Application in biomedical analytics to enhance cardiac tissue image analysis
Speaker: Jennifer Rodgers
Date: April 12
Hypoxia (low oxygen) due to acute respiratory failure is the most common cause of ICU admission in patients. Oxygen therapy is a first-line treatment for patients with life-threatening hypoxia. High levels of oxygen is also known to result in harmful effects in patients. Despite this, there is still a tendency in critical care settings to provide hypoxic patients with excessive oxygen. Our lab has previously reported arrhythmias and cardiac remodeling in mice after 72 hours of high oxygen therapy. Based on this data, we hypothesized that there is a time-dependent nature to high oxygen-induced electrical disturbances and cardiac remodeling in mice. Therefore, we have studied oxygen therapy in mice, in a time course study, in order to generate incremental data regarding the onset of the cardiac impact of high oxygen exposure, using analytic techniques with machine learning applications. As a result, we have developed an application to enhance cardiac tissue image analysis.
Global regularity for a rapidly rotating convection model of tall columnar structure with weak dissipation
Speaker: Yanqiu Guo
Date: April 5
This presentation is based on our analysis of a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. Global well-posedness for strong solutions is shown provided the model is regularized by a weak dissipation term. This is a joint project with Cao and Titi.
Nonlinear waves and singularities in nonlinear optics, plasmas and biology
Speaker: Pavel Lushnikov
Date: March 8
Many nonlinear partial differential equations have a striking phenomenon of spontaneous formation of singularities in a finite time (blow up). Blow up is often accompanied by a dramatic contraction of the spatial extent of solution, which is called by collapse. Near singularity point there is usually a qualitative change in underlying nonlinear phenomena, reduced models loose their applicability with diverse singularity regularization mechanisms become important such as optical breakdown and formation of plasma in nonlinear optical media, excluded volume constraints in bacterial aggregation or dissipation of breaking water waves. Collapses occur in numerous physical and biological systems including a nonlinear Schrodinger equation, Keller-Segel equation, Davey–Stewartson equation and many others. Wavebreaking is another example of spontaneous formation of singularities corresponding to the breaking of initially smooth smooth fluid's free surface. It can be reduced to the motion of complex singularities outside of fluid with wavebreaking resulting from the approach of these singularities to the free surface. The recent progress in collapse theory will be reviewed with multiple applications ranging from laser fusion to bacterial dynamics addressed.
Numerical simulation for wave propagation and imaging
Speaker: Kai Huang
Date: March 1
A direct imaging algorithm for point and extended targets is presented.
The algorithm is based on a physical factorization of the response matrix of a transducer array.
An efficient algorithm proposed for simulating wave propagation over long distance with both weak and strong scatters.
A high order finite difference method with subcell resolution for stiff multispecies detonation in under-resolved mesh
Speaker: Wei Wang
Date: Feb. 22
In this talk, we propose a high order finite difference WENO method with Harten's ENO subcell resolution idea for the chemical reactive flows. In the reaction problems, when the reaction time scale is very small, the problems will become very stiff. Wrong propagation of discontinuity occurs due to the underresolved numerical solutions in both the space and time. The proposed method is a modified fractional step method which solves the convection step and reaction step separately. A fifth-order WENO is used in convection step. In the reaction step, a modified ODE solver is applied but with the flow variables in the discontinuity region modified by the subcell resolution idea.
Blind source separations in spectroscopy
Speaker: Yuanchang Sun
Date: Feb. 15
We shall start with a framework for extracting spectral structures from mixed data when partial knowledge of the mixtures are available. Then computational modeling and methods will be introduced for data fitting with distortions.
On the stochastic Navier Stokes equations
Speaker: Annie Millet
Date: Feb. 8
This talk will give an overview on some results on the Navier Stokes equation subject to a stochastic perturbation: global well posedness for general 2D hydrodynamical models, anisotropic 3D Navier Stokes equation with some Brinkman Forchheimer regularization, exponential concentration of the distribution when the strength of the noise/ the viscosity converges to 0, strong speed of convergence of time discretization schemes. These are joint results with H. Bessaih and I. Chueshov.
An Introduction to Nonlinear Waves, Solitons and Collapses
Speaker: Kai Yang
Date: Feb. 1
We demonstrate several solution profiles for different types of Nonlinear wave equations.
Introduction to Statistical Learning with an Emphasis on Bayesian Logic Multiple Classifications
Speaker: Wensong Wu
Date: Jan. 25
This presentation has three parts. It will start with an introduction to Statistical Learning, which is a framework for machine learning from statistical perspective. Then I will talk about my current research on Two-Step Bayesian Multiple Classification with Logic Expressions, which utilizes Bayesian decision theoretic framework and Logistic regression together with some data mining methods. If time permits we will briefly talk about the route from Logistic regression to Neural Network and Deep Learning.
Some recent results on two phase flow models
Speaker: Theodore Tachim Medjo
Date: Jan. 18
The purpose of this talk is to present some recent results on two phase flow models. We will consider both the Cahn-Hilliard-Navier-Stokes systems and the Allen-Cahn-Navier-Stokes system (deterministic and stochastic version).