Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Birth-death processes with disaster and instantaneous resurrection

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Molecular evolution and phylogeny of elapid snake venom three-finger toxins

Animal venom components are of considerable interest to researchers across a wide variety of disciplines, including molecular biology, biochemistry, medicine, and evolutionary genetics. The three-finger family of snake venom peptides is a particularly interesting and biochemically complex group of venom peptides, because they are encoded by a large multigene family and display a diverse array of functional activities. In addition, understanding how this complex and highly varied multigene family evolved is an interesting question to researchers investigating the biochemical diversity of these peptides and their impact on human health. Therefore, the purpose of our study was to investigate the long-term evolutionary patterns exhibited by these snake venom toxins to understand the mechanisms by which they diversified into a large, biochemically diverse, multigene family. Our results show a much greater diversity of family members than was previously known, including a number of subfamilies that did not fall within any previously identified groups with characterized activities. In addition, we found that the long-term evolutionary processes that gave rise to the diversity of three-finger toxins are consistent with the birth-and-death model of multigene family evolution. It is anticipated that this three-finger toxin toolkit will prove to be useful in providing a clearer picture of the diversity of investigational ligands or potential therapeutics available within this important family.

Molecular Sieve Silica (MSS) Membranes for Gas Separation and Reaction Processes

Weakly branched silica films formed by the two-step sol-gel process allow for the formation of high selectivity membranes for gas separation. 29Si NMR and gas permeation showed that reduced crosslinking leads to He/CH4 selectivity improvement from 300 to 1000. Applied in membrane reactor for cyclohexane conversion to benzene, conversions were achieved at 14 fold higher than a conventional reactor at 250°C. Hydrothermal stability studies showed that carbon templating of silica is required for hydrothermally stable membranes. From our work it was shown that with correct application of chemistry, practical membrane systems can be built to suit gas separation (e. g. hydrogen fuel) and reactor systems.

Altered adhesion, proliferation and death in neural cultures from adults with schizophrenia

The causes of schizophrenia are unknown, but there is evidence linking subtle deviations in neural development with schizophrenia. Embryonic brain development cannot be studied in an adult with schizophrenia, but neurogenesis and early events in neuronal differentiation can be investigated throughout adult life in the human olfactory epithelium. Our past research has demonstrated that neuronal cultures can be derived from biopsy of the human adult olfactory epithelium. In the present study, we examined mechanisms related to neurogenesis and neuronal differentiation in adults with schizophrenia versus well controls. Forty biopsies were collected under local anaesthesia from ten individuals with DSM III-R schizophrenia and ten age- and sex-matched well controls. All patients, except one, were receiving antipsychotic medication at the time of the biopsy, Immunostaining for neuronal markers indicated that neurogenesis occurred in the biopsies from both patients and controls since all contained cells expressing tubulin and/or olfactory marker protein. The major findings of this study are: 1. biopsies from patients with schizophrenia showed a significantly reduced ability to attach to the culture slide: 29.9% of patient biopsies attached compared to 73.5% of control biopsies; 2. biopsies from patients with schizophrenia had a significantly greater proportion of cells undergoing mitosis: 0.69% in the patients compared to 0.29% in the controls; and 3. dopamine (10 mu M) significantly increased the proportion of apoptotic cells in the control cultures but significantly decreased the proportion in patients' cultures. (C) 1999 Elsevier Science B.V. All rights reserved.

Quantum measurement and stochastic processes in mesoscopic conductors

In quantum measurement theory it is necessary to show how a, quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of Buttiker and the Fermi quantum stochastic calculus for mesoscopic systems.

Community structure of Quaternary coral reefs compared with Recent life and death assemblages

This paper assesses the reliability with which fossil reefs record the diversity and community structure of adjacent Recent reefs. The diversity and taxonomic composition of Holocene raised fossil reefs was compared with those of modern reef coral life and death assemblages in adjacent moderate and low-energy shallow reef habitats Of Madang Lagoon, Papua New Guinea. Species richness per sample area and Shannon-Wiener diversity (H') were highest in the fossil reefs, intermediate in the life assemblages, and lowest in the death assemblages. The taxonomic composition of the fossil reefs was most similar to the combination of the life and death assemblages from the modern reefs adjacent to the two fossil reefs. Depth zonation was recorded accurately in the fossil reefs. The Madang fossil reefs represent time-averaged composites of the combined life and death assemblages as they existed at the time the reef was uplifted. Because fossil reefs include overlapping cohorts from the life and death assemblages, lagoonal facies of fossil reefs are dominated by the dominant sediment-producing taxa, which are not necessarily the most abundant in the life assemblage. Rare or slow-growing taxa accumulate more slowly than the encasing sediments and are underrepresented in fossil reef lagoons. Time-averaging dilutes the contribution of rare taxa, rather than concentrating their contribution. Consequently, fidelity indices developed for mollusks in sediments yield low values in coral reef death and fossil assemblages. Branching corals dominate lagoonal facies of fossil reefs because they are abundant, they grow and produce sediment rapidly, and most of the sediment they produce is not exported. Fossil reefs distinguished kilometer-scale variations in community structure more clearly than did the modern life assemblages. This difference implies that fossil,reefs may provide a better long-term record of community structure than modern reefs. This difference also suggests that modern kilometer-scale variation in coral reef community structure may have been reduced by anthropogenic degradation, even in the relatively unimpacted reefs of Madang Lagoon. Holocene and Pleistocene fossil reefs provide a time-integrated historical record of community composition and may be used as long-term benchmarks for comparison with modern, degraded, nearshore reefs. Comparisons between fossil reefs and degraded modern reefs display gross changes in community structure more effectively than they demonstrate local extinction of rare taxa.

The effect of emotional and attentional processes on blink startle modulation and on electrodermal responses

Emotional accounts of startle modulation predict that startle is facilitated if elicited during aversive foreground stimuli. Attentional accounts hold that startle is enhanced if startle-eliciting stimulus and foreground stimulus are in the same modality. Visual and acoustic foreground stimuli and acoustic startle probes were employed in aversive differential conditioning and in a stimulus discrimination task. Differential conditioning was evident in electrodermal responses and blink latency shortening in both modalities, but effects on magnitude facilitation were found only for visual stimuli. In the discrimination task, skin conductance responses, blink latency shortening, and blink magnitude facilitation were larger during to-be-attended stimuli regardless of stimulus modality. The present results support the notion that attention and emotion can affect blink startle modulation during foreground stimuli.

Variation in length, fecundity and survival of pink wax scale, Ceroplastes rubens Maskell (Hemiptera: Coccidae), on umbrella trees

We investigated some of the factors that may lead to outbreaks of pink wax scale, Ceroplastes rubens Maskell, on umbrella trees, Schefflera actinophylla (Endl.). Estimates of birth and death rates of pink wax scale were high and variable within and among trees; variation in these rates was not related to scale density. Adult fecundity correlated significantly but weakly with adult test length; mean fecundity was 292 eggs per female with a range of 5-1178. Adult test length and its variance decreased weakly with increasing density. Field experiments showed that mortality of C. rubens is greatest during the first 24 hours after hatching when approximately half disappear. The rate of loss decreases over time with 0.3% of initial motile first-instar nymphs surviving to maturity. Rates of loss varied significantly between trees, indicating that some trees are more suitable for scale colonisation and survival.