Postdoctoral Fellows Seminars – Spring 2012

Reviewing Paper and Grant Applications

January 25, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Richard L. Smith, SAMSI and UNC-Chapel Hill


Sequential data assimilation with multiple models

February 1, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Akil Narayan, Purdue University

Abstract

Realistic systems are often complicated with multiple kinds of physics, different scales of dynamics, and various sources of uncertainty. While one mathematical system alone may be insufficient to capture global dynamics, several different models may be faithful to evolution of the system in their own ways. In addition to these predictive models, one often has access to sparse, incomplete, and noisy empirical data.

We explore the problem of assimilation of these multiple models and data into a single predictive state of the system. We propose a method that assimilates these models and data in a consistent and robust fashion. With a single model and a single source of data our method reverts to the celebrated Kalman Filter, and we show that our method sensibly handles the case when state vectors have singular covariance matrices (useful, for example, in imposing constraints).


The effect of antibody attachment on a diffusing population of virus

February 8, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Alex Chen, SAMSI

Abstract

We study the diffusion of a virus population through a mucus layer and the attachment of antibodies to the surface of individual virions. Many studies on viral infectivity assume a well-mixed regime of viruses and antibodies, while introducing the virus-antibody mixture directly into a population of cells. As a result, they tend to overestimate the quantity of antibodies present in the system and ignore the role of antibodies in arresting the diffusion of virus in the mucus layer.

Our study focuses on the interaction of virus and antibodies inside the mucus layer with more physically realistic parameters. In particular, we will study the distribution of the “antibody copy number”, the number of attached antibodies to each virion. We introduce several models, those based purely on stochastic path simulation, those based on a continuum PDE model, and hybrid models that incorporate both path simulation and PDE. We examine the relative advantages of each model in terms of approximating the true nature of the system and in computation speed. Several semi-analytical estimates for scaling behavior with respect to various physical parameters in the system are also derived.


Preliminary UQ for smart materials

February 15, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Nathanial Burch, SAMSI

Abstract

In this talk, we present some preliminary uncertainty quantification results for smart material models. The smart material of interest is lead zirconate titanate (PZT), which exhibits a strong piezoelectric effect and hysteretic behavior. The homogenized energy model provides a multi-scale, unified framework for modeling hysteresis. A Bayesian framework and MCMC is used to estimate posterior densities for a set of parameters in a model for a PZT actuator. We present the results and discuss in detail the triumphs and failures of this endeavor. A model for a macro-fiber composite actuator is introduced, which is the subject of future research directions.


February 15, 2012, 1:30pm – 2:30pm

February 22, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: David Sivakoff, SAMSI and Duke

Abstract

Bootstrap percolation is a simple cellular automaton model of nucleation and cascade dynamics that has been studied on various network structures. I will discuss the behavior of this model on the Hamming graph. When the process is started from a product measure on vertices with density p we can make rather precise statements about the probability that the model percolates.


Simulating rare random graphs using importance sampling schemes based on large deviations

February 29, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Chia Ying Lee, SAMSI

Abstract

We discuss some recent concentration of measure results and large deviations results for the Erdos-Renyi graph, and in particular its implications for the probability of rare graphs with large triangle counts. In the high temperature regime, two proofs of the large deviations result, one using a exponential random graph tilt and the other using an inhomogeneous graph tilt, provide different classes of tilted measures on which to build the importance sampling scheme. We analyse the asymptotic optimality of the two tilts and compare how they perform numerically. If time permits, we will briefly discuss the low temperature regime in which much less is known about the rare event of interest.
(Joint work with S. Bhamidi, J. Nolen, J. Hannig)


Models for model discrepancy

March 14, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Jenný Brynjarsdóttir, SAMSI

Abstract

Model discrepancy is an important source of uncertainty in computer models. Yet it is usually not accounted for due to the added complexity it brings to the analysis. Through a simple example we explore using both stationary and non-stationary Gaussian Processes to model the model-discrepancy and the effect on calibration of physical parameters and prediction.


Estimating change-points in extreme values

March 21, 2012 – 1:30am – 2:30am
SAMSI, Room 150
Speaker: Ying Sun, SAMSI

Abstract

Motivated by modeling heat waves for non-stationary time series, we consider the distribution of a random process which might change at some point. Although the change in the distribution can be exhibited in many different ways, much of the literature looks for changes in location of scale when carrying out a change-point analysis. We are focusing on looking for changes in the extremes of the distribution. We examine different change-point detection methods for extremes in the literature and then propose other approaches as alternatives. The results of a simulation study comparing the performances of all methods are discussed including the computational speed and the power of detection. The multiple change-points detection generalization is also discussed.


A semiparametric functional multiple-discrete choice model for profiling consumers’ preferences

March 28, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Silvie Tchumtchoua, SAMSI and Duke

Abstract

Advances in technology and data collection methods have led to the availability of large datasets with complex structure in Marketing. An application which motivated this study is the Nielsen household panel data consisting of geographically representative households recruited to continually provide information — such as brand or product purchased, price paid, date purchased, or retailer shopped — about their purchases. Often the data exhibit irregular and sparse structures, and multiple discreteness (households buy more than one brand of a given product on a shopping trip). Multiple discreteness precludes the use of standard multinomial logit/probit models. Another characteristic of these data is their high-dimensionality: the number of households and the number of brands or time periods are often large. We develop a semiparametric functional multiple-discrete choice model for profiling consumers’preferences for product characteristics and responses to marketing mix variables. The methodology is applied to a panel of household purchases for ready-to-eat cereals.


Bridging cell and tissue scale models for nutrient diffusion and uptake in articular cartilage

April 11, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Andreas Aristotelous, SAMSI

Abstract

Nutrient diffusion and nutrient loss due to cellular uptake are crucial mechanisms influencing homeostasis in articular cartilage. Using reaction-diffusion finite-element simulations, we study relationships between models in which cells are represented explicitly and models in which cellular contributions are aggregated via a cell volume fraction and macroscopic nutrient loss term. Uncertainty due to volume fraction and configuration is studied with the aim of identifying optimal representations for the nutrient loss term in the macroscopic models.


Rolling the dice on Big Data

April 25, 2012, 1:30pm – 2:30pm
SAMSI, Room 150
Speaker: Ilse Ipsen, SAMSI and N.C. State University (Mathematics)

Abstract

What do Facebook, the Large Hadron Collider and health care have in common? They each produce massive amounts of data. Get a close-up look at how mathematicians use the Monte Carlo method and other tools to wrestle with this deluge.

[This is an “outreach” talk about my research for NCSU alumni (and their spouses) in the College of Physical & Mathematical Sciences. At the end of the seminar, I will briefly explain several of the design choices for such a broad and largely non-expert audience.]