N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice

The N-tree approximation scheme, introduced in the context of random directed polymers, is here applied to the computation of the maximum Lyapunov exponent in a coupled map lattice. We discuss both an exact implementation for small tree-depth $n$ and a numerical implementation for larger $n$s. We find that the phase-transition predicted by the mean field approach shifts towards larger values of the coupling parameter when the depth $n$ is increased. We conjecture that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure

Transport properties in chaotic and non-chaotic many particles systems

Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting as a thermal bath. The second is the same except for the shape of the particles, which is now square. The basic difference of these two systems lies in the interaction: hard core elastic collisions make the dynamics of the disks chaotic whereas that of squares is not. Remarkably, this difference is not reflected in the transport properties of the two systems: simulations show that the diffusion coefficients, velocity correlations and response functions of the heavy impurity are in agreement with kinetic theory for both the chaotic and the non-chaotic model. The relaxation to equilibrium, however, is very sensitive to the kind of interaction. These observations are used to reconsider and discuss some issues connected to chaos, statistical mechanics and diffusion.Comment: 23 pgs with 8 Figure

Brownian motion and diffusion: from stochastic processes to chaos and beyond

One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian Motion and more general diffusive behaviours. Then, we focus on the problems concerning the determination of the microscopic nature of diffusion by means of data analysis. Finally, we discuss the general conditions required for the onset of large scale diffusive motion.Comment: RevTeX-4, 11 pages, 5 ps-figures. Chaos special issue "100 Years of Brownian Motion

Thermodynamic formalism for the Lorentz gas with open boundaries in dd dimensions

A Lorentz gas may be defined as a system of fixed dispersing scatterers, with a single light particle moving among these and making specular collisions on encounters with the scatterers. For a dilute Lorentz gas with open boundaries in $d$ dimensions we relate the thermodynamic formalism to a random flight problem. Using this representation we analytically calculate the central quantity within this formalism, the topological pressure, as a function of system size and a temperature-like parameter \ba. The topological pressure is given as the sum of the topological pressure for the closed system and a diffusion term with a \ba-dependent diffusion coefficient. From the topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller, the topological entropy, and the partial information dimension.Comment: 7 pages, 5 figure

Diffusion, super-diffusion and coalescence from single step

From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field \bu(\bx), we derive different dynamical regimes when \bu(\bx) is iterated to build a velocity field. First we show that spatially uncorrelated fields \bu(\bx) lead to both standard and anomalous diffusion equation. When the field \bu(\bx) is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field \bu(\bx) induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement-displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes, in the one-dimensional system, is shown through computer simulations and a simple theoretical argument.Comment: RevTeX (iopstyle) 19 pages, 5 eps-figure

Transition to Stochastic Synchronization in Spatially Extended Systems

Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if the maximum Lyapunov exponent becomes negative for sufficiently large noise amplitude. Moreover, noise can suppress also the non-linear mechanism of information propagation, that may be present in the spatially extended system. A first example of phase transition is observed when both the linear and the non-linear mechanisms of information production disappear at the same critical value of the noise amplitude. The corresponding critical properties can be hardly identified numerically, but some general argument suggests that they could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely, when the non-linear mechanism prevails on the linear one, another type of phase transition to stochastic synchronization occurs. This one is shown to belong to the universality class of directed percolation.Comment: 21 pages, Latex - 14 EPS Figs - To appear on Physical Review

Metabolomics Fingerprint Predicts Risk of Death in Dilated Cardiomyopathy and Heart Failure

BACKGROUND: Heart failure (HF) is a leading cause of morbidity and mortality worldwide. Metabolomics may help refine risk assessment and potentially guide HF management, but dedicated studies are few. This study aims at stratifying the long-term risk of death in a cohort of patients affected by HF due to dilated cardiomyopathy (DCM) using serum metabolomics via nuclear magnetic resonance (NMR) spectroscopy. METHODS: A cohort of 106 patients with HF due to DCM, diagnosed and monitored between 1982 and 2011, were consecutively enrolled between 2010 and 2012, and a serum sample was collected from each participant. Each patient underwent half-yearly clinical assessments, and survival status at the last follow-up visit in 2019 was recorded. The NMR serum metabolomic profiles were retrospectively analyzed to evaluate the patient's risk of death. Overall, 26 patients died during the 8-years of the study. RESULTS: The metabolomic fingerprint at enrollment was powerful in discriminating patients who died (HR 5.71, p = 0.00002), even when adjusted for potential covariates. The outcome prediction of metabolomics surpassed that of N-terminal pro b-type natriuretic peptide (NT-proBNP) (HR 2.97, p = 0.005). Metabolomic fingerprinting was able to sub-stratify the risk of death in patients with both preserved/mid-range and reduced ejection fraction [hazard ratio (HR) 3.46, p = 0.03; HR 6.01, p = 0.004, respectively]. Metabolomics and left ventricular ejection fraction (LVEF), combined in a score, proved to be synergistic in predicting survival (HR 8.09, p = 0.0000004). CONCLUSIONS: Metabolomic analysis via NMR enables fast and reproducible characterization of the serum metabolic fingerprint associated with poor prognosis in the HF setting. Our data suggest the importance of integrating several risk parameters to early identify HF patients at high-risk of poor outcomes

The anti-apoptotic effect of ASC-exosomes in an in vitro ALS model and their proteomic analysis

Stem cell therapy represents a promising approach in the treatment of several neurodegenerative disorders, including amyotrophic lateral sclerosis (ALS). The beneficial effect of stem cells is exerted by paracrine mediators, as exosomes, suggesting a possible potential use of these extracellular vesicles as non-cell based therapy. We demonstrated that exosomes isolated from adipose stem cells (ASC) display a neuroprotective role in an in vitro model of ALS. Moreover, the internalization of ASC-exosomes by the cells was shown and the molecules and the mechanisms by which exosomes could exert their beneficial effect were addressed. We performed for the first time a comprehensive proteomic analysis of exosomes derived from murine ASC. We identified a total of 189 proteins and the shotgun proteomics analysis revealed that the exosomal proteins are mainly involved in cell adhesion and negative regulation of the apoptotic process. We correlated the protein content to the anti-apoptotic effect of exosomes observing a downregulation of pro-apoptotic proteins Bax and cleaved caspase-3 and upregulation of anti-apoptotic protein Bcl-2 \u3b1, in an in vitro model of ALS after cell treatment with exosomes. Overall, this study shows the neuroprotective effect of ASC-exosomes after their internalization and their global protein profile, that could be useful to understand how exosomes act, demonstrating that they can be employed as therapy in neurodegenerative diseases