Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Understanding graphicacy : students’ making sense of graphics in mathematics assessment tasks

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed: 1) factors which contribute to success or hinder performance on tasks with various graphical representations; and 2) how the literacy and graphical demands of tasks influence the mathematical sense making of students. The outcomes of this study highlight the changing nature of assessment in school mathematics and identify the function and influence of graphics in the design of assessment tasks.

Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

From cultural to creative industries : theory, industry, and policy implications

Across post-industrial societies worldwide, the creative industries are increasingly seen as a key economic driver. These industries - including fields as diverse as advertising, art, computer games, crafts, design, fashion, film, museums, music, performing arts, publishing, radio, theatre and TV - are built upon individual creativity and innovation and have the potential to create wealth and employment through the mechanism of intellectual property. Creative Industries: Critical Readings brings together the key writings - drawing on both journals and books - to present an authoritative and wide-ranging survey of this emerging field of study. The set is presented with an introduction and the writings are divided into four volumes, organized thematically: Volume 1: Concepts - focuses on the concept of creativity and the development of government and industry interest in creative industries; Volume 2: Economy - maps the role and function of creative industries in the economy at large; Volume 3: Organization - examines the ways in which creative institutions organize themselves; and Volume 4: Work - addresses issues of creative work, labour and careers This major reference work will be invaluable to scholars in economics, cultural studies, sociology, media studies and organization studies.

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.

Speeding by young novice drivers : what can personal characteristics and psychosocial theory add to our understanding?

Purpose: Young novice drivers continue to be overrepresented in fatalities and injuries arising from crashes even with the introduction of countermeasures such as graduated driver licensing (GDL). Enhancing countermeasures requires a better understanding of the variables influencing risky driving. One of the most common risky behaviours performed by drivers of all ages is speeding, which is particularly risky for young novice drivers who, due to their driving inexperience, have difficulty in identifying and responding appropriately to road hazards. Psychosocial theory can improve our understanding of contributors to speeding, thereby informing countermeasure development and evaluation. This paper reports an application of Akers’ social learning theory (SLT), augmented by Gerrard and Gibbons’ prototype/willingness model (PWM), in addition to personal characteristics of age, gender, car ownership, and psychological traits/states of anxiety, depression, sensation seeking propensity and reward sensitivity, to examine the influences on self-reported speeding of young novice drivers with a Provisional (intermediate) licence in Queensland, Australia. Method: Young drivers (n = 378) recruited in 2010 for longitudinal research completed two surveys containing the Behaviour of Young Novice Drivers Scale, and reported their attitudes and behaviours as pre-Licence/Learner (Survey 1) and Provisional (Survey 2) drivers and their sociodemographic characteristics. Results: An Akers’ measurement model was created. Hierarchical multiple regressions revealed that (1) personal characteristics (PC) explained 20.3%; (2) the combination of PC and SLT explained 41.1%; and (3) the combination of PC, SLT and PWM explained 53.7% of variance in self-reported speeding. Whilst there appeared to be considerable shared variance, the significant predictors in the final model included gender, car ownership, reward sensitivity, depression, personal attitudes, and Learner speeding. Conclusions: These results highlight the capacity for psychosocial theory to improve our understanding of speeding by young novice drivers, revealing relationships between previous behaviour, attitudes, psychosocial characteristics and speeding. The findings suggest multi-faceted countermeasures should target the risky behaviour of Learners, and Learner supervisors should be encouraged to monitor their Learners’ driving speed. Novice drivers should be discouraged from developing risky attitudes towards speeding.

Collaborative academic/practitioner research in project management : theory and models

Purpose – The purpose of this paper is to provide of a review of the theory and models underlying project management (PM) research degrees that encourage reflective learning. Design/methodology/approach – Review of the literature and reflection on the practice of being actively involved in conducting and supervising academic research and disseminating academic output. The paper argues the case for the potential usefulness of reflective academic research to PM practitioners. It also highlights theoretical drivers of and barriers to reflective academic research by PM practitioners. Findings – A reflective learning approach to research can drive practical results though it requires a great deal of commitment and support by both academic and industry partners. Practical implications – This paper suggests how PM practitioners can engage in academic research that has practical outcomes and how to be more effective at disseminating these research outcomes. Originality/value – Advanced academic degrees, in particular those completed by PM practitioners, can validate a valuable source of innovative ideas and approaches that should be more quickly absorbed into the PM profession’s sources of knowledge. The value of this paper is to critically review and facilitate a reduced adaptation time for implementation of useful reflective academic research to industry.

A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Transition to day care for older people in Taiwan : a grounded theory study

Adult day care centres provide a means whereby frail or disabled older people can remain living at home particularly when their family care-givers engage in waged work. In Taiwan, adult day care services appear to meet the cultural needs of both older people and their families for whom filial care is vital. Little research attention has been paid to the use of day care services in Taiwan, the uptake rate of which is low. This grounded theory study explored the ways in which older people and family care-givers construct meanings around the use of day care services in Taiwan. Forty-four semi-structured interviews were undertaken with older people, care-givers and day care centre managers. The findings from grounded theory data analysis bring focus to the assumptions and structures that underpin the process of transition to day care services. A key feature of this process is the reconstruction of personal identity as both the older people and family care-givers work to make sense of the relationship between the self and a changing social structure. Reconstructing identity in a shifting world is the core category of the study and reflects a process of reframing whereby older people came to new definitions of social responsibility and independence within the context of the day care centre. Similarly, the family care-givers actively reformulated the concept of filial piety as they interacted with and interpreted the changes in economic and social conditions in Taiwan.

An investigation of market segmentation theory and its impact on effective fundraising

This paper presents the findings of an indepth study into the effects and success of marketing segmentation, target marketing and fundraising. Organisations are constantly seeking new ways and more efficient means to raise funds so that they can fulfill their objectives. These organisations review and evaluate their resources to gain competitive advantage and increased fundraising success...

Tests and Models of Non-compositional Concepts

The question of under what conditions conceptual representation is compositional remains debatable within cognitive science. This paper proposes a well developed mathematical apparatus for a probabilistic representation of concepts, drawing upon methods developed in quantum theory to propose a formal test that can determine whether a specific conceptual combination is compositional, or not. This test examines a joint probability distribution modeling the combination, asking whether or not it is factorizable. Empirical studies indicate that some combinations should be considered non-compositionally.

Homo- and heteronuclear meso,meso-(E)-Ethene-1,2-diyl-Linked Diporphyrins : preparation, X-ray crystal structure, electronic absorption and emission spectra and density functional theory calculations

Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.