A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Irregular mixing due to a vortex pair interacting with a fixed vortex

The paper examines scalar advection caused by a point–vortex pair encountering a fixed point vortex in a uniform flow. The interaction produces two types of vortex motion. First is unbounded as the pair moves unrestrictedly after encountering the fixed vortex. The scalar exchanging between the pair's bubble and fixed vortex's neighbourhood is numerically estimated. Second is bounded as the pair's vortices periodically oscillate about the fixed vortex. The pair's periodic motion perturbs scalar motion causing a portion of scalar trajectories to manifest chaotic behaviour. We analyse scalar transport using Poincaré sections, which reveal regular and chaotic transport regions.     

Analog computation through high-dimensional physical chaotic neuro-dynamics

Conventional von Neumann computers have difficulty in solving complex and ill-posed real-world problems. However, living organisms often face such problems in real life, and must quickly obtain suitable solutions through physical, dynamical, and collective computations involving vast assemblies of neurons. These highly parallel computations through high-dimensional dynamics (computation through dynamics) are completely different from the numerical computations on von Neumann computers (computation through algorithms). In this paper, we explore a novel computational mechanism with high-dimensional physical chaotic neuro-dynamics. We physically constructed two hardware prototypes using analog chaotic-neuron integrated circuits. These systems combine analog computations with chaotic neuro-dynamics and digital computation through algorithms. We used quadratic assignment problems (QAPs) as benchmarks. The first prototype utilizes an analog chaotic neural network with 800-dimensional dynamics. An external algorithm constructs a solution for a QAP using the internal dynamics of the network. In the second system, 300-dimensional analog chaotic neuro-dynamics drive a tabu-search algorithm. We demonstrate experimentally that both systems efficiently solve QAPs through physical chaotic dynamics. We also qualitatively analyze the underlying mechanism of the highly parallel and collective analog computations by observing global and local dynamics. Furthermore, we introduce spatial and temporal mutual information to quantitatively evaluate the system dynamics. The experimental results confirm the validity and efficiency of the proposed computational paradigm with the physical analog chaotic neuro-dynamics.     

Duffing振子微弱信号检测方法的统计特性研究

利用混沌振子可以检测极其微弱的信号，并且具有很多优点，本文根据随机微分方程理论，通过对噪声经过Ｄｕｆｉｉｎｇ系统后统计特性的分析，确定了采用此方法检测的信噪改善比，从而为该方法的实际应用提供了指导，并且，本文针对周期系数线性微分方程的特点，提出了其输出统计特性的求法。     

A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

四相zcz序列的交织构造

为了弥补四相正交序列周期短的缺陷,将最佳四相正交序列应用于零相关区(ZCZ,Zero Correlation Zone)序列中,提出一种用交织法构建四相ZCZ序列的方法。首先选择合适的移位序列,经交织变换生成具有更长周期的ZCZ序列,再用正交矩阵将该序列进行扩展而得到新的序列集,实现了最佳四相正交序列和正交矩阵的结合。该方法构造的序列具有更大的周期和较大的容量,从而可以更好地在实际工程中加以利用。     

级联GMW序列的三项式特性

利用有限域上迹函数的性质,讨论了一类非线性扩频序列:级联GMW序列的三项式特性,即移位相加性。给出了此类序列的三项式时,并对级联GMW序列的性质作了一些讨论。     

A self-adaptive weighted affinity propagation clustering for key frames extraction on human action recognition

In this paper, we propose a novel approach for key frames extraction on human action recognition from 3D video sequences. To represent human actions, an Energy Feature (EF), combining kinetic energy and potential energy, is extracted from 3D video sequences. A Self-adaptive Weighted Affinity Propagation (SWAP) algorithm is then proposed to extract the key frames. Finally, we employ SVM to recognize human actions on the EFs of selected key frames. The experiments show the information including whole action course can be effectively extracted by our method, and we obtain good recognition performance without losing classification accuracy. Moreover, the recognition speed is greatly improved.