No Correlation between Endo- and Exoskeletal Regenerative Capacities in Teleost Species

The regeneration of paired appendages in certain fish and amphibian lineages is a well established and extensively studied regenerative phenomenon. The teleost fin is comprised of a proximal endoskeletal part (considered homologous to the Tetrapod limb) and a distal exoskeletal one, and these two parts form their bony elements through different ossification processes. In the past decade, a significant body of literature has been generated about the biology of exoskeletal regeneration in zebrafish. However, it is still not clear if this knowledge can be applied to the regeneration of endoskeletal parts. To address this question, we decided to compare endo- and exoskeletal regenerative capacity in zebrafish (Danio rerio) and mudskippers (Periophthalmus barbarous). In contrast to the reduced endoskeleton of zebrafish, Periophthalmus has well developed pectoral fins with a large and easily accessible endoskeleton. We performed exo- and endoskeletal amputations in both species and followed the regenerative processes. Unlike the almost flawless exoskeletal regeneration observed in zebrafish, regeneration following endoskeletal amputation is often impaired in this species. This difference is even more pronounced in Periophthalmus where we could observe no regeneration in endoskeletal structures. Therefore, regeneration is regulated differentially in the exo- and endoskeleton of teleost species.

Two limit theorems for ergodically regenerated stochastic processes

There is a subtle difference between the recurrent event of Feller and the regenerative phenomenon of Kingman: The former regenerates an entire ambient process, whereas the latter regenerates only itself. This paper generalizes Feller's definition to a discrete regenerative phenomenon E in association with an arbitrary discrete-time stochastic process X. Two limit theorems of a general character are proved for the process X when it is regenerated by an ergodic phenomenon E. The first implies that X becomes strictly stationary at a uniform rate which is determined solely by the asymptotic behaviour of E. The second is essentially a mixing convergence theorem which implies the asymptotic independence of regenerating and regenerated events. Applications include (1) the outright independence of the regenerating events and the regenerated events which occur ‘at the end of time’, and (2) the identification of the transient features of X with the null sets of the stationary limiting probability. Numerous open questions are posed.

Lattice-valued random walks with Markov chain dependent steps

The probability of ever returning to the origin and the mean square displacement after n steps are studied for some lattice-valued random walks, whose successive steps constitute a Markov chain on a finite state space with transition probabilities of a simple kind, and such that the returns to the origin form a regenerative phenomenon. The case of walks on a diamond lattice with no immediate reversals is included: this example is relevant as a polymer chain building model. The numerical evaluation of the return probabilities of some three-dimensional walks is discussed and examples given.

A bivariate distribution in regeneration

The joint distribution of the time since last exit, and the time until next entrance, into a unique boundary point is given in Formula (1) below. The boundary point may be replaced by a regenerative phenomenon.

A bivariate distribution in regeneration

The joint distribution of the time since last exit, and the time until next entrance, into a unique boundary point is given in Formula (1) below. The boundary point may be replaced by a regenerative phenomenon.

Runs of a discrete time regenerative phenomenon

The limiting behavior of the number of runs up to time n of a regenerative phenomenon on the positive integers is related to the one of the number of regenerations. Applications are considered in fluctuation theory, and for the GI/G/1 queue.

Runs of a discrete time regenerative phenomenon

The limiting behavior of the number of runs up to time n of a regenerative phenomenon on the positive integers is related to the one of the number of regenerations. Applications are considered in fluctuation theory, and for the GI/G/1 queue.

Slow and Spike Potentials Recorded from Retinula Cells of the Honeybee Drone in Response to Light

Responses to light recorded by means of intracellular microelectrodes in isolated heads kept in oxygenated Ringer solution consist of a slow depolarization. Light adaptation increases the rates of depolarization and repolarization and decreases the amplitude of the response. Qualitatively these changes are similar to those observed in Limulus by Fuortes and Hodgkin. They are rapidly reversible during dark adaptation. In retinula cells of the drone eye a large single spike is recorded superimposed on the rising phase of the slow potential. The spike is a regenerative phenomenon; it can be triggered with electric current and is markedly reduced, sometimes abolished by tetrodotoxin. In rare cases cells were found which responded to light with a train of spikes. This behavior was only found under "unusual" experimental conditions; i.e., towards the end of a long experiment, during impalement, or at the beginning of responses to steps of strongly light-adapted preparations.