Mathematics

In this talk, I will describe a smoothed particle hydrodynamics method for simulating the motion and deformation of red blood cells. After validating the model and numerical method using the dynamics of healthy red cells in shear and channel flows, we focus on the loss of red cell deformability as a result of malaria infection. The current understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of about 3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out 3D numerical simulations of RBC stretching tests by optical tweezers to demonstrate this mechanism. Our results show that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. Thus, the previous interpretation of RBC-deformation data in terms of membrane stiffness alone is flawed. With the solid inclusion, the apparently contradictory data can be reconciled, and the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.

• Cell biology imaging techniques
  • 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
  • 2. Fluorescence microscopy: Fluorescent labelling biological samples |
    Epifluorescence microscopy |
    Confocal fluorescence microscopy
  • 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging
    (time permitting)
  • 4. FRAP data and modelling integrin dynamics

• Cell biology imaging techniques
  • 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
  • 2. Fluorescence microscopy: Fluorescent labelling biological samples |
    Epifluorescence microscopy |
    Confocal fluorescence microscopy
  • 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging
    (time permitting)
  • 4. FRAP data and modelling integrin dynamics

• Cell biology imaging techniques
  • 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
  • 2. Fluorescence microscopy: Fluorescent labelling biological samples |
    Epifluorescence microscopy |
    Confocal fluorescence microscopy
  • 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging
    (time permitting)
  • 4. FRAP data and modelling integrin dynamics

Central to Alan Turing's posthumous reputation is his work with British codebreaking during the Second World War. This relationship is not well understood, largely because it stands on the intersection of two technical fields, mathematics and cryptology, the second of which also has been shrouded by secrecy. This lecture will assess this relationship from an historical cryptological perspective. It treats the mathematization and mechanization of cryptology between 1920-50 as international phenomena. It assesses Turing's role in one important phase of this process, British work at Bletchley Park in developing cryptanalytical machines for use against Enigma in 1940-41. It focuses on also his interest in and work with cryptographic machines between 1942-46, and concludes that work with them served as a seed bed for the development of his thinking about computers.

Turing 2012 - Calgary

This talk is part of a series celebrating the Alan Turing Centenary in Calgary. The following mathtube videos are part of this series

1. Alan Turing and the Decision Problem, Richard Zach.
2. Turing's Real Machine, Michael R. Williams.
3. Alan Turing and Enigma, John R. Ferris.