Analysis of Round Off Errors with Reversibility Test as a Dynamical Indicator

We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analysed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described.Comment: International Journal of Bifurcation and Chaos, 201

Deterministic and stochastic chaos characterize laboratory earthquakes

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical changes associated with the transition from stable to unstable motion. We find that the seismic cycle exhibits characteristics of a low-dimensional system with average dimension similar to that of natural slow earthquakes (<5). We also investigate local properties of the attractor and find maximum instantaneous dimension ≳10, indicating that some regions of the phase space require a high number of degrees of freedom (dofs). Our analysis does not preclude deterministic chaos, but the lab seismic cycle is best explained by a random attractor based on rate- and state-dependent friction whose dynamics is stochastically perturbed. We find that minimal variations of 0.05% of the shear and normal stresses applied to the experimental fault influence the large-scale dynamics and the recurrence time of labquakes. While complicated motion including period doubling is observed near the stability transition, even in the fully unstable regime we do not observe truly periodic behavior. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics. As applied to tectonic faults, our results imply that even small stress field fluctuations (≲150 kPa) can induce coefficient of variations in earthquake repeat time of a few percent. Moreover, these perturbations can drive an otherwise fast-slipping fault, close to the critical stability condition, into a mixed behavior involving slow and fast ruptures

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Timescale of Emplacement and Rheomorphism of the Green Tuff Ignimbrite (Pantelleria, Italy)

We present a multidisciplinary study based on Differential Scanning Calorimetry (DSC), paleomagnetic analysis, and numerical modeling to gain information on the timescales of syn- and post-depositional ductile deformation of the strongly welded and rheomorphic Green Tuff ignimbrite (GT; Pantelleria, Italy). DSC measurements allow the determination of glass fictive temperatures (Tf; i.e., the parameter accounting for the cooling dependence of glass structure and properties). Using a Tf-based geospeedometry procedure, we infer the cooling rate (qc) experienced by the glassy phases in different lithofacies within the GT formation. Glass shards from the basal pumice fall deposit record a fast qc of ∼10°C/s. In contrast, the ignimbrite body returns slow qc values depending on the stratigraphic position and lithofacies (basal/upper vitrophyres, fiamme-rich and rheomorphic layers), ranging from ∼10−2 to ∼10−6 °C/s. Moreover, paleomagnetic analyses of the natural remanent magnetization of ignimbrite matrix and embedded lithic clasts indicate an emplacement temperature higher than 550–600°C. By integrating calorimetric and paleomagnetic datasets, we constrain a conductive cooling model, describing the ignimbrite's temperature-time-viscosity (T–t–η) evolution from the eruptive temperature to below Tf. Outcomes suggest that the upper and basal vitrophyres deformed and quenched over hours, indicating that the entire GT underwent intense syn-depositional ductile deformation. Furthermore, the central body remained above Tf for a much longer timespan (>1 month), enabling post-emplacement rheomorphic flow. Lastly, we discuss the critical role of mechanisms such as shear heating and retrograde solubility of volatiles, in locally controlling the rheological behavior of the GT

Extreme value statistics for dynamical systems with noise

We study the distribution of maxima ( extreme value statistics ) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former case, we show that, by perturbing rational or irrational rotations with additive noise, an extreme value law appears, regardless of the intensity of the noise, while unperturbed rotations do not admit such limiting distributions. In the case of deterministic chaotic dynamics, we will consider observables specially designed to study the recurrence properties in the neighbourhood of periodic points. Hence, the exponential limiting law for the distribution of maxima is modified by the presence of the extremal index , a positive parameter not larger than one, whose inverse gives the average size of the clusters of extreme events. The theory predicts that such a parameter is unitary when the system is perturbed randomly. We perform sophisticated numerical tests to assess how strong the impact of noise level is when finite time series are considered. We find agreement with the asymptotic theoretical results but also non-trivial behaviour in the finite range. In particular, our results suggest that, in many applications where finite datasets can be produced or analysed, one must be careful in assuming that the smoothing nature of noise prevails over the underlying deterministic dynamics

Signatures of the 1976-1977 Regime Shift in the North Pacific Revealed by Statistical Analysis

Regime shifts are abrupt changes in an ecosystem that may propagate through multiple trophic levels and have pronounced effects on the biotic and abiotic environment, potentially resulting in ecosystem reorganization. There are multiple mechanisms that could cause such abrupt events including natural and anthropogenic factors. In the North Pacific, a major shift in the physics of the system, including a sudden increase in sea surface temperature, was reported in 1977 with a prominent biological response in the lower trophic levels and subsequent effects on the fisheries and economy of the region. Here we investigate the statistics of physical processes that could have triggered and maintained the late 1970s shift. The hypothesis of an extreme sea level pressure event abruptly changing the oceanic conditions in winter 1976–1977, which was maintained by long‐term changes in air‐sea interaction processes, is tested. Using dynamical proxies, we show the occurrence of an extreme atmospheric event, specifically a persistent Aleutian Low during winter 1976–1977, which constitutes a substantial part of the triggering mechanism of the regime shift. Subsequent sudden changes in the net heat flux occurred in the western North Pacific, particularly in the Kuroshio Extension region, which contributed to the maintenance of the new regime

Covid-19 vaccine hesitancy in systemic sclerosis

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Analysis of a nanoparticle‑enriched fraction of plasma reveals miRNA candidates for down syndrome pathogenesis

Down syndrome (DS) is caused by the presence of part or all of a third copy of chromosome 21. DS is associated with several phenotypes, including intellectual disability, congenital heart disease, childhood leukemia and immune defects. Specific microRNAs (miRNAs/miR) have been described to be associated with DS, although none of them so far have been unequivocally linked to the pathology. The present study focuses to the best of our knowledge for the first time on the miRNAs contained in nanosized RNA carriers circulating in the blood. Fractions enriched in nanosized RNA-carriers were separated from the plasma of young participants with DS and their non-trisomic siblings and miRNAs were extracted. A microarray-based analysis on a small cohort of samples led to the identification of the three most abundant miRNAs, namely miR-16-5p, miR-99b-5p and miR-144-3p. These miRNAs were then profiled for 15 pairs of DS and non‑trisomic sibling couples by reverse transcription-quantitative polymerase chain reaction (RT-qPCR). Results identified a clear differential expression trend of these miRNAs in DS with respect to their non-trisomic siblings and gene ontology analysis pointed to their potential role in a number of typical DS features, including ‘nervous system development’, ‘neuronal cell body’ and certain forms of ‘leukemia’. Finally, these expression levels were associated with certain typical quantitative and qualitative clinical features of DS. These results contribute to the efforts in defining the DS‑associated pathogenic mechanisms and emphasize the importance of properly stratifying the miRNA fluid vehicles in order to probe biomolecules that are otherwise hidden and/or not accessible to (standard) analysis