On the use of aggregated human mobility data to estimate the reproduction number.

The reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated 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.

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

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.

Seascape connectivity of European anchovy in the Central Mediterranean Sea revealed by weighted Lagrangian backtracking and bio-energetic modelling.

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.

General characteristics of relative dispersion in the ocean.

The multi-scale and nonlinear nature of the ocean dynamics dramatically affects the spreading of matter, like pollutants, marine litter, etc., of physical and chemical seawater properties, and the biological connectivity inside and among different basins. Based on the Finite-Scale Lyapunov Exponent analysis of the largest available near-surface Lagrangian data set from the Global Drifter Program, our results show that, despite the large variety of flow features, relative dispersion can ultimately be described by a few parameters common to all ocean sub-basins, at least in terms of order of magnitude.

Seasonal heterogeneity of ocean warming: a mortality sink for ectotherm colonizers.

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.

Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.

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.

The role of hydrodynamic processes on anchovy eggs and larvae distribution in the sicily channel (mediterranean sea): a case study for the 2004 data set.

Knowledge of the link between ocean hydrodynamics and distribution of small pelagic fish species is fundamental for the sustainable management of fishery resources. Both commercial and scientific communities are indeed seeking to provide services that could "connect the dots" among in situ and remote observations, numerical ocean modelling, and fisheries. In the Mediterranean Sea and, in particular, in the Sicily Channel the reproductive strategy of the European Anchovy (Engraulis encrasicolus) is strongly influenced by the oceanographic patterns, which are often visible in sea surface temperature satellite data.

Nonlinear stability of traffic models and the use of Lyapunov vectors for estimating the traffic state.

Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter.

Distribution of first-return times in correlated stationary signals.

We present an analytical expression for the first return time (FRT) probability density function of a stationary correlated signal. Precisely, we start by considering a stationary discrete-time Ornstein-Uhlenbeck (OU) process with exponential decaying correlation function. The first return time distribution for this process is derived by adopting a well-known formalism typically used in the study of the FRT statistics for nonstationary diffusive processes.

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 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).

Properties making a chaotic system a good pseudo random number generator.

We discuss the properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy, high dimensionality of the parent dynamical system, and very large period of the generated sequence. We propose the multidimensional 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 state version of the map.

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. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J.

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 hKS and the production rate of the coarse-grained Gibbs entropy rG. 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 pseudochaos. The basic reason for this is in the asymptotic (with respect to time) nature of hKS, while rG is a quantity related to short-time features of a system.

Non-Poisson dichotomous noise: higher-order correlation functions and aging.

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 two-time correlation functions. The transition of psi (tau) from the exponential to the nonexponential 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.

Absorption and emission in the non-Poissonian case.

This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential 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.

Generalized master equation via aging continuous-time random walks.

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 density psi(t) that is assumed to be an inverse power law with the power index micro.

Power-law time distribution of large earthquakes.

We study the statistical properties of time distribution of seismicity 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.