Definition and Empirical Characterization of Creative Processes

Creative processes exhibit a new, thus far unrecognized, form of dynamical behavior distinct from the known classes of mechanical and chaotic dynamics. We present quantitative methods of time series analysis that distinguish creative processes from random and chaotic systems. Creative processes exhibit diversification, indicating an expanding phase space volume, which contrasts with processes that converge to equilibrium, or to periodic or chaotic attractors. Creative processes exhibit novelty, that is, they produce less recurrence than obtains from random series. Creative processes exhibit arrangement, a measure of patterned recurrences that indicates nonrandom complexity. These three measures, diversification, novelty, and arrangement, reliably identify creative dynamics and distinguish creativity from chaos and from randomness.     

Psychophysiology,Cortical Arousal and Dynamical Complexity (DCX)

Recent studies in brain dynamics have utilized a dependent variable calculated from the electroencephalogram (EEG) known as dimensional complexity (DC _x ), where variables such as scalp locus, cognitive task difficulty, or cortical arousal, are manipulated to test quantitative hypotheses regarding brain-state changes. The technique has been criticised on technical and theoretical grounds, yet its application to experimental time series in many domains has succeeded in yielding information about cortical activity which either complements or surpasses spectral band analysis, and other linear-stochastic techniques. The aim of this paper is to provide a pedagogical review of the contribution of dimensional complexity studies in understanding the psychophysiology of cortical arousal by outlining strategies for the successful estimation of DC _x as an empirical measure.     

Comment on the Shiner–Davison–Landsberg Measure

The complexity measure from Shiner et al. [Physical Review E 59, 1999, 1459–1464] (henceforth abbreviated as SDL-measure) has recently been the subject of a fierce debate. We discuss the properties and shortcomings of this measure, from the point of view of our recently constructed fundamental, statistical mechanics-based measures of complexity C_s(γ,β) [Stoop et al., J. Stat. Phys. 114, 2004, 1127–1137]. We show explicitly, what the shortcomings of the SDL-measure are: It is over-universal, and the implemented temperature dependence is trivial. We also show how the original SDL-approach can be modified to rule out these points of critique. Results of this modification are shown for the logistic parabola.     

动力系统的复杂性刻划

本文扼要地综述了近年来提出的刻划动力系统复杂性的各种度量．着重点在于将复杂性同随机性区分开．由此对于过去为刻划混沌而提出的度量,其中包括Ｌｙａｐｕｎｏｖ指数、拓扑熵、测度熵和Ｋｏｌｍｏｇｏｒｏｖ复杂性等,作了简单回顾．从自动机和信息论的观点对于包括ＡＣ、ＳＣ、ＥＭＣ在内的新提出的复杂性度量作了阐述．通过单峰映射和一维元胞自动机等例子对上述复杂性度量进行了比较,并较详细地介绍了利用形式语言和自动机来分析动力系统的方法．      

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(ɛ ₀/ɛ)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.     

Bios data analyzer

The Bios Data Analyzer (BDA) is a set of computer programs (CD-ROM, in Sabelli et al., Bios. A Study of Creation, 2005) for new time series analyses that detects and measures creative phenomena, namely diversification, novelty, complexes, nonrandom complexity. We define a process as creative when its time series displays these properties. They are found in heartbeat interval series, the exemplar of bios .just as turbulence is the exemplar of chaos, in many other empirical series (galactic distributions, meteorological, economic and physiological series), in biotic series generated mathematically by the bipolar feedback, and in stochastic noise, but not in chaotic attractors. Differencing, consecutive recurrence and partial autocorrelation indicate nonrandom causation, thereby distinguishing chaos and bios from random and random walk. Embedding plots distinguish causal creative processes (e.g. bios) that include both simple and complex components of variation from stochastic processes (e.g. Brownian noise) that include only complex components, and from chaotic processes that decay from order to randomness as the number of dimensions is increased. Varying bin and dimensionality show that entropy measures symmetry and variety, and that complexity is associated with asymmetry. Trigonometric transformations measure coexisting opposites in time series and demonstrate bipolar, partial, and uncorrelated opposites in empirical processes and bios, supporting the hypothesis that bios is generated by bipolar feedback, a concept which is at variance with standard concepts of polar and complementary opposites.     

A perturbation method for estimation of dynamic systems

A novel framework called the Perturbed Jth Moment Extended Kalman Filter (PJMEKF), based on a classical perturbation technique is proposed for estimating the states of a nonlinear dynamical system from sensor measurements. This method falls under a class of architectures under investigation primarily to study the interplay of major issues in nonlinear estimation such as nonlinearity, measurement sparsity, and initial condition uncertainty in an environment with low levels of process noise. Taylor series expansion of the departure motion dynamics about the best estimate is used to derive a series representation of the unforced motion. It is found that such series representation evolves as a set of differential equations that force each other in a cascade manner, adding up to give the unforced motion (in a so-called “triangular” structure). This formal perturbation solution for the departure motion dynamics is used in deriving the differential equations governing the time evolution of the high order statistical moments of the estimation error. These tensor differential equations are found to possess a similar high order triangular structure in addition to being symmetric (in N tensorial dimensions and we appropriately term the evolution equations as Tensor Lyapunov Equations of statistical moment perturbations). Elegance of the tensor differential equations thus derived is accompanied by the computational advantages due to symmetry in all tensorial dimensions. A vector matrix representation of tensors is proposed with which the representation and solution of the tensor differential equations can be carried out effectively. Approximations are introduced to incorporate low levels of process noise forcing function in the propagation phase of the moment equations. The statistics thus propagated are used in a filtering framework to estimate the state vector of a nonlinear system from noisy measurements, within the traditional Kalman update paradigm. The Kalman gain thus determined is utilized in updating all high order moments in preparation for the subsequent propagation phase leading to improved estimation accuracy. The filter developed is applied to an orbit estimation problem and comparisons are presented with classical extended Kalman filter.     

Combustion process in a spark ignition engine: analysis of cyclic peak pressure and peak pressure angle oscillations

In this paper we analyze the cycle-to-cycle variations of peak pressure p _max and peak pressure angle α _pmax in a four-cylinder spark ignition engine. We examine the experimental time series of p _max and α _pmax for three different spark advance angles. Using standard statistical techniques such as return maps and histograms we show that depending on the spark advance angle, there are significant differences in the fluctuations of p _max and α _pmax . We also calculate the multiscale entropy of the various time series to estimate the effect of randomness in these fluctuations. Finally, we explain how the information on both p _max and α _pmax can be used to develop optimal strategies for controlling the combustion process and improving engine performance.     

软件系统的复杂网络研究进展

互联网给软件带来了革命性的转变------软件网络化,这种趋势使软件作为全局性的资源,以网络为媒介向大众用户提供各种信息资源的应用服务.软件的计算模式、应用模式、产品形态以及盈利模式都会发生很大的变化,例如今后软件的应用方式就像打电话一样, 通过网络租用软件来实现.网络化软件正会成为联接各种网络资源、数据资源、计算资源的核心,成为数据和数据交换的基础. 同时, 网络化软件系统也将成为复杂系统,而复杂性也是软件开发困难、质量难以保证的关键.软件工程是将系统化、规范化、可度量的方法应用于软件的开发、运行和维护.复杂网络理论的最新研究成果,为复杂系统的软件工程提供了新的数学基础和方法. 分析了软件的复杂性,介绍了复杂网络与软件复杂性结合的研究工作,包括软件系统的拓扑特性、形成机理、演化规律以及软件复杂性度量和评估,对软件网络的研究现状进行了小结, 并列举了需要进一步研究的问题.提出软件网络观(软件在网络中生长、可以用网络来刻画软件)将有助于我们深入理解和认识软件的复杂性本质.      

Approximate MPA-based method for performing incremental dynamic analysis

In performance based earthquake engineering, it is important to accurately predict the seismic demand and capacities of structures. One recent estimation method is incremental dynamic analysis (IDA), which requires a series of nonlinear response history analyses (RHA) of the structure under various ground motions, each scaled to multiple levels of intensity, selected to cover entire range of structural response from elasticity, to yield and finally global dynamic instability. The implementation of IDA requires intensive computation and detailed knowledge of the nonlinear RHA of structures. In response to the complexity of IDA, an approximate method based on modal pushover analysis (MPA-based IDA) was developed. In MPA-based IDA, seismic demands are computed using the nonlinear RHA of the equivalent SDF systems instead of using nonlinear RHA of MDF systems. The objective of this study is to develop a simpler MPA-based IDA procedure that can avoid nonlinear RHA of equivalent SDF systems. For this purpose, MPA-based IDA employs the empirical equation of the inelastic displacement ratio (C _R ), defined as the ratio of peak displacement of the inelastic SDF system to that of the corresponding elastic SDF system given the strength ratio R, and that of the collapse strength ratio (R _c), which is the ratio of collapse intensity to yield strength. The proposed procedure is verified by comparing the seismic demands and capacities of 6-, 9-, and 20-story steel moment frames as determined by the proposed method and exact IDA.     

Viscosity and compliance from molar mass distributions using double reptation models

Various empirical correlations between linear viscoelastic properties and molar mass distribution of linear polymers have been proposed. Many of these summarize the distribution in terms of the first few moments. This is sufficient when studying samples of limited variability. In parallel, various fundamental models that enable calculation of these rheological characteristics from the full distribution have been proposed. The advantage of the modeling approach is the ease of creating distributions, thus enabling independent control of moments up to any desired order. It is the goal of this contribution to explore this advantage and compare the findings of the single exponential (DRSE) and modified time-dependent diffusion (DRmTDD) double reptation models with the empirical relations. The models predict that η ₀ is primarily a function of the weight-average molar mass M _w, with subtle dependence on polydispersity. Furthermore, the model depends mainly on a combination of the second (M _z/M _w) and third (M _z+1/M _z) polydispersity index. The DRmTDD model shows that conventional moment-based fit equations are only valid for limited distribution parameter ranges. General fit equations are proposed based on genetic programming. The details of the predictions are sensitive to the precise physical model formulation and need to be validated from experiments.     

A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity

Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I ₁ of the Cauchy–Green strain tensor, is a simple logarithmic function of I ₁ and involves just two material parameters, the shear modulus μ and a parameter J _m which measures a limiting value for I ₁−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Padè approximant for this function. The constants μ and J _m in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function. This revised version was published online in June 2006 with corrections to the Cover Date.     

Canonical ensemble for static elastic structures with random microstructures

A constant-(N,V,T,θ) ensemble is proposed to describe the elastostatics of random solid structures. Within the harmonic approximation, the energy of such a solid structure is the sum of a thermal and a strain component without mutual interaction. Systems in this ensemble thus draw energies from two separate baths: one thermal and the other mechanical. A mechanical entropy and an effective temperature (θ) can then be defined on the same rigorous basis as the thermal entropy and the Kelvin temperature (T). This ensemble approach can be used to calculate the properties of solid structures sharing similar microstructural randomness.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N = 19,625 elements that must be filled with the given data. A substantial number of practical time series have fewer elements than 19,625. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series of any length 5 ≤ N ≤ 19,625. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short-time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. In addition to external noise, the hyperparameter (bias) used in entropy calculation also plays a critical role. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal-to-Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

     

基于物理统一存储大规模数字导航地图道路网拓扑自动生成算法

道路网络的拓扑信息是GIS进行空间分析,如最优路径、地图匹配等算法的数据基础。目前,获取和建立道路网络的拓扑信息非常繁琐,不仅费时、费力,并且容易出错。采用逻辑分幅物理统一的存储策略,在探讨了拓扑生成的一般算法的前提下,提出了大规模超大规模数字地图自动生成道路网络拓扑关系的步骤和算法。该算法采用网格索引检索每个子图的元素,用hash索引映射实体ID和实体对象信息,并将整图的拓扑信息生成转化为对每个子图的拓扑求取,并对跨子图道路拓扑求解特别讨论。然后,对算法复杂度进行了分析,并且通过建立不同道路数的多个虚拟道路网络子图对算法性能进行了测试和比较。最后用本算法跟踪处理了南京市道路网络（部分）,并给出了结果。本算法在保留地理数据完整性的前提下,解决了常规方法的内存限制,并且具有准线性的运算代价,并能够自动恢复数据处理。     

PFC2D平节理模型细观参数标定方法

细观参数的快速准确确定对PFC正确模拟岩石力学性能非常重要.目前,平节理模型细观参数的标定研究均未考虑对泊松比和压拉比有很大影响的黏结比例φb和影响岩石强度及裂纹产生难易程度的黏结强度变异系数Rsd这两个细观参数,且未考虑作为判断围岩损伤范围重要指标的宏观参数起裂强度σci在参数中新增φb,Rsd和σci,采用正交数值试验方法研究了平节理模型8个细观参数与岩石6个宏观参数之间的相关性,确定了各宏观参数与主要细观参数之间的拟合关系,并分析了宏细观参数间的趋势关系.在此基础上,提出了平节理模型细观参数的标定流程,然后根据片麻花岗岩物理试验的宏观力学参数确定了模型的细观参数并进行数值试验,模拟结果与物理试验结果基本吻合,说明标定流程可行.     

A comparative study of crack propagation models for PMMA and PVC

An analysis of examining the validity of a unified approach proposed earlier by the authors for the fatigue crack propagation (FCP) of engineering materials to include PMMA and PVC is described. The proposed formulation has been shown capable of characterizing a diversified range of materials with a master FCP diagram and expressed as da/dN = A(ΔG)^m/(G_c − G_max).An experimental program is undertaken to measure fatigue growth rate with the standard compact tension specimen. The FCP results are for the first instance analysed for each material using the unified formulation. The validity of the formulation for producing a master FCP diagram is verified when the fatigue crack growth rates of the materials are successfully characterized in one master diagram, yielding an excellent coefficient of correlation of 0.993. No such success is attained using a number of conventional FCP laws considered most acceptable to characterize polymeric materials.     

Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields

The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E ₁ , E ₂ , ν ₁₂ , G ₁₂ ) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moiré interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article).