Monday, February 8, 2010 at 3:00 AM in SAS 4201
Marc Millstone, Courant Institute NYU
Localized Optimization: Exploiting non-orthogonality to efficiently minimize the Kohn-Sham Energy
With the constantly increasing power of computers, the realm of experimental chemistry is increasingly being brought in contact with the field of computational mathematics. In particular, the ability to compute the charge density, i.e., the probabilistic location of a molecule's electrons, allows numerous properties of matter to be displayed graphically, as opposed to investigated in the chemistry lab.
As many current methods scale at a rate proportional to the cube of the number of atoms, such problems are still too large for direct {it ab initio} computations. This work describes a new algorithm for minimizing the Kohn-Sham energy that not only avoids local minima, but also guarantees the expensive energy function is only evaluated at sparse iterates. Preliminary results on a realistic model problem as well as small
molecular systems will be given.
Tuesday, March 2, 2010 at 3:00 PM in SAS 4201
Yi Sun, NCSU
Network dynamics of Hodgkin-Huxley neurons
The reliability and predictability of neuronal network dynamics is a central question in neuroscience. We present a numerical analysis of the dynamics of all-to-all pulsed-coupled Hodgkin-Huxley (HH) neuronal networks. Since this is a non-smooth dynamical system, we propose a pseudo-Lyapunov exponent (PLE) that captures the long-time predictability of HH neuronal networks. The PLE can capture very well the dynamical regimes of the network. Furthermore, we present an efficient library-based numerical method for simulating HH neuronal networks. Our pre-computed high resolution data library can allow us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations. By using the library-based method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity. Moreover, our large time steps using the library method can overcome the stability requirement of standard ODE methods for the original dynamics.Thursday, April 15, 2010 at 4:00 PM in Burlington Labs
Mike Eldred, Sandia National Laboratories
TBA
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Seminar Organizers: Pierre Gremaud, Ilse Ipsen, Tim Kelley