Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes

This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Hemolymph Functions In Mytilus-Californianus - Cytochemistry Of Hemocytes And Their Responses To Foreign Implants And Hemolymph Factors In Phagocytosis

The hemocytes of Mytilus californianus are of three types: small and large basophils and large granular acidophils. The basophils contain lysosomal enzymes and phagocytose colloidal carbon. Agglutinins for yeast and human A Rh+ve erythrocytes are present in plasma, but are not needed for effective phagocytosis; in vitro both acidophilic and basophilic hemocytes rapidly phagocytose these particles. Plasma proteins, analyzed electrophoretically, are under strong homeostatic control. When Mya arenaria mantle is placed orthotopically on M. californianus mantle, the implant is invaded by host hemocytes in a manner consistent with that described in other published reports on molluscan graft rejection. Steady state is achieved by 26 days postimplant. Second- and third-set implants are rejected more rapidly than are first-set implants, but this is not a specific response. Third-set implants elicit a host cellular response that is more localized than the response to first-set implants. These data do not permit conclusions with respect to memory in these molluscan immune responses, but do imply a qualitative “improvement” in this quasi-immune response of M. californianus.

Consequences of a simulated rapid ocean acidification event for benthic ecosystem processes and functions

Whilst the biological consequences of long-term, gradual changes in acidity associated with the oceanic uptake of atmospheric carbon dioxide (CO2) are increasingly studied, the potential effects of rapid acidification associated with a failure of sub-seabed carbon storage infrastructure have received less attention. This study investigates the effects of severe short-term (8 days) exposure to acidified seawater on infaunal mediation of ecosystem processes (bioirrigation and sediment particle redistribution) and functioning (nutrient concentrations). Following acidification, individuals of Amphiura filiformis exhibited emergent behaviour typical of a stress response, which resulted in altered bioturbation, but limited changes in nutrient cycling. Under acidified conditions, A. filiformis moved to shallower depths within the sediment and the variability in occupancy depth reduced considerably. This study indicated that rapid acidification events may not be lethal to benthic invertebrates, but may result in behavioural changes that could have longer-term implications for species survival, ecosystem structure and functioning.

Generalized ocean color inversion model for retrieving marine inherent optical properties

Ocean color measured from satellites provides daily, global estimates of marine inherent optical properties (IOPs). Semi-analytical algorithms (SAAs) provide one mechanism for inverting the color of the water observed by the satellite into IOPs. While numerous SAAs exist, most are similarly constructed and few are appropriately parameterized for all water masses for all seasons. To initiate community-wide discussion of these limitations, NASA organized two workshops that deconstructed SAAs to identify similarities and uniqueness and to progress toward consensus on a unified SAA. This effort resulted in the development of the generalized IOP (GIOP) model software that allows for the construction of different SAAs at runtime by selection from an assortment of model parameterizations. As such, GIOP permits isolation and evaluation of specific modeling assumptions, construction of SAAs, development of regionally tuned SAAs, and execution of ensemble inversion modeling. Working groups associated with the workshops proposed a preliminary default configuration for GIOP (GIOP-DC), with alternative model parameterizations and features defined for subsequent evaluation. In this paper, we: (1) describe the theoretical basis of GIOP; (2) present GIOP-DC and verify its comparable performance to other popular SAAs using both in situ and synthetic data sets; and, (3) quantify the sensitivities of their output to their parameterization. We use the latter to develop a hierarchical sensitivity of SAAs to various model parameterizations, to identify components of SAAs that merit focus in future research, and to provide material for discussion on algorithm uncertainties and future emsemble applications.