arXiv subjects

Massimiliano Ignaccolo

Publications and source records attributed to Massimiliano Ignaccolo.

8 recordsLinked to original sources

arXiv2012

Metastatistics of Extreme Values and its Application in Hydrology

We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of data with statistical inhomogeneities. By use of artificial sequences, we show that the metastatistics produce the correct predictions while the traditional approach based on the generalized extreme value distribution does not. An application of the metastatistics methodology to the case of extreme event to rainfall daily precipitation is also presented.

stat.AP↗

arXiv2012

Phase space parametrization of rain: the inadequacy of the gamma distribution

We show that the Gamma distribution is not an adequate fit for the probability density function of drop diameters using the Kolmogorov-Smirnov goodness of fit test. We propose a different parametrization of drop size distributions, which not depending by any particular functional form, is based on the adoption of standardized central moments. The first three standardized central moments are sufficient to characterize the distribution of drop diamters at the ground. These parameters together with the drop count form a 4-tuple which fully describe the variability of the drop size distributions. The Cartesian product of this 4-tuple of parameters is the rainfall phase space. Using disdrometer data from 10 different locations we identify invariant, not depending on location, properties of the rainfall phenomenon.

physics.ao-ph↗

arXiv2010

Time and ensemble averaging in time series analysis

In many applications expectation values are calculated by partitioning a single experimental time series into an ensemble of data segments of equal length. Such single trajectory ensemble (STE) is a counterpart to a multiple trajectory ensemble (MTE) used whenever independent measurements or realizations of a stochastic process are available. The equivalence of STE and MTE for stationary systems was postulated by Wang and Uhlenbeck in their classic paper on Brownian motion (Rev. Mod. Phys. 17, 323 (1945)) but surprisingly has not yet been proved. Using the stationary and ergodic paradigm of statistical physics -- the Ornstein-Uhlenbeck (OU) Langevin equation, we revisit Wang and Uhlenbeck's postulate. In particular, we find that the variance of the solution of this equation is different for these two ensembles. While the variance calculated using the MTE quantifies the spreading of independent trajectories originating from the same initial point, the variance for STE measures the spreading of two correlated random walkers. Thus, STE and MTE refer to two completely different dynamical processes. Guided by this interpretation, we introduce a novel algorithm of partitioning a single trajectory into a phenomenological ensemble, which we name a threshold trajectory ensemble (TTE), that for an ergodic system is equivalent to MTE. We find that in the cohort of healthy volunteers, the ratio of STE and TTE asymptotic variances of stage 4 sleep electroencephalogram is equal to 1.96 \pm 0.04 which is in agreement with the theoretically predicted value of 2.

physics.data-an↗

arXiv2009

A non arbitrary definition of rain event: the case of stratiform rain

A long standing issue in Hydrology is the arbitrariness of the rain "event" definition. In this manuscript, we show that 1) the event definition resting on the occurrence of a minimum rainless period and the one resting a sequence of consecutive wet intervals are statistically equivalent. 2) In the case of stratiform rain, a non arbitrary definition of rain event is possible. The dynamical properties of stratiform rain indicate the range [1.5,4] h as the proper one for the choice of a minimum rainless period for Chilbolton, UK. 3) The intra event dynamical variability is "described" by an alternate sequence of quiescent and active phases.

physics.ao-ph↗

arXiv2007

Brain, Music and non-Poisson Renewal Processes

In this paper we show that both music composition and brain function, as revealed by the Electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the non-ergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a techniques of statistical analysis recently developed by our group, the Aging Experiment (AE). First, we find that in both cases the distances between two consecutive events are described by non-exponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities $Ψ(t)$ are well fitted by stretched exponentials ($Ψ(t) \propto exp(-(γt)^α$), with $0.5 <α<1$.) The second step rests on the adoption of the AE, which shows that these are renewal processes. We show that the renewal stretched exponential is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index $μ= 1 + α$. We find that both EEG and music composition yield $μ< 2$. On the basis of the recently discovered complexity matching effect, according to which a complex system $S$ with $μ_S < 2$ responds only to a complex driving signal $P$ with $μ_P = μ_S$, we conclude that the results of our analysis may explain the influence of music on human brain.

q-bio.NC↗

arXiv2006

Renewal Aging as Emerging Property of Phase Synchronization

In this letter we examine a model recently proposed to produce phase synchronization [K. Wood et al, Phys. Rev. Lett. 96, 145701 (2006)] and we show that the onset to synchronization corresponds to the emergence of an intermittent process that is non-Poisson and renewal at the same time. We argue that this makes the model appropriate for the physics of blinking quantum dots, and the dynamics of human brain as well.

cond-mat.stat-mech↗

arXiv2003

Vortex dynamics in evolutive flows: a weakly chaotic phenomenon

We study the vortex dynamics in an evolutive flow. We carry out the statistical analysis of the resulting time series by means of the joint use of a compression and an entropy diffusion method. This approach to complexity makes it possible for us to establish that the time series emerging from the wavelet analysis of the vortex dynamics is a weakly chaotic process driven by a hidden dynamic process. The complexity of the hidden driving process is shown to be located at the border between the stationary and non-stationary state.

cond-mat.stat-mech↗

arXiv2000

A non-extensive approach to the time evolution of Lyapunov coefficients

We study sporadic randomness by means of a non-extensive form of Lyapunov coefficient. We recover from a different perspective the same conclusion as that of an earlier work, namely, that the ordinary Pesin theorem applies (P.Gaspard and X.-J. Wang, Proc. Natl. Acad. Sci. USA {\bf85}, 4591 (1988)). However, our theoretical analysis allows us to organize the numerical calculations so as to reveal the slow transition from a temporary form of non-extensive thermodynamics, corresponding to the prediction of a recent paper (M. Buiatti, P. Grigolini, A. Montagnini, Phys. Rev. Lett {\bf 82}, 3383 (1999)), to the ordinary extensive thermodynamics. We show that the transition takes place with a slow decay corresponding to the regression from a non-equilibrium initial condition to equilibrium condition.

cond-mat.stat-mech↗