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The green biflagellated algae Chlamydomonas nivalis has a prolate spheroidal body and has two long, thin flagella attached at one end which are propelled to cause the swimming of the organism. The length of the cell body and flagella is approx. same as 10 micro meter and the flagella beat at approx. 50 hertz. C. nivalis is usually considered to swim in a human breast-stroke manner with an effective-recovery style, approximately in the direction of its axis of symmetry. However, the latest research proved that this is not exactly the accurate swimming stroke.
The approximation known as Resistive Force Theory (RFT) was established by Gray & Hancock (1953) and states that the normal and tangential components of force and torque on an element of a flagellum is directly proportional to the normal and tangential components of the fluid velocity relative to that element. RFT was used by Jones et al. (1994) to model the swimming of a single cell of C. nivalis in a viscous flow of low Reynolds number. Analytical and numerical techniques were used to calculate the magnitude and direction of the cell's swimming velocity and angular velocity.
The aim of our work is to extend the Jones et al. model to calculate the the cell's swimming velocity and angular velocity in the vicinity of a stationary no-slip boundary or sphere using appropriate image system techniques. Finally, we will model interactions of two algae cells using RFT and image systems and calculate the magnitude and direction of both cell's swimming velocity and angular velocity.
Maximum likelihood (ML), and least squares (LS) techniques, while incredibly common, are not the only methods available for parameter estimation. In this talk I will introduce Markov Chain Monte Carlo (MCMC) methods; these are especially useful in high dimensional (of order 10,000) models, and situations where data is missing or incomplete. While I will work exclusively in a Bayesian framework, MCMC is also applicable in frequentist settings. I will focus on key ideas in Bayesian and Markov theory, with attention to MCMC implementation algorithms and a discussion of stochastic epidemic models (SEIR type) with missing data.
One of the main goals in theoretical biology is to discover or explain unifying organizational principles across a wide range of observed structures and functions. Assigning subunits of these structures and their interactions to nodes and edges of a graph can often prove helpful in the development of such theories. In fact, much understanding can often be directly obtained by studying the properties of the resulting graph, or network. This mode of investigation is called "network biology." In this SURVEY I will highlight several results in network biology that I am familiar with and discuss some tools that prove useful for studying networks.