Related papers: Complexity, multiresolution, non-stationarity and …
A complex process is often a balance between non-stationary and stationary components. We show how the non-extensive Tsallis q-entropy indicator may be interpreted as a measure of non-stationarity in time series. This is done by applying…
The multiresolution diffusion entropy analysis is used to evaluate the stochastic information left in a time series after systematic removal of certain non-stationarities. This method allows us to establish whether the identified patterns…
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…
This paper is devoted to the problem of statistical mechanics raised by the analysis of an issue of sociological interest: the teen birth phenomenon. It is expected that these data are characterized by correlated fluctuations, reflecting…
Fine particulate matter (PM2.5) measured at a given location is a mix of pollution generated locally and pollution traveling long distances in the atmosphere. Therefore, the identification of spatial scales associated with health effects…
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 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…
In this work, a study of epitaxial growth was carried out by means of wavelets formalism. We showed the existence of a dynamic scaling form in wavelet discriminated linear MBE equation where diffusion and noise are the dominant effects. We…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
A multiresolution technique on tessellation graphs for particle dynamics is proposed. This allows to split spatial field data given on millions of discrete particle positions into scale-dependent contributions. The Delaunay tessellation is…
We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes.…
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…
The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
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…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
We argue that a process of social interest is a balance of order and randomness, thereby producing a departure from a stationary diffusion process. The strength of this effect vanishes if the order to randomness intensity ratio vanishes,…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…