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JUNE, 2014

2014 Theses

It is the end of Spring 2014 and our graduates students have submitted their theses. The defended theses this year were:

Cross-sectional MRI Data Analysis Based On Shearlet Transformation
Hao Zhao, Department of Mathematics, Washington University in St.Louis
April 28, 2014
2:00pm to 3:00pm
M.A. in Statistics with Thesis
Abstract: Alzheimer s disease is most common form of dementia. The cause and development of Alzheimer's disease are not completely understood. Studies results show that the disease is associated with plaques and tangles in the brain (Tiraboschi, P., et al., 2004). Alzheimer's disease is diagnosed among people who are over 65 years old and the incidence rates increases exponentially after 65 years of age (Brookmeyer, 1998). Several studies have indicated that structural MRI can help study AD. The typical set of MRI data contains full brain scanned images from different individuals, with intensities on the same two-dimensional domain for each slice. The main purpose of this type of image data is to combine all the information from images to make statistical inferences about the effects on the populations represented in the images (Morris, Jeffrey S., et al. 2010). The Open Access Series of Imaging Studies (OASIS) project freely distributes magnetic resonance imaging (MRI) data sets of the brain. Shearlets are becoming one of the best frameworks for representing the multidimensional data efficiently. Shearlet decomposition is applied to the MRI data set by choosing a configuration. After decompositions, we had a large sparse coefficients matrix. We used different methods for data size reduction in order to perform a meaningful statistical analysis. Variable ranking feature selection method is applied and then Principle Components Analysis was used for feather data reduction. At last, logistic regression was applied to the OASIS data set with principle components. In the result of the logistic regression, gender, age, education and some principle components significantly affect the CDR, which is a measurement for AD.
Location: Cupples I, Room 199
Host: Prof. Jiming Ding

Nonlinear Mixed Effect Model for Wavelet-transformed Longitudinal MRI Data in Non-demented and Demented Older Adults
Tianhui Gu, Department of Mathematics, Washington University in St.Louis
April 24, 2014
1:00pm to 2:00pm
M.A. in Statistics with Thesis
Abstract: Alzheimer's disease (AD) is the most common form of dementia. How AD affects brain structure and tissues has aroused a lot of attention. Due to the high dimensionality of Magnetic Resonance Imaging data, it is difficult to conduct data analysis on them. My thesis uses data from Open Access Series of Imaging Studies, a longitudinal collection of 373 MRI sessions from 150 subjects aged 60 to 96. Instead of processing images directly, I use wavelet transformation to change image data into the wavelet domain for more efficient data reduction. A linear mixed effect model is then fitted for every dominating wavelet coefficient that contains the major information of the images. I discover that the association between the clinical covariates and the features of the brain images that are represented by the dominating wavelet coefficients is monotone but nonlinear over the index of the coefficients. To capture such a nonlinear trend and integrate all features in one model, I try to fit a nonlinear mixed effect model. The estimates from nonlinear least square models are used as the initial values for the parameters. For the better interpretation and visualization of the estimates, I predict the wavelet coefficients from the model and reconstruct the predicted images. After reconstruction, the effects of Clinical Dementia Rating and baseline age can be easily observed while gender has a significant effect.
Location: Cupples I, Room 199
Host: Prof. Jimin Ding

Using the Wavelet Transformation to Analyze Cross-Sectional MRI Data
Yuyang Zhang, Department of Mathematics, Washington University in St.Louis
April 24, 2014
11:00am to 12:00pm
M.A. in Statistics with Thesis
Abstract:Alzheimer's Disease (AD) is a serious disease which is frequently in the news nowadays. Almost 1/3 of elderly people have this disease. Some biological factors are found to be associated with it, such as gender, age and education level. The governments all over the world have paid a large amount of money to solve this problem, but the result is not as good as people expected. AD cannot be cured at this time. To find as soon as possible whether a person has AD is the best way to control AD. My goal in this thesis is to describe some models to help discover the presence of AD in clinical trials. The original data is collected by OASIS (Open Access Series of Imaging Studies). We have about 400 subjects in this research. Due to some problems about protection, only 235 subjects have provided the entire information. I will consider these 235 subjects in this thesis, and 100 of them have AD. To analyze the image data of AD in the brain, the high dimension of the image is the most important problem that should be solved. Principal Component Analysis (PCA) and wavelet transformation are the two popular methods to solve this problem. I will do Logistic Regression based on PCA to consider whether a person has AD as the predicted variable in the first part. And I will use the functional linear model to consider the wavelet coefficients as the predicted variables in the second part. Finally, I will discuss the advantages and disadvantages of these analysis methods.
Location: Cupples I, Room 215
Host: Prof. Jiming Ding

Study of the Mini-Mental State Examination: Checking Validity, Relationships to Demographical variables and Alcohol-related Variables
Chong Bian, Mathematics, Washington University in St.Louis
April 17, 2014
3:00pm to 4:00pm
M.A. in Statistics with Thesis
Abstract: Thesis about checking the validity of construction of the MMSE using factor analysis. And study the relationships between MMSE and demographic variables and alcohol-related variables, respectively.
Location: Cupples I, Room 199
Host: Prof. Edward Spitznagel

Looking to contact a past graduate? Visit our Recent Ph.D.'s page⇨
2014 Mathematics Theses from WUSTL's Open Scholarship are soon to appear. Meanwhile, you can download a 2012-2013 Mathematics Theses from WUSTL's Open Scholarship⇨

Liked this story? See also 2013 Theses in Mathematics and Statistics⇨ and 2012 Theses in Mathematics and Statistics⇨

— Math news, stories, videos, and interviews by Marie C. Taris, http://www.math.wustl.edu/marietaris/math.html⇨

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