Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description

Cooper pair correlations and energetic knock-out reactions

Two-nucleon removal (or knock-out) reactions at intermediate energies are a developing tool for both nuclear spectroscopy and for the study of certain nucleon correlations in very exotic and some stable nuclei. We present an overview of these reactions with specific emphasis on the nature of the two-nucleon correlations that can be probed. We outline future possibilities and tests needed to fully establish these sensitivities.Comment: 12 pages, 3 figures: Contribution to the Volume 50 years of Nuclear BCS edited by World Scientifi

Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Research and technology program perspectives for general aviation and commuter aircraft

The uses, benefits, and technology needs of the U.S. general aviation industry were studied in light of growing competition from foreign general aviation manufacturers, especially in the commuter and business jet aircraft markets

The role of Guanxi on Chinese leadership innovation:the pilot study on the electric motor sector

This research aims to examine the existence and nature of complex business-social relationships in the Chinese context (Guanxi) and evaluate how these relationships influence the behaviors of managers in State-owned Chinese engineering firms. Research on Guanxi is comprehensive though little work investigates internal influences and how internal relationships may mirror or replicate external Guanxi. This study uses a snowball sample of 66 senior managers across the key functional disciplines in typical large Chinese firms and explores how often strategic level problems in the firm are solved through relationships outside, inside or between the companies. Do Guanxi networks penetrate the organization itself and are there relationships that are unique to internal networks? The research finds that problem solving at strategic levels are often through internal and external networks, rather than internal management structures, but also that different problems complexities typically demonstrate unique problem-solving networks. The research identifies three different forms that these relationships take: Internal, inter-firm and hybrid relationship modes. Implications for this work suggest problem solving in Chinese firms is enhanced through cooperation and mutual respect, and likely to be inhibited by traditional Western approaches to management

A study of the usefulness of Skylab EREP data for earth resources studies in Australia

The author has identified the following significant results. The stereo cover of the Skylab photos, their clarity, and their resolution put them far above the ERTS imagery not only in distinguishing between patterns but also in determining the nature of the country. The following land systems: (1) plains with sand dunes; (2) ridges, foothills, and alluvial plains; (3) dune-covered country with stony hills; and (4) alluvial plains were indistinguishable on the ERTS imagery. However, the same places are clearly distinguishable on the Skylab photos, together with the character of the dunes (parallel, reticulate, or irregular)