数据分析、统计与概率
The topological charge of an electromagnetic vortex beam depends on its wavefront helicity. For mixed vortex beams composed of several different coaxial vortices, the topological charge spectrum can be obtained by Fourier transform.…
The problem of embedding the Tsallis and R\'{e}nyi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES related to measured spaces. We prove that both of…
The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods…
The unfolding problem formulation for correcting experimental data distortions due to finite resolution and limited detector acceptance is discussed. A novel validation of the problem solution is proposed. Attention is drawn to fact that…
We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and…
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…
One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means…
The Omega-preprocessing was introduced to improve phase noise rejection by using a least square algorithm. The associated variance is the PVAR which is more efficient than MVAR to separate the different noise types. However, unlike AVAR and…
In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high…
This paper presents a complete strategy for the geometry estimation of large microphone arrays of arbitrary shape. Largeness is intended here in both number of microphones (hundreds) and size (few meters). Such arrays can be used for…
This article covers the problem of processing of Big Data that describe process of complex networks and network systems operation. It also introduces the notion of hierarchical network systems combination into associations and conglomerates…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
Observer models were developed to process data in list-mode format in order to perform binary discrimination tasks for use in an arms-control-treaty context. Data used in this study was generated using GEANT4 Monte Carlo simulations for…
With the standard deviation for the logarithm of the re-scaled range $\langle |F(t+\tau)-F(t)|\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \cite{q14}, the method of least squares is adopted to determine…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
Efficient processing of particulate products across various manufacturing steps requires that particles possess desired attributes such as size and shape. Controlling the particle production process to obtain required attributes will be…
Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record…