Past Junior Applied Mathematics Seminar

8 March 2011
13:15
Sophie Kershaw
Abstract

How best to use the cellular Potts model? This is a boundary dynamic method for computational cell-based modelling, in which evolution of the domain is achieved through a process of free energy minimisation. Historically its roots lie in statistical mechanics, yet in modern day it has been implemented in the study of metallic grain growth, foam coarsening and most recently, biological cells. I shall present examples of its successful application to the Steinberg cell sorting experiments of the early 1960s, before examining the specific case of the colorectal crypt. This scenario highlights the somewhat problematic nuances of the CPM, and provides useful insights into the process of selecting a cell-based framework that is suited to the complex biological tissue of interest.

  • Junior Applied Mathematics Seminar
22 February 2011
13:15
Yi Ming Lai
Abstract
&nbsp;We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modelling<br />populations of neurons. In particular, we use the example of a interacting<br />populations of excitatory and inhibitory neurons (E-I networks). As each<br />network consists of a large but finite number of neurons that fire<br />stochastically, we can study the effect of this intrinsic noise using a master<br />equation formulation. In the parameter regime where each E-I network acts as a<br />limit cycle oscillator, we combine phase reduction and averaging to study the<br />stationary distribution of phase differences in an ensemble of uncoupled E-I<br />oscillators, and explore how the intrinsic noise disrupts synchronization due<br />to a common external noise source.<pre> </pre>
  • Junior Applied Mathematics Seminar
25 January 2011
13:15
Hermes Gadelha
Abstract

Abstract: Flagella and cilia are ubiquitous in biology as a means of motility and critical for male gametes migration in reproduction, to mucociliary clearance in the lung, to the virulence of devastating parasitic pathogens such as the Trypanosomatids, to the filter feeding of the choanoflagellates, which are constitute a critical link in the global food chain. Despite this ubiquity and importance, the details of how the ciliary or flagellar waveform emerges from the underlying mechanics and how the cell, or the environs, may control the beating pattern by regulating the axoneme is far from fully understood. We demonstrate in this talk that mechanics and modelling can be utilised to interpret observations of axonemal dynamics, swimming trajectories and beat patterns for flagellated motility impacts on the science underlying numerous areas of reproductive health, disease and marine ecology. It also highlights that this is a fertile and challenging area of inter-disciplinary research for applied mathematicians and demonstrates the importance of future observational and theoretical studies in understanding the underlying mechanics of these motile cell appendages.

  • Junior Applied Mathematics Seminar
30 November 2010
13:15
Almut Eisentrager
Abstract
<p>In a healthy human brain, cerebrospinal fluid (CSF), a water-like liquid, fills a system of cavities, known as ventricles, inside the brain and also surrounds the brain and spinal cord. Abnormalities in CSF dynamics, such as hydrocephalus, are not uncommon and can be fatal for the patient. We will consider two types of models for the so-called infusion test, during which additional fluid is injected into the CSF space at a constant rate, while measuring the pressure continuously, to get an insight into the CSF dynamics of that patient.</p> <p>&nbsp;</p> <p>In compartment type models, all fluids are lumped into compartments, whose pressure and volume interactions can be modelled with compliances and resistances, equivalent to electric circuits. Since these models have no spatial variation, thus cannot give information such as stresses in the brain tissue, we also consider a model based on the theory of poroelasticity, but including strain-dependent permeability and arterial blood as a second fluid interacting with the CSF only through the porous elastic solid.</p>
  • Junior Applied Mathematics Seminar
16 November 2010
13:15
Chris Lustri
Abstract
We investigate the behaviour of free-surface waves on time-varying potential flow in the limit as the Froude number becomes small. These waves are exponentially small in the Froude number, and are therefore inaccessible to ordinary asymptotic methods. As such, we demonstrate how exponential asymptotic techniques may be applied to the complexified free surface in order to extract information about the wave behaviour on the free surface, using a Lagrangian form of the potential flow equations. We consider the specific case of time-varying flow over a step, and demonstrate that the results are consistent with the steady state case.
  • Junior Applied Mathematics Seminar
2 November 2010
13:15
Athanasios Tsanas
Abstract
<p>This work demonstrates how we can extract clinically useful patterns</p><p>extracted from time series data (speech signals) using nonlinear signal<br /> processing and how to exploit those patterns using robust statistical<br /> machine learning tools, in order to estimate remotely and accurately<br /> average Parkinson's disease symptom severity.&nbsp;</p> <p>&nbsp;</p>
  • Junior Applied Mathematics Seminar
19 October 2010
13:15
Abstract
<p>We explore two different threading approaches on a graphics processing<br /> unit (GPU) exploiting two different characteristics of the current GPU<br /> architecture. The fat thread approach tries to minimise data access time<br /> by relying on shared memory and registers potentially sacrificing<br /> parallelism. The thin thread approach maximises parallelism and tries to<br /> hide access latencies. We apply these two approaches to the parallel<br /> stochastic simulation of chemical reaction systems using the stochastic<br /> simulation algorithm (SSA) by Gillespie. In these cases, the proposed<br /> thin thread approach shows comparable performance while eliminating the<br /> limitation of the reaction system's size.</p><p>Link to paper:&nbsp;</p> <p><a target="_blank" href="http://people.maths.ox.ac.uk/erban/papers/paperCUDA.pdf">http://people.maths.ox.ac.uk/erban/papers/paperCUDA.pdf</a></p>
  • Junior Applied Mathematics Seminar
15 June 2010
13:15
Cara Morgan
Abstract

Following work done by the 'Oxford Spies' we uncover more secrets of 'surface-active Agents'. In modern-day applications we refer to these agents as surfactants, which are now extensively used in industrial, chemical, biological and domestic applications. Our work focuses on the dynamic behaviour of surfactant and polymer-surfactant mixtures.

In this talk we propose a mathematical model that incorporates the effects of diffusion, advection and reactions to describe the dynamic behaviour of such systems and apply the model to the over-flowing-cylinder experiment (OFC). We solve the governing equations of the model numerically and, by exploiting large parameters in the model, obtain analytical asymptotic solutions for the concentrations of the bulk species in the system. Thus, these solutions uncover secrets of the 'surface-active Agents' and provide an important insight into the system behaviour, predicting the regimes under which we observe phase transitions of the species in the system. Finally, we suggest how our models can be extended to uncover the secrets of more complex systems in the field.

  • Junior Applied Mathematics Seminar
1 June 2010
13:15
Sara-Jane Dunn
Abstract

Colorectal cancer (CRC) is one of the leading causes of cancer-related death worldwide, demanding a response from scientists and clinicians to understand its aetiology and develop effective treatment. CRC is thought to originate via genetic alterations that cause disruption to the cellular dynamics of the crypts of Lieberkűhn, test-tube shaped glands located in both the small and large intestine, which are lined with a monolayer of epithelial cells. It is believed that during colorectal carcinogenesis, dysplastic crypts accumulate mutations that destabilise cell-cell contacts, resulting in crypt buckling and fission. Once weakened, the corrupted structure allows mutated cells to migrate to neighbouring crypts, to break through to the underlying tissue and so aid the growth and malignancy of a tumour. To provide further insight into the tissue-level effects of these genetic mutations, a multi-scale model of the crypt with a realistic, deformable geometry is required. This talk concerns the progress and development of such a model, and its usefulness as a predictive tool to further the understanding of interactions across spatial scales within the context of colorectal cancer.

  • Junior Applied Mathematics Seminar
4 May 2010
13:15
Guido Klingbeil
Abstract
Graphics processing units (GPU) are well suited to decrease the computational in- tensity of stochastic simulation of chemical reaction systems. We compare Gillespie’s Direct Method and Gibson-Bruck’s Next Reaction Method on GPUs. The gain of the GPU implementation of these algorithms is approximately 120 times faster than on a CPU. Furthermore our implementation is integrated into the Systems Biology Toolbox for Matlab and acts as a direct replacement of its Matlab based implementation.
  • Junior Applied Mathematics Seminar

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