相关论文: Scaling detection in time series: diffusion entrop…

We address the problem of the statistical analysis of a time series generated by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA) (Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the Shannon…

Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation…

We present a modification to the diffusion entropy analysis method for detecting temporal scaling. Diffusion entropy analysis detects temporal scaling in a data set by converting a time-series into a diffusion trajectory and using the…

This paper presents a global air and sea temperature anomalies analysis based upon a combination of the wavelet multiresolution analysis and the scaling analysis methods of a time series. The wavelet multiresolution analysis decomposes the…

We analyze the waiting time distribution of time distances $\tau$ between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function…

We introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the probability flux analysis (PFA). The advantages of this method…

By means of the concept of balanced estimation of diffusion entropy we evaluate reliable scale-invariance embedded in different sleep stages and stride records. Segments corresponding to Wake, light sleep, REM, and deep sleep stages are…

Diffusion models perform remarkably well on high-dimensional data such as images, often using only a modest number of reverse-time steps. Despite this practical success, existing convergence theory does not fully explain why such samplers…

This paper introduces a new methodology for detecting anomalies in time series data, with a primary application to monitoring the health of (micro-) services and cloud resources. The main novelty in our approach is that instead of modeling…

A new concept, called balanced estimator of diffusion entropy, is proposed to detect scalings in short time series. The effectiveness of the method is verified by means of a large number of artificial fractional Brownian motions. It is used…

Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system, are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by…

In this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets. The scaling behaviors of four representative stock markets, Dow Jones Industrial Average, Standard&Poor 500, Heng Seng Index,…

We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored…

This study develops a data-driven group variable selection method for data envelopment analysis (DEA), a non-parametric linear programming approach to the estimation of production frontiers. The proposed method extends the group Lasso…

Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…

We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…

In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…