Development of a genetic method to estimate effective spawner numbers in the NPF and Queensland tiger prawn fisheries

OBJECTIVES: 1. To critically evaluate a variety of mathematical methods of calculating effective population size (Ne) by conducting comprehensive computer simulations and by analysis of empirical data collected from the Moreton Bay population of tiger prawns. 2. To lay the groundwork for the application of the technology in the NPF. 3. To produce software for the calculation of Ne, and to make it widely available.

A formal representation of assumptions in process modelling

In this work, we present a systematic approach to the representation of modelling assumptions. Modelling assumptions form the fundamental basis for the mathematical description of a process system. These assumptions can be translated into either additional mathematical relationships or constraints between model variables, equations, balance volumes or parameters. In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The smallest indivisible syntactical element, the so called assumption atom has been identified as a triplet. With this syntax a modelling assumption can be described as an elementary assumption, i.e. an assumption consisting of only an assumption atom or a composite assumption consisting of a conjunction of elementary assumptions. The above syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and necessary conditions for checking them are given. These transformations can be used in several ways and their implications can be analysed by formal methods. The modelling assumptions define model hierarchies. That is, a series of model families each belonging to a particular equivalence class. These model equivalence classes can be related to primal assumptions regarding the definition of mass, energy and momentum balance volumes and to secondary and tiertinary assumptions regarding the presence or absence and the form of mechanisms within the system. Within equivalence classes, there are many model members, these being related to algebraic model transformations for the particular model. We show how these model hierarchies are driven by the underlying assumption structure and indicate some implications on system dynamics and complexity issues. (C) 2001 Elsevier Science Ltd. All rights reserved.

Surface diffusion and adsorption of hydrocarbons in activated carbon

Adsorption and diffusion in a porous media were studied theoretically and experimentally with a differential transient permeation method. The porous medium is allowed to equilibrate at some specified loading, and then the time trajectory of the permeation process is followed after a small difference between the pressures at the end faces of the porous medium is introduced at time t = 0 +. Such a trajectory us. time would contain adsorption and diffusion characteristics of the system. By studying this for various surface loadings, pore and surface diffusions can be fully characterized. Mathematical modeling of transient permeation is detailed for pure gases or vapors diffusion and adsorption in porous media. Effects of nonlinearity of adsorption isotherm, pressure, temperature and heat effects were considered in the model. Experimental data of diffusion and adsorption of propane, n-butane and n-hexane in activated carbon at different temperatures and loadings show the potential of this method as a useful tool to study adsorption kinetics in porous media. Validity of the model is best tested against the transient data where the kinetics curves exhibit sigmoidal shape, which is a result of the diffusion and adsorption rate during the initial stage of permeation.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

Using a non-invasive stable isotope tracer to measure the absorption of water in humans

The development of solutions that prevent dehydration or promote adequate re-hydration play a vital role in preventing fatigue during exercise, however, the methods commonly used to assess the hydration ability of such solutions are invasive and often assess the components of absorption separately. This paper describes using a non-invasive deuterium tracer technique that assesses gastric emptying and intestinal absorption simultaneously to evaluate the uptake of water during rest and exercise. The kinetics of absorption are further examined by mathematical modelling of the data generated. For the rest group, 0.05 g/kg of body weight of deuterium, contained in gelatine capsules, was ingested with ordinary tap water and saliva samples were collected every 5 min for one hour while the subject remained seated. The deuterium was administered as above for the exercise group but sample collection was during one hour of exercise on a treadmill at 55% of the subject's maximum heart rate. The enrichment data for each subject were mathematically modelled and the parameters obtained were compared across groups using an independent samples t-test. Compared with the rest condition, the exercise group showed delayed absorption of water as indicated by significant differences for the modelling parameters t(2), t(1/2), maximum absorption rate and solution absorption amount at t(1). Labelling with a deuterium tracer is a good measure of the relative rate ingested fluids are absorbed by the body. Mathematical modelling of the data generates rates of maximum absorption and allows calculation of the percentage of the solution that is absorbed at any given time during the testing period. Copyright (C) 2004 John Wiley Sons, Ltd.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

On the optimal ratio of heavy to light chain genes for efficient recombinant antibody production by CHO cells

Monoclonal antibodies (Mab) are heterotetramers consisting of an equimolar ratio of heavy chain (HC) and light chain (LC) polypeptides. Accordingly, most recombinant Mab expression systems utilize an equimolar ratio of heavy chain (he) to light chain (lc) genes encoded on either one or two plasmids. However, there is no evidence to suggest that this gene ratio is optimal for stable or transient production of recombinant Mab. In this study we have determined the optimal ratio of hc:lc genes for production of a recombinant IgG(4) Mab, cB72.3, by Chinese hamster ovary (CHO) cells using both empirical and mathematical modeling approaches. Polyethyleneimine-mediated transient expression of cB72.3 at varying ratios of hc:lc genes encoded on separate plasmids yielded an optimal Mab titer at a hc:lc gene ratio of 3:2; a conclusion confirmed by separate mathematical modeling of the Mab folding and assembly process using transient expression data. On the basis of this information, we hypothesized that utilization of he genes at low hc:lc gene ratios is more efficient. To confirm this, cB72.3 Mab was transiently produced by CHO cells at constant he and varying lc gene dose. Under these conditions, Mab yield was increased with a concomitant increase in lc gene dose. To determine if the above findings also apply to stably transfected CHO cells producing recombinant Mab, we compared the intra- and extracellular ratios of HC and LC polypeptides for three GS-CHO cells lines transfected with a 1:1 ratio of hc:lc genes and selected for stable expression of the same recombinant Mab, cB72.3. Intra- and extracellular HC:LC polypeptide ratios ranged from 1:2 to 1:5, less than that observed on transient expression of the same Mab in parental CHO cells using the same vector. In conclusion, our data suggest that the optimal ratio of hc:lc genes used for transient and stable expression of Mab differ. In the case of the latter, we infer that optimal Mab production by stably transfected cells represents a compromise between HC abundance limiting productivity and the requirement for excess LC to render Mab folding and assembly more efficient.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

A probabilistic switch model of information flow in social networks: Application for virtual circuits to organizational design

Network building and exchange of information by people within networks is crucial to the innovation process. Contrary to older models, in social networks the flow of information is noncontinuous and nonlinear. There are critical barriers to information flow that operate in a problematic manner. New models and new analytic tools are needed for these systems. This paper introduces the concept of virtual circuits and draws on recent concepts of network modelling and design to introduce a probabilistic switch theory that can be described using matrices. It can be used to model multistep information flow between people within organisational networks, to provide formal definitions of efficient and balanced networks and to describe distortion of information as it passes along human communication channels. The concept of multi-dimensional information space arises naturally from the use of matrices. The theory and the use of serial diagonal matrices have applications to organisational design and to the modelling of other systems. It is hypothesised that opinion leaders or creative individuals are more likely to emerge at information-rich nodes in networks. A mathematical definition of such nodes is developed and it does not invariably correspond with centrality as defined by early work on networks.

Modelling of two-stage anaerobic digestion using the IWA Anaerobic Digestion Model No. 1 (ADM1)

The aim of the study presented was to implement a process model to simulate the dynamic behaviour of a pilot-scale process for anaerobic two-stage digestion of sewage sludge. The model implemented was initiated to support experimental investigations of the anaerobic two-stage digestion process. The model concept implemented in the simulation software package MATLAB(TM)/Simulink(R) is a derivative of the IWA Anaerobic Digestion Model No.1 (ADM1) that has been developed by the IWA task group for mathematical modelling of anaerobic processes. In the present study the original model concept has been adapted and applied to replicate a two-stage digestion process. Testing procedures, including balance checks and 'benchmarking' tests were carried out to verify the accuracy of the implementation. These combined measures ensured a faultless model implementation without numerical inconsistencies. Parameters for both, the thermophilic and the mesophilic process stage, have been estimated successfully using data from lab-scale experiments described in literature. Due to the high number of parameters in the structured model, it was necessary to develop a customised procedure that limited the range of parameters to be estimated. The accuracy of the optimised parameter sets has been assessed against experimental data from pilot-scale experiments. Under these conditions, the model predicted reasonably well the dynamic behaviour of a two-stage digestion process in pilot scale. (C) 2004 Elsevier Ltd. All rights reserved.

Molecular classification of cutaneous malignant melanoma by gene expression profiling

The most common human cancers are malignant neoplasms of the skin(1,2). Incidence of cutaneous melanoma is rising especially steeply, with minimal progress in non-surgical treatment of advanced disease(3,4). Despite significant effort to identify independent predictors of melanoma outcome, no accepted histopathological, molecular or immunohistochemical marker defines subsets of this neoplasm(2,3). Accordingly, though melanoma is thought to present with different 'taxonomic' forms, these are considered part of a continuous spectrum rather than discrete entities(2). Here we report the discovery of a subset of melanomas identified by mathematical analysis of gene expression in a series of samples. Remarkably, many genes underlying the classification of this subset are differentially regulated in invasive melanomas that form primitive tubular networks in vitro, a feature of some highly aggressive metastatic melanomas(5). Global transcript analysis can identify unrecognized subtypes of cutaneous melanoma and predict experimentally verifiable phenotypic characteristics that may be of importance to disease progression.

Using Lindenmayer systems to model morphogenesis in a tropical pasture legume Stylosanthes scabra

This paper summarizes the processes involved in designing a mathematical model of a growing pasture plant, Stylosanthes scabra Vog. cv. Fitzroy. The model is based on the mathematical formalism of Lindenmayer systems and yields realistic computer-generated images of progressive plant geometry through time. The processes involved in attaining growth data, retrieving useful growth rules, and constructing a virtual plant model are outlined. Progressive output morphological data proved useful for predicting total leaf area and allowed for easier quantification of plant canopy size in terms of biomass and total leaf area.

Model for gas-liquid flow through wet porous medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra-fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re approximate to 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.