Searcharxiv⌕ Search

arXiv subjects

Luigi Palatella

Publications and source records attributed to Luigi Palatella.

At least 19 recordsLinked to original sources
arXiv2024

Cell Motility in Cancer, Crucial Events, Criticality, and Lévy Walks

The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Levy random walks is presented herein. We study such walks occurring on a two-dimensional plane where the walk is similar to the motion of a bird flying with a constant velocity, but with random changes of direction in time. The intelligence of the bird is signaled by the instantaneous changes of flying direction, which become invisible in the time series obtained by projecting the 2D walk either on the x axis or the y axis. We establish that the projected 1D time series share the statistical complexity of time series frequently used to monitor physiological processes, shedding light on the role of crucial events (CE-s) in pathophysiology. Such CE-s are signified by abrupt changes of flying direction which are invisible in the 1D physiological time series. We establish a connection between the complex scaling index δgenerated by the CE-s through μ_{R} = 2 - δ, where μ_{R} is the inverse power law index of the probability density function of the time interval between consecutive failures of the process of interest. We argue that the identification of empirical indices along with their theoretical relations afford important measures to control cancer.

nlin.AO↗
arXiv2022

Noise-induced intermittence

We study a form of noise-induced intermittence originated by an out of equilibrium process yielding events in time with a survival probability that in the case of an infinitely aged condition coincides with the Mittag-Leffler function. In contrast with the Pomeau-Manneville intermittence, the aging process does not have any effect on the inverse power law of the large time scale but on the short-time stretched exponential regime.

physics.bio-ph↗
arXiv2021

A phenomenological estimate of the Covid-19 true scale from primary data

Estimation of prevalence of undocumented SARS-CoV-2 infections is critical for understanding the overall impact of the Covid-19 disease. In fact, unveiling uncounted cases has fundamental implications for public policy interventions strategies. In the present work, we show a basic yet effective approach to estimate the actual number of people infected by Sars-Cov-2, by using epidemiological raw data reported by official health institutions in the largest EU countries and USA.

physics.soc-ph↗
arXiv2020

Epidemic response to physical distancing policies and their impact on the outbreak risk

We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of 'lockdown' to reduce the number of new infections. Specifically we use a collisional approach to an infection-age structured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical proximity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distancing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interactions among people, which may help policy makers to improve remote-working organizational structure.

physics.soc-ph↗
arXiv2007

Macroscopic equations for the adiabatic piston

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 on 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 gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).

nlin.CD↗
arXiv2006

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

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.

physics.soc-ph↗
arXiv2005

Properties making a chaotic system a good Pseudo Random Number Generator

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.

nlin.CD↗
arXiv2005

Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the growth with time of the Boltzmann entropy, S_B, in this system as a function of the coarse graining resolution. We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse graining 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 depends essentially on the single-particle chaotic dynamics (for t not too small). It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.

nlin.CD↗
arXiv2004

Correlation function and generalized master equation of arbitrary age

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.

cond-mat.stat-mech↗
arXiv2004

The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?

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.

nlin.CD↗
arXiv2004

Absorption and Emission in the non-Poisson case

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.

cond-mat.other↗
arXiv2003

Activity autocorrelation in financial markets. A comparative study between several models

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.

cond-mat.stat-mech↗
arXiv2003

Cognitive scale-free networks as a model for intermittency in human natural language

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.

cond-mat.stat-mech↗
arXiv2003

Detection of invisible and crucial events: from seismic fluctuations to the war against terrorism

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.

cond-mat.stat-mech↗
arXiv2003

Intermittency and scale-free networks: a dynamical model for human language complexity

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.

cond-mat.stat-mech↗
arXiv2003

In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures

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.

cond-mat.stat-mech↗
arXiv2003

Breakdown of the Onsager principle as a sign of aging

We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution psi(t) that is assumed to be an inverse power law. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless the nature of the waiting time distribution. As a consequence of this procedure we create a GME that it is a "bona fide" master equation, in spite of being non-Markovian. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light into the problem of how to unravel non-Markovian master equations.

cond-mat.stat-mech↗