Related papers: Joint multifractal analysis based on the partition…
An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA)…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of…
Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional…
The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In…
Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…