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.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

A new approach to control of MIMO processes with static nonlinearities using an extended IMC framework

In this paper, a new control design method is proposed for stable processes which can be described using Hammerstein-Wiener models. The internal model control (IMC) framework is extended to accommodate multiple IMC controllers, one for each subsystem. The concept of passive systems is used to construct the IMC controllers which approximate the inverses of the subsystems to achieve dynamic control performance. The Passivity Theorem is used to ensure the closed-loop stability. (c) 2005 Elsevier Ltd. All rights reserved.

On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Let S be a countable set and let Q = (q(ij), i, j is an element of S) be a conservative q-matrix over S with a single instantaneous state b. Suppose that we are given a real number mu >= 0 and a strictly positive probability measure m = (m(j), j is an element of S) such that Sigma(i is an element of S) m(i)q(ij) = -mu m(j), j 0 b. We prove that there exists a Q-process P(t) = (p(ij) (t), i, j E S) for which m is a mu-invariant measure, that is Sigma(i is an element of s) m(i)p(ij)(t) = e(-mu t)m(j), j is an element of S. We illustrate our results with reference to the Kolmogorov 'K 1' chain and a birth-death process with catastrophes and instantaneous resurrection.

Linking physiological processes with mangrove forest structure: phosphorus deficiency limits canopy development, hydraulic conductivity and photosynthetic carbon gain in dwarf Rhizophora mangle

Spatial gradients in mangrove tree height in barrier islands of Belize are associated with nutrient deficiency and sustained flooding in the absence of a salinity gradient. While nutrient deficiency is likely to affect many parameters, here we show that addition of phosphorus (P) to dwarf mangroves stimulated increases in diameters of xylem vessels, area of conductive xylem tissue and leaf area index (LAI) of the canopy. These changes in structure were consistent with related changes in function, as addition of P also increased hydraulic conductivity (K-s), stomatal conductance and photosynthetic assimilation rates to the same levels measured in taller trees fringing the seaward margin of the mangrove. Increased xylem vessel size and corresponding enhancements in stern hydraulic conductivity in P fertilized dwarf trees came at the cost of enhanced midday loss of hydraulic conductivity and was associated with decreased assimilation rates in the afternoon. Analysis of trait plasticity identifies hydraulic properties of trees as more plastic than those of leaf structural and physiological characteristics, implying that hydraulic properties are key in controlling growth in mangroves. Alleviation of P deficiency, which released trees from hydraulic limitations, reduced the structural and functional distinctions between dwarf and taller fringing tree forms of Rhizophora mangle.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Fractal analysis of pyramidal cells in the visual cortex of the galago (Otolemur garnetti): Regional variation in dendritic branching patterns between visual areas

Previously it has been shown that the branching pattern of pyramidal cells varies markedly between different cortical areas in simian primates. These differences are thought to influence the functional complexity of the cells. In particular, there is a progressive increase in the fractal dimension of pyramidal cells with anterior progression through cortical areas in the occipitotemporal (OT) visual stream, including the primary visual area (V1), the second visual area (V2), the dorsolateral area (DL, corresponding to the fourth visual area) and inferotemporal cortex (IT). However, there are as yet no data on the fractal dimension of these neurons in prosimian primates. Here we focused on the nocturnal prosimian galago (Otolemur garnetti). The fractal dimension (D), and aspect ratio (a measure of branching symmetry), was determined for I I I layer III pyramidal cells in V1, V2, DL and IT. We found, as in simian primates, that the fractal dimension of neurons increased with anterior progression from V1 through V2, DL, and IT. Two important conclusions can be drawn from these results: (1) the trend for increasing branching complexity with anterior progression through OT areas was likely to be present in a common primate ancestor, and (2) specialization in neuron structure more likely facilitates object recognition than spectral processing.

Prismatic dentine in the Australian lungfish, Neoceratodus forsteri (Osteichthyes : Dipnoi)

The Australian lungfish, Neoceratodus forsteri, has a dentition consisting of enamel, mantle dentine and bone, enclosing circumdenteonal, core and interdenteonal dentines. Branching processes from cells that produce interdenteonal dentine leave the cell surface at different angles, with collagen fibrils aligned parallel to the long axis of each process. In the interdenteonal dentine, crystals of calcium hydroxyapatite, form within fibrils of collagen, and grow within a matrix of non-collagenous protein. Crystals are aligned parallel to the cell process, as are the original collagen fibrils. Because the processes are angled to the cell surface, the crystals within the core or interdenteonal dentine are arranged in bundles set at angles to each other. Apatite crystals in circumdenteonal dentine are finer and denser than those of the interdenteonal dentine, and form outside the fibrils of collagen. In mature circumdenteonal dentine the crystals of circumdenteonal dentine form a dense tangled mass, linked to interdenteonal dentine by isolated crystals. The functional lungfish tooth plate contains prisms of large apatite crystals in the interdenteonal dentine and masses of fine tangled crystals around each denteon. This confers mechanical strength on a structure with little enamel that is subjected to heavy wear. (c) 2006 Elsevier Ltd. All rights reserved.

Microbial quantification in activated sludge: the hits and misses

Since the implementation of the activated sludge process for treating wastewater, there has been a reliance on chemical and physical parameters to monitor the system. However, in biological nutrient removal (BNR) processes, the microorganisms responsible for some of the transformations should be used to monitor the processes with the overall goal to achieve better treatment performance. The development of in situ identification and rapid quantification techniques for key microorganisms involved in BNR are required to achieve this goal. This study explored the quantification of Nitrospira, a key organism in the oxidation of nitrite to nitrate in BNR. Two molecular genetic microbial quantification techniques were evaluated: real-time polymerase chain reaction (PCR) and fluorescence in situ hybridisation (FISH) followed by digital image analysis. A correlation between the Nitrospira quantitative data and the nitrate production rate, determined in batch tests, was attempted. The disadvantages and advantages of both methods will be discussed.

Yield behaviour of a melt-compounded polyethylene-intercalated montmorillonite nanocomposite

The yield behaviour of a series of melt-mixed polyethylene-modified montmorillonite nanocomposites has been studied as a function of temperature and strain rate and compared to the behaviour of the base polymer. The processing conditions used gave an intercalated structure as assessed by X-ray diffraction. Although there was a modest improvement in stiffness with clay content, the yield behaviour was insensitive to the addition of the clay. Both the base polymer and the nanocomposites showed double yield points. These were analysed as activated rate processes, with the activation energies consistent with the low strain yield point being associated with the alpha(2) molecular relaxation and the higher strain yield point with W axis slip. (C) 2003 Society of Chemical Industry.

Genetic effects of kangaroo harvesting

There is concern that the commercial harvest of kangaroos (Macropus spp.) is affecting species fitness and evolutionary potential because the harvest selects for larger individuals, particularly males. This paper reviews the likely effect of selective harvesting on specific traits associated with fitness, including size, and on adaptive genotypes through generalised loss of gene diversity. Heritability for traits associated with fitness is low generally. The intensity of selection imposed by harvesting is low for several reasons: the geographic size of genetic populations is much larger than the harvest localities, which are therefore not closed but open with immigration acting to correct any change in allele frequencies through harvesting; the harvest targets kangaroos above a threshold weight that includes all adult males, not the largest males specifically; larger, older males may not confer significant fitness benefits on offspring; fitness traits are inherited through both sexes while males are targeted predominantly; populations are not at a selective equilibrium because food availability fluctuates, and the fittest is unlikely to be the largest. Comparisons of harvested and unharvested populations do not show any loss of gene diversity as a result of harvesting. The likelihood of a long-term genetic impact of kangaroo harvesting as currently practiced is negligible.

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.

Exposing extinction risk analysis to pathogens: Is disease just another form of density dependence?

In the United States and several other countries., the development of population viability analyses (PVA) is a legal requirement of any species survival plan developed for threatened and endangered species. Despite the importance of pathogens in natural populations, little attention has been given to host-pathogen dynamics in PVA. To study the effect of infectious pathogens on extinction risk estimates generated from PVA, we review and synthesize the relevance of host-pathogen dynamics in analyses of extinction risk. We then develop a stochastic, density-dependent host-parasite model to investigate the effects of disease on the persistence of endangered populations. We show that this model converges on a Ricker model of density dependence under a suite of limiting assumptions, including. a high probability that epidemics will arrive and occur. Using this modeling framework, we then quantify: (1) dynamic differences between time series generated by disease and Ricker processes with the same parameters; (2) observed probabilities of quasi-extinction for populations exposed to disease or self-limitation; and (3) bias in probabilities of quasi-extinction estimated by density-independent PVAs when populations experience either form of density dependence. Our results suggest two generalities about the relationships among disease, PVA, and the management of endangered species. First, disease more strongly increases variability in host abundance and, thus, the probability of quasi-extinction, than does self-limitation. This result stems from the fact that the effects and the probability of occurrence of disease are both density dependent. Second, estimates of quasi-extinction are more often overly optimistic for populations experiencing disease than for those subject to self-limitation. Thus, although the results of density-independent PVAs may be relatively robust to some particular assumptions about density dependence, they are less robust when endangered populations are known to be susceptible to disease. If potential management actions involve manipulating pathogens, then it may be useful to. model disease explicitly.

Areal specialization of pyramidal cell structure in the visual cortex of the tree shrew: a new twist revealed in the evolution of cortical circuitry

Cortical pyramidal cells, while having a characteristic morphology, show marked phenotypic variation in primates. Differences have been reported in their size, branching structure and spine density between cortical areas. In particular, there is a systematic increase in the complexity of the structure of pyramidal cells with anterior progression through occipito-temporal cortical visual areas. These differences reflect area-specific specializations in cortical circuitry, which are believed to be important for visual processing. However, it remains unknown as to whether these regional specializations in pyramidal cell structure are restricted to primates. Here we investigated pyramidal cell structure in the visual cortex of the tree shrew, including the primary (V1), second (V2) and temporal dorsal (TD) areas. As in primates, there was a trend for more complex branching structure with anterior progression through visual areas in the tree shrew. However, contrary to the trend reported in primates, cells in the tree shrew tended to become smaller with anterior progression through V1, V2 and TD. In addition, pyramidal cells in V1 of the tree shrew are more than twice as spinous as those in primates. These data suggest that variables that shape the structure of adult cortical pyramidal cells differ among species.