Applied Math Seminar

Mathematical model of cardiovascular system

09/05/2016 - 4:15pm
09/05/2016 - 5:15pm
Speaker: 
Marina Chugunova (CGU)
Abstract: 

The talk will be based on the analytical and numerical results obtained by a group of mathematicians during Industrial Problem Solving Workshop
at Fields Institute (Summer, 2016).
We will show that instead of a statistical approach to data analysis, which fails to produce a valuable result in our case, one can use a simple mathematical model to perform qualitative analysis of parameters.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Representation Theorems of R-trees and Brownian motions indexed by R-trees

05/02/2016 - 4:15pm
05/02/2016 - 5:15pm
Speaker: 
Qidi Peng (CGU)
Abstract: 

Authors: Asuman Aksoy, Monairah Al-ansari and Qidi Peng Abstract: We provide a new representation of R-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between these sets of metric rays, and the R-trees with radial and river metrics. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by R-trees.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Different Differences

03/21/2016 - 4:15pm
03/21/2016 - 5:15pm
Speaker: 
Ron Buckmire (Occidental College)
Abstract: 

From calculus we know that a derivative of a a function can be approximated using a difference quotient. There are different forms of the difference quotient, such as the forward difference (most common), backward difference and centered difference. I will introduce and discuss ``Mickens differences," which are decidedly different differences for approximating the derivatives in differential equations. Professor Ronald Mickens is an African-American Physics Professor at Clark Atlanta University who has written nearly 300 journal articles on this and related topics. These nonstandard finite differences can produce discrete solutions to a wide variety of differential equations with improved accuracy over standard numerical techniques. Applications drawn from first-semester Calculus to advanced computation fluid dynamics will be given. Students are very welcome to attend. Knowledge of elementary derivatives/anti-derivatives and Taylor Approximations will be assumed.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

CFD Simulations and Particulate Deposition Before and After Intervention in Patient with Tracheal Stenosis

04/25/2016 - 4:15pm
04/25/2016 - 5:15pm
Speaker: 
Shahab Taherian (California State University, Long Beach)
Abstract: 

The existence of obstructions such as tracheal stenosis has major impacts on respiratory functions. Therapeutic effectiveness of inhaled medications is influenced by tracheal stenosis, and particle transport and deposition pattern are modified. The majority of studies have focused on obstructions in branches of the airways, where air is diverted to the other branches to meet the needed oxygen intake. In this study we have investigated the effects of trachea with and without stenosis/obstruction on particle depositions and air flow in a human respiratory system, using patient-specific Computational Fluid Dynamics (CFD) simulations and CT-scans.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Viscosity Solutions of Path Dependent PDEs

04/11/2016 - 4:15pm
04/11/2016 - 5:15pm
Speaker: 
Jianfeng Zhang (USC)
Abstract: 

Abstract: Path dependent PDEs considers continuous paths as its variable. It is a convenient tool for stochastic optimization/games in non-Markovian setting, and has natural applications on non-Markovian financial models with drift and/or volatility uncertainty. For example, a martingale can be viewed as a solution to a path dependent heat equation, and we are particularly interested in path dependent HJB equations and Isaacs equations. In path dependent case, even a heat equation typically does not have a classical solution, where smoothness is defined through Dupire's functional Ito calculus, so a viscosity theory is desirable. There are two major difficulties in the project: (i) the state space of (continuous paths) is not locally compact, and thus one cannot apply many tools in standard viscosity theory; (ii) fully nonlinear PPDEs involve a nonlinear expectation under which the dominated convergence theorem fails. In this talk, we will motivate our definition of viscosity solutions and give an overview of the recent developments of the theory.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Adaptive Finite Element Method for PDEs on Surfaces

02/22/2016 - 4:15pm
02/22/2016 - 5:15pm
Speaker: 
Ryan S. Szypowski (Cal Poly, Pomona)
Abstract: 

The finite element method is a powerful technique for approximating
solutions to partial differential equations (PDEs) that is based on
rich theory and is efficiently implementable. When used in an adaptive
fashion, the method is provably convergent for a wide array of
problems. The recently developed Finite Element Exterior Calculus
formalism allows the method to be applied to problems with geometric
content. This talk will introduce the basics of this formalism,
specifically in the context of PDEs on surfaces, and provide some
recent theoretical and numerical results.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Verblunsky Coefficients (and Related Ideas)

04/04/2016 - 4:15pm
04/04/2016 - 5:15pm
Speaker: 
Angel Chavez (Pomona College)
Abstract: 

Verblunsky coefficients provide a remarkable correspondence between sequences of points in the unit disk and ``non-trivial” probability measures on the unit circle. In this talk, we’ll give an overview of this Verblunksy correspondence and then discuss progress on two projects pertaining to Verblunsky coefficients (and related ideas).

Where: 
Emmy Noether Room Millikan 1021 Pomona College

A Strong Law and a Law of the Single Logarithm for Arrays of Row-wise Independent Random Variables

02/01/2016 - 4:15pm
02/01/2016 - 5:15pm
Speaker: 
Tien-Chung Hu (Department of Mathematics, National Tsing Hua University )
Abstract: 

 See the attachment

Where: 
Millikan 1021 Pomona College

An estimate for the probability of heads on a coin whose relative error is independent of the true value

02/29/2016 - 4:15pm
02/29/2016 - 5:15pm
Speaker: 
Mark Huber (Claremont McKenna College)
Abstract: 

Consider a coin with an unknown probability $ p $ of heads that can be flipped as many times as needed. In this talk I will present a new estimate $ \hat p $ for $ p $ such that the relative error $ (\hat p/p) - 1 $ has a distribution that is independent of $ p $. This has applications in several Monte Carlo algorithms, including using acceptance/rejection to give approximations of high dimensional integrals and sums. In addition, this idea can also be used to obtain an estimate with similar properties for the mean of a sequence of independent, identically distributed Poisson random variables.

Where: 
Millikan 1021 Pomona College

Multiphase flow modeling of cell adhesion and migration

03/07/2016 - 4:15pm
03/07/2016 - 5:15pm
Speaker: 
Damir Khismatullin (Biomedical Engineering, Tulane U.)
Abstract: 

One of the fundamental properties of living cells is their ability to migrate from one region of space to another in response to specific chemical stimuli. Cell migration often involves adhesion to the surrounding tissue, chemoattractant-mediated intracellular signaling, and intracellular force generation. We have developed state-of-the-art three-dimensional computational algorithms, known as VECAM and VECAM-Active, to simulate cell-substrate adhesion and active, amoeboid migration of motile cells. These algorithms are based on the multiphase flow approach and account for cell and substrate deformability, rheological properties, multiple cellular compartments, receptor-ligand binding, transport of chemical activators (chemokines, cytokines), intracellular force generation due to actin polymerization, and physiologic shear flow conditions. In this talk, I will first present recent experimental data of my laboratory on circulating cell adhesion to activated vascular endothelium. Then I will show VECAM data on passive migration of cells in microchannels with different geometry (straight, Y-junction bifurcation, cross-flow, grooves and pillars), deformable cell adhesion to a receptor-coated substrate, and chemotactic and haptotactic migration of cells in a microchannel.

Where: 
Emmy Noether Room Millikan 1021 Pomona College
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