数据分析、统计与概率

This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed for small amplitudes. It is shown that a…

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…

A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images.…

In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…

Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations n on many more variables p, a scenario that we denote as p>>n. Traditional data processing methods are often…

We propose a pattern recognition method that identifies the common tangent lines of a set of ellipses. The detection of the tangent lines is attained by applying the Legendre transform on a given set of ellipses. As context, we consider a…

We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so introduced…

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…

Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…

In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed…

It is shown that whenever the multiplicative normalization of a fitting function is not known, least square fitting by $\chi^2$ minimization can be performed with one parameter less than usual by converting the normalization parameter into…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…

Alternating projection (AP) of various forms, including the Parallel AP (PAP), Real-constrained AP (RAP) and the Serial AP (SAP), are proposed to solve phase retrieval with at most two coded diffraction patterns. The proofs of geometric…

We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…

A model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT), dynamical (ridge) or other correlation functions, that have a nearly L\'evy or…

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

Detection of hydroacoustic transmissions is a key enabling technology in applications such as depth measurements, detection of objects, and undersea mapping. To cope with the long channel delay spread and the low signal-to-noise ratio,…

Iafrate, Miller, and Strauch [Equipartition and a Distribution for Numbers: A Statistical Model for Benford's Law," arXiv:1503.08259] construct and test a statistical model for partitioning a conserved quantity. One consequence of their…