Langevin formulation of a subdiffusive continuous time random walk in physical time

Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous time random walk (CTRW). Stochastic trajectories of a CTRW can be described mathematically in terms of a subordination of a normal diffusive process by an inverse Levy-stable process. Here, we propose a simpler Langevin formulation of CTRWs without subordination. By introducing a new type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multi-point statistics of this noise and compare it with the noise driving scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive behaviour. Interestingly, these two noises are identical up to the level of the 2nd order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields, and compare our results with those of SBM.Comment: 11 pages, 4 figures - The new version contains corrected figures and new paragraphs in the main tex

Forecasting transitions in systems with high dimensional stochastic complex dynamics: A Linear Stability Analysis of the Tangled Nature Model

We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean field equations. Numerical analysis of the high dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation is found to be a good early-warning of the transitions occurring intermittently.Comment: 4 pages and 4 figures - The new version contains a corrected Figure

Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity

Stochastic processes play a key role for mathematically modeling a huge variety of transport problems out of equilibrium. To formulate models of stochastic dynamics the mainstream approach consists in superimposing random fluctuations on a suitable deterministic evolution. These fluctuations are sampled from probability distributions that are prescribed a priori, most commonly as Gaussian or Levy. While these distributions are motivated by (generalised) central limit theorems they are nevertheless unbounded. This property implies the violation of fundamental physical principles such as special relativity and may yield divergencies for basic physical quantities like energy. It is thus clearly never valid in real-world systems by rendering all these stochastic models ontologically unphysical. Here we solve the fundamental problem of unbounded random fluctuations by constructing a comprehensive theoretical framework of stochastic processes possessing finite propagation velocity. Our approach is motivated by the theory of Levy walks, which we embed into an extension of conventional Poisson-Kac processes. Our new theory possesses an intrinsic flexibility that enables the modelling of many different kinds of dynamical features, as we demonstrate by three examples. The corresponding stochastic models capture the whole spectrum of diffusive dynamics from normal to anomalous diffusion, including the striking Brownian yet non Gaussian diffusion, and more sophisticated phenomena such as senescence. Extended Poisson-Kac theory thus not only ensures by construction a mathematical representation of physical reality that is ontologically valid at all time and length scales. It also provides a toolbox of stochastic processes that can be used to model potentially any kind of finite velocity dynamical phenomena observed experimentally.Comment: 25 pages, 5 figure

Towards a Comprehensive Framework for the Analysis of Anomalous Diffusive Systems

PhDThe modelling of transport processes in biological systems is one of the main theoretical challenges in physics, chemistry and biology. This is motivated by their essential role in the emergence of diseases, like tumour metastases, which originate from the spontaneous migration of cancer cells. Thus, improvements in their understanding could potentially pave the way for an outstanding innovation of present-day techniques in medicine. These processes often exhibit anomalous properties, which are qualitatively described by the power-law scaling of their mean square displacement, compared to the linear one of normal diffusion. Such behaviour has been often successfully explained by the celebrated continuous-time random walk model. However, recent experimental studies revealed the existence of both more complicated mean square displacement behaviour and anomalous features in other characteristic observables, e.g. the position-velocity statistics or the two point correlation functions of either the velocity or the position. Thus, in order to understand the anomalous diffusion recorded in these experiments and assess the microscopic processes underlying the observed macroscopic dynamics, one needs to have a complete tool-kit of techniques and models that can be readily compared with the experimental datasets. In this Thesis, we contribute to the construction of such a complete framework by fully characterising anomalous processes, which are described by means of a continuoustime random walk with general waiting time distributions and/or external forces that are exerted both during the jumps (as in the original model) and the waiting times. In the first case we derive both the joint statistics of these processes and their observables, specifically by obtaining a generalised fractional Feynman-Kac formula, and their multipoint correlation functions and employ them to fit the mean square displacement data of diffusing mitochondria. This result supports the experimental relevance of our formalism, which comprises general formulas for several quantities that can provide readily predictable tests to be checked in experiments. In the second case, we characterise the new anomalous processes by means of Langevin equations driven by a novel type of non Gaussian noise, which reproduces the typical fluctuations of a free diffusive continuous-time random walk. For a constant external force, we also obtain the fractional evolution equations of their position probability density function and show that, contrarily to continuous-time random walks, they are weak Galilean invariant, i.e., their position distribution in different Galilean frames is obtained by shifting the sample variable according to the relative motion of the frames. Thus, these processes provide a suitable frame-invariant framework, that could be employed to investigate the stochastic thermodynamics of anomalous diffusive processes

In the folds of the Central Limit Theorem: L\'evy walks, large deviations and higher-order anomalous diffusion

This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply. Notwithstanding this property, their higher-order moments display anomalous scaling properties, whenever the statistics of the transition times possesses power-law tails. This phenomenon is perfectly consistent with the classical Central Limit Theorem, as it involves the convergence properties towards the normal distribution. This phenomenon is closely related to the property that the higher order moments of normalized sums of $N$ independent random variables possessing finite variance may deviate, for $N$ tending to infinity, to those of the normal distribution. The thermodynamic implications of these results are thoroughly analyzed by motivating the concept of higher-order anomalous diffusion.Comment: 24 pages, 9 figure

Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let

Making visible the cost of informal caregivers’ time in Latin America : a case study for major cardiovascular, cancer and respiratory diseases in eight countries

BACKGROUND: Informal care is a key element of health care and well-being for society, yet it is scarcely visible and rarely studied in health economic evaluations. This study aims to estimate the time use and cost associated with informal care for cardiovascular diseases, pneumonia and ten different cancers in eight Latin American countries (Argentina, Brazil, Chile, Colombia, Costa Rica, Ecuador, Mexico and Peru). METHODS: We carried out an exhaustive literature review on informal caregivers' time use, focusing on the selected diseases. We developed a survey for professional caregivers and conducted expert interviews to validate this data in the local context. We used an indirect estimate through the interpolation of the available data, for those cases in which we do not found reliable information. We used the proxy good method to estimate the monetary value of the use of time of informal care. National household surveys databases were processed to obtain the average wage per hour of a proxy of informal caregiver. Estimates were expressed in 2020 US dollars. RESULTS: The study estimated approximately 1,900 million hours of informal care annually and $ 4,300 million per year in average informal care time cost for these fifteen diseases and eight countries analyzed. Cardiovascular diseases accounted for an informal care burden that ranged from 374 to 555 h per year, while cancers varied from 512 to 1,825 h per year. The informal care time cost share on GDP varied from 0.26% (Mexico) to 1.38% (Brazil), with an average of 0.82% in the studied American countries. Informal care time cost represents between 16 and 44% of the total economic cost (direct medical and informal care cost) associated with health conditions. CONCLUSIONS: The study shows that there is a significant informal care economic burden -frequently overlooked- in different chronic and acute diseases in Latin American countries; and highlights the relevance of including the economic value of informal care in economic evaluations of healthcare

The health, economic and social burden of smoking in Argentina, and the impact of increasing tobacco taxes in a context of illicit trade

Tobacco tax increases, the most cost-effective measure in reducing consumption, remain underutilized in low and middle-income countries. This study estimates the health and economic burden of smoking in Argentina and forecasts the benefits of tobacco tax hikes, accounting for the potential effects of illicit trade. Using a probabilistic Markov microsimulation model, this study quantifies smoking-related deaths, health events, and societal costs. The model also estimates the health and economic benefits of different increases in the price of cigarettes through taxes. Annually, smoking causes 45,000 deaths and 221,000 health events in Argentina, costing USD 2782 million in direct medical expenses, USD 1470 million in labor productivity loss costs, and USD 1069 million in informal care costs-totaling 1.2% of the national gross domestic product. Even in a scenario that considers illicit trade of tobacco products, a 50% cigarette price increase through taxes could yield USD 8292 million in total economic benefits accumulated over a decade. Consequently, raising tobacco taxes could significantly reduce the health and economic burdens of smoking in Argentina while increasing fiscal revenue