*Image reconstruction methods for atomic force microscopy*

**January 23, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Alex Chen, UNC and SAMSI

### Abstract

Atomic force microscopy (AFM) images have become increasingly useful in the study of biological, chemical and physical processes at the atomic level. The acquisition of AFM images takes more time than the acquisition of most optical images, so that the avoidance of unnecessary scanning becomes important. Details that are unclear from a scan may be enhanced using various image processing techniques. This talk consists of two parts.

The first part reviews image reconstruction methods. We further consider their application to AFM images. Lower-resolution AFM data is simulated by subsampling the number of scan lines in an image, and reconstruction methods are used to recreate an image on the original domain. These techniques are evaluated based on qualitative and quantitative measures, showing the extent to which scans times can be reduced while preserving the essence of the original features.

Secondly, the challenge of fast imaging by AFM has motivated the study of non-raster scan paths. Various errors can arise for such scan paths, such as the gradual error in the height signal resulting from thermal changes in the scanning apparatus during the imaging process. Herein proposed is an algorithm for self-intersecting scan paths which, unlike traditional correction methods, does not cause distortions as a result of surface geometry. This approach is shown to outperform an analogous algorithm to the classical raster methods when tilt is present, or when the sample contains a large feature.

*Dimension reduction in exponential families via generalized SVD*

**January 30, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Garvesh Raskutti, SAMSI

### Abstract

Singular value decomposition (SVD) is a very important and widely used tool for dimension reduction. When data is Gaussian, SVD is well-motivated as a solution to a constrained maximum likelihood problem, and the singular values and vectors have concrete statistical interpretations. In this talk I present ongoing work analyzing a proposed generalization of SVD to exponential family data. The goal is to determine to what extent the singular vectors and singular values of the generalized SVD algorithm has a concrete statistical interpretation.

## Postdoc Seminar

**February 6, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: TBA

## NO SEMINAR TODAY!

**February 13, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

*Methodologies for bridging cell and tissue scale models for nutrient transport and uptake in articular cartilage*

**February 20, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Andreas Aristotelous, Duke and SAMSI

### Abstract

Nutrient diffusion and nutrient loss due to cellular uptake are crucial mechanisms influencing homeostasis in articular cartilage. Using a hybrid discrete finite-element modeling paradigm, 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. The aim is the development of methodologies to systematically identify optimal representations for the nutrient loss term in the macroscopic models.

*Regression in high dimensions via Geometric Multi-Resolution Analysis*

**February 27, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: David Lawlor, SAMSI

### Abstract

In this talk we present a framework for high-dimensional regression using the GMRA data structure. In analogy to a classical wavelet decomposition of function spaces, a GMRA is a tree-based decomposition of a data set into local linear projections. Moreover, for new points, GMRA admits a fast algorithm for computing the projection coefficients on the already-learned dictionary. Within each node of the tree one can also assign regression coefficients in any manner; here we study the simple case of weighted linear regression. We discuss some preliminary empirical results using galactic spectra from the Sloan Digital Sky Survey as well as future research directions.

## Postdoc Seminar

March 6, 2013 – 1:45pm – 2:45pm

SAMSI, Room 150

Speaker: Yi Grace Wang, SAMSI

*Non-negative matrix factorization with partially labeled data*

**March 20, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Kenny Lopiano

### Abstract

Non-negative matrix factorization (NMF) is a popular unsupervised learning method used in various applications. In this talk we review the foundations of NMF and several of the applications of non-negative matrix factorization. Then, we discuss how non-negative matrix factorization can be used in semi-supervised and supervised learning algorithms. In particular, we consider the use of NMF to reduce the number of covariates used in a supervised learning framework for handwritten digit recognition. We compare the performance of learning algorithms using the reduced dimensions learned using NMF versus using the reduced dimensions derived from principal components analysis.

*Designing importance sampling schemes for simulating rare events in stochastic differential equations*

**March 27, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Chia Ying Lee, UNC and SAMSI

### Abstract

We consider stochastic processes which are stochastic differential equations (SDEs) or reflected SDEs with a small white-noise perturbation. We look at some associated rare events, such as the event that the trajectory of the process exits from a given domain. An important question for us is to numerically compute the probabilities of these rare events. Since Monte Carlo simulation is very inefficient for generating rare trajectories, we turn to the importance sampling technique, which allows us to generate trajectories that are more likely to exit the given domain. A main ingredient in designing the importance sampling scheme is the concept that there is an optimal path that the trajectory should follow in order to exit the domain with the least cost. We use this optimal path idea when generating trajectories to guide the trajectory out of the domain. If time permits, we also discuss the connection to the Hamilton-Jacobi equation.

*Dimension reduction for diffusion tensor images*

**April 3, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Dan Yang, SAMSI

### Abstract

Diffusion Tensor Imaging (DTI) data can be used to understand brain structure and connectivity. It is intrinsically high-dimensional, which requires dimension reduction. But it has its own feature, namely, for each voxel in a three dimensional space, there a symmetric positive definite matrix associated with it. How to reduce the dimensionality of this type of data to visualize and improve our understanding is an interesting problem. The past work in this direction essentially is a variant of nonnegative matrix factorization by flattening the three dimensional object into a vector, which neglects the spatial structure and results in a solution that is of lower dimension than the original data, but still large. We would like to approach the problem through tensor perspective, which keeps the spatial information and has the potential of further dimension reduction. The challenge is the combination of tensor decomposition method with symmetric positive definite and nonnegative constraints. In this talk, we will address the above issues through series of algorithms, which together will tackle the problem.

*Parameter estimation and prediction for smart material models*

**April 10, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Nate Burch, NCSU and SAMSI

### Abstract

We consider parameter estimation and prediction for models of smart material systems. As an example, we consider an experiment and model of a cantilever beam with surface-mounted lead zirconate titanate (PZT) patches. Using experimental data and a statistical model for the observation errors, we compute approximate posterior distributions of the underlying model parameters via Bayesian techniques. The residuals, however, provide evidence that the errors are not iid normal as assumed and, in fact, exhibit strong serial correlation. This necessitates the incorporation of a model discrepancy term in the statistical model formulation as well. In this talk, we present several attempts at understanding such a model discrepancy term and its implications on parameter estimation and prediction.

*Learning about physical parameters: the importance of model discrepancy*

**April 17, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Jenný Brynjarsdóttir, Duke and SAMSI

### Abstract

Science-based simulation models are widely used to predict the behaviour of complex physical systems. It is also common to use observations of the physical system to learn about the values of parameters within the model, a process usually called calibration. The values of parameters in the model may be of intrinsic scientific interest, so learning about them contributes to the underlying science. Another reason for calibration is to improve the predictive performance of the simulator.

In order to make appropriate use of observations of the physical system, however, it is important to recognise model discrepancy, the difference between reality and the simulator output. We illustrate through a simple example that an analysis that does not account for model discrepancy will lead to biased and over-confident parameter estimates and predictions.

The challenge with incorporating model discrepancy in a statistical analysis of computer models is the confounding with calibration parameters, which will only be resolved with meaningful priors. For our simple example, we model the model-discrepancy via a Gaussian Process and demonstrate that by accounting for model discrepancy our prediction within the range of data is correct. However, only with realistic priors on model discrepancy do we uncover true parameters.

*Seasonal Tropical Cyclone Forecast*

**April 24, 2013, 1:15pm – 2:15pm**

SAMSI, Room 150

Speaker: Dorit Hammerling, SAMSI

### Abstract

Tropical cyclones such as Hurricane Sandy are events of high societal relevance often causing large damage. The formation of tropical cyclones is inherently a chaotic phenomenon and predicting a specific occurrence more than weeks ahead will likely remain elusive. There is, however, the possibility to conduct seasonal forecasts, which are typically based on annually or decadally varying climatic modes and patterns.

In a joint effort between the Department of Marine, Earth, and Atmospheric Sciences and the Department of Statistics, a team at NC State has been working and providing such seasonal forecasts of tropical cyclones for the Atlantic basin. The forecasts are based on a Poisson regression model. For this year’s forecast, we have made some methodological changes including a broader selection of potential predictors, introducing a Lasso-based variable selection method, and allowing for the selection of a different set of predictors for each region. Advantages of this approach include the direct interpretability of the effect of the climate indices on the number of predicted hurricanes, which might be of scientific relevance, especially how they differ between regions.

I will show the forecast for the 2013 Atlantic hurricane season, which we predict to be an above-average year, discuss the lack of predictability for landfalls, and provide an overview of the data used in the Undergraduate Modeling Workshop.