相关论文: L\'{e}vy scaling: the Diffusion Entropy Analysis a…

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where…

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…

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…

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…

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…

We propose a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures. The technique interpolates between standard Statistical Energy Analysis (SEA) and full ray tracing…

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…

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…

Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model…

This paper presents a statistical methodology for analyzing a complex phenomenon in which deterministic and scaling components are superimposed. Our approach is based on the wavelet multiresolution analysis combined with the scaling…

Data Envelopment Analysis (DEA) appears more than just an instrument of measurement. DEA models can be seen as a mathematical structure for democratic voicing within decisional contexts. Such an important aspect of DEA is enhanced through…

High-throughput sequencing of RNA transcripts (RNA-seq) has become the method of choice for detection of differential expression (DE). Concurrent with the growing popularity of this technology there has been a significant research effort…

We propose a new method of statistical analysis of nucleotide sequences yielding the true scaling without requiring any form of de-trending. With the help of artificial sequences that are proved to be statistically equivalent to the real…

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…

The Automatic Dependent Surveillance Broadcast protocol is one of the latest compulsory advances in air surveillance. While it supports the tracking of the ever-growing number of aircraft in the air, it also introduces cybersecurity issues…

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…

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…

We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in…

We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied…