Multidimensional sticky Brownian motions as limits of exclusion processes

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and the entire particle system is slowed down until the ``collision'' is resolved. We show that under diffusive scaling of space and time such processes converge to what one might refer to as a sticky reflected Brownian motion in the wedge. The latter behaves as a Brownian motion with constant drift vector and diffusion matrix in the interior of the wedge, and reflects at the boundary of the wedge after spending an instant of time there. In particular, this leads to a natural multidimensional generalization of sticky Brownian motion on the half-line, which is of interest in both queuing theory and stochastic portfolio theory. For instance, this can model a market, which experiences a slowdown due to a major event (such as a court trial between some of the largest firms in the market) deciding about the new market leader.Comment: Published at http://dx.doi.org/10.1214/14-AAP1019 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Radiodiagnostic method for studying the dynamics of Anguillicola crassus (Nematoda: Dracunculoidea) infection and pathological status of the swimbladder in Lake Balaton eels

Swimbladder changes resulting from Anguillicola crassus infection of the European eel Anguilla anguilla have been the subject of several studies reported in the literature. These investigations, however, studied exclusively the status of infection at a given point in time and did not deal with changes in swimbladder infection in eels suffering from anguillicolosis over a period of time. In this study, A. crassus-induced pathological changes were monitored in 78 eels naturally infected in Lake Balaton and subsequently kept in the laboratory, thus excluding the possibility of further infection. During the 3 mo study, the status of the swimbladder was checked by radiographic examination on 4 occasions. At the end of the study the eels were dissected and the gross pathological changes in the swimbladders were compared with the radiographic findings. As compared to their starting condition, by the end of the study the pathological status of the swimbladder had deteriorated in 55 % and remained the same in 37 % of the cases. Tendency to improvement (1 %) and variable findings (7 %) were recorded in a low percentage of cases only. With the help of the radiographs presented, the dynamics of A. crassus infection and of changes in the swimbladder of individual eel specimens can be monitored easily

Intraoligochaete development of Myxobolus intimus (Myxosporea: Myxobolidae), a gill myxosporean of the roach (Rutilus rutilus)

The infection with Myxobolus intimus Zaika, 1965 in the gills of the roach Rutilus rutilus (L.) from Lake Balaton was recorded in 28 out of the 39 fish examined. Developing and mature plasmodia were detected on the gills exclusively in the spring. The Myxobolus intimus infection was found only in 2- to 3-year-old fish. In histological sections, young plasmodia were found in capillaries of the secondary lamellae. More mature, round plasmodia 0.4-0.6 mm in diameter, deformed the respiratory lamellae. The intraoligochacte development of M. intimus was studied in experimentally infected oligochaetes. In two experiments, uninfected Tubifex tubifex Muller and Limnodrilus hoffmeisteri (Claparede) were exposed to mature myxospores of M. intimus. In both experiments, typical triactinospores developed in T. tubifex specimens but no infection was found in L. hoffmeisteri. In semithin sections, developmental stages, pansporocysts and actinospores, were found within the proliferated gut epithelium of T. tubifex. Triactinospores were first released from oligochaetes 37 and 58 days after initial exposure in the two experiments, respectively. Each triactinospore had three pyriform polar capsules and a cylindrical sporoplasm with 32 secondary cells. The spore body joined the 3 caudal projections with a moderately long style

Can one hear the shape of a population history?

Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we provide tight bounds on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certain level of accuracy. In practice, coalescence times are estimated from sequence data and so our lower bounds should be taken as rather conservative.Comment: 22 pages, 7 figures; v2 is significantly revised from v

Front motion in an A+B→CA+B\to C type reaction-diffusion process: Effects of an electric field

We study the effects of an external electric field on both the motion of the reaction zone and the spatial distribution of the reaction product, $C$, in an irreversible $A^- +B^+ \to C$ reaction-diffusion process. The electrolytes $A\equiv (A^+,A^-)$ and $B\equiv (B^+,B^-)$ are initially separated in space and the ion-dynamics is described by reaction-diffusion equations obeying local electroneutrality. Without an electric field, the reaction zone moves diffusively leaving behind a constant concentration of $C$-s. In the presence of an electric field which drives the reagents towards the reaction zone, we find that the reaction zone still moves diffusively but with a diffusion coefficient which slightly decreases with increasing field. The important electric field effect is that the concentration of $C$-s is no longer constant but increases linearly in the direction of the motion of the front. The case of an electric field of reversed polarity is also discussed and it is found that the motion of the front has a diffusive, as well as a drift component. The concentration of $C$-s decreases in the direction of the motion of the front, up to the complete extinction of the reaction. Possible applications of the above results to the understanding of the formation of Liesegang patterns in an electric field is briefly outlined.Comment: 13 pages, 13 figures, submitted to J. Chem. Phy