Alzheimer's disease (AD) disrupts selectively and progressively (increasing with severity) functional connectivity of intrinsic brain networks (IBNs), most prominent in the default mode network. Given that IBNs' functional connectivity depends on structural connectivity, we hypothesize for our study selective and progressive changes of IBN based structural… (More)
On the basis of integral representations we propose numerical methods to solve the stochastic wave equation and the stochastic Klein-Gordon equation. The algorithms are exact in a probabilistic sense. 1 The Cauchy problem for stochastic wave equation. Integral representation Let us consider the Cauchy problem for the stochastic wave equation ∂ 2 u ∂t 2 (t,… (More)
On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense. 1 Statement of the problem and integral representations Consider the stochastic wave equation ∂ 2 X ∂t 2 (t,… (More)
To solve boundary value problems for linear systems of stochastic differential equations we propose and justify a numerical method based on the Gibbs sampler. In contrast to the technique which yields for linear systems an " exact " numerical solution, the proposed method is simpler to generalize for stochastic partial differential equations and nonlinear… (More)
Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for… (More)
Analysis of crossing fibers is a challenging topic in recent diffusion-weighted imaging (DWI). Resolving crossing fibers is expected to bring major changes to present tractography results based on the standard tensor model. Model free approaches, like Q-ball or diffusion spectrum imaging, as well as multi-tensor models are used to unfold the different… (More)
On this Web page we present results of our cooperative research aiming at computation of fractal dimension. You can find here a few papers, references and corresponding software to simulate fractals and estimate fractal dimension.
The aim of the paper is to study by Monte Carlo simulation statistical properties of two numerical methods (the extended counting method and the variance counting method) developed to estimate the Hausdorff dimension of a time series and applied to the fractional Brownian motion.