Uncertainty principles in time-frequency analysis

Speaker: 

Bernie Russo

Institution: 

UCI

Time: 

Thursday, July 8, 2004 - 3:00pm

Location: 

MSTB 254

Time-frequency analysis is a modern branch of harmonic analysis. It uses translations and modulations (multiplication by an exponential) for the analysis of functions and operators. It is a form of local Fourier
analysis treating time and frequency simultaneously and symmetrically. The subject is motivated by applications in signal analysis and quantum mechanics.

An introduction to the subject is the book: Foundations of Time-Frequency Analysis by Karlheinz Grochenig 2001.

Evolution of the universe

Speaker: 

Prof. Don Saari

Institution: 

UCI

Time: 

Monday, November 1, 2004 - 4:00pm

Location: 

MSTB 254

We know that the Newtonian N-body problem cannot be solved in a normal sense. On the other hand, we can find all possible asymptotic behaviors as time goes to infinity of all possible solutions for all possible values of N. That is, we can describe the evolution of Newton's universe. In doing so, I will introduce some of the history of the problem showing where "chaos" came from, etc.

An application of von Neumann algebras to Gabor frames

Speaker: 

Bernie Russo

Institution: 

University of California, Irvine

Time: 

Friday, October 29, 2004 - 2:00pm

Location: 

MSTB 256

A sketch of the proof of Daubechies, Landau and Landau (1995) using elementary von Neumann algebra theory of Rieffel's (1981) incompleteness theorem: If ab>1, then there does not exist a square integrable function g whose Gabor lattice G(g,a,b) is dense in L^2.

Weak Wave Turbulence and its Challengers

Speaker: 

Dr. Laura Biven

Institution: 

Max-Planck-Institut fur Physik Komplexer Systeme

Time: 

Monday, November 8, 2004 - 4:00pm

Location: 

MSTB 122

I will begin my talk with a brief overview of WWT during which I aim to give an intuitive picture of the phenomenon using the example of surface water waves. This example will be revisited throughout the talk. Next I will try to give a welcoming (although selective) introduction to the calculations of WWT. Equipped with the results of these calculations, I will discuss the relationship between WWT, power-law spectra (both Kolmogorov-Zakharov and MMT) and intermittency. The challengers to WWT are highly nonlinear events, breakdown and the alternative symmetries of the governing equation. I will make some remarks which point out the interconnectedness of these phenomena and, simultaneously, the goals of my research interests.

A Tale of Two Topologies: Canonical Forms for Ion Channel Data Analysis

Speaker: 

Dr. John Pearson

Institution: 

Los Alamos National Laboratory

Time: 

Tuesday, November 2, 2004 - 1:00pm

Location: 

MSTB 254

In this talk I will introduce the manifest interconductance rank (MIR) form and contrast it to another long-known canonical form used in the
data-driven identification of ion channel gating kinetics: the uncoupled model (UCM). (The UCM has every open state connected to every closed state and vice versa). MIR form has significantly fewer parameters and provides more insight into gating kinetics than the uncoupled model. Beyond the new canonical form the principle results to be presented are
(1)All topologies with interconductance rank=1 and with the same number of open and closed states result in identical steady-state statistics
(2)detailed balance is preserved under transformation to either UCM or MIR forms and
(3) a general detailed balance preserving transformation. These results should facilitate maximum likelihood methods for finding models that best fit a given data set.

Pages

Subscribe to UCI Mathematics RSS