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2010 Journal article Open Access OPEN
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), vol. 10 (issue 7), pp. 1647-1661

See at: CNR IRIS Open Access | CNR IRIS Restricted


2010 Journal article Open Access OPEN
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, vol. 82 (issue 1), pp. 015103-1-015103-4
DOI: 10.1103/physreve.82.015103
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See at: CNR IRIS Open Access | pre.aps.org Open Access | Physical Review E Restricted | CNR IRIS Restricted


2010 Journal article Open Access OPEN
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, vol. 1, pp. 128-129
DOI: 10.3389/fphys.2010.00128
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See at: Frontiers in Physiology Open Access | Frontiers in Physiology Open Access | CNR IRIS Open Access | DOAJ-Articles Open Access | Frontiers in Physiology Open Access | www.frontiersin.org Open Access | CNR IRIS Restricted


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), vol. 127 (issue 1), pp. 131-151
DOI: 10.1007/s10546-007-9250-1
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See at: Boundary-Layer Meteorology Restricted | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.springerlink.com Restricted


2005 Journal article Open Access OPEN
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, vol. 123 (issue 17), pp. 174704-1-174704-10
DOI: 10.1063/1.2102903
DOI: 10.48550/arxiv.cond-mat/0509608
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See at: arXiv.org e-Print Archive Open Access | The Journal of Chemical Physics Open Access | CNR IRIS Open Access | jcp.aip.org Open Access | The Journal of Chemical Physics Restricted | doi.org Restricted | CNR IRIS Restricted


2006 Journal article Restricted
Periodic trend and fluctuations: The case of strong correlation
Oc 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, vol. 371 (issue 2), pp. 157-170
DOI: 10.1016/j.physa.2006.04.054
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See at: Physica A Statistical Mechanics and its Applications Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.sciencedirect.com Restricted


2009 Journal article Open Access OPEN
Spontaneous brain activity as a source of ideal 1/f noise
Paolo Allegrini, Danilo Menicucci, Remo Bedini, Leone Fronzoni, Angelo Gemignani, Paolo Grigolini, Bj 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, vol. 80 (issue 6), pp. 061914-1-061914-13
DOI: 10.1103/physreve.80.061914
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See at: Physical Review E Open Access | CNR IRIS Open Access | pre.aps.org Open Access | Physical Review E Restricted | CNR IRIS Restricted


2006 Journal article Open Access OPEN
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, vol. 73 (issue 4), pp. 046136-1-046136-13
DOI: 10.1103/physreve.73.046136
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See at: Physical Review E Open Access | CNR IRIS Open Access | pre.aps.org Open Access | Physical Review E Restricted | CNR IRIS Restricted


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, vol. 34, pp. 11-18
DOI: 10.1016/j.chaos.2007.01.045
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See at: Chaos Solitons & Fractals Restricted | CNR IRIS Restricted | CNR IRIS Restricted


2012 Journal article Open Access OPEN
Dynamical and statistical downscaling of precipitation and temperature in a Mediterranean area
Pizzigalli C, Palatella L, Zampieri M, Lionello P, Miglietta M, Paradisi P
In this paper we present and discuss a comparison between statistical and regional climate modeling techniques for downscaling GCM prediction. The comparison is carried out over the Capitanata region, an area of agricultural interest in south-eastern Italy, for current (1961-1990) and future (2071-2100) climate. The statistical model is based on Canonical Correlation Analysis (CCA), associated with a data pre-filtering obtained by a Principal Component Analysis (PCA), whereas the Regional Climate Model REGCM3 was used for dynamical downscaling. Downscaling techniques were applied to estimate rainfall, maximum and minimum temperatures and average number of consecutive wet and dry days. Both methods have comparable skills in estimating stations data. They show good results for spring, the most important season for agriculture. Both statistical and dynamical models well reproduce the statistical properties of precipitation, the crucial variable for the growth of crops.Source: ITALIAN JOURNAL OF AGRONOMY (ONLINE), vol. 7 (issue e2), pp. 3-12
DOI: 10.4081/ija.2012.e2
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See at: Italian Journal of Agronomy Open Access | Italian Journal of Agronomy Open Access | CNR IRIS Open Access | Italian Journal of Agronomy Open Access | www.agronomy.it Open Access | CNR IRIS Restricted


2012 Contribution to journal Restricted
Sleep unconsciousness and the fragmentation of the global workspace
Allegrini P, Paradisi P, Laurino M, Menicucci D, Piarulli A, Gemignani A
While several mental functions, from visual perception up to working memory, are characterized by parallel computation performed by integrated moduli in the cortex, consciousness is sustained by a serial process of global integration, insofar as a single scene at a time takes place. Rigorous studies on the theoretical physics of second order phase transition (i.e. critical phenomena) show that the so called order parameters, defined as the macroscopic variables (i.e. thermodynamically measurable quantities that integrate the activity of many components) that respond to external fields (i.e. interactions), display, in the absence of interactions, coordinated fluctuations with an intermittent serial structure when the system is at the transition, termed critical state. This "criticality" state is operationally defined by the presence of avalanches with inverse-power-law (scale-free) distribution densities of sizes and inter-event times (duration of metastable states, i.e. states without events). Criticality is a state of maximal complexity, with maximal redundancies in the dynamical patterns, and complex topologies supporting the structure of cross correlations between different areas. The state of criticality has been established by our group in human brain dynamics in basal conditions, by studying abrupt transitions (RTPs, or rapid transition processes) to and from stationary states, via multichannel EEGs (electroencephalograms). RTPs are the events that delimit quasi-stationary (sometimes called metastable) epochs with constant frequencies and amplitude. It remained unsolved whether this complex behavior correlates with consciousness or, alternatively, with a non-task-driven default mode activity of the brain, also present in non-conscious states, such as NREM sleep. This does not mean that default mode and consciousness are in conceptual contrast, but that so far we had not assessed whether our finding of critical neural dynamics was a correlate of either the former or the latter. Here we show that in NREM sleep this serial dynamical behavior breaks down, insofar as the inverse-power-law distributions of the inter-event times are replaced, in the long-time regime, by exponential cutoffs whose time scales correlate with the average time between episodes of neural bistability,marked in EEGs by Sleep SlowOscillations (SSOs). During REM sleep the dynamics turns back to the scale-free behavior observed during the pre-sleep wakefulness. We demonstrate that the dynamics of passage between quasi stationary states in unconscious NREM sleep has a spatial connectivity not significantly different from the spatial connectivity of wakefulness and REM sleep. However, NREM RTPs are not dynamically compatible with a serial (single time) scenario, with a strong discrepancy with respect to the serial behavior of wakefulness and REM sleep, where consciousness takes place. This is ultimately due to the fact that the global workspace, the most used model to describe consciousness, cannot emerge due to NREM neural bistability.Source: INTERNATIONAL JOURNAL OF PSYCHOPHYSIOLOGY, vol. 85 (issue 3), pp. 332-333
DOI: 10.1016/j.ijpsycho.2012.06.117
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See at: International Journal of Psychophysiology Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.sciencedirect.com Restricted


2014 Journal article Restricted
Source identification by a statistical analysis of backward trajectories based on peak pollution events
Cesari R, Paradisi P, Allegrini P
Back-trajectory techniques are extensively used to identify the most probable source locations, starting from the known pollutants concentration data at some receptor sites. In this paper, we review the trajectory statistical methods (TSMs) that are most used in literature for source identification, which are essentially based on the concept of residence time (RT), and we introduce a novel statistical method. To validate this method, artificial receptor data at two receptor sites are derived from numerical simulations with a given aerial source, using the Lagrangian dispersion model (LSM) FLEXPART in forward mode. Then the RTs are computed using again the model FLEXPART, but in backward mode. Then, the new statistical methodology, which is based on the use of peak concentration events, is applied to reconstruct the spatial distribution of emission sources. Our approach requires simulation times shorter than those required in other methods and could overcome the problem of ghost sources.Source: INTERNATIONAL JOURNAL OF ENVIRONMENT AND POLLUTION, vol. 55 (issue 1-4), pp. 94-103
DOI: 10.1504/ijep.2014.065909
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See at: International Journal of Environment and Pollution Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.inderscience.com Restricted


2011 Journal article Open Access OPEN
A fast model for pollutant dispersion at the neighbourhood scale
Di Sabatino S, Buccolieri R, Paradisi P, Palatella L, Corrado R
This paper is devoted to the development and evaluation of a fast three-dimensional Eulerian model for dispersion inside and above the urban canopy layer. Spatially averaged wind and diffusivity coefficient profiles obtained from the commercial Computational Fluid Dynamics (CFD) code FLUENT are used as input in the developed model. This model is numerically solved by means of a finite volume method and mean concentration outputs are compared with the corresponding results from FLUENT. We considered several canopies made of arrays of cubes laid in staggered position. Results from the comparison suggest the potential of this type of simple modelling approach. As the spatially averaged wind and diffusivity profiles are strongly dependent from the mean morphometry properties of the urban canopy, these results, though preliminary, highlight the necessity of using specific turbulence closure models where building effects at the neighbourhood scale arc taken into account.Source: INTERNATIONAL JOURNAL OF ENVIRONMENT AND POLLUTION, vol. 47 (issue 1-4), pp. 207-215
DOI: 10.1504/ijep.2011.047335
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See at: Archivio Istituzionale della Ricerca- Università del Salento Open Access | International Journal of Environment and Pollution Restricted | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.inderscience.com Restricted


2013 Journal article Restricted
Is temporal scaling at the basis of allometry? Comment on "Physiologic time: A hypothesis" by West and West
Allegrini P, Paradisi P, Menicucci D, Gemignani A
This is a commentary to the paper West D, West BJ. Physiologic time: a hypothesis. Physics of Life Reviews 2013;10(2):210-24 discussing about allometry and universal power-laws in living systems.Source: PHYSICS OF LIFE REVIEWS, vol. 10 (issue 2), pp. 233-234
DOI: 10.1016/j.plrev.2013.04.009
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See at: Physics of Life Reviews Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.sciencedirect.com Restricted


2013 Journal article Restricted
Sleep unconsciousness and breakdown of serial critical intermittency: New vistas on the global workspace
Allegrini P, Paradisi P, Menicucci D, Bedini R, Piarulli A, Gemignani A
While several mental functions are characterized by parallel computation performed by moduli in the cortex, consciousness is sustained by a serial global integration: a single scene at a time takes place. Studies on complex systems show that macroscopic variables, integrating many components activities, undergo fluctuations with an intermittent serial structure when the system is in a state called "criticality", characterized by avalanches with inverse-power-law (scale-free) distribution densities of sizes and inter-event times. Criticality has been established in human brain dynamics during wakefulness. Here we review how the critical hypothesis is able to explain many recent studies on brain complex dynamics. We focus, in particular, on the global, serial, intermittent behavior that can be assessed via high-density electroencephalograms, studying transitions between metastable states. Established as it is during wakefulness, it remained unsolved whether this global intermittent dynamics correlates with consciousness or with a non-task-driven default mode, also present in non-conscious states, like deep (NREM) sleep. Here we show that in NREM sleep seriality breaks down, and re-establishes during REM sleep (dreams), with unaltered spacial structure, in terms of complex branching of avalanches. We conjecture that this connectivity is exploited in NREM sleep by neural bistability, resetting and "parallelizing" portions of the cortex. (C) 2013 Elsevier Ltd. All rights reserved.Source: CHAOS, SOLITONS AND FRACTALS, vol. 55, pp. 32-43
DOI: 10.1016/j.chaos.2013.05.019
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See at: Chaos Solitons & Fractals Restricted | CNR IRIS Restricted | CNR IRIS Restricted | www.sciencedirect.com Restricted


2013 Conference article Restricted
Scaling and intermittency of brain events as a manifestation of consciousness
Paradisi P, Allegrini P, Gemignani A, Laurino M, Menicucci D, Piarulli A
We discuss the critical brain hypothesis and its relationship with intermittent renewal processes displaying power-law decay in the distribution of waiting times between two consecutive renewal events. In particular, studies on complex systems in a "critical" condition show that macroscopic variables, integrating the activities of many individual functional units, undergo fluctuations with an intermittent serial structure characterized by avalanches with inverse-power-law (scale-free) distribution densities of sizes and inter-event times. This condition, which is denoted as "fractal intermittency", was found in the electroencephalograms of subjects observed during a resting state wake condition. It remained unsolved whether fractal intermittency correlates with the stream of consciousness or with a non-task-driven default mode activity, also present in non-conscious states, like deep sleep. After reviewing a method of scaling analysis of intermittent systems based of event-driven random walks, we show that during deep sleep fractal intermittency breaks down, and re-establishes during REM (Rapid Eye Movement) sleep, with essentially the same anomalous scaling of the pre-sleep wake condition. From the comparison of the pre-sleep wake, deep sleep and REM conditions we argue that the scaling features of intermittent brain events are related to the level of consciousness and, consequently, could be exploited as a possible indicator of consciousness in clinical applications.DOI: 10.1063/1.4776519
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See at: doi.org Restricted | CNR IRIS Restricted | CNR IRIS Restricted | scitation.aip.org Restricted


2013 Conference article Restricted
A trajectory statistical method for the identification of sources associated with concentration peak events
Cesari R, Paradisi P, Allegrini P
We briefly review the Trajectory Statistical Methods (TSMs) most used in literature for source identification, essentially based on the concept of Residence Time. Then, we introduce a statistical methodology that, starting from the Concentration Field method, takes into account only the peak values in the concentration time series measured at multiple receptor sites. We use virtual simulations to evaluate the performance of our approach. In order to derive concentration time series at multiple receptors, the Lagrangian Dispersion Model (LSM) FLEXPART is used, in the time forward mode, to simulate dispersion from a known emission source. Then, virtual concentration data are available in the receptor sites. As in many TSMs, Residence Times need to be computed and, to this goal, we use FLEXPART, but in the backward mode, that is, FLEXPART is applied to compute the backward trajectories from the receptor sites. Then, our proposed statistical method is applied to the computed Residence Times and to the concentration data to reconstruct the spatial distribution of emission sources. The numerical results show that our approach could overcome the problem of ghost sources. Further, the proposed method requires simulation times shorter that those required in other methods, since it makes use of a relatively small set of trajectories. This could be of some interest in the characterization of impact studies and local climatic scenarios.

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2013 Other 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.

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2013 Other 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 ?

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2014 Conference article Open Access OPEN
Biochemical reactions as renewal processes: the case of mRNA degradation
Paradisi P, Chiarugi D
Biochemical processes are typically described in terms of Continuous Time Markov Chains (CTMCs), which is the stochastic pro- cess associated with the well-known Gillespie's Chemical Master Equa- tion (CME). However, this approach is limited by the basic features of CTMC, that is, Markov property, time-invariance and, consequently, exponential decay of both correlation functions and distribution of Wait- ing Times (WTs) between successive reactions. Here we propose a model based on the theory of renewal point processes, i.e., stochastic processes defined as sequences of critical events occurring randomly in time and in- dependent from each other. Renewal theory allows to generalize CTMC modeling to the case of non-exponential behavior observed in many bio- chemical systems at the cell scale and is the natural framework for the study of intermittent time series. In particular, renewal modeling allows to include directly in a simple way non-exponential WT distribution such as slow power-law decay or stretched exponential. In the specific appli- cation of mRNA degradation, a renewal model can include whatever functional form of the degradation rate.

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