Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

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.

Population pharmacokinetic analysis of mycophenolic acid in renal transplant recipients following oral administration of mycophenolate mofetil

Aim To develop a population pharmacokinetic model for mycophenolic acid in adult kidney transplant recipients, quantifying average population pharmacokinetic parameter values, and between- and within-subject variability and to evaluate the influence of covariates on the pharmacokinetic variability. Methods Pharmacokinetic data for mycophenolic acid and covariate information were previously available from 22 patients who underwent kidney transplantation at the Princess Alexandra Hospital. All patients received mycophenolate mofetil 1 g orally twice daily. A total of 557 concentration-time points were available. Data were analysed using the first-order method in NONMEM (version 5 level 1.1) using the G77 FORTRAN compiler. Results The best base model was a two-compartment model with a lag time (apparent oral clearance was 271 h(-1), and apparent volume of the central compartment 981). There was visual evidence of complex absorption and time-dependent clearance processes, but they could not be successfully modelled in this study. Weight was investigated as a covariate, but no significant relationship was determined. Conclusions The complexity in determining the pharmacokinetics of mycophenolic acid is currently underestimated. More complex pharmacokinetic models, though not supported by the limited data collected for this study, may prove useful in the future. The large between-subject and between-occasion variability and the possibility of nonlinear processes associated with the pharmacokinetics of mycophenolic acid raise questions about the value of the use of therapeutic monitoring and limited sampling strategies.

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.

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.

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.

Strain-dependent fluid flow defined through rock mass classification schemes

Strain-dependent hydraulic conductivities are uniquely defined by an environmental factor, representing applied normal and shear strains, combined with intrinsic material parameters representing mass and component deformation moduli, initial conductivities, and mass structure. The components representing mass moduli and structure are defined in terms of RQD (rock quality designation) and RMR (rock mass rating) to represent the response of a whole spectrum of rock masses, varying from highly fractured (crushed) rock to intact rock. These two empirical parameters determine the hydraulic response of a fractured medium to the induced-deformations The constitutive relations are verified against available published data and applied to study one-dimensional, strain-dependent fluid flow. Analytical results indicate that both normal and shear strains exert a significant influence on the processes of fluid flow and that the magnitude of this influence is regulated by the values of RQD and RMR.

The shoot controls zeatin riboside export from pea roots. Evidence from the branching mutant rms4

The rms4 mutant of pea (Pisum sativum L.) was used in grafting studies and cytokinin analyses of the root xylem sap to provide evidence that, at least for pea, the shoot can modify the import of cytokinins from the root. The rms4 mutation, which confers a phenotype with increased branching in the shoot, causes a very substantial decrease (down to 40-fold less) in the concentration of zeatin riboside (ZR) in the xylem sap of the roots. Results from grafts between wild-type (WT) and rms4 plants indicate that the concentration of cytokinins in the xylem sap of the roots is determined almost entirely by the genotype of the shoot. WT scions normalize the cytokinin concentration in the sap of rms4 mutant roots, whereas mutant scions cause WT roots to behave like those of self-grafted mutant plants. The mechanism whereby rms4 shoots of pea cause a down-regulation in the export of cytokinins from the roots is unknown at this time. However, our data provide evidence that the shoot transmits a signal to the roots and thereby controls processes involved in the regulation of cytokinin biosynthesis in the root.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Cloning of a catalytic subunit of cAMP-dependent protein kinase from the honeybee (Apis mellifera) and its localization in the brain

In the honeybee the cAMP-dependent signal transduction cascade has been implicated in processes underlying learning and memory, The cAMP-dependent protein kinase (PKA) is the major mediator of cAMP action. To characterize the PKA system in the honeybee brain we cloned a homologue of a PKA catalytic subunit from the honeybee,The deduced amino acid sequence shows 80-94% identity with catalytic subunits of PKA from Drosophila melanogaster, Aplysia californica and mammals. The corresponding gene is predominantly expressed in the mushroom bodies, a structure that is involved in learning and memory processes. However, expression can also be found in the antennal and optic lobes,The level of expression varies within all three neuropiles.

Kinase-dependent and kinase-independent functions of EphA4 receptors in major axon tract formation in vivo

The EphA4 receptor tyrosine kinase regulates the formation of the corticospinal tract (CST), a pathway controlling voluntary movements, and of the anterior commissure (AC), connecting the neocortical temporal robes. To study EphA4 kinase signaling in these processes, we generated mice expressing mutant EphA4 receptors either lacking kinase activity or with severely downregulated kinase activity. We demonstrate that EphA4 is required for CST formation as a receptor for which it requires an active kinase domain. In contrast, the formation of the AC is rescued by kinase-dead EphA4, suggesting that in this structure EphA4 acts as a ligand for which its kinase activity is not required. Unexpectedly, the cytoplasmic sterile-alpha motif (SAM) domain is not required for EphA4 functions. Our findings establish both kinase-dependent and kinase-independent functions of EphA4 in the formation of major axon tracts.

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Indirect evidence of density-dependent population regulation in Aponomma hydrosauri (Acari : Ixodidae), an ectoparasite of reptiles

The extent to which density-dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density-dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long-term dataset on the distribution of ticks among individual hosts. If density-dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host-parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re-analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density-dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population-scale increase in the aggregation coefficient is indirect evidence of a density-dependent process or processes sufficiently strong to produce a population-wide pattern, and thus also likely to influence population regulation. The direct observation of a density-dependent process is evidence of at least part of the responsible mechanism.

Asymmetric blasting: a rock mass dependent blast design method

Blasting has been the most frequently used method for rock breakage since black powder was first used to fragment rocks, more than two hundred years ago. This paper is an attempt to reassess standard design techniques used in blasting by providing an alternative approach to blast design. The new approach has been termed asymmetric blasting. Based on providing real time rock recognition through the capacity of measurement while drilling (MWD) techniques, asymmetric blasting is an approach to deal with rock properties as they occur in nature, i.e., randomly and asymmetrically spatially distributed. It is well accepted that performance of basic mining operations, such as excavation and crushing rely on a broken rock mass which has been pre conditioned by the blast. By pre-conditioned we mean well fragmented, sufficiently loose and with adequate muckpile profile. These muckpile characteristics affect loading and hauling [1]. The influence of blasting does not end there. Under the Mine to Mill paradigm, blasting has a significant leverage on downstream operations such as crushing and milling. There is a body of evidence that blasting affects mineral liberation [2]. Thus, the importance of blasting has increased from simply fragmenting and loosing the rock mass, to a broader role that encompasses many aspects of mining, which affects the cost of the end product. A new approach is proposed in this paper which facilitates this trend 'to treat non-homogeneous media (rock mass) in a non-homogeneous manner (an asymmetrical pattern) in order to achieve an optimal result (in terms of muckpile size distribution).' It is postulated there are no logical reasons (besides the current lack of means to infer rock mass properties in the blind zones of the bench and onsite precedents) for drilling a regular blast pattern over a rock mass that is inherently heterogeneous. Real and theoretical examples of such a method are presented.

Phosphatidylinositol 3-kinase C2 alpha is essential for ATP-dependent priming of neurosecretory granule exocytosis

Neurotransmitter release and hormonal secretion are highly regulated processes culminating in the calcium-dependent fusion of secretory vesicles with the plasma membrane. Here, we have identified a role for phosphatidylinositol 3-kinase C2 alpha (PI3K-C2 alpha) and its main catalytic product, PtdIns3P, in regulated exocytosis. In neuroendocrine cells, PI3K-C2 alpha is present on a subpopulation of mature secretory granules. Impairment of PI3K-C2 alpha function specifically inhibits the ATP-dependent priming phase of exocytosis. Overexpression of wild-type PI3K-C2 alpha enhanced secretion, whereas transfection of PC12 cells with a catalytically inactive PI3K-C2 alpha mutant or a 2xFYVE domain sequestering PtdIns3P abolished secretion. Based on these results, we propose that production of PtdIns3P by PI3K-C2 alpha is required for acquisition of fusion competence in neurosecretion.