Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

Collapse of spatiotemporal chaos

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.     

Transient activation in a network of coupled map neurons

The focus of this Letter is on the activity of a network of neurons pairwise coupled by inhibitory connections. Each neuron is represented by a two-dimensional map capable, when isolated, of a rich variety of complex dynamical regimes. It is shown that the network exhibits a stimulus-dependent sequential activation and inactivation of subgroups of neurons. This complex behavior is rather similar to some spatiotemporal features observed in the first stages of the olfaction process in some insects and suggests the possibility of large scale simulation of these processes by using reasonable computational capabilities.     

Scale-invariant structure of energy fluctuations in real earthquakes

Earthquakes are obviously complex phenomena associated with complicated spatiotemporal correlations, and they are generally characterized by two power laws: the Gutenberg-Richter (GR) and the Omori-Utsu laws. However, an important challenge has been to explain two apparently contrasting features: the GR and Omori-Utsu laws are scale-invariant and unaffected by energy or time scales, whereas earthquakes occasionally exhibit a characteristic energy or time scale, such as with asperity events. In this paper, three high-quality datasets on earthquakes were used to calculate the earthquake energy fluctuations at various spatiotemporal scales, and the results reveal the correlations between seismic events regardless of their critical or characteristic features. The probability density functions (PDFs) of the fluctuations exhibit evidence of another scaling that behaves as a q-Gaussian rather than random process. The scaling behaviors are observed for scales spanning three orders of magnitude. Considering the spatial heterogeneities in a real earthquake fault, we propose an inhomogeneous Olami-Feder-Christensen (OFC) model to describe the statistical properties of real earthquakes. The numerical simulations show that the inhomogeneous OFC model shares the same statistical properties with real earthquakes.     

Revealing the building blocks of spatiotemporal chaos: deviations from extensivity

We have performed high-precision computational studies of the fractal dimension as a function of system length for spatiotemporal chaotic states of the one-dimensional complex Ginzburg-Landau equation. Our data show deviations from extensivity on a length scale consistent with the chaotic length scale, indicating that this spatiotemporal chaotic system is composed of weakly interacting building blocks, each containing about 2 degrees of freedom. Our results also suggest an explanation of some of the "windows of periodicity" found in spatiotemporal systems of moderate size.     

A self-adapting image encryption algorithm based on spatiotemporal chaos and ergodic matrix

To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.     

Penta-hepta defect chaos in a model for rotating hexagonal convection

In a model for rotating non-Boussinesq convection with mean flow, we identify a regime of spatiotemporal chaos that is based on a hexagonal planform and is sustained by the induced nucleation of dislocations by penta-hepta defects. The probability distribution function for the number of defects deviates substantially from the usually observed Poisson-type distribution. It implies strong correlations between the defects in the form of density-dependent creation and annihilation rates of defects. We extract these rates from the distribution function and also directly from the defect dynamics.     

Lateral membrane waves constitute a universal dynamic pattern of motile cells

We have monitored active movements of the cell circumference on specifically coated substrates for a variety of cells including mouse embryonic fibroblasts and T cells, as well as wing disk cells from fruit flies. Despite having different functions and being from multiple phyla, these cell types share a common spatiotemporal pattern in their normal membrane velocity; we show that protrusion and retraction events are organized in lateral waves along the cell membrane. These wave patterns indicate both spatial and temporal long-range periodic correlations of the actomyosin gel.     

基于模糊模型的耦合时空混沌H_\infty$跟踪控制

由于子系统的时空耦合作用，实现耦合时空混沌的跟踪控制比较困难。然而模型未知的耦合时空混沌的子系统可由一系列模糊逻辑模型逼近，每个模糊逻辑模型代表子系统在特定运行点的局部线性化模型。基于该系列模糊模型，采用模糊跟踪控制方法实现了耦合时空混沌的模型参考跟踪控制，并用线性矩阵不等式的凸优化方法求解控制器参数，确保系统的全局渐近稳定性。仿真验证了方案的有效性。     

Optical manipulation of molecular function by chromophore-assisted light inactivation

In addition to simple on/off switches for molecular activity, spatiotemporal dynamics are also thought to be important for the regulation of cellular function. However, their physiological significance and in vivo importance remain largely unknown. Fluorescence imaging technology is a powerful technique that can reveal the spatiotemporal dynamics of molecular activity. In addition, because imaging detects the correlations between molecular activity and biological phenomena, the technique of molecular manipulation is also important to analyze causal relationships. Recent advances in optical manipulation techniques that artificially perturb molecules and cells via light can address this issue to elucidate the causality between manipulated target and its physiological function. The use of light enables the manipulation of molecular activity in microspaces, such as organelles and nerve spines. In this review, we describe the chromophore-assisted light inactivation method, which is an optical manipulation technique that has been attracting attention in recent years.     

Mutual spatiotemporal coherence of optical fields in an amplitude-splitting interferometer

We have considered cross correlations of wave perturbations formed by optical fields at different points of space at the exit of an interferometer with the splitting of the amplitude of the initial wave field. Expressions for the longitudinal spatiotemporal cross-correlation function of perturbations on the optical axis of a Michelson interferometer have been obtained and analyzed. We have determined spatial and temporal intervals in which the wave fields excite mutually coherent perturbations in the exit channel of the interferometer in the free space and in the image space of the lens system. We have found that, in the free space, mutually correlated perturbations arise simultaneously in identical longitudinal intervals, whereas, in the image space, they arise at different times in spatial and temporal intervals varying along the optical axis of the lens. The influence of cross correlations of the wave fields on the interferometer signal has been analyzed.

     

在空间-时间域测量飞秒脉冲

依据飞秒脉冲测量中的空间-时间耦合理论,通过采用空间分辨和光谱分辨在时间和空间域对飞秒脉冲强度和相位进行测量.测量装置主要由两个光学元件组成,实现了空间和光谱干涉.待测脉冲和参考脉冲通过一个绕中心轴转过某一角度的二维衍射光栅,产生倾斜的二维阵列全息图;一个带通滤波片对全息图进行分离,从而每个全息图含有一个唯一的频率.用照相机记录下所有的全息图,可以在时间和空间域再现出待测脉冲,并给出了测量结果. 关键词： 飞秒脉冲 时间-空间耦合 二维衍射光栅 带通滤光片     

Convective lyapunov exponents and propagation of correlations

We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatiotemporal chaos (the complex Ginzburg-Landau equation); (iii) experimental data taken from a CO2 laser with delayed feedback. In the last case, the convective Lyapunov exponent is determined directly from the experimental data.     

Concentration dependence of the collective dynamics of swimming bacteria

At concentrations near the maximum allowed by steric repulsion, swimming bacteria form a dynamical state exhibiting extended spatiotemporal coherence. The viscous fluid into which locomotive energy of individual microorganisms is transferred also carries interactions that drive the coherence. The concentration dependence of correlations in the collective state is probed here with a novel technique that herds bacteria into condensed populations of adjustable concentration. For the particular thin-film geometry employed, the correlation lengths vary smoothly and monotonically through the transition from individual to collective behavior.     

Spatiotemporal synchronization of coupled oscillators in a laboratory plasma

The spatiotemporal synchronization between two plasma instabilities of autonomous glow discharge tubes is observed experimentally. For this purpose, two tubes are placed separately and two chaotic waves interact with each other through a coupler. When the coupling strength is changed, the coupled oscillators exhibit synchronization in time and space. This is the first experimental evidence of spatiotemporal synchronization by mutual chaotic wave interaction in plasma.     

A hierarchical feature graph matching method for recognition of complex human activities

Complex human activities in natural videos are often composed of several atomic-level actions organized hierarchically. We should not only consider the appearance variability of these action units, but also model the spatiotemporal relationships between them when recognizing such high-level complex activities. In this paper, we focus on the problem of recognition of complex human activities in an example-based video retrieval framework and propose a new method based on hierarchical feature-graph matching. A video depicting an activity is represented as a high-level feature graph (HLFG), and each node of the HLFG is a mid-level feature graph (MLFG) constructed on a local collection of spatiotemporal interest points. MLFG, the first level of our two-level graph structure, describes the local feature contents and spatiotemporal arrangements of interest points. HLFG, the second level, describes the appearance variability and spatiotemporal arrangements of atomic-level actions in a way. Final recognition is accomplished by matching the HLFGs of the query and test videos, and matching two HLFGs involves matching the MLFGs between them. We use an efficient spectral method to solve these two graph-matching problems. Our method does not require any preprocessing and gives reasonable results with even a small number of query examples. We evaluate our approach with one publicly available complex human activity dataset and achieve results comparable to other systems that have studied this problem.     

Spatiotemporal antiphase dynamics in coupled extended optical media

Experimental evidence of spatiotemporal antiphase dynamics is given for an extended system made of two liquid crystal slices that are optically coupled by two equal amplitude counterpropagating pumping beams. Theory and experiments carried out in a transverse one-dimensional configuration show that roll patterns are generated in each slice. These rolls are spatially in-phase or antiphase for a focusing or a defocusing nonlinearity type, respectively. These in-phase or antiphase dynamics remain robust even for complex spatiotemporal regimes such as dislocation regimes.     

Highly efficient single-pass source of pulsed single-mode twin beams of light

We report the realization of a bright ultrafast type II parametric down-conversion source of twin beams free of any spatiotemporal correlations in a periodically poled KTiOPO4 (PP-KTP) waveguide. From a robust, single-pass setup it emits pulsed two-mode squeezed vacuum states: photon-number entangled pairs of single-mode pulses or, in terms of continuous variables quantum optics, pulsed Einstein-Podolsky-Rosen states in the telecom wavelength regime. We verify the single-mode character of our source by measuring Glauber correlation functions g(2) and demonstrate with a pump energy as low as 75 pJ per pump pulse a mean photon number of 2.5.     

One-way hash function construction based on the spatiotemporal chaotic system

Based on the spatiotemporal chaotic system,a novel algorithm for constructing a one-way hash function is proposed and analysed.The message is divided into fixed length blocks.Each message block is processed by the hash compression function in parallel.The hash compression is constructed based on the spatiotemporal chaos.In each message block,the ASCII code and its position in the whole message block chain constitute the initial conditions and the key of the hash compression function.The final hash value is generated by further compressing the mixed result of all the hash compression values.Theoretic analyses and numerical simulations show that the proposed algorithm presents high sensitivity to the message and key,good statistical properties,and strong collision resistance.     

Self-Organization in Coupled Map Scale-Free Networks

We study the self-organization of phase synchronization in coupled map scale-free networks with chaotic logistic map at each node and find that a variety of ordered spatiotemporal patterns emerge spontaneously in a regime of coupling strength. These ordered behaviours will change with the increase of the average finks and are robust to both the system size and parameter mismatch. A heuristic theory is given to explain the mechanism of self-organization and to figure out the regime of coupling for the ordered spatiotemporal patterns.