22 research outputs found
The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts
The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe
Time-fractional Caputo derivative versus other integro-differential operators in generalized Fokker-Planck and generalized Langevin equations
Fractional diffusion and Fokker-Planck equations are widely used tools to
describe anomalous diffusion in a large variety of complex systems. The
equivalent formulations in terms of Caputo or Riemann-Liouville fractional
derivatives can be derived as continuum limits of continuous time random walks
and are associated with the Mittag-Leffler relaxation of Fourier modes,
interpolating between a short-time stretched exponential and a long-time
inverse power-law scaling. More recently, a number of other
integro-differential operators have been proposed, including the
Caputo-Fabrizio and Atangana-Baleanu forms. Moreover, the conformable
derivative has been introduced. We here study the dynamics of the associated
generalized Fokker-Planck equations from the perspective of the moments, the
time averaged mean squared displacements, and the autocovariance functions. We
also study generalized Langevin equations based on these generalized operators.
The differences between the Fokker-Planck and Langevin equations with different
integro-differential operators are discussed and compared with the dynamic
behavior of established models of scaled Brownian motion and fractional
Brownian motion. We demonstrate that the integro-differential operators with
exponential and Mittag-Leffler kernels are not suitable to be introduced to
Fokker-Planck and Langevin equations for the physically relevant diffusion
scenarios discussed in our paper. The conformable and Caputo Langevin equations
are unveiled to share similar properties with scaled and fractional Brownian
motion, respectively.Comment: 26 pages, 7 figures, RevTe
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
A Statistical Approach to the Alignment of fMRI Data
Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods
A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium
When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available