拟并证明了系统在较大的参数范围内都能实现同步，模拟了混沌调制速率200Mb/s和调制频率1.4GHz的保密通信应用. 还通过键控调制注入光的相位相移对激光混沌态进行了编码，通过同步与非同步进行混沌解码，数值模拟了具有调制速率10Mb/s的混沌相位键控编码通信应用. 关键词： 混沌 同步 激光器 相位     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

The impact of competing time delays in coupled stochastic systems

We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays at each element. We establish the scaling theory for the phase boundary of synchronization and for the steady-state fluctuations in the synchronizable regime. Further, we provide the asymptotic behavior near the boundary of the synchronizable regime. Our results also imply the potential for optimization and trade-offs in synchronization problems with time delays.