Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Refined plastic hinge analysis of steel frame structures comprising non-compact sections : II : verification

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A refined plastic hinge method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in a companion paper. The method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established in this paper by comparison with a comprehensive range of analytical benchmark frame solutions. The refined plastic hinge method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Distributed plasticity analysis of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A primary objective was to produce a comprehensive range of new distributed plasticity analytical benchmark solutions for verification of the concentrated plasticity methods. A distributed plasticity model was developed using shell finite elements to explicitly account for the effects of gradual yielding and spread of plasticity, initial geometric imperfections, residual stresses and local buckling deformations. The model was verified by comparison with large-scale steel frame test results and a variety of existing analytical benchmark solutions. This paper presents a description of the distributed plasticity model and details of the verification study.

Pseudo plastic zone analysis of steel frame structures comprising non-compact sections

Application of `advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Large-scale testing of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A series of large-scale tests were performed in order to provide experimental results for verification of the new analytical models. Each of the test frames comprised non-compact sections, and exhibited significant local buckling behaviour prior to failure. This paper presents details of the test program including the test specimens, set-up and instrumentation, procedure, and results.

Non-invasive clinical measurement of the viscoelastic properties of tendon using acoustic wave transmission

Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.

Learning processes in creative service teams : towards a dynamic systems theory

The fastest-growing segment of jobs in the creative sector are in those firms that provide creative services to other sectors (Hearn, Goldsmith, Bridgstock, Rodgers 2014, this volume; Cunningham 2014, this volume). There are also a large number of Creative Services (Architecture and Design, Advertising and Marketing, Software and Digital Content occupations) workers embedded in organizations in other industry sectors (Cunningham and Higgs 2009). Ben Goldsmith (2014, this volume) shows, for example, that the Financial Services sector is the largest employer of digital creative talent in Australia. But why should this be? We argue it is because ‘knowledge-based intangibles are increasingly the source of value creation and hence of sustainable competitive advantage (Mudambi 2008, 186). This value creation occurs primarily at the research and development (R and D) and the marketing ends of the supply chain. Both of these areas require strong creative capabilities in order to design for, and to persuade, consumers. It is no surprise that Jess Rodgers (2014, this volume), in a study of Australia’s Manufacturing sector, found designers and advertising and marketing occupations to be the most numerous creative occupations. Greg Hearn and Ruth Bridgstock (2013, forthcoming) suggest ‘the creative heart of the creative economy […] is the social and organisational routines that manage the generation of cultural novelty, both tacit and codified, internal and external, and [cultural novelty’s] combination with other knowledges […] produce and capture value’. 2 Moreover, the main “social and organisational routine” is usually a team (for example, Grabher 2002; 2004).

Multi-party computation with conversion of secret sharing

Classical results in unconditionally secure multi-party computation (MPC) protocols with a passive adversary indicate that every n-variate function can be computed by n participants, such that no set of size t < n/2 participants learns any additional information other than what they could derive from their private inputs and the output of the protocol. We study unconditionally secure MPC protocols in the presence of a passive adversary in the trusted setup (‘semi-ideal’) model, in which the participants are supplied with some auxiliary information (which is random and independent from the participant inputs) ahead of the protocol execution (such information can be purchased as a “commodity” well before a run of the protocol). We present a new MPC protocol in the trusted setup model, which allows the adversary to corrupt an arbitrary number t < n of participants. Our protocol makes use of a novel subprotocol for converting an additive secret sharing over a field to a multiplicative secret sharing, and can be used to securely evaluate any n-variate polynomial G over a field F, with inputs restricted to non-zero elements of F. The communication complexity of our protocol is O(ℓ · n 2) field elements, where ℓ is the number of non-linear monomials in G. Previous protocols in the trusted setup model require communication proportional to the number of multiplications in an arithmetic circuit for G; thus, our protocol may offer savings over previous protocols for functions with a small number of monomials but a large number of multiplications.

Distinguishing attack on SOBER-128 with linear masking

We present a distinguishing attack against SOBER-128 with linear masking. We found a linear approximation which has a bias of 2^− − 8.8 for the non-linear filter. The attack applies the observation made by Ekdahl and Johansson that there is a sequence of clocks for which the linear combination of some states vanishes. This linear dependency allows that the linear masking method can be applied. We also show that the bias of the distinguisher can be improved (or estimated more precisely) by considering quadratic terms of the approximation. The probability bias of the quadratic approximation used in the distinguisher is estimated to be equal to O(2^− − 51.8), so that we claim that SOBER-128 is distinguishable from truly random cipher by observing O(2^103.6) keystream words.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Gossip we can trust: Defamation law and non-fiction

Drawing on two case studies, this article considers the allegation of a disgruntled author: ’Defamation was framed to protect the reputations of 19th century gentlemen hypocrites'. The first case study considers the litigation over Bob Ellis' unreliable political memoir, ’Goodbye Jerusalem', published by Random House. The second case study focuses upon the litigation over the allegation by Media Watch that Richard Carleton had plagarised a documentary entitled ’Cry from the Grave'. The article considers the meaning of defamatory imputations, the range of defences, and the available remedies. It highlights the competing arguments over the protection of reputation and privacy, artistic expression, and the freedom of speech. This article concludes that defamation law should foster ’gossip we can trust'.

Refined Plastic Hinge Analysis of Steel Frame Structures Comprising Non-Compact Sections: I: Formulation

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity formulation suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. This formulation, referred to as the refined plastic hinge method, implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling.

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Micropolar flow in a porous channel with high mass transfer

Two dimensional flow of a micropolar fluid in a porous channel is investigated. The flow is driven by suction or injection at the channel walls, and the micropolar model due to Eringen is used to describe the working fluid. An extension of Berman's similarity transform is used to reduce the governing equations to a set of non-linear coupled ordinary differential equations. The latter are solved for large mass transfer via a perturbation analysis where the inverse of the cross-flow Reynolds number is used as the perturbing parameter. Complementary numerical solutions for strong injection are also obtained using a quasilinearisation scheme, and good agreement is observed between the solutions obtained from the perturbation analysis and the computations.

Curvilinear relationships between the job demands-resources (JD-R) model, and work engagement : a police service case study

The current study aims to investigate the non-linear relationship between the JD-R model and work engagement. Previous research has identified linear relationships between these constructs; however there are strong theoretical arguments for testing curvilinear relationships (e.g., Warr, 1987). Data were collected via a self-report online survey from officers of one Australian police service (N = 2,626). Results demonstrated a curvilinear relationship between job demands and job resources and engagement. Gender (as a control variable) was also found to be a significant predictor of work engagement. The results indicated that male police officers experienced significantly higher job demands and colleague support than female officers. However, female police officers reported significantly higher levels of work engagement than male officers. This study emphasises the need to test curvilinear relationships, as well as simple linear associations, when measuring psychological health.