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1.
近似熵是一个有效的非线性动力学指数,能够用于表征时间序列的复杂性,通过滑动窗口技术,近似熵对于一维时间序列的动力学结构突变具有一定的识别能力,但其突变检测结果依赖于子序列长度的选择,且不能准确定位突变点.鉴于此,本文提出了一种新的突变检测方法——滑动移除近似熵.测试结果表明,滑动移除近似熵具有检测结果稳定性好、准确性高等特点,明显优于滑动近似熵和Mann-Kendall方法,其在实际观测资料中的应用进一步证实了新方法的可靠性.
关键词:
近似熵
滑动移除近似熵
突变检测 相似文献
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信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系--兼论玻尔兹曼熵和克劳修斯熵是否等价 总被引:6,自引:0,他引:6
论述了信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系;由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式;指出玻尔兹曼熵与克劳修斯熵不是等价关系,而是玻尔兹曼熵包含克劳修斯熵,信息熵又包含玻尔兹曼熵。 相似文献
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对麻醉的SD大鼠在癫痫发作前后两种状态的皮层脑电(ECoG)的时间序列,用多种有效的方法和分析技术,使得大量的ECoG时间序列得以正确的分析,并得出重要的结论.首先利用延时坐标法重构吸引子;计算互信息函数,取互信息函数第一次达到最小值的延时为重构延时时间,提出将伪邻点法和Cao法相结合的方法确定最佳嵌入维数.然后采用非线性预报和替代数据法相结合的方法确定ECoG为混沌时间序列,从不同角度得出了ECoG不是低维混沌的结论.在ECoG相空间重构的基础上,计算了最大Lyapunov指数(LLE).应用了近似熵这一标量对ECoG进行刻画,计算结果表明:癫痫发作前的皮层脑电的最大Lyapunov指数和近似熵都明显地高于癫痫发作后的,这可能为理解癫痫发病机理,预报癫痫发作和治疗提供一定的思路.
关键词:
皮层脑电
互信息
伪邻点法
最大Lyapunov指数
近似熵 相似文献
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提出一种多变量混沌时间序列相空间重构的条件熵扩维方法.首先使用互信息法求解每个变量的时间延迟,其次按条件熵最大原则逐步扩展相空间的嵌入维数,使得重构坐标从低维到高维的转换保持较强的独立性,最终的重构相空间具有较低的冗余度,为多变量时间序列的预测构造了有效的模型输入向量.通过对几个经典多变量混沌时间序列进行数值实验,结果表明该方法比单变量预测和已有多变量预测方法具有更好的预测效果,说明了该重构方法的有效性.
关键词:
多变量混沌时间序列
相空间重构
条件熵
神经网络预测 相似文献
11.
Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal. 相似文献
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We consider a holographic extended phase space in the presence of Reissner-Nordstrom-Anti-de Sitter(RNAdS) and Born-Infeld-Anti-de Sitter(BI-AdS) black holes in the bulk. In this extended phase space the cosmological constant is investigated as pressure and volume is defined as the codimension one-time slice in the bulk geometry enclosed by the minimal area appearing in the computation of the holographic entanglement entropy. These thermodynamics quantities can serve as probes of the underlying phase transition dictated by black hole thermodynamics, but do not describe different structures. We find that the isocharges on the pressure-volume plane exhibit a Van der Waals-like structure, for RN-AdS black holes in the background. For BI-AdS black holes, we observe the analogy with a Van der Waals liquid-gas system for βQ 1/2 and Reentrant phase transition for βQ 1/2 in the holographic extended phase space. The same holographic thermodynamic behavior is observed when we use the fidelity susceptibility as the volume and the cosmological constant as the pressure for RN-AdS black hole in the background. 相似文献
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Francesca Al Francesca Miraglia Alessandro Orticoni Elda Judica Maria Cotelli Paolo Maria Rossini Fabrizio Vecchio 《Entropy (Basel, Switzerland)》2020,22(11)
Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments. 相似文献
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Recent mathematical investigations have shown that under very general conditions, exponential mixing implies the Bernoulli property. As a concrete example of statistical mechanics that are exponentially mixing we consider the Bernoulli shift dynamics by Chebyshev maps of arbitrary order , which maximizes Tsallis entropy rather than the ordinary Boltzmann-Gibbs entropy. Such an information shift dynamics may be relevant in a pre-universe before ordinary space-time is created. We discuss symmetry properties of the coupled Chebyshev systems, which are different for even and odd N. We show that the value of the fine structure constant is distinguished as a coupling constant in this context, leading to uncorrelated behaviour in the spatial direction of the corresponding coupled map lattice for . 相似文献
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From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordströmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system. 相似文献
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Subhash Kak 《International Journal of Theoretical Physics》2007,46(4):860-876
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown
pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this,
we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and
the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary
evolution. Such complementarity is also at the basis of the so-called interaction-free measurement. 相似文献
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In this paper, we present the concept of the logical entropy of order m, logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions and is always less than the sum of the logical entropy of the variables and . We define the logical Shannon entropy and logical metric permutation entropy to an information system and examine the properties of this kind of entropy. Finally, we examine the amount of the logical metric entropy and permutation logical entropy for maps. 相似文献
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Yunus A. engel 《Entropy (Basel, Switzerland)》2021,23(6)
The term entropy is used in different meanings in different contexts, sometimes in contradictory ways, resulting in misunderstandings and confusion. The root cause of the problem is the close resemblance of the defining mathematical expressions of entropy in statistical thermodynamics and information in the communications field, also called entropy, differing only by a constant factor with the unit ‘J/K’ in thermodynamics and ‘bits’ in the information theory. The thermodynamic property entropy is closely associated with the physical quantities of thermal energy and temperature, while the entropy used in the communications field is a mathematical abstraction based on probabilities of messages. The terms information and entropy are often used interchangeably in several branches of sciences. This practice gives rise to the phrase conservation of entropy in the sense of conservation of information, which is in contradiction to the fundamental increase of entropy principle in thermodynamics as an expression of the second law. The aim of this paper is to clarify matters and eliminate confusion by putting things into their rightful places within their domains. The notion of conservation of information is also put into a proper perspective. 相似文献
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In this note we use the method of invariant to calculate the phase space
path integral appearing in our previous article. 相似文献