Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either first time derivative or second space a of fractional order. The fundamental solutions these equations provide probability density functions, evolving on variable in space, which are related class stable distributions. This property is noteworthy generalization what happens for standard and can be relevant treating financial economical problems where distributions play key role.

We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we global properties simultaneously occurring among two or more electrodes termed coincidences. convert coincidences into diffusion process three distinct rules that can yield same $\ensuremath{\mu}$ only in case where are driven by renewal...

We present a modeling approach for diffusion in complex medium characterized by random length scale. The resulting stochastic process shows subdiffusion with behavior qualitative agreement single-particle tracking experiments living cells, such as ergodicity breaking, $p$ variation, and aging. In particular, this recapitulates characteristic features previously described part the fractional Brownian motion continuous-time walk. Moreover, proper distribution of scale, single parameter...

The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development novel modelling approaches for description anomalous diffusion in systems, such as complex heterogeneous cell environment. Nevertheless, many questions still open, joint manifestation statistical features agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk fractional Brownian motion. To overcome these...

Inspired by the success of dimensional analysis in continuum mechanics and nondimensional numbers such as Péclet, Schmidt, Lewis, Prandtl, we introduce study Brownian motion parameter M=conservativeforce/nonconservativeforce. In particular, nondimensionalise Langevin equation for a particle mass m moving fluid viscosity γ with diffusivity coefficient σ under action conservative force form harmonic oscillator constant k. We identify all possible time-scales T, associated length-scales L, on...

By fractional diffusive waves we mean the solutions of so-called time-fractional diffusion-wave equation. This equation is obtained from classical D'Alembert wave by replacing second-order time derivative with a order β∈(0,2) and expected to govern evolution processes intermediate between diffusion propagation when β∈(1,2). Here it shown stress in viscoelastic media which, exhibiting power law creep, are relevance acoustics seismology since their quality factor turns out be independent...

Criticality reportedly describes brain dynamics. The main critical feature is the presence of scale-free neural avalanches, whose auto-organization determined by a branching ratio neural-excitation spreading. Other features, directly associated to second-order phase transitions, are: (i) scale-free-network topology functional connectivity, stemming from suprathreshold pairwise correlations, superimposable, in waking activity, with that ferromagnets at Curie temperature; (ii) temporal...

We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$ probabilities occurrence each mechanism, then anomalousness parameter $\beta (0,1)$ results to be \simeq 1 - 1/\{1 + \log[(1-p)/p]\}$. Ensemble single-particle observables this model have been studied they match main characteristics as typically measured in living systems....

We study time series produced by the blinking quantum dots, means of an aging experiment, and we examine results this experiment in light two distinct approaches to complexity, renewal slow modulation. find that approach fits result while modulation perspective does not. make also attempt at establishing existence intermediate condition.

Abstract. In this paper we produce projections of seasonal precipitation for four Mediterranean areas: Apulia region (Italy), Ebro river basin (Spain), Po valley (Italy) and Antalya province (Turkey). We performed the statistical downscaling using Canonical Correlation Analysis (CCA) in two versions: one case Principal Component (PCA) filter is applied only to predictor other both predictand. After performing a validation test, CCA after PCA on predictand has been chosen. Sea level pressure...

OPINION article Front. Behav. Neurosci., 07 September 2021 | https://doi.org/10.3389/fnbeh.2021.709365

The partial differential equation of diffusion is generalized by replacing the first time derivative a fractional order /spl alpha/. This shown to govern propagation stress waves in viscoelastic solids, which exhibit power law creep degree p with 0<p<1, provided that 1</spl alpha/=2-p<2. For basic Cauchy and signaling problems corresponding Green functions are expressed terms an entire function for integral series representations provided. Numerical results presented show transition from...

We consider two different approaches, to which we refer as renewal and modulation, generate time series with a nonexponential distribution of waiting times. show that the same are not necessarily statistically equivalent, might physical properties. Renewal generates aging anomalous scaling, while modulation yields no significant either ordinary or diffusion, according dynamic prescription adopted. show, in fact, realization classes events. The events first class determined by persistent use...

We propose a model for the passage between metastable states of mind dynamics. As changing points we use rapid transition processes simultaneously detectable in EEG signals related to different cortical areas. Our consists non-Poissonian intermittent process, which that brain is condition complexity, upon Poisson process superimposed. provide an analytical solution waiting-time distribution model, well obeyed by physiological data. Although role remains unexplained, able reproduce many...

We discuss the critical brain hypothesis and its relationship with intermittent renewal processes displaying power-law decay in distribution of waiting times between two consecutive events. In particular, studies on complex systems a "critical" condition show that macroscopic variables, integrating activities many individual functional units, undergo fluctuations an serial structure characterized by avalanches inverse-power-law (scale-free) densities sizes inter-event times. This condition,...

Abstract. We investigate the time intermittency of turbulent transport associated with birth-death self-organized coherent structures in atmospheric boundary layer. apply a threshold analysis on increments fluctuations to extract sequences rapid acceleration events, which is marker transition between structures. The inter-event distributions show power-law decay ψ(τ) ~ 1/τμ, strong dependence index μ threshold. A recently developed method based application event-driven walking rules generate...