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2010 Journal article Unknown

Climate change assessment for Mediterranean agricultural areas by statistical downscaling
Palatella L., Miglietta M. M., Paradisi P., Lionello P.
In this paper we produce projections of seasonal precipitation for four Mediterranean areas: Apulia region (Italy), Ebro river basin (Spain), Po valley (Italy) and An- talya province (Turkey). We performed the statistical down- scaling using Canonical Correlation Analysis (CCA) in two versions: in one case Principal Component Analysis (PCA) filter is applied only to predictor and in the other to both pre- dictor and predictand. After performing a validation test, CCA after PCA filter on both predictor and predictand has been chosen. Sea level pressure (SLP) is used as predictor. Downscaling has been carried out for the scenarios A2 and B2 on the basis of three GCM's: the CCCma-GCM2, the Csiro-MK2 and HadCM3. Three consecutive 30-year pe- riods have been considered. For Summer precipitation in Apulia region we also use the 500 hPa temperature (T500) as predictor, obtaining comparable results. Results show dif- ferent climate change signals in the four areas and confirm the need of an analysis that is capable of resolving internal differences within the Mediterranean region. The most ro- bust signal is the reduction of Summer precipitation in the Ebro river basin. Other significative results are the increase of precipitation over Apulia in Summer, the reduction over the Po-valley in Spring and Autumn and the increase over the Antalya province in Summer and Autumn.Source: Natural hazards and earth system sciences (Print) 10 (2010): 1647–1661.

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2010 Journal article Open Access

Complex intermittency blurred by noise: theory and application to neural dynamics
Allegrini P., Menicucci D., Bedini R., Gemignani A., Paradisi P.
We propose a model for the passage between metastable states of mind dynamics. As changing points we use the rapid transition processes simultaneously detectable in EEG signals related to different cortical areas. Our model consists of a non-Poissonian intermittent process, which signals that the brain is in a condition of complexity, upon which a Poisson process is superimposed. We provide an analytical solution for the waiting- time distribution for the model, which is well obeyed by physiological data. Although the role of the Poisson process remains unexplained, the model is able to reproduce many behaviors reported in literature, although they seem contradictory.Source: Physical review. E, Statistical, nonlinear and soft matter physics (Online) 82 (2010): 015103-1–015103-4. doi:10.1103/PhysRevE.82.015103
DOI: 10.1103/physreve.82.015103
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2010 Journal article Open Access

Fractal complexity in spontaneous EEG metastable-state transitions: new vistas on integrated neural dynamics
Allegrini P., Paradisi P., Menicucci D., Gemignani A.
Resting-state EEG signals undergo Rapid Transition Processes (RTPs) that glue otherwise stationary epochs. We study the fractal properties of RTPs in space and time, supporting the hypothesis that the brain works at a critical state. We discuss how the global intermittent dynamics of collective excitations is linked to mentation, namely non-constrained non-task-oriented mental activity.Source: Frontiers in physiology 1 (2010): 128–129. doi:10.3389/fphys.2010.00128
DOI: 10.3389/fphys.2010.00128
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2008 Journal article Restricted

A simple model for spatially-averaged wind profiles within and above an urban canopy
Di Sabatino S., Solazzo E., Paradisi P., Britter R.
This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as ?f and ?p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of ?f .Source: Boundary-layer meteorology (Dordrecht. Online) 127 (2008): 131–151. doi:10.1007/s10546-007-9250-1
DOI: 10.1007/s10546-007-9250-1
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2005 Journal article Open Access

Fluorescence intermittency in blinking quantum dots: Renewal or slow modulation?
Simone Bianco, Paolo Grigolini, Paolo Paradisi
We study the time series produced by blinking quantum dots, by means of an aging experiment, and we examine the results of this experiment in the light of two distinct approaches to complexity, renewal and slow modulation. We find that the renewal approach fits the result of the aging experiment, while the slow modulation perspective does not. We make also an attempt at establishing the existence of an intermediate condition.Source: The Journal of chemical physics 123 (2005): 174704-1–174704-10. doi:10.1063/1.2102903
DOI: 10.1063/1.2102903
DOI: 10.48550/arxiv.cond-mat/0509608
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2006 Journal article Restricted

Periodic trend and fluctuations: The case of strong correlation
O. C. Akin, Paolo Paradisi, Paolo Grigolini
We study the effects of an external periodic perturbation on a Poisson rate process, with special attention to the perturbation-induced sojourn-time patterns. We show that these patterns correspond to turning a memory-less sequence into a sequence with memory. The memory effects are stronger the slower the perturbation. The adoption of a de-trending technique, applied with no caution, might generate the impression that no fluctuation-periodicity correlation exists. We find that this is due to the fact that the perturbation-induced memory is a global property and that the result of a local in time analysis would not find any memory effect, insofar as the process under study is locally a Poisson process. We find that an efficient way to detect this memory effect is to analyze the moduli of the de-trended sequence. We turn the sequence to analyze into a diffusion process, and we evaluate the Shannon entropy of the resulting diffusion process. We find that both the original sequence and the suitably processed de-trended sequence yield the same dependence of entropy on time, namely, an initial scaling larger than ordinary scaling, and a sequel of weak oscillations, which are a clear signature of the external perturbation, in both cases. This is a clear indication of the fluctuation-periodicity correlation.Source: Physica. A (Print) 371 (2006): 157–170. doi:10.1016/j.physa.2006.04.054
DOI: 10.1016/j.physa.2006.04.054
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2009 Journal article Open Access

Spontaneous brain activity as a source of ideal 1/f noise
Paolo Allegrini, Danilo Menicucci, Remo Bedini, Leone Fronzoni, Angelo Gemignani, Paolo Grigolini, B. J. West, Paolo Paradisi
We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same \mu only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index \mu about 2 corresponding to ideal 1 / f noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that 1 / f noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.Source: Physical review. E, Statistical, nonlinear and soft matter physics (Online) 80 (2009): 061914-1–061914-13. doi:10.1103/PhysRevE.80.061914
DOI: 10.1103/physreve.80.061914
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2006 Journal article Open Access

Renewal, modulation, and superstatistics in times series
Paolo Allegrini, Francesco Barbi, Paolo Grigolini, Paolo Paradisi
We consider two different approaches, to which we refer to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times. We show that different time series with the same waiting time distribution are not necessarily statistically equivalent, and might generate different physical properties. Renewal generates aging and anomalous scaling, while modulation yields no significant aging and either ordinary or anomalous diffusion, according to the dynamic prescription adopted. We show, in fact, that the physical realization of modulation generates two classes of events. The events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time, and consequently are numerous; the events of the second class are identified with the abrupt changes from one to another exponential prescription, and consequently are rare. The events of the second class, although rare, determine the scaling of the diffusion process, and for this reason we term them as crucial events. According to the prescription adopted to produce modulation, the distribution density of the time distances between two consecutive crucial events might have, or not, a diverging second moment. In the former case the resulting diffusion process, although going through a transition regime very extended in time, will eventually become anomalous. In conclusion, modulation rather than ruling out the action of renewal events, produces crucial events hidden by clouds of exponential events, thereby setting the challenge for their identification.Source: Physical review. E, Statistical, nonlinear and soft matter physics (Online) 73 (2006): 046136-1–046136-13. doi:10.1103/PhysRevE.73.046136
DOI: 10.1103/physreve.73.046136
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2007 Journal article Restricted

Aging and renewal events in sporadically modulated systems
Allegrini P., Barbi F., Grigolini P., Paradisi P.
We describe a form of modulation, namely a dishomogeneous Poisson process whose event rate changes sporadically and randomly in time with a chosen prescription, so as to share many statistical properties with a corresponding non- Poisson renewal process. Using our prescription the correlation function and the waiting time distribution between events are the same. If we study a continuous-time random walk, where the walker has only two possible velocities, randomly established at the times of the events, we show that the two processes also share the same second moment. ? However, the modulated diffusion process undergoes a dynamical transition between superstatistics and a Levy walk process, sharing the scaling properties of the renewal process only asymptotically. The aging experiment - based on the evaluation of the waiting time for the next event, given a certain time distance between another previous event and the beginning of the observation - seems to be the key experiment to discriminate between the two processes.Source: Chaos, solitons and fractals 34 (2007): 11–18. doi:10.1016/j.chaos.2007.01.045
DOI: 10.1016/j.chaos.2007.01.045
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2013 Contribution to conference Restricted

Linking fractional calculus to real data
Paradisi P.
I will review some well-known theoretical findings about fractional calculus and, in particular, the links between fractal intermittency, the Continuous Time Random Walk (CTRW) model and the emergence of Fractional Diffu- sion Equations (FDE) for anomalous diffusion. In this framework, I will show how fractional operators are associated with the existence of renewal events, a typical feature of complex systems. I will also discuss the possibile connections with critical phenomena. Then, I will introduce some statistical methods allowing to understand when a real system could be described by means of fractional models. Finally, I will show some applications to real data from nano-crystal fluores- cence intermittency, human brain dynamics and atmospheric turbulence.Source: FCPNLO 2014 - Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments. A workshop on the occasion of the retirement of Francesco Mainardi, Bilbao, Spain, 6-8 November 2013

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2013 Contribution to conference Restricted

Renewal and fractionality in the brain
Paradisi P.
Renewal theory is the basic ingredient of Continuous Time Random Walk (CTRW) models and our analyses show that the intermittent behavior of brain events can be modelled through fractal renewal processes. In the long-time limit, CTRW models with appropriate scaling properties, are known to obey generalized diffusion equations with fractional derivatives in time and/or space. Is it possible to develop a CTRW model for the anomalous transport of information in the brain and, consequently, to derive a fractional model of the brain ?Source: Chaos, Solitons and Fractals Conference, Amsterdam, The Netherlands, 29 November 2013

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2014 Contribution to conference Restricted

Statistical analysis of time series in anomalous diffusion generated by fractal intermittency
Paradisi P.
The interest towards self-organized and cooperative systems has rapidly increased in recent years. This is related to the increasing interest in the evolution of complex networks, such as the web and, more in general, social dynamics (not only associated with web applications), but also biological applications such as neural networks, human brain dynamics and metabolic networks in the cell. This hot research field is sometimes denoted as complexity science. A fully accepted definition of "complex system" does not yet exist, but there's some agreement on some general features. For example, a complex system is typically made of many individual units with strong non-linear interactions. The global dynamics of this multi-component systems is characterized by emergent properties, i.e., the emergence of cooperative, self-organized, coherent structures that are hardly explained in terms of microscopic dynamics. Thus, the typical approach is focused on emergent properties and their dynamical evolution. Along this line, a crucial property that has been observed is given by the meta-stability of the emerging self-organized structures, that is, the dynamics of a complex system is characterized by a birth-death process of cooperation [Allegrini et al., 2009]. In time series analysis, this is mathematically described in the framework of renewal point processes [Cox, 1962] as a sequence of critical short-time events, with abrupt memory decays, thus dividing the time series into separate segments with long-range memory [Paradisi et al., 2013; Allegrini et al., 2013; Fingelkurts et al., 2008]. As a consequence, the inter- event times are statistically distributed according to a inverse power-law, a condition also denoted as fractal intermittency. The sequence of renewal events with fractal distribution of inter-event times are associated with anomalous diffusion processes. Here we will show how simple random walks driven by complex (i.e., fractal intermittent) events generate anomalous diffusion and long-range correlation despite the presence of memory erasing events in the time series. Then, we discuss different approaches for the statistical characterization of diffusion scaling in time series with intermittent events. We discuss the robustness of diffusion scaling generated by event-driven random walks with respect to the presence of noisy events, here modelled as events with Poisson statistics, as such events are not able to generate anomalous diffusion, but only normal diffusion (i.e., variance linearly increasing in time). [l] Allegrini et al., Phys. Rev. E 80, 061914 (2009). [2] D.R. Cox, Renewal Theory Ed.: Methuen, London (1962). [3] Paradisi et al., AIP Conf. Proc. 1510, 151 (2013). [4] Allegrini et al., Chaos Solit. Fract. 55, 32 (2013). [5] Fingelkurts and Fingelkurts, Open Neuroimaging J. 2, 73 (2008).Source: SIGMAPHI2014 - International Conference on Statistical Physics, pp. 125–126, Rodi, Greece, 7-11 July 2014

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2015 Journal article Open Access

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency
Paradisi P., Allegrini P.
In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth-death process of coop- eration. This is found to be described by a renewal point process, i.e., a sequence of crucial birth-death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occur- rence of crucial events is typically associated with a fast memory drop, which is the reason for the renewal condition. Consequently, these complex systems display a power-law decay and, thus, a long-range or scale-free behavior, in both time correlations and distribution of inter-event times, i.e., fractal intermittency. The emergence of fractal intermittency is then a signature of complexity. However, the scaling features of complex systems are, in general, affected by the presence of added white or short-term noise. This has been found also for fractal intermittency. In this work, after a brief review on metastability and noise in complex systems, we discuss the emerging paradigm of Temporal Complexity. Then, we propose a model of noisy fractal in- termittency, where noise is interpreted as a renewal Poisson process with event rate r p . We show that the presence of Poisson noise causes the emergence of a normal diffusion scaling in the long-time range of diffusion generated by a telegraph signal driven by noisy fractal intermittency. We analytically derive the scaling law of the long-time normal diffusivity coef- ficient. We find the surprising result that this long-time normal diffusivity depends not only on the Poisson event rate, but also on the parameters of the complex component of the signal: the power exponent Î¼ of the inter-event time distribution, denoted as complexity index, and the time scale T needed to reach the asymptotic power-law behavior marking the emergence of complexity. In particular, in the range Î¼ < 3, we find the counter-intuitive result that normal diffusivity increases as the Poisson rate decreases. Starting from the diffusivity scaling law here derived, we propose a novel scaling analysis of complex signals being able to estimate both the complexity index Î¼ and the Poisson noise rate r_p .Source: Chaos, solitons and fractals 81 (2015): 451–462. doi:10.1016/j.chaos.2015.07.003
DOI: 10.1016/j.chaos.2015.07.003
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2016 Journal article Open Access

A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation
Pagnini G., Paradisi P.
The stochastic solution with Gaussian stationary increments is established for the symmetric space-time fractional diffusion equation when 0 < ? < ? <= 2, where 0 < ? <= 1 and 0 < ? <= 2 are the fractional derivation orders in time and space, respectively. This solution is provided by imposing the identity between two probability density functions resulting (i) from a new integral representation formula of the fundamental solution of the symmetric space-time fractional diffusion equation and (ii) from the product of two independent random variables. This is an alternative method with respect to previous approaches such as the scaling limit of the continuous time random walk, the parametric subordination and the subordinated Langevin equation. A new integral representation formula for the fundamental solution of the space-time fractional diffusion equation is firstly derived. It is then shown that, in the symmetric case, a stochastic solution can be obtained by a Gaussian process with stationary increments and with a random wideness scale variable distributed according to an arrangement of two extremal Lévy stable densities. This stochastic solution is self-similar with stationary increments and uniquely defined in a statistical sense by the mean and the covariance structure. Numerical simulations are carried out by choosing as Gaussian process the fractional Brownian motion. Sample paths and probability densities functions are shown to be in agreement with the fundamental solution of the symmetric space-time fractional diffusion equation.Source: Fractional Calculus & Applied Analysis (Online) 19 (2016): 408–440. doi:10.1515/fca-2016-0022
DOI: 10.1515/fca-2016-0022
DOI: 10.48550/arxiv.1603.05300
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2018 Journal article Open Access

Langevin equation in complex media and anomalous diffusion
Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G.
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.Source: Journal of the Royal Society interface (Print) 15 (2018). doi:10.1098/rsif.2018.0282
DOI: 10.1098/rsif.2018.0282
DOI: 10.48550/arxiv.1806.11508
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2019 Journal article Open Access

Gaussian processes in complex media: new vistas on anomalous diffusion
Di Tullio F., Paradisi P., Spigler R., Pagnini G.
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions defines anomalous diffusion, thus a nonlinear growth in time of the variance and/or a non-Gaussian displacement distribution. Motivated by the idea that anomalous diffusion emerges from standard diffusion when it occurs in a complex medium, we discuss a number of anomalous diffusion models for strongly heterogeneous systems. These models are based on Gaussian processes and characterized by a population of scales, population that takes into account the medium heterogeneity. In particular, we discuss diffusion processes whose probability density function solves space- and time-fractional diffusion equations through a proper population of time-scales or a proper population of length-scales. The considered modeling approaches are: the continuous time random walk, the generalized gray Brownian motion, and the time-subordinated process. The results show that the same fractional diffusion follows from different populations when different Gaussian processes are considered. The different populations have the common feature of a large spreading in the scale values, related to power-law decay in the distribution of population itself. This suggests the key role of medium properties, embodied in the population of scales, in the determination of the proper stochastic process underlying the given heterogeneous medium.Source: Frontiers in Physics 7 (2019): 123-1–123-11. doi:10.3389/fphy.2019.00123
DOI: 10.3389/fphy.2019.00123
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2018 Journal article Open Access

Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion
D'Ovidio M., Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G.
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.Source: Fractional Calculus & Applied Analysis (Print) 21 (2018): 1420–1435. doi:10.1515/fca-2018-0074
DOI: 10.1515/fca-2018-0074
DOI: 10.48550/arxiv.1806.11351
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2019 Journal article Open Access

Finite-energy Levy-type motion through heterogeneous ensemble of Brownian particles
Sliusarenko O. Y., Vitali S., Sposini V., Paradisi P., Chechkin A., Castellani G., Pagnini G.
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem.Source: Journal of physics. A, Mathematical and theoretical (Print) 52 (2019). doi:10.1088/1751-8121/aafe90
DOI: 10.1088/1751-8121/aafe90
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2017 Contribution to book Open Access

Intermittency-driven complexity in signal processing
Paradisi P., Allegrini P.
In this chapter, we rst discuss the main motivations that are causing an increasing interest of many research elds and the interdisciplinary eort of many research groups towards the new paradigm of complexity. Then, without claiming to include all possible complex systems, which is much beyond the cope of this review, we introduce a possible denition of complexity. Along this line, we also introduce our particular approach to the analysis and modeling of complex systems. This is based on the ubiquitous observation of metastability of self-organization, which triggers the emergence of intermittent events with fractal statistics. This condition, named fractal intermittency, is the signature of a particular class of complexity here referred to as Intermittency-Driven Complexity (IDC) . Limiting to the IDC framework, we give a survey of some recently developed statistical tools for the analysis of complex behavior in multi-component systems and we review recent applications to real data, especially in the eld of human physiology. Finally, we give a brief discussion about the role of complexity paradigm in human health and wellness.Source: Complexity and Nonlinearity in Cardiovascular Signals, edited by Barbieri R.; Scilingo E.; Valenza G., pp. 161–195. London: Springer, 2017
DOI: 10.1007/978-3-319-58709-7_6
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2016 Journal article Open Access

Fractional kinetics emerging from ergodicity breaking in random media
Molina-García D., Pham T. M., Paradisi P., Manzo C., Pagnini G.
We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.Source: Physical review. E (Print) 94 (2016). doi:10.1103/PhysRevE.94.052147
DOI: 10.1103/physreve.94.052147
DOI: 10.48550/arxiv.1508.01361
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