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The measurement of transpiration at plant level is a challenging topic in crop water requirements research, e.g. for irrigation scheduling and for the partitioning of plant transpiration and soil evaporation in modelling crop evapotranspiration process. The thermal dissipation method (TD) is widely applied for transpiration estimates of tree species, however some studies reported underestimations of transpiration measurements performed with the TD method when using the equation proposed by Granier. In particular, large underestimation of transpiration flux was reported in vineyards. The underestimation is ascribed to the equation, and its parameters, used to calculate the sapwood flux density from the heat transfer equations in the original Granier’s model and site-specific calibration is required. In this study, using measurements performed in a 2-year field experiment, the TD method was recalibrated at field scale in a vineyard cultivated in a Mediterranean region (Sicily, southern Italy), comparing transpiration flux determined by the TD method with transpiration calculated by the partitioning flux-variance similarity (FVS) method. FVS is a relatively new and innovative method for partitioning water fluxes in transpiration and evaporation through EC data. In this study, transpiration calculated through the equation proposed by Granier was, on average, 26% lower than transpiration determined by FVS. The results show that a new exponential function to calculate the sapwood flux density performed better than the power function in the original equation proposed by Granier. The results also showed that species and site-specific relationships are needed to accurately determine transpiration through the TD method. The ratio T/ET when T is calculated by the recalibrated TD function was equal to 0.77.

The CoViD-19 pandemic ceased to be describable by a susceptible-infected-recovered (SIR) model when lockdowns were enforced. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 (Sudden Acute Respiratory Syndrome Coronavirus 2) in terms of individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

Ecological connectivity is one of the most important processes that shape marine populations and ecosystems, determining their distribution, persistence, and productivity. Here we use the synergy of Lagrangian back-trajectories, otolith-derived ages of larvae, and satellite-based chlorophyll-a to identify spawning areas of European anchovy from ichthyoplanktonic data, collected in the Strait of Sicily (Central Mediterranean Sea), i.e., the crucial channel in between the European and African continents. We obtain new evidence of ecosystem connectivity between North Africa and recruitment regions off the southern European coasts. We assess this result by using bio-energetic modeling, which predicts species-specific responses to environmental changes by producing quantitative information on functional traits. Our work gives support to a collaborative and harmonized use of Geographical Sub-Areas, currently identified by the General Fisheries Commission for the Mediterranean. It also confirms the need to incorporate climate and environmental variability effects into future marine resources management plans, strategies, and directives.

The flux-variance similarity (FVS) partitioning method to estimate transpiration/photosynthesis and evaporation/respiration, using only high frequency Eddy Covariance (EC) measurements, was studied. The FVS method was applied to two crops in successive growing seasons of a typical cropping system in Mediterranean region: fava bean followed by winter wheat. FVS applies the flux-variance arguments derived from Monin-Obukhov similarity theory separately to the stomatal (photosynthesis and transpiration) and non-stomatal (respiration and evaporation) processes. The leaf-level water use efficiency, an input of FVS method, is here calculated by using EC outputs and estimated humidity after the direct measurement of surface infrared temperature. The two experimental seasons were characterized by exceptionally rainy periods (262 mm in 85 days in 2014, 344 mm in 149 days in 2015). Nevertheless, the partitioning results are consistent with expected trends and absolute values of flux components throughout both seasons. In particular, heterotrophic soil respiration measured by chamber systems and modelled FVS respiration components are comparable at the beginning and at the end of the growing crop cycles, when crop biomass and leaf area are very low. Furthermore, the coupling of FVS method and root exclusion method for measuring soil respiration is able to give the heterotrophic and autotrophic components of respiration. Finally, the results showed that the succession fava bean to wheat permits a mitigation of the loss of carbon to the atmosphere and increases carbon sequestration.

In this paper we propose a C++-software package implementing the algorithm EKF-AUS-NL (Extended Kalman Filter with Assimilation in the Unstable Space with NonLinear evolution) designed to perform data assimilation in the unstable space when the Jacobian of the differential equation cannot be calculated. We also propose a simple approach to take into account the presence of the model error in the framework of the EKF-AUS-NL. The software performs the data assimilation using the EKF-AUS-NL algorithm with a dynamical systems defined as a generic time evolution routine separately implemented. We present two illustrative examples based on the Lorenz96 and SLAM systems. Keywords: Kalman-Filter, AUS, Lorenz96, SLAM

Estimation of the prevalence of undocumented SARS-CoV-2 infections is critical for understanding the overall impact of CoViD-19, and for implementing effective public policy intervention strategies. We discuss a simple yet effective approach to estimate the true number of people infected by SARS-CoV-2, using raw epidemiological data reported by official health institutions in the largest EU countries and the USA.

The effect of vertical shear on the horizontal dispersion properties of passive tracer particles on the continental shelf of the South Mediterranean is investigated by means of observation and model data. In situ current measurements reveal that vertical gradients of horizontal velocities in the upper mixing layer decorrelate quite fast ( ∼ 1 day), whereas an eddy-permitting ocean model, such as the Mediterranean Forecasting System, tends to overestimate such decorrelation time because of finite resolution effects. Horizontal dispersion, simulated by the Mediterranean sea Forecasting System, is mostly affected by: (1) unresolved scale motions, and mesoscale motions that are largely smoothed out at scales close to the grid spacing; (2) poorly resolved time variability in the profiles of the horizontal velocities in the upper layer. For the case study we have analysed, we show that a suitable use of deterministic kinematic parametrizations is helpful to implement realistic statistical features of tracer dispersion in two and three dimensions. The approach here suggested provides a functional tool to control the horizontal spreading of small organisms or substance concentrations, and is thus relevant for marine biology, pollutant dispersion as well as oil spill applications.

When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

Multidisciplinary studies are recently aiming to define diagnostic tools for fishery sustainability by coupling ichthyoplanktonic datasets, physical and bio-geochemical oceanographic measurements, and ocean modelling. The main goal of these efforts is to understand those processes that control the dispersion and fate of fish larvae and eggs, and thus tuning the inter-annual variability of the biomass of small pelagic fish species. In this paper we analyse the distribution of eggs and larvae as well as the biological features of the two species of pelagic fish, Engraulis encrasicolus and Sardinella aurita in the north-eastern sector of the Sicily Channel (Mediterranean Sea) from ichthyoplanktonic data collected during the 2010 and 2011 summer cruises. We use Lagrangian simulations and satellite data (i.e., sea surface temperature, wind, and chlorophyll-a concentration) to recognize the main oceanographic patterns that mark eggs and larvae transport processes. We provide a mechanistic explanation of a cross-shore transport process by using a potential vorticity (PV) model that takes into account the role of wind stress in generating cold filaments. Our results show that the strong offshore transport towards Malta occurred in 2010 was likely due to a persistent Mistral wind forcing that generated high-PV cold filaments. This phenomenon was not found in the 2011 analysis, which indeed showed an along-shore transport towards the retention area of Capo Passero. Since, for the first time, we describe the spatial distribution of the early life stage of Sardinella aurita in the northern part of the Sicily Channel and we clarify the link between the ocean dynamics and the fate of small pelagic fish larvae, this work provides a useful, diagnostic tool for the sustainable management of fishery resources.

Scanlon and Sahu (Water Resour Res 44(10): W10418, 2008) proposed an interesting method to estimate assimilation, respiration, evaporation and transpiration directly using high-frequency eddy-covariance measurements. In this note we critically revise this method and, in particular, using the Descartes' rule of sign, we show that one branch of solutions can be directly neglected reducing the analytical complexity of the procedure. We also discuss the stability of the results of the method with respect to the input parameters, especially to the water-use efficiency.

Distribution shifts are a common adaptive response of marine ectotherms to climate change but the pace of redistribution depends on species-specific traits that may promote or hamper expansion to northern habitats. Here we show that recently, the loggerhead turtle (Caretta caretta) has begun to nest steadily beyond the northern edge of the species’ range in the Mediterranean basin. This range expansion is associated with a significant warming of spring and summer sea surface temperature (SST) that offers a wider thermal window suitable for nesting. However, we found that post-hatchlings departing from this location experience low winter SST that may affect their survival and thus hamper the stabilization of the site by self-recruitment. The inspection of the Intergovernmental Panel on Climate Change model projections and observational data on SST trends shows that, despite the annual warming for this century, winter SST show little or no trends. Therefore, thermal constraints during the early developmental phase may limit the chance of population growth at this location also in the near future, despite increasingly favourable conditions at the nesting sites. Quantifying and understanding the interplay between dispersal and environmental changes at all life stages is critical for predicting ectotherm range expansion with climate warming.

We discuss a route to intermittency based on the concept of reflexivity, namely on the interaction between observer and stochastic reality. A simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1 / f -noise. In the absence of noise the model yields a symmetry-induced equilibrium manifold with two stable states. Noise makes this equilibrium manifold unstable, with an escape rate becoming lower and lower upon time increase, thereby generating an inverse power law distribution of waiting times. The distribution of the times of permanence in the basin of attraction of the equilibrium manifold are analytically predicted through the adoption of a first-passage time technique. Finally we discuss the possible extension of our approach to deal with the intermittency of complex systems in different fields.

15 pages.-- PACS numbers: 05.45.−a; 05.60.−k; 05.45.Jn.-- Final full-text version of the paper available at: http://dx.doi.org/10.1016/j.physa.2007.06.036., We introduce a high-dimensional symplectic map, modeling a large system, to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the initial growth of the Boltzmann entropy, SB, as a function of the coarse-graining resolution (the late stage of the evolution is trivial, as the system is subjected to no external drivings). We show that a characteristic scale emerges, and that the behavior of SB vs t, at variance with the Gibbs entropy, does not depend on the resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth, in its early stage, depends essentially on the single-particle chaotic dynamics. It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.

Multidisciplinary studies are recently seeking to define diagnostic tools for fishery sustainability by coupling ichthyoplanktonic datasets, physical and bio-geochemical oceanographic measurements, and ocean modelling. The main goal of these efforts is the understanding of those processes that control fate and dispersion of fish larvae and eggs and thus tune the inter-annual variability of biomass of fish species. We here analyzed eggs and larvae distribution and biological features of Sardinella aurita in the northeast sector of the Sicily Channel (Mediterranean Sea) collected during the 2010 and 2011 summer cruises. We make use of satellite sea surface temperature, wind, and chlorophyll data to recognize the main oceanographic patterns that mark eggs and larvae transport processes and we pair these data with Lagrangian runs. To provide a physical explanation of the transport processes that we observe, we hire a potential vorticity (PV) model that takes into account the role of wind stress in generating those cold filaments responsible for the offshore delivery of eggs and larvae. Our results show that the strong offshore transport towards Malta occurring in 2010 is related to a persistent wind forcing along the southern Sicilian coast that generated an observable cold filament. Such a pattern is not found in the 2011 analysis, which indeed shows a more favorable condition for sardinella larvae recruiting with a weak offshore transport. Our results want to add some insights regarding operational oceanography for sustainable fishery.

The effect of vertical shear on the horizontal dispersion properties of passive tracer particles on the continental shelf of South Mediterranean is investigated by means of observative and model data. In-situ current measurements reveal that vertical velocity gradients in the upper mixed layer decorrelate quite fast (∼ 1 day), whereas basin-scale ocean circulation models tend to overestimate such decorrelation time because of finite resolution effects. Horizontal dispersion simulated by an eddy-permitting ocean model, like, e.g., the Mediterranean Forecasting System, is mosty affected by: (1) unresolved scale motions, and mesoscale motions that are largely smoothed out; (2) poorly resolved time variability of vertical velocity profiles in the upper layer. For the case study we have analysed, we show that a suitable use of kinematic parameterisations is helpful to implement realistic statistical features of tracer dispersion in two and three dimensions. The approach here suggested provides a functional tool to control the horizontal spreading of small organisms or substance concentrations, and is thus relevant for marine biology, pollutant dispersion as well as oil spill applications.

When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.

The present work briefly summarizes the results obtained in Palatella et al. Eur. Phys. J. B 38 (2004) 671 using the Diffusion Entropy technique and adds some new results regarding the Dow Jones Index time series. We show that time distances between peaks of volatility or activity are distributed following an asymptotic power-law which ultimately recovers an exponential behavior. We discuss these results in comparison with the TARCH model, the Ornstein-Uhlenbeck stochastic volatility model and a multi-agent model. We conclude that both ARCH and stochastic volatility models better describe the observed experimental evidences. © 2005 Elsevier B.V. All rights reserved.

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects., 30 pages

A spectroscopic analysis of nonlinear energy transfer in BaY 2 F 8 and LiYF 4 doped with Er 3+ is reported. We developed a new method to measure the upconversion parameter based on the sinusoidal modulation of the pump beam intensity and on the intensity spectrum analysis of the green fluorescence. We also present cw laser results in the 2 μm wavelength region of a Tm,Ho : LiYF 4 crystal with 30% slope efficiency at room temperature.

We study the time evolution of a quantum system without classical counterpart, undergoing a process of entropy increase due to the environment influence. We show that if the environment-induced decoherence is interpreted in terms of wave-function collapses, a symbolic sequence can be generated. We prove that the Kolmogorov-Sinai entropy of this sequence coincides with rate of von Neumann entropy increase., 5 pages, 2 figures

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 reproduce the statistical properties of precipitation well, the crucial variable for the growth of crops.

This work describes the results obtained by the statistical downscaling technique for the assessment of changes in precipitation (P), potential evaporation (PE). In turn P and PE are used for computing two indexes of water availability, namely the index of water deficit (WDI) and the aridity index (AI). The analysis is carried out for the Capitanata plain (South-East of Italy) and the A2 scenario of the IPCC Assessment Report 4 (AR4). The large-scale temperature at the 1000hPa level and sea level pressure fields are used as predictors. The local precipitation and potential evaporation time series are used as predictands. The statistical downscaling technique used is based on Canonical Correlation Analysis. A validation procedure of the model is performed and the same technique is used for climatic projections of P, PE and consequently WDI and AI. Climate analysis and projections at this local space scale is an important issue not only for current water management and planning, but also for improving the irrigation efficiency considering future climate change scenarios. © L. Palatella et al., 2012.

In the first part of this paper, we review some important results on atmospheric predictability, from the pioneering work of Lorenz to recent results with operational forecasting models. Particular relevance is given to the connection between atmospheric predictability and the theory of Lyapunov exponents and vectors. In the second part, we briefly review the foundations of data assimilation methods and then we discuss recent results regarding the application of the tools typical of chaotic systems theory described in the first part to well established data assimilation algorithms, the Extended Kalman Filter (EKF) and Four Dimensional Variational Assimilation (4DVar). In particular, the Assimilation in the Unstable Space (AUS), specifically developed for application to chaotic systems, is described in detail.

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: in one case Principal Component Analysis (PCA) filter is applied only to predictor and in the other to both predictor 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 periods have been considered. For Summer precipitation in Apulia region we also use the 500 hPa temperature (T500) as predictor, obtaining comparable results. Results show different 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 robust 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.

12 pages.-- PACS numbers: 05.70.Ln, 05.40.-a.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.76.051103., Auxiliary material available at: http://netserver.aip.org/cgi-bin/epaps?ID=E-PLEEE8-76-106710., A simplified version of a classical problem in thermodynamics -the adiabatic piston- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained in the left and right chambers of the piston are always in equilibrium that is, the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution after any collision with the piston. Then by using kinetic theory we derive the collision statistics, from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables namely, the piston average velocity and position, the velocity variance, and the temperatures of the two compartments. The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of a gas devised to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables that catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache, and Lesne [J. Stat. Phys. 108, 669 (2002); 112, 1177 (2003)]., This work has been partially supported by MIUR, PRIN2003 "Complex Systems and Many Body Problems", and PRIN2005 "Statistical Mechanics of Complex Systems". S.P. has benefited from a MEC-MIUS joint program (Italy-Spain Integral Actions).

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power-law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. We also in terms of the DEA revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description., 16 pages, 7 figures

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation based respectively on the Generalized Master Equation formalism, on a Liouville-like approach and on a trajectory perspective., 11 pages, 1figure

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed., 10 pages, 3 figures, new version, title changed and minor corrections

We discuss the connection between the Kolmogorov-Sinai entropy, $h_{KS}$, and the production rate of the coarse grained Gibbs entropy, $r_G$. Detailed numerical computations show that the (often accepted) identification of the two quantities does not hold in systems with intermittent behavior and/or very different characteristic times and in systems presenting pseudo-chaos. The basic reason of this fact is in the asymptotic (with respect to time) nature of $h_{KS}$, while $r_G$ is a quantity related to short time features of a system., 8 pages, 5 figures Submitted to PRE

We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.

This article is a reply to a comment by A. Helmstetter and D. Sornette about the article 'Power-Law Time Distribution of Large Earthquakes' from 2003.

We prove the efficiency of a new method for the detection of crucial events that might have useful applications to the war against terrorism. This has to do with the search for rare but significant events, a theme of research that has been made of extreme importance by the tragedy of September 11. This method is applied here to defining the statistics of seismic main-shocks, as done in cond-mat/0212529. The emphasis here is on the conceptual issues behind the results obtained in cond-mat/0212529 than on geophysics. This discussion suggests that the method has a wider range of validity. We support this general discussion with a dynamic model originally proposed in cond-mat/0107597 for purposes different from geophysical applications. However, it is a case where the crucial events to detect are under our control, thereby making it possible for us to check the accuracy of the method of detection of invisible and crucial events that we propose here for a general purpose, including the war against terrorism. For this model an analytical treatment has been recently found [cond-mat/0209038], supporting the claims that we make in this paper for the accuracy of the method of detection. For the reader's convenience, the results on the seismic fluctuations are suitably reviewed, and discussed in the light of the more general perspective of this paper. We also review the model for seismic fluctuations, proposed in the earlier work of cond-mat/0212529. This model shares with the model of cond-mat/0107597 the property that the crucial events are imbedded in a sea of secondary events, but it allows us to reveal with accuracy the statistics of the crucial events for different mathematical reasons.

With the help of the Diffusion Entropy technique we show the non-Poisson statistics of the distances between consecutive Omori's swarms of earthquakes. We give an analytical proof of the numerical results of an earlier paper [cond-mat/0212529, Mega et al., Phys. Rev. Lett. 90 (2003) 188501], Comment: Frontiers of Science 2003, Pavia,Italy

This letter adresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a non-exponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics., Comment: 4 pages 3 figures. accepted for publication on Physical Review Letters

In this work, we observe experimentally the dynamics of the defects of a periodic convective pattern obtained in a liquid crystal n-(4-methoxybenziliden)-4-butylamilin 98% cell subjected to electro-nematic instability by means of an ac electric field. We perform a check of the validity of the theoretical prescriptions regarding the interaction of these defects with the external phase-field gradient. We found results in a good agreement with the theory.

We model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. Using a time series approach, the diffusion entropy method (DE), we compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The model yields the famous Zipf's law in terms of the generalized central limit theorem., Conference FRACTAL 2004

We analyze $\mathrm{RR}$ heartbeat sequences with a dynamic model that satisfactorily reproduces both the long- and the short-time statistical properties of heart beating. These properties are expressed quantitatively by means of two significant parameters, the scaling $\ensuremath{\delta}$ concerning the asymptotic effects of long-range correlation, and the quantity $1\ensuremath{-}\ensuremath{\pi}$ establishing the amount of uncorrelated fluctuations. We find a correlation between the position in the phase space $(\ensuremath{\delta},\ensuremath{\pi})$ of patients with congestive heart failure and their mortality risk.

We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent $\mu=2.06 \pm 0.01$. We propose the Long-Range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes., Comment: 4 pages, 3 figures. Revised version accepted for publication. Typos corrected, more detailed discussion on the method used, refs added. Phys. Rev. Lett. (2003) in press

In this paper we try to model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. We use a time series approach, the diffusion entropy method (DE), to compute the complexity of an italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The network complexity is independently measured on the same corpus, looking at the co-occurrence of nouns and verbs. This connection of cognitive complexity with long-range time correlations also provides an explanation for the famous Zipf's law in terms of the generalized central limit theorem.

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work., Comment: 27 pages, 9 figures

We investigate on a possible way to connect the presence of Low-Complexity Sequences (LCS) in DNA genomes and the nonstationary properties of base correlations. Under the hypothesis that these variations signal a change in the DNA function, we use a new technique, called Non-Stationarity Entropic Index (NSEI) method, and we prove that this technique is an efficient way to detect functional changes with respect to a random baseline. The remarkable aspect is that NSEI does not imply any training data or fitting parameter, the only arbitrarity being the choice of a marker in the sequence. We make this choice on the basis of biological information about LCS distributions in genomes. We show that there exists a correlation between changing the amount in LCS and the ratio of long- to short-range correlation.

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences., Comment: 15 pages, 4 figures

We describe two types of memory and illustrate each using artificial and actual heartbeat data sets. The first type of memory, yielding anomalous diffusion, implies the inverse power-law nature of the waiting time distribution and the second the correlation among distinct times, and consequently also the occurrence of many pseudoevents, namely, not genuinely random events. Using the method of diffusion entropy analysis, we establish the scaling that would be determined by the real events alone. We prove that the heart beating of healthy patients reveals the existence of many more pseudoevents than in the patients with congestive heart failure.

We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored with a window of size $L << N$. The DEM makes a wise use of the statistical information available and, consequently, in spite of the modest size of the window used, does succeed in revealing local statistical properties, and it shows how they change upon moving the windows along the experimental sequence. The method is expected to work also to predict catastrophic events before their occurrence., FRACTAL 2002 (Spain)