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The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical…
Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and…
Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
Multimodal sentiment analysis (MSA) is a research field that recognizes human sentiments by combining textual, visual, and audio modalities. The main challenge lies in integrating sentiment-related information from different modalities,…
Rank-Ordered Multifractal Analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of…
Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity,…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Unsupervised evaluation of segmentation quality is a crucial step in image segmentation applications. Previous unsupervised evaluation methods usually lacked the adaptability to multi-scale segmentation. A scale-constrained evaluation…
Multimodal Sentiment Analysis (MSA) aims to recognize human emotions by exploiting textual, acoustic, and visual modalities, and thus how to make full use of the interactions between different modalities is a central challenge of MSA.…
We introduce a method of estimating parameters associated with a fractal random scattering medium, which utilizes the multiscale properties of the scattered field. The example of ray-density fluctuations beyond a phase screen with fractal…
We introduce a novel way to extract information from turbulent datasets by applying an ARMA statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded…
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…
Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of…
Advanced MAVKA software for the approximation of extrema observations is used to analyze the variability of the brightness of pulsating and eclipsing stars, but may be useful in analyzing signals of any nature. A new algorithm using a…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…