Passage time from four to two blocks of opinions in the voter model and walks in the quarter plane

A random walk in $Z_+^2$ spatially homogeneous in the interior, absorbed at the axes, starting from an arbitrary point $(i_0,j_0)$ and with step probabilities drawn on Figure 1 is considered. The trivariate generating function of probabilities that the random walk hits a given point $(i,j)\in Z_+^2$ at a given time $k\geq 0$ is made explicit. Probabilities of absorption at a given time $k$ and at a given axis are found, and their precise asymptotic is derived as the time $k\to\infty$. The equivalence of two typical ways of conditioning this random walk to never reach the axes is established. The results are also applied to the analysis of the voter model with two candidates and initially, in the population $Z$, four connected blocks of same opinions. Then, a citizen changes his mind at a rate proportional to the number of its neighbors that disagree with him. Namely, the passage from four to two blocks of opinions is studied.Comment: 11 pages, 1 figur

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient

Identification and Phylogenetic Analysis of Tityus pachyurus and Tityus obscurus Novel Putative Na+-Channel Scorpion Toxins

Background: Colombia and Brazil are affected by severe cases of scorpionism. In Colombia the most dangerous accidents are caused by Tityus pachyurus that is widely distributed around this country. In the Brazilian Amazonian region scorpion stings are a common event caused by Tityus obscurus. The main objective of this work was to perform the molecular cloning of the putative Na+-channel scorpion toxins (NaScTxs) from T. pachyurus and T. obscurus venom glands and to analyze their phylogenetic relationship with other known NaScTxs from Tityus species. Methodology/Principal Findings: cDNA libraries from venom glands of these two species were constructed and five nucleotide sequences from T. pachyurus were identified as putative modulators of Na+-channels, and were named Tpa4, Tpa5, Tpa6, Tpa7 and Tpa8; the latter being the first anti-insect excitatory b-class NaScTx in Tityus scorpion venom to be described. Fifteen sequences from T. obscurus were identified as putative NaScTxs, among which three had been previously described, and the others were named To4 to To15. The peptides Tpa4, Tpa5, Tpa6, To6, To7, To9, To10 and To14 are closely related to the a-class NaScTxs, whereas Tpa7, Tpa8, To4, To8, To12 and To15 sequences are more related to the b-class NaScTxs. To5 is possibly an arthropod specific toxin. To11 and To13 share sequence similarities with both a and b NaScTxs. By means of phylogenetic analysis using the Maximum Parsimony method and the known NaScTxs from Tityus species, these toxins were clustered into 14 distinct groups. Conclusions/Significance: This communication describes new putative NaScTxs from T. pachyurus and T. obscurus and their phylogenetic analysis. The results indicate clear geographic separation between scorpions of Tityus genus inhabiting the Amazonian and Mountain Andes regions and those distributed over the Southern of the Amazonian rainforest. Based on the consensus sequences for the different clusters, a new nomenclature for the NaScTxs is proposed

The Power-Series Algorithm for Markovian Queueing Networks

A newversion of the Power-Series Algorithm is developed to compute the steady-state distribution of a rich class of Markovian queueing networks. The arrival process is a Multi-queue Markovian Arrival Process, which is a multi-queue generalization of the BMAP. It includes Poisson, fork and round-robin arrivals. At each queue the service process is a Markovian Service Process, which includes sequences of phase-type distributions, setup times and multi-server queues. The routing is Markovian. The resulting queueing network model is extremely general, which makes the Power-Series Algorithm a useful tool to study load-balancing, capacity-assignment and sequencing problems.

Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms

We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop an algorithm to check whether the invariant measure of a given random walk is a sum of geometric terms. We also provide the explicit form of the invariant measure if it is a sum of geometric terms. Secondly, for random walks of which the invariant measure is not a sum of geometric terms, we provide an approximation scheme to obtain error bounds for the performance measures. Finally, some numerical examples are provided

Neuronal degeneration and reorganization: a mutual principle in pathological and in healthy interactions of limbic and prefrontal circuits.

Teuchert-Noodt G. Neuronal degeneration and reorganization: a mutual principle in pathological and in healthy interactions of limbic and prefrontal circuits. J Neural Transm Suppl. 2000;(60):315-333.Based on developmental principles and insights from animal research about neuroplasticity in cell assemblies, this article is to propose a view of plasticity that promotes a link between hippocampal and prefrontal structure and function. Both the mitotic activity (counting of BrdU-labeled cells) in hippocampal dentatus and the maturation of dopamine fibres (quantitative immunochemistry of mesoprefrontal projection) in the prefrontal cortex proved to be a measurable combination for investigating the complex chain of events that relate activity dependent neuroplasticity to normal as well as to pathological maturational processes. With our animal model we demonstrate that both rearing conditions and neuroactive substances can effectively interfere with developmental plasticity and induce a malfunctional adaptation of prefrontal structures and neurotransmitter systems (dopamine, GABA). In the hippocampal dentatus, where ontogenetic plasticity proved to be preserved by continued neuro- and synaptogenesis, serious damage can be internalized without simultaneous disruption of neural dynamics offering an approach to reverse dysfunctional reorganization in the prefrontal cortex