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.

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.

Extinction times for a general birth, death and catastrophe process

The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data, This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

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.

Finite element modelling of rock alteration and metamorphic process in hydrothermal systems

We use the finite element method to simulate the rock alteration and metamorphic process in hydrothermal systems. In particular, we consider the fluid-rock interaction problems in pore-fluid saturated porous rocks. Since the fluid rock interaction takes place at the contact interface between the pore-fluid and solid minerals, it is governed by the chemical reaction which usually takes place very slowly at this contact interface, from the geochemical point of view. Due to the relative slowness of the rate of the chemical reaction to the velocity of the pore-fluid flow in the hydrothermal system to be considered, there exists a retardation zone, in which the conventional static theory in geochemistry does not hold true. Since this issue is often overlooked by some purely numerical modellers, it is emphasized in this paper. The related results from a typical rock alteration and metamorphic problem in a hydrothermal system have shown not only the detailed rock alteration and metamorphic process, but also the size of the retardation zone in the hydrothermal system. Copyright (C) 2001 John Wiley & Sons, Ltd.

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.

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.

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.

Urban birth and migrant status as risk factors for psychosis: An Australian case-control study

Background Urban birth and migrant status have been identified as risk factors for psychosis in North American and European studies. The aim of this study was to explore these variables in an Australian case-control study. Method Country of birth of subjects and their parents, and place of birth of Australian-born subjects, were examined in individuals with psychosis drawn from a prevalence study (n = 310) and well controls recruited from the same catchment area (n = 303). Results Migrant status was associated with a significantly decreased odds of having a psychotic disorder. For those born in Australia, neither migrant status of parents nor urban birth was associated with having a psychotic disorder. Conclusions The lack of effect for urban birth and second-generation migrant status may help generate candidate environmental risk factors that operate in Europe but not in Australia.

Learning about life and death in early childhood

Inagaki and Hatano (2002) have argued that young children initially understand biological phenomena in terms of vitalism, a mode of construal in which life or life-force is the central causal-explanatory concept. This study investigated the development of vitalistic reasoning in young children's concepts of life, the human body and death. Sixty preschool children between the ages of 3 years, 7 months and 5 years, 11 months participated. All children were initially given structured interviews to assess their knowledge of (1) human body function and (2) death. From this sample 40 children in the Training group were taught about the human body and how it functions to maintain life. The Control group (n = 20) received no training. All 60 children were subsequently reassessed on their knowledge of human body function and death. Results from the initial interviews indicated that young children who spontaneously appealed to vitalistic concepts in reasoning about human body functioning were also more sophisticated in their understanding of death. Results from the posttraining interviews showed that children readily learned to adopt a vitalistic approach to human body functioning, and that this learning coincided with significant development in their understanding of human body function, and of death. The overall pattern of results supports the claim that the acquisition of a vitalistic causal-explanatory framework serves to structure children's concepts and facilitates learning in the domain of biology. (C) 2003 Elsevier Science (USA). All rights reserved.

Inter-organisational networks, value creation and the process of technology integration in research and development

Traditional methods of R&D management are no longer sufficient for embracing innovations and leveraging complex new technologies to fully integrated positions in established systems. This paper presents the view that the technology integration process is a result of fundamental interactions embedded in inter-organisational activities. Emerging industries, high technology companies and knowledge intensive organisations owe a large part of their viability to complex networks of inter-organisational interactions and relationships. R&D organisations are the gatekeepers in the technology integration process with their initial sanction and motivation to develop technologies providing the first point of entry. Networks rely on the activities of stakeholders to provide the foundations of collaborative R&D activities, business-to-business marketing and strategic alliances. Such complex inter-organisational interactions and relationships influence value creation and organisational goals as stakeholders seek to gain investment opportunities. A theoretical model is developed here that contributes to our understanding of technology integration (adoption) as a dynamic process, which is simultaneously structured and enacted through the activities of stakeholders and organisations in complex inter-organisational networks of sanction and integration.