Past 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
9 March 2010
13:15
Aaron Smith
Abstract
The visceral endoderm (VE) is an epithelium of approximately 200 cells encompassing the early post-implantation mouse embryo. At embryonic day 5.5, a subset of around 20 cells differentiate into morphologically distinct tissue, known as the anterior visceral endoderm (AVE), and migrate away from the distal tip, stopping abruptly at the future anterior. This process is essential for ensuring the correct orientation of the anterior-posterior axis, and patterning of the adjacent embryonic tissue. However, the mechanisms driving this migration are not clearly understood. Indeed it is unknown whether the position of the future anterior is pre-determined, or defined by the movement of the migrating cells. Recent experiments on the mouse embryo, carried out by Dr. Shankar Srinivas (Department of Physiology, Anatomy and Genetics) have revealed the presence of multicellular ‘rosettes’ during AVE migration. We are developing a comprehensive vertex-based model of AVE migration. In this formulation cells are treated as polygons, with forces applied to their vertices. Starting with a simple 2D model, we are able to mimic rosette formation by allowing close vertices to join together. We then transfer to a more realistic geometry, and incorporate more features, including cell growth, proliferation, and T1 transitions. The model is currently being used to test various hypotheses in relation to AVE migration, such as how the direction of migration is determined, what causes migration to stop, and what role rosettes play in the process.
  • Junior Applied Mathematics Seminar
23 February 2010
13:15
Siddharth Arora
Abstract
Abstract: Nonlinear models have been widely employed to characterize the underlying structure in a time series. It has been shown that the in-sample fit of nonlinear models is better than linear models, however, the superiority of nonlinear models over linear models, from the perspective of out-of-sample forecasting accuracy remains doubtful. We compare forecast accuracy of nonlinear regime switching models against classical linear models using different performance scores, such as root mean square error (RMSE), mean absolute error (MAE), and the continuous ranked probability score (CRPS). We propose and investigate the efficacy of a class of simple nonparametric, nonlinear models that are based on estimation of a few parameters, and can generate more accurate forecasts when compared with the classical models. Also, given the importance of gauging uncertainty in forecasts for proper risk assessment and well informed decision making, we focus on generating and evaluating both point and density forecasts. Keywords: Nonlinear, Forecasting, Performance scores.
  • Junior Applied Mathematics Seminar
26 January 2010
13:00
Trevor Wood
Abstract
<i>The background for the multitarget tracking problem is presented along with a new framework for solution using the theory of random finite sets. A range of applications are presented including submarine tracking with active SONAR, classifying underwater entities from audio signals and extracting cell trajectories from biological data.</i>
  • Junior Applied Mathematics Seminar
4 December 2009
16:30
to
5 December 2009
17:00
Ornella Cominetti
Abstract
<span style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 8px; line-height: normal; font-size-adjust: none; font-stretch: normal; font-family: Helvetica"><span style="font-size: small" class="Apple-style-span"><span class="Apple-style-span" style="font-size: 12px">Soft (fuzzy) clustering techniques are often used in the study of high-dimensional datasets, such as microarray and other high-throughput bioinformatics data. The most widely used method is Fuzzy C-means algorithm (FCM), but it can present difficulties when dealing with nonlinear clusters. In this talk, we will overview and compare different clustering methods. We will introduce DifFUZZY, a novel spectral fuzzy clustering algorithm applicable to a larger class of clustering problems than FCM. This method is better at handling datasets that are curved, elongated or those which contain clusters of different dispersion. We will present examples of datasets (synthetic and real) <span class="Apple-style-span" style="font-size: medium"><span style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 8px; line-height: normal; font-size-adjust: none; font-stretch: normal; font-family: Helvetica"><span style="font-size: small" class="Apple-style-span"><span class="Apple-style-span" style="font-size: 12px">for which this method outperforms other frequently used algorithms</span></span></span></span></span></span></span>
  • Junior Applied Mathematics Seminar
20 November 2009
16:30
Jason Zhong
Abstract
Hairsine-Rose (HR) model is the only multi sediment size soil erosion model. The HR model is modifed by considering the effects of sediment bedload and bed elevation. A two step composite Liska-Wendroff scheme (LwLf4) which designed for solving the Shallow Water Equations is employed for solving the modifed Hairsine-Rose model. The numerical approximations of LwLf4 are compared with an independent MOL solution to test its validation. They are also compared against a steady state analytical solution and experiment data. Buffer strip is an effective way to reduce sediment transportation for certain region. Modifed HR model is employed for solving a particular buffer strip problem. The numerical approximations of buffer strip are compared with some experiment data which shows good matches.
  • Junior Applied Mathematics Seminar
6 November 2009
16:30
Abstract
Abstract: Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs.
  • Junior Applied Mathematics Seminar
23 October 2009
16:30
Abstract
Dislocation channel-veins and Persist Slip Band (PSB) structures are characteristic configurations in material science. To find out the formation of these structures, the law of motion of a single dislocation should be first examined. Analogous to the local expansion in electromagnetism, the self induced stress is obtained. Then combining the empirical observations, we give a smooth mobility law of a single dislocation. The stability analysis is carried our asymptotically based on the methodology in superconducting vortices. Then numerical results are presented to validate linear stability analysis. Finally, based on the evidence given by the linear stability analysis, numerical experiments on the non-linear evolution are carried out.
  • Junior Applied Mathematics Seminar

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