485 research outputs found

    Growth:Visualisation of predictive mathematical models using 3D computer graphics and animation

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    ‘Growth’ is a short film created as a result of a multidisciplinary collaboration between artists and scientists from the University of Dundee. The author worked with mathematicians to investigate how techniques and technologies used in 3D computer animation and visual effects industries might support the enhanced visualisation of predictive mathematical modelling of solid tumour growth. This paper will discuss the practical and artistic processes of this visualisation research, including the technical innovations required in undertaking this work – such as the creation of custom tools for ‘reading’ data, or the addition of stereoscopic output. By transforming numerical data into three-dimensional ‘objects’, artists can provide new ways of ‘seeing’ information and identifying patterns or results. Developing visualisation techniques can be used to improve the communication of cancer growth to patients (by increasing patient understanding and relieving their fears) through the use of new and innovative visual material.<br/

    Ignition conditions for inertial confinement fusion targets with a nuclear spin-polarized DT fuel

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    The nuclear fusion cross-section is modified when the spins of the interacting nuclei are polarized. In the case of deuterium?tritium it has been theoretically predicted that the nuclear fusion cross-section could be increased by a factor d = 1.5 if all the nuclei were polarized. In inertial confinement fusion this would result in a modification of the required ignition conditions. Using numerical simulations it is found that the required hot-spot temperature and areal density can both be reduced by about 15% for a fully polarized nuclear fuel. Moreover, numerical simulations of a directly driven capsule show that the required laser power and energy to achieve a high gain scale as d-0.6 and d-0.4 respectively, while the maximum achievable energy gain scales as d0.9

    Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

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    The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

    Cauchy's infinitesimals, his sum theorem, and foundational paradigms

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    Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

    Resumen topográfico e histórico de Menorca [Manuscrito]

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    Copia digital. Madrid : Ministerio de Cultura. Subdirección General de Coordinación Bibliotecaria, 200

    Armida [Manuscrito] : tragèdia en tres actes

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    Copia digital. Madrid : Ministerio de Cultura. Subdirección General de Coordinación Bibliotecaria, 200
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