Time correlations for the parabolic Anderson model

We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a finite cumulant generating function. We use these results to give precise asymptotics for statistical moments of positive order. Furthermore, we show what the potential peaks that contribute to the intermittency picture look like and how they are distributed in space. We also investigate for how long intermittency peaks remain relevant in terms of ageing properties of the model.Comment: 28 page

Precise asymptotics for the parabolic Anderson model with a moving catalyst or trap

We consider the solution $u\colon [0,\infty) \times\mathbb{Z}^d\rightarrow [0,\infty)$ to the parabolic Anderson model, where the potential is given by $(t,x)\mapsto\gamma\delta_{Y_t}(x)$ with $Y$ a simple symmetric random walk on $\mathbb{Z}^d$. Depending on the parameter $\gamma\in[-\infty,\infty)$, the potential is interpreted as a randomly moving catalyst or trap. In the trap case, i.e., $\gamma<0$, we look at the annealed time asymptotics in terms of the first moment of $u$. Given a localized initial condition, we derive the asymptotic rate of decay to zero in dimensions 1 and 2 up to equivalence and characterize the limit in dimensions 3 and higher in terms of the Green's function of a random walk. For a homogeneous initial condition we give a characterisation of the limit in dimension 1 and show that the moments remain constant for all time in dimensions 2 and higher. In the case of a moving catalyst ($\gamma>0$), we consider the solution $u$ from the perspective of the catalyst, i.e., the expression $u(t,Y_t+x)$. Focusing on the cases where moments grow exponentially fast (that is, $\gamma$ sufficiently large), we describe the moment asymptotics of the expression above up to equivalence. Here, it is crucial to prove the existence of a principal eigenfunction of the corresponding Hamilton operator. While this is well-established for the first moment, we have found an extension to higher moments.Comment: In honour of J\"urgen G\"artner on the occasion of his 60th birthday, 20 page

STRATEGY FOR ASSESSING IMPACTS OF THYROID DISRUPTING CHEMICALS IN TELEOSTEANS

Peer reviewe

Interfollicular fibrosis and organohalogens in the thyroid of the harbour porpoise (phocoena phocoena) of the British and Belgian coasts

Previous studies have described high levels of polychlorobiphenyls (PCB), p,p`-dichlordiphenyl-dichlorethen (DDT), p,p`-dichlordiphenyl-trichlorethan (DDE) and polybrominated diphenylether (PBDE) in the blubber of the harbour porpoise (Phocoena phocoena) from the North Sea raising the question of a potential endocrine disruption in this species. In the present study, the thyroids of 36 harbour porpoises from the British and the Belgian coast have been collected for histological and immunohistological investigations. The number and mean diameter of follicles and the relative distribution of follicular, connective and vascular tissues (%) were quantified in the thyroid of each individual. Then, the relationship between the thyroid morphometry data and previously described organic compounds (namely PCB, DDT, DDE and PBDE) was investigated using factor analysis and multiple regressions. The results of this work were compared to the previous study of harbour porpoises from the German (North and Baltic Seas), Norwegian and Icelandic coasts. Thyroid morphology was similar between the harbour porpoises from the British and Belgian coast. Compared to the previous study, the thyroids differed strongly between sampling sites. Porpoises from the German (North and Baltic Seas) and Norwegian coasts displayed a high percentage of connective tissues between 30 and 38% revealing severe inter-follicular fibrosis. The thyroids of Icelandic coasts displayed only a light inter-follicular fibrosis (percentage of connective tissue of 3%). The thyroids of the porpoises from the British and Belgian coasts occupied an intermediary place with a moderate fibrosis (percentage of connective tissue of 10%). A relation between mean diameter of follicles and the body size and mass suggesting a downward trend of activity of the thyroid with increasing body size and mass and thus, the age of the porpoises. A correlation-based principal component analysis (PCA) revealed one principal components explaining 69% of the total variance. The variables PCB, PBDE, DDT, and DDE compounds loaded highest on PC1. Our results pointed out a relationship between PCBs, PBDE, DDE and DDT (PC1) compounds and interfollicular fibrosis in the thyroids of harbour porpoises from the German coast of the Baltic Sea. The present report supports the hypothesis of a contaminant-induced thyroid fibrosis in harbour porpoises raising the question of the long term-viability in highly polluted area

Thyroid dysfunction in sea bass (Dicentrarchus labrax): Underlying mechanisms and effects of polychlorinated biphenyls on thyroid hormone physiology and metabolism

peer reviewedaudience: researcher, professional, student, popularization, otherThe current study examines the effect of subchronic exposure to a mixture of Aroclor standards on thyroid hormone physiology and metabolism in juvenile sea bass. The contaminant mixture was formulated to reflect the persistent organic pollution to which the European sea bass population could conceivably be exposed (0.3, 0.6 and 1.0 g 7PCBs per g food pellets) and higher (10 g 7PCBs per g food pellets). After 120 days of exposure, histomorphometry of thyroid tissue, muscular thyroid hormone concentration and activity of enzymes involved in metabolism of thyroid hormones were assessed. Mean concentrations of 8, 86, 142, 214 and 2279 ng g−1 ww ( 7 ICES PCB congeners) were determined after 120 days exposure. The results show that the effects of PCB exposures on the thyroid system are dose-dependent. Exposure to environmentally relevant doses of PCB (0.3–1.0 g 7PCBs per g food pellets) induced a larger variability of the follicle diameter and stimulated hepatic T4 outer ring deiodinase. Muscular thyroid hormone levels were preserved thanks to the PCB induced changes in T4 dynamics. At 10 times higher concentrations (10 g 7PCBs per g food pellets) an important depression of T3 and T4 levels could be observed which are apparently caused by degenerative histological changes in the thyroid tissue

Occurrence of legacy and emerging organic pollutants in whitemouth croakers from Southeastern Brazil

The whitemouth croaker (Micropogonias furnieri) is one of the most commercially important species along the Atlantic coast of South America. Moreover, some of its biological traits (long life span, inshore feeding, high trophic position) make this species a suitable sentinel of coastal pollution. Here, we investigated contamination by multiple legacy and emerging organic pollutants, such as brominated and chlorinated flame retardants, polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs), in whitemouth croakers from two estuaries (Guanabara and Sepetiba Bays) located in industrialized and urbanized areas in Rio de Janeiro State, Southeastern Brazil. Furthermore, we assessed how biological and ecological features could explain the observed contamination patterns. Regarding brominated flame retardants, concentrations of polybrominated diphenyl ethers (PBDEs) varied from 7.6 to 879.7 pg g-1 wet weight (w.w.), with high contribution of tetra-, penta-, hexa- and deca-BDEs. The sum of chlorinated flame retardants (dechlorane-related compounds, ΣDRC) ranged from <LOD to 41.1 pg g-1 w.w., mostly represented by Dechlorane 603 and Dechlorane Plus (DP). Concentrations of PCDDs and PCDFs varied from <LOD to 1.7 pg g-1 w.w., while the Toxic Equivalent (TEQ-PCDD/Fs) levels ranged from 0.1 to 0.2 pg g-1 w.w. Positive correlations between δ15N and concentrations of tri-, tetra- and penta-BDEs, as well as ΣDRC, DP and anti-DP isomers suggested that ecological factors (namely biomagnification along the food web) influence contamination of whitemouth croakers in the estuaries studied. Moreover, the sum of PBDEs (ΣPBDE), tri- and tetra-BDEs concentrations were negatively correlated with fish size, suggesting that depuration by fishes and/or habitat shift throughout the whitemouth croaker’s life cycle might also influence concentrations. Overall, our study emphasized the need for further investigations to help understand the complex patterns of bioaccumulation and biomagnification that seem to exist in Southeastern Brazil