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The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling…
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and…
This paper is devoted to problem of detecting critical events at finiacial markets using methods of multifractal analysis. Namely, the local regularity of time-series is studied. As a result, one can find out a special behavior or signal of…
Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…
We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solutions are locally H{\"o}lder continuous Lp valued functions…
Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively…
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity…
We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which…
Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
We propose an analysis of heart rate marathon runners implemented by computing a multifractal spectrum based on p-exponents. We draw physiological conclusions about their performance. Finally, we link this analysis with the disturbances of…
We study the asymptotic power means of the coefficients associated with the Schneider continued fraction map on $p\mathbb{Z}_p$. Using tools from thermodynamic formalism, we compute the Hausdorff dimension of the corresponding level sets…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Local H\"older regularity is established for certain weak solutions to a class of parabolic fractional $p$-Laplace equations with merely measurable kernels. The proof uses DeGiorgi's iteration and refines DiBenedetto's intrinsic scaling…
The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality,…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
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…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…