Matching Items (133)
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Coherent vortices are ubiquitous structures in natural flows that affect mixing and transport of substances and momentum/energy. Being able to detect these coherent structures is important for pollutant mitigation, ecological conservation and many other aspects. In recent years, mathematical criteria and algorithms have been developed to extract these coherent structures in turbulent flows. In this study, we will apply these tools to extract important coherent structures and analyze their statistical properties as well as their implications on kinematics and dynamics of the flow. Such information will aide representation of small-scale nonlinear processes that large-scale models of natural processes may not be able to resolve.
ContributorsCass, Brentlee Jerry (Author) / Tang, Wenbo (Thesis director) / Kostelich, Eric (Committee member) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Video object segmentation (VOS) is an important task in computer vision with a lot of applications, e.g., video editing, object tracking, and object based encoding. Different from image object segmentation, video object segmentation must consider both spatial and temporal coherence for the object. Despite extensive previous work, the problem is still challenging. Usually, foreground object in the video draws more attention from humans, i.e. it is salient. In this thesis we tackle the problem from the aspect of saliency, where saliency means a certain subset of visual information selected by a visual system (human or machine). We present a novel unsupervised method for video object segmentation that considers both low level vision cues and high level motion cues. In our model, video object segmentation can be formulated as a unified energy minimization problem and solved in polynomial time by employing the min-cut algorithm. Specifically, our energy function comprises the unary term and pair-wise interaction energy term respectively, where unary term measures region saliency and interaction term smooths the mutual effects between object saliency and motion saliency. Object saliency is computed in spatial domain from each discrete frame using multi-scale context features, e.g., color histogram, gradient, and graph based manifold ranking. Meanwhile, motion saliency is calculated in temporal domain by extracting phase information of the video. In the experimental section of this thesis, our proposed method has been evaluated on several benchmark datasets. In MSRA 1000 dataset the result demonstrates that our spatial object saliency detection is superior to the state-of-art methods. Moreover, our temporal motion saliency detector can achieve better performance than existing motion detection approaches in UCF sports action analysis dataset and Weizmann dataset respectively. Finally, we show the attractive empirical result and quantitative evaluation of our approach on two benchmark video object segmentation datasets.
ContributorsWang, Yilin (Author) / Li, Baoxin (Thesis advisor) / Wang, Yalin (Committee member) / Cleveau, David (Committee member) / Arizona State University (Publisher)
Created2013
Description
Learning from high dimensional biomedical data attracts lots of attention recently. High dimensional biomedical data often suffer from the curse of dimensionality and have imbalanced class distributions. Both of these features of biomedical data, high dimensionality and imbalanced class distributions, are challenging for traditional machine learning methods and may affect the model performance. In this thesis, I focus on developing learning methods for the high-dimensional imbalanced biomedical data. In the first part, a sparse canonical correlation analysis (CCA) method is presented. The penalty terms is used to control the sparsity of the projection matrices of CCA. The sparse CCA method is then applied to find patterns among biomedical data sets and labels, or to find patterns among different data sources. In the second part, I discuss several learning problems for imbalanced biomedical data. Note that traditional learning systems are often biased when the biomedical data are imbalanced. Therefore, traditional evaluations such as accuracy may be inappropriate for such cases. I then discuss several alternative evaluation criteria to evaluate the learning performance. For imbalanced binary classification problems, I use the undersampling based classifiers ensemble (UEM) strategy to obtain accurate models for both classes of samples. A small sphere and large margin (SSLM) approach is also presented to detect rare abnormal samples from a large number of subjects. In addition, I apply multiple feature selection and clustering methods to deal with high-dimensional data and data with highly correlated features. Experiments on high-dimensional imbalanced biomedical data are presented which illustrate the effectiveness and efficiency of my methods.
ContributorsYang, Tao (Author) / Ye, Jieping (Thesis advisor) / Wang, Yalin (Committee member) / Davulcu, Hasan (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation constructs a new computational processing framework to robustly and precisely quantify retinotopic maps based on their angle distortion properties. More generally, this framework solves the problem of how to robustly and precisely quantify (angle) distortions of noisy or incomplete (boundary enclosed) 2-dimensional surface to surface mappings. This framework builds upon the Beltrami Coefficient (BC) description of quasiconformal mappings that directly quantifies local mapping (circles to ellipses) distortions between diffeomorphisms of boundary enclosed plane domains homeomorphic to the unit disk. A new map called the Beltrami Coefficient Map (BCM) was constructed to describe distortions in retinotopic maps. The BCM can be used to fully reconstruct the original target surface (retinal visual field) of retinotopic maps. This dissertation also compared retinotopic maps in the visual processing cascade, which is a series of connected retinotopic maps responsible for visual data processing of physical images captured by the eyes. By comparing the BCM results from a large Human Connectome project (HCP) retinotopic dataset (N=181), a new computational quasiconformal mapping description of the transformed retinal image as it passes through the cascade is proposed, which is not present in any current literature. The description applied on HCP data provided direct visible and quantifiable geometric properties of the cascade in a way that has not been observed before. Because retinotopic maps are generated from in vivo noisy functional magnetic resonance imaging (fMRI), quantifying them comes with a certain degree of uncertainty. To quantify the uncertainties in the quantification results, it is necessary to generate statistical models of retinotopic maps from their BCMs and raw fMRI signals. Considering that estimating retinotopic maps from real noisy fMRI time series data using the population receptive field (pRF) model is a time consuming process, a convolutional neural network (CNN) was constructed and trained to predict pRF model parameters from real noisy fMRI data
ContributorsTa, Duyan Nguyen (Author) / Wang, Yalin (Thesis advisor) / Lu, Zhong-Lin (Committee member) / Hansford, Dianne (Committee member) / Liu, Huan (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2022
Description
Retinotopic map, the map between visual inputs on the retina and neuronal activation in brain visual areas, is one of the central topics in visual neuroscience. For human observers, the map is typically obtained by analyzing functional magnetic resonance imaging (fMRI) signals of cortical responses to slowly moving visual stimuli on the retina. Biological evidences show the retinotopic mapping is topology-preserving/topological (i.e. keep the neighboring relationship after human brain process) within each visual region.
Unfortunately, due to limited spatial resolution and the signal-noise ratio of fMRI, state of art retinotopic map is not topological.
The topic was to model the topology-preserving condition mathematically, fix non-topological retinotopic map with numerical methods, and improve the quality of retinotopic maps.
The impose of topological condition, benefits several applications.
With the topological retinotopic maps, one may have a better insight on human retinotopic maps, including better cortical magnification factor quantification, more precise description of retinotopic maps, and potentially better exam ways of in Ophthalmology clinic.
ContributorsTu, Yanshuai (Author) / Wang, Yalin (Thesis advisor) / Lu, Zhong-Lin (Committee member) / Crook, Sharon (Committee member) / Yang, Yezhou (Committee member) / Zhang, Yu (Committee member) / Arizona State University (Publisher)
Created2022
Description
Neural tissue is a delicate system comprised of neurons and their synapses, glial cells for support, and vasculature for oxygen and nutrient delivery. This complexity ultimately gives rise to the human brain, a system researchers have become increasingly interested in replicating for artificial intelligence purposes. Some have even gone so far as to use neuronal cultures as computing hardware, but utilizing an environment closer to a living brain means having to grapple with the same issues faced by clinicians and researchers trying to treat brain disorders. Most outstanding among these are the problems that arise with invasive interfaces. Optical techniques that use fluorescent dyes and proteins have emerged as a solution for noninvasive imaging with single-cell resolution in vitro and in vivo, but feeding in information in the form of neuromodulation still requires implanted electrodes. The implantation process of these electrodes damages nearby neurons and their connections, causes hemorrhaging, and leads to scarring and gliosis that diminish efficacy. Here, a new approach for noninvasive neuromodulation with high spatial precision is described. It makes use of a combination of ultrasound, high frequency acoustic energy that can be focused to submillimeter regions at significant depths, and electric fields, an effective tool for neuromodulation that lacks spatial precision when used in a noninvasive manner. The hypothesis is that, when combined in a specific manner, these will lead to nonlinear effects at neuronal membranes that cause cells only in the region of overlap to be stimulated. Computational modeling confirmed this combination to be uniquely stimulating, contingent on certain physical effects of ultrasound on cell membranes. Subsequent in vitro experiments led to inconclusive results, however, leaving the door open for future experimentation with modified configurations and approaches. The specific combination explored here is also not the only untested technique that may achieve a similar goal.
ContributorsNester, Elliot (Author) / Wang, Yalin (Thesis advisor) / Muthuswamy, Jitendran (Committee member) / Towe, Bruce (Committee member) / Arizona State University (Publisher)
Created2022
Description
Beta-Amyloid(Aβ) plaques and tau protein tangles in the brain are now widely recognized as the defining hallmarks of Alzheimer’s disease (AD), followed by structural atrophy detectable on brain magnetic resonance imaging (MRI) scans. However, current methods to detect Aβ/tau pathology are either invasive (lumbar puncture) or quite costly and not widely available (positron emission tomography (PET)). And one of the particular neurodegenerative regions is the hippocampus to which the influence of Aβ/tau on has been one of the research projects focuses in the AD pathophysiological progress.
In this dissertation, I proposed three novel machine learning and statistical models to examine subtle aspects of the hippocampal morphometry from MRI that are associated with Aβ /tau burden in the brain, measured using PET images. The first model is a novel unsupervised feature reduction model to generate a low-dimensional representation of hippocampal morphometry for each individual subject, which has superior performance in predicting Aβ/tau burden in the brain. The second one is an efficient federated group lasso model to identify the hippocampal subregions where atrophy is strongly associated with abnormal Aβ/Tau. The last one is a federated model for imaging genetics, which can identify genetic and transcriptomic influences on hippocampal morphometry. Finally, I stated the results of these three models that have been published or submitted to peer-reviewed conferences and journals.
ContributorsWu, Jianfeng (Author) / Wang, Yalin (Thesis advisor) / Li, Baoxin (Committee member) / Liang, Jianming (Committee member) / Wang, Junwen (Committee member) / Wu, Teresa (Committee member) / Arizona State University (Publisher)
Created2022
Description
Structural Magnetic Resonance Imaging analysis is a vital component in the study of Alzheimer’s Disease pathology and several techniques exist as part of the existing research conducted. In particular, volumetric approaches in this field are known to be beneficial due to the increased capability to express morphological characteristics when compared to manifold methods. To aid in the improvement of the field, this paper aims to propose an intrinsic volumetric conic system that can be applied to bounded volumetric meshes to enable a more effective study of subjects. The computation of the metric involves the use of heat kernel theory and conformal parameterization on genus-0 surfaces extended to a volumetric domain. Additionally, this paper also explores the use of the ’TetCNN’ architecture on the classification of hippocampal tetrahedral meshes to detect features that correspond to Alzheimer’s indicators. The model tested was able to achieve remarkable results with a measured classification accuracy of above 90% in the task of differentiating between subjects diagnosed with Alzheimer’s and normal control subjects.
ContributorsGeorge, John Varghese (Author) / Wang, Yalin (Thesis advisor) / Hansford, Dianne (Committee member) / Gupta, Vikash (Committee member) / Arizona State University (Publisher)
Created2023
Description
Climate change is one of the most pressing issues affecting the world today. One of the impacts of climate change is on the transmission of mosquito-borne diseases (MBDs), such as West Nile Virus (WNV). Climate is known to influence vector and host demography as well as MBD transmission. This dissertation addresses the questions of how vector and host demography impact WNV dynamics, and how expected and likely climate change scenarios will affect demographic and epidemiological processes of WNV transmission. First, a data fusion method is developed that connects non-autonomous logistic model parameters to mosquito time series data. This method captures the inter-annual and intra-seasonal variation of mosquito populations within a geographical location. Next, a three-population WNV model between mosquito vectors, bird hosts, and human hosts with infection-age structure for the vector and bird host populations is introduced. A sensitivity analysis uncovers which parameters have the most influence on WNV outbreaks. Finally, the WNV model is extended to include the non-autonomous population model and temperature-dependent processes. Model parameterization using historical temperature and human WNV case data from the Greater Toronto Area (GTA) is conducted. Parameter fitting results are then used to analyze possible future WNV dynamics under two climate change scenarios. These results suggest that WNV risk for the GTA will substantially increase as temperature increases from climate change, even under the most conservative assumptions. This demonstrates the importance of ensuring that the warming of the planet is limited as much as possible.
ContributorsMancuso, Marina (Author) / Milner, Fabio A (Thesis advisor) / Kuang, Yang (Committee member) / Kostelich, Eric (Committee member) / Eikenberry, Steffen (Committee member) / Manore, Carrie (Committee member) / Arizona State University (Publisher)
Created2023