Junior Applied Mathematics Seminar
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Tue, 26/01/2010 13:00 |
Trevor Wood (OCIAM Oxford) |
Junior Applied Mathematics Seminar  |
DH 1st floor SR |
| 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. | |||
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Tue, 23/02/2010 13:15 |
Siddharth Arora (University of Oxford) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| 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. | |||
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Tue, 09/03/2010 13:15 |
Aaron Smith (University of Oxford) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| 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. | |||
