Discrete Data Assimilation in the 2D Navier--Stokes Equations

Speaker: 

Professor Eric Olson

Institution: 

University of Nevada - Reno

Time: 

Monday, May 16, 2011 - 4:00pm

Location: 

RH 306

Consider a continuous dynamical system for which partial
information about its current state is observed at a sequence of
discrete times. Discrete data assimilation inserts these observational
measurements of the reference dynamical system into an approximate
solution by means of an impulsive forcing. In this way the
approximating solution is coupled to the reference solution at a
discrete sequence of points in time. This paper studies discrete data
assimilation for the incompressible two-dimensional Navier--Stokes
equations. In both cases we obtain bounds on the time interval
between subsequent observations which guarantee the convergence of the
approximating solution obtained by discrete data assimilation to the
reference solution.

Data assimilation for impact-produced shock-wave dynamics

Speaker: 

Professor Sarah Eichhorn

Institution: 

UCI

Time: 

Monday, May 9, 2011 - 4:00pm

Location: 

RH 306

Model assimilation of data strives to determine optimally the state of an evolving physical system from a limited number of observations. The first attempt of applying the extended Kalman filter (EKF) method of data assimilation to shock-wave dynamics induced by high-speed impact will be presented. Additionally, we will mention current work on estimating hydrocode model parameters using EKF.

True amplitude wave equation imaging methods and their applications to seismic exploration

Speaker: 

Deputy Global Research Manager and Distinguished Expert at CGGVeritas Yu Zhang

Institution: 

CGGVeritas

Time: 

Monday, March 28, 2011 - 4:00pm

Location: 

RH 306

Prestack depth imaging/migration transforms the seismic data into an image, which reveals the subsurface geology. The imaging technology has made rapid progress in the past decade. Especially the wave propagation based migrations are considered to be the methods of choice for imaging complex structures. In the meantime, we have seen the demand for imaging technology to move from its heuristic roots to mathematically sound techniques.
Traditionally, One-way Wave Equation Migration (OWEM) was considered as a rough and intuitive inversion method. Based on Zhang (1994) and Bleistein (1987), we reformulated one-way wave equations to provide accurate amplitude as well as traveltime. We developed true amplitude OWEM theory in both shot domain and reflection angle domain. Especially, we found that the angle domain true amplitude migration is a stable inversion algorithm. Therefore, we have built OWEM on a solid theoretical base.
Later, we generalized our theory to Reverse Time Migration (RTM) and developed a 3D true amplitude migration theory in reflection/azimuth angle domain. Anisotropy and visco-acoustic absorption can also be incorporated in a migration to calibrate the image.
We will use many real data examples to show how the imaging technology evolutions have greatly improved our capability to image the interior of the earth.

Applications of Computational Quasiconformal Geometry on Medical Morphometry and Computer Graphics

Speaker: 

Alvin Wong

Institution: 

UCLA

Time: 

Monday, April 25, 2011 - 4:00pm

Location: 

RH 306

Conformal mappings have been widely applied in medical imaging and computer graphics, such as in brain registration and texture mapping, where the mappings are constructed to be as conformal as possible to reduce geometric distortions. A direct generalization of conformal mappings is quasiconformal mappings, where the mappings are allowed to have bounded conformality distortions. In this talk, we explore how the theories of quasiconformal mappings and their computations can be applied to areas where conformal mappings are used traditionally. These includes registration of biological surfaces, shape analysis, medical morphometry, compression and refinement of texture mappings, and the inpainting of surface diffeomorphisms.

BEYOND ITO AND STRATONOVITCH

Speaker: 

Professor Janek Wehr

Institution: 

University of Arizona

Time: 

Monday, April 11, 2011 - 4:00pm

Location: 

RH 306

Recent experiments show that the Langevin equation
describing the motion of Brownian particle in a diffusion gradient should be
interpreted according to the backwards Ito definition of the
stochastic integral---different from Ito or Stratonovitch. I
will explain this result mathematically and show that other stochastic
integrals, including new, nonstandard ones, should be expected in further
experiments.

The Adaptive Perfectly Matched Layer Method for Time-harmonic Acoustic and Electromagnetic Scattering Problems

Speaker: 

Professor Zhiming Chen

Institution: 

Chinese Academy of Sciences

Time: 

Friday, April 1, 2011 - 3:00pm

Location: 

RH 306

We first develop efficient and robust adaptive edge element
methods for the Maxwell cavity problem in 3D which are of optimal
computational complexity. Then we report our recent efforts in developing
adaptive PML method for solving time-harmonic scattering problems.
The adaptive PML method provides a complete way to solve
the scattering problem with error control in the FE framework in
which the total computational costs are insensitive to the thickness
of the PML absorbing layer. This talk is based on the joint work
with Tao Cui and Linbo Zhang.

Automated Analysis of Large Text Collections using Statistical Topic Models

Speaker: 

Professor Padhraic Smyth

Institution: 

UCI

Time: 

Friday, March 4, 2011 - 4:00pm

Location: 

RH 306

With the proliferation of digital document collections in recent years (Web
pages, blogs, online news articles, etc) there has been an increasing
interest in automated tools that can automatically summarize, classify, and
annotate such text. In this talk I will provide an overview of statistical
topic models (also known as latent Dirichlet allocation models), which
provide a flexible framework for statistical modeling of high-dimensional
count data, in particular, for word counts in text documents.The talk will
begin by discussing the underlying statistical principles of these models,
including their interpretation within a general probabilistic
matrix-decomposition framework and contrasting them with techniques such as
principal component analysis and clustering. Estimation methods and
algorithms will be reviewed, with a focus on Gibbs sampling approaches. This
introduction will be followed by an illustration of how these models can be
to generate high-level summaries of document collections and to
automatically uncovering thematic trends in text over time. The remainder of
the talk will focus on extensions of the basic topic modeling framework,
with applications in document classification, document retrieval, as well as
discussion of parallel algorithms for scaling to very large data sets. A
number of different text data sets will be used during the talk as
illustrative examples, including archives of New York Times articles,
historical records of the Pennsylvania Gazette from the 18th century, large
databases of scientific publications such as PubMed and CiteSeer, and
publicly-available emails from the Enron corporation.

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