Junior Applied Mathematics Seminar
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Tue, 25/01/2011 13:15 |
Hermes Gadelha (CMB) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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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. |
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Tue, 22/02/2011 13:15 |
Yi Ming Lai (OCCAM) |
Junior Applied Mathematics Seminar |
Gibson Grd floor SR |
| We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modellingpopulations of neurons. In particular, we use the example of a interactingpopulations of excitatory and inhibitory neurons (E-I networks). As eachnetwork consists of a large but finite number of neurons that firestochastically, we can study the effect of this intrinsic noise using a masterequation formulation. In the parameter regime where each E-I network acts as alimit cycle oscillator, we combine phase reduction and averaging to study thestationary distribution of phase differences in an ensemble of uncoupled E-Ioscillators, and explore how the intrinsic noise disrupts synchronization dueto a common external noise source. | |||
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Tue, 08/03/2011 13:15 |
Sophie Kershaw (Comlab) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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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. |
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