Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$ could be either a set of saddle (exit) points of the well, or a set of further (meta)stable configurations. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which has three important attributes. First, it is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. Second, it relies only on the natural hypothesis that the mean hitting time to $G$ is asymptotically longer than the mean recurrence time to $x_0$ or $G$. Third, despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature so to eliminate potential sources of confusion. This is specially relevant for evolutions of infinite-volume systems, whose treatment depends on whether and how relevant parameters (temperature, fields) are adjusted. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions

Application of Neurochemical Markers for Assessing Health Effects after Developmental Methylmercury and PCB Coexposure

Cholinergic muscarinic receptors (MRs) and monoamine oxidase activity (MAO-B), expressed both in brain and blood cells, were investigated in animals and exposed subjects to assess (i) MeHg (0.5–1 mg/kg/day GD7-PD7) and/or PCB153 (20 mg/kg/day GD10–GD16) effects on cerebellar MAO-B and MRs, and lymphocyte MRs, in dams and offspring 21 days postpartum; (ii) MAO-B in platelets and MRs in lymphocytes of a Faroese 7-year-old children cohort, prenatally exposed to MeHg/PCBs. Animal Data. MAO-B was altered in male cerebellum by MeHg, PCB153, and their combination (35%, 45%, and 25% decrease, resp.). Cerebellar MRs were enhanced by MeHg alone in dams (87%) and male pups (27%). PCB153 alone and in mixture did not modify cerebellar MRs. Similarly to brain, lymphocyte MRs were enhanced in both dams and offspring by MeHg alone. All changes were caused by 1 MeHg mg/kg/day, the lower dose was ineffective. Human Data. Both biomarkers showed homogeneous distributions within the cohort (MRs, range 0.1–36.78 fmol/million cells; MAO-B, 0.95–14.95 nmol/mg protein/h). No correlation was found between the two biomarkers and neurotoxicant concentrations in blood (pre- and postnatally)

Metastability for reversible probabilistic cellular automata with self--interaction

The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. %The characterization of the metastable behavior %of a system in the context of parallel dynamics is a very difficult task, %since all the jumps in the configuration space are allowed. Our strategy is based on recent powerful approaches, not needing a complete description of the fixed points of the dynamics, but relying on few model dependent results. We compute the exit time, in the sense of logarithmic equivalence, and characterize the critical droplet that is necessarily visited by the system during its excursion from the metastable to the stable state. We need to supply two model dependent inputs: (1) the communication energy, that is the minimal energy barrier that the system must overcome to reach the stable state starting from the metastable one; (2) a recurrence property stating that for any configuration different from the metastable state there exists a path, starting from such a configuration and reaching a lower energy state, such that its maximal energy is lower than the communication energy

Spatio-temporal analysis of prodelta dynamics by means of new satellite generation: the case of Po river by Landsat-8 data

Abstract This paper describes a procedure to perform spatio-temporal analysis of river plume dispersion in prodelta areas by multi-temporal Landsat-8-derived products for identifying zones sensitive to water discharge and for providing geostatistical patterns of turbidity linked to different meteo-marine forcings. In particular, we characterized the temporal and spatial variability of turbidity and sea surface temperature (SST) in the Po River prodelta (Northern Adriatic Sea, Italy) during the period 2013–2016. To perform this analysis, a two-pronged processing methodology was implemented and the resulting outputs were analysed through a series of statistical tools. A pixel-based spatial correlation analysis was carried out by comparing temporal curves of turbidity and SST hypercubes with in situ time series of wind speed and water discharge, providing correlation coefficient maps. A geostatistical analysis was performed to determine the spatial dependency of the turbidity datasets per each satellite image, providing maps of correlation and variograms. The results show a linear correlation between water discharge and turbidity variations in the points more affected by the buoyant plumes and along the southern coast of Po River delta. Better inverse correlation was found between turbidity and SST during floods rather than other periods. The correlation maps of wind speed with turbidity show different spatial patterns depending on local or basin-scale wind effects. Variogram maps identify different spatial anisotropy structures of turbidity in response to ambient conditions (i.e. strong Bora or Scirocco winds, floods). Since the implemented processing methodology is based on open source software and free satellite data, it represents a promising tool for the monitoring of maritime ecosystems and to address water quality analyses and the investigations of sediment dynamics in estuarine and coastal waters

BeppoSAX Observations of the Radio Galaxy Centaurus A

We present preliminary results from two observations of the radio galaxy Centaurus A performed by the BeppoSAX satellite. We did not detect any spectral variation of the nuclear continuum in spite of the long-term flux change (by a factor 1.3) between the two observations. At both epochs, the nuclear point-like emission was well fitted with a strongly absorbed power law with an exponential cutoff at high energies (E_cutoff>200 keV). We also observed a significant flux variation of the iron line between the two observations. The flux of the line and of the continuum changed in the opposite sense. The line is more intense at the first epoch, when the nuclear source was at the lower intensity level. The implied delay between the continuum and line variations strongly suggests that the cold material responsible for the iron line production is not located very near to the primary X-ray source. There is also evidence that the line profile changed between the two epochs, being broader and slightly blueshifted when the source was fainter. It is possible that the emission feature is a blend of cold and ionized iron lines produced in separate regions surrounding the nuclear source.Comment: 4 pages, 4 figures, accepted for publication in Advances in Space Research, proceedings of 32nd COSPAR Symposium (1998