单调递增分形函数上、下界的估计

Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure.In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f(x)(it is a monotone increasing fractal function)and its some applications.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

大理岩非分叉断裂的随机分形模型

本文建立了大理岩沿晶、穿晶及沿晶穿晶偶合断裂的随机分形模型，该模型能与大理岩的整体晶态结构自洽，且模型的分维值与测量值有很好的吻合。     

分形理论在雷达天线中的应用

分形维数大于其相应的拓扑维数,使得分形结构在空间中能够充分填充,以八木天线阵为例,详细说明了分形理论在雷达天线中的应用,并仿真设计了一个一次迭代的六元分形八木天线。所得实测结果与仿真结果一致,说明了分形理论在雷达天线小型化设计应用的可行性和准确性,也为雷达提供了一种性能优良的天线。     

基于Krawtchouk矩不变量和核模糊聚类的快速分形编码

针对基于分类的快速分形编码方法存在着编码速度与解码质量间的矛盾,鉴于Krawtchouk矩不变量具有在仿射变换下保持不变的特性和核模糊聚类在处理非线性问题上的突出优势,本文首次将这两者引入到分形编码中,提出了基于Krawtchouk矩不变量和核模糊聚类的自适应分类快速分形编码方法。首先根据Domain块的方差将其粗分类,再根据Domain块的Krawtchouk矩不变量利用核模糊聚类对Domain块细分类。实验结果表明,与其他基于分类的快速分形编码方法相比,在解码图像质量提高的同时,大大加快了分形编码的速度。     

基于分形理论的麻醉监测诱发脑电信号识别方法研究

提出了一种基于分形理论的麻醉监测诱发脑电信号识别方法.首先给出了麻醉监测中潜伏期听觉诱发脑电信号的数学模型,产生与实际信号相符的模拟脑电信号,然后对脑电信号进行小波降噪,提取降噪后脑电信号的关联维数,最后通过关联维数的大小识别麻醉状态下中潜伏期听觉诱发脑电信号的类型.实验仿真结果表明:提出的识别方法具有较高的识别率.     

分形物体转动惯量的计算

由分形物体的自相似性、转动惯量的量纲和平行轴定理,分别计算并得到分形三角形、分形正方体、分形四面体和科赫雪花的转动惯量.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

分形图形周界和面积的关系

 本文讨论分形图形周界和面积的关系；指出：在现实存在的有限层次自相似结构的近似分形图形中，Mandelbrot的周界-面积分维关系不适用。这可能是一些用此方法测出的分维值随码尺大小变化的根本原因。