OCCAM Wednesday Morning Event
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Wed, 25/01/2012 10:10 |
Eric Keaveny ((Imperial College, London)) |
OCCAM Wednesday Morning Event  |
OCCAM Common Room (RI2.28) |
| Many swimming microorganisms inhabit heterogeneous environments consisting of solid particles immersed in viscous fluid. Such environments require the organisms attempting to move through them to negotiate both hydrodynamic forces and geometric constraints. Here, we study this kind of locomotion by first observing the kinematics of the small nematode and model organism Caenorhabditis elegans in fluid-filled, micro-pillar arrays. We then compare its dynamics with those given by numerical simulations of a purely mechanical worm model that accounts only for the hydrodynamic and contact interactions with the obstacles. We demonstrate that these interactions allow simple undulators to achieve speeds as much as an order of magnitude greater than their free-swimming values. More generally, what appears as behavior and sensing can sometimes be explained through simple mechanics. | |||
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Wed, 15/02/2012 10:15 |
Chuan Xue (Ohio State University) |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
| Mathematical models of chemotactic movement of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular signaling chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities that ar biologically unrealistic. Here we present a microscopic model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We show that this model permits travelling wave solutions and predicts the formation of other bacterial patterns such as radial and spiral streams. We also present connections of this microscopic model with macroscopic models of bacterial chemotaxis. This is joint work with Radek Erban, Benjamin Franz, Hyung Ju Hwang, and Kevin J. Painter. | |||
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Wed, 07/03/2012 10:15 |
Mihai Cucuringu (Princeton) |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
| The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. We introduce the ASAP algorithm, for the graph realization problem in R^d, given a sparse and noisy set of distance measurements associated to the edges of a globally rigid graph. ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in R^3, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. The reflections and rotations are estimated using a recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. Furthermore, the algorithm successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose SP-ASAP, a faster version of ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that ASAP and SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms. Time permitting, we briefly discuss the analogy between the graph realization and the low-rank matrix completion problems, as well as an application of synchronization over Z_2 and its variations to bipartite multislice networks. | |||
