Junior Applied Mathematics Seminar
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Tue, 01/05/2012 13:15 |
Lucas Jeub |
Junior Applied Mathematics Seminar  |
DH 1st floor SR |
| With the advent of powerful computers and the internet, our ability to collect and store large amounts of data has improved tremendously over the past decades. As a result, methods for extracting useful information from these large datasets have gained in importance. In many cases the data can be conveniently represented as a network, where the nodes are entities of interest and the edges encode the relationships between them. Community detection aims to identify sets of nodes that are more densely connected internally than to the rest of the network. Many popular methods for partitioning a network into communities rely on heuristically optimising a quality function. This approach can run into problems for large networks, as the quality function often becomes near degenerate with many near optimal partitions that can potentially be quite different from each other. In this talk I will show that this near degeneracy, rather than being a severe problem, can potentially allow us to extract additional information | |||
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Tue, 15/05/2012 13:15 |
Katie Leonard |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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The use of tissue engineered implants could facilitate unions in situations where there is loss of bone or non-union, thereby increasing healing time, reducing the risk of infections and hence reducing morbidity. Currently engineered bone tissue is not of sufficient quality to be used in widespread clinical practice. In order to improve experimental design, and thereby the quality of the tissue-constructs, the underlying biological processes involved need to be better understood. In conjunction with experimentalists, we consider the effect hydrodynamic pressure has on the development and regulation of bone, in a bioreactor designed specifically for this purpose. To answer the experimentalists’ specific questions, we have developed two separate models; in this talk I will present one of these, a multiphase partial differential equation model to describe the evolution of the cells, extracellular matrix that they deposit, the culture medium and the scaffold. The model is then solved using the finite element method using the deal.II library. |
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Tue, 29/05/2012 13:15 |
Huy Vu |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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Higher-order transformations are ubiquitous within data management. In relational databases, higher-order queries appear in numerous aspects including query rewriting and query specification. In XML databases, higher-order functions are natural due to the close connection of XML query languages with functional programming. We investigate higher-order query languages that combine higher- order transformations with ordinary database query languages. We define higher-order query languages based on Relational Algebra and XQuery. We also study basic problems for these query languages including evaluation, containment, and type inference. We show that even though evaluating these higher-order query languages is non-elementary, there are subclasses that are polynomially reducible to evaluation for ordinary query languages. |
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Tue, 12/06/2012 13:15 |
Joseph Parker |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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Nuclear fusion offers the prospect of abundant clean energy production, but the physical and engineering challenges are very great. In nuclear fusion reactors, the fuel is in the form of a plasma (charged gas) which is confined at high temperature and density using a toroidal magnetic field. This configuration is susceptible to turbulence, which transports heat out of the plasma and prevents fusion. It is believed that rotating the plasma suppresses turbulence, but experiments are expensive and even modest numerical simulation requires hundreds of thousands of CPU hours. We present a numerical technique for one of the five phase-space dimensions that both improves the accuracy of the calculation and greatly reduces the resolution required. |
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