Matching Items (164)
Description
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2013
Description
Functional magnetic resonance imaging (fMRI) has been widely used to measure the retinotopic organization of early visual cortex in the human brain. Previous studies have identified multiple visual field maps (VFMs) based on statistical analysis of fMRI signals, but the resulting geometry has not been fully characterized with mathematical models. This thesis explores using concepts from computational conformal geometry to create a custom software framework for examining and generating quantitative mathematical models for characterizing the geometry of early visual areas in the human brain. The software framework includes a graphical user interface built on top of a selected core conformal flattening algorithm and various software tools compiled specifically for processing and examining retinotopic data. Three conformal flattening algorithms were implemented and evaluated for speed and how well they preserve the conformal metric. All three algorithms performed well in preserving the conformal metric but the speed and stability of the algorithms varied. The software framework performed correctly on actual retinotopic data collected using the standard travelling-wave experiment. Preliminary analysis of the Beltrami coefficient for the early data set shows that selected regions of V1 that contain reasonably smooth eccentricity and polar angle gradients do show significant local conformality, warranting further investigation of this approach for analysis of early and higher visual cortex.
ContributorsTa, Duyan (Author) / Wang, Yalin (Thesis advisor) / Maciejewski, Ross (Committee member) / Wonka, Peter (Committee member) / Arizona State University (Publisher)
Created2013
Description
In blindness research, the corpus callosum (CC) is the most frequently studied sub-cortical structure, due to its important involvement in visual processing. While most callosal analyses from brain structural magnetic resonance images (MRI) are limited to the 2D mid-sagittal slice, we propose a novel framework to capture a complete set of 3D morphological differences in the corpus callosum between two groups of subjects. The CCs are segmented from whole brain T1-weighted MRI and modeled as 3D tetrahedral meshes. The callosal surface is divided into superior and inferior patches on which we compute a volumetric harmonic field by solving the Laplace's equation with Dirichlet boundary conditions. We adopt a refined tetrahedral mesh to compute the Laplacian operator, so our computation can achieve sub-voxel accuracy. Thickness is estimated by tracing the streamlines in the harmonic field. We combine areal changes found using surface tensor-based morphometry and thickness information into a vector at each vertex to be used as a metric for the statistical analysis. Group differences are assessed on this combined measure through Hotelling's T2 test. The method is applied to statistically compare three groups consisting of: congenitally blind (CB), late blind (LB; onset > 8 years old) and sighted (SC) subjects. Our results reveal significant differences in several regions of the CC between both blind groups and the sighted groups; and to a lesser extent between the LB and CB groups. These results demonstrate the crucial role of visual deprivation during the developmental period in reshaping the structural architecture of the CC.
ContributorsXu, Liang (Author) / Wang, Yalin (Thesis advisor) / Maciejewski, Ross (Committee member) / Ye, Jieping (Committee member) / Arizona State University (Publisher)
Created2013
Description
Sparsity has become an important modeling tool in areas such as genetics, signal and audio processing, medical image processing, etc. Via the penalization of l-1 norm based regularization, the structured sparse learning algorithms can produce highly accurate models while imposing various predefined structures on the data, such as feature groups or graphs. In this thesis, I first propose to solve a sparse learning model with a general group structure, where the predefined groups may overlap with each other. Then, I present three real world applications which can benefit from the group structured sparse learning technique. In the first application, I study the Alzheimer's Disease diagnosis problem using multi-modality neuroimaging data. In this dataset, not every subject has all data sources available, exhibiting an unique and challenging block-wise missing pattern. In the second application, I study the automatic annotation and retrieval of fruit-fly gene expression pattern images. Combined with the spatial information, sparse learning techniques can be used to construct effective representation of the expression images. In the third application, I present a new computational approach to annotate developmental stage for Drosophila embryos in the gene expression images. In addition, it provides a stage score that enables one to more finely annotate each embryo so that they are divided into early and late periods of development within standard stage demarcations. Stage scores help us to illuminate global gene activities and changes much better, and more refined stage annotations improve our ability to better interpret results when expression pattern matches are discovered between genes.
ContributorsYuan, Lei (Author) / Ye, Jieping (Thesis advisor) / Wang, Yalin (Committee member) / Xue, Guoliang (Committee member) / Kumar, Sudhir (Committee member) / Arizona State University (Publisher)
Created2013
Description
Food system and health characteristics were evaluated across the last Waorani hunter-gatherer group in Amazonian Ecuador and a remote neighboring Kichwa indigenous subsistence agriculture community. Hunter-gatherer food systems like the Waorani foragers may not only be nutritionally, but also pharmaceutically beneficial because of high dietary intake of varied plant phytochemical compounds. A modern diet that reduces these dietary plant defense phytochemicals below levels typical in human evolutionary history may leave humans vulnerable to diseases that were controlled through a foraging diet. Few studies consider the health impact of the recent drastic reduction of plant phytochemical content in the modern global food system, which has eliminated essential components of food because they are not considered "nutrients". The antimicrobial and anti-inflammatory nature of the food system may not only regulate infectious pathogens and inflammatory disease, but also support beneficial microbes in human hosts, reducing vulnerability to chronic diseases. Waorani foragers seem immune to certain infections with very low rates of chronic disease. Does returning to certain characteristics of a foraging food system begin to restore the human body microbe balance and inflammatory response to evolutionary norms, and if so, what implication does this have for the treatment of disease? Several years of data on dietary and health differences across the foragers and the farmers was gathered. There were major differences in health outcomes across the board. In the Waorani forager group there were no signs of infection in serious wounds such as 3rd degree burns and spear wounds. The foragers had one-degree lower body temperature than the farmers. The Waorani had an absence of signs of chronic diseases including vision and blood pressure that did not change markedly with age while Kichwa farmers suffered from both chronic diseases and physiological indicators of aging. In the Waorani forager population, there was an absence of many common regional infectious diseases, from helminthes to staphylococcus. Study design helped control for confounders (exercise, environment, genetic factors, non-phytochemical dietary intake). This study provides evidence of the major role total phytochemical dietary intake plays in human health, often not considered by policymakers and nutritional and agricultural scientists.
ContributorsLondon, Douglas (Author) / Tsuda, Takeyuki (Thesis advisor) / Beezhold, Bonnie L (Committee member) / Hruschka, Daniel (Committee member) / Eder, James (Committee member) / Arizona State University (Publisher)
Created2012
Description
Over 2 billion people are using online social network services, such as Facebook, Twitter, Google+, LinkedIn, and Pinterest. Users update their status, post their photos, share their information, and chat with others in these social network sites every day; however, not everyone shares the same amount of information. This thesis explores methods of linking publicly available data sources as a means of extrapolating missing information of Facebook. An application named "Visual Friends Income Map" has been created on Facebook to collect social network data and explore geodemographic properties to link publicly available data, such as the US census data. Multiple predictors are implemented to link data sets and extrapolate missing information from Facebook with accurate predictions. The location based predictor matches Facebook users' locations with census data at the city level for income and demographic predictions. Age and relationship based predictors are created to improve the accuracy of the proposed location based predictor utilizing social network link information. In the case where a user does not share any location information on their Facebook profile, a kernel density estimation location predictor is created. This predictor utilizes publicly available telephone record information of all people with the same surname of this user in the US to create a likelihood distribution of the user's location. This is combined with the user's IP level information in order to narrow the probability estimation down to a local regional constraint.
ContributorsMao, Jingxian (Author) / Maciejewski, Ross (Thesis advisor) / Farin, Gerald (Committee member) / Wang, Yalin (Committee member) / Arizona State University (Publisher)
Created2012
Description
This document presents a new implementation of the Smoothed Particles Hydrodynamics algorithm using DirectX 11 and DirectCompute. The main goal of this document is to present to the reader an alternative solution to the largely studied and researched problem of fluid simulation. Most other solutions have been implemented using the NVIDIA CUDA framework; however, the proposed solution in this document uses the Microsoft general-purpose computing on graphics processing units API. The implementation allows for the simulation of a large number of particles in a real-time scenario. The solution presented here uses the Smoothed Particles Hydrodynamics algorithm to calculate the forces within the fluid; this algorithm provides a Lagrangian approach for discretizes the Navier-Stockes equations into a set of particles. Our solution uses the DirectCompute compute shaders to evaluate each particle using the multithreading and multi-core capabilities of the GPU increasing the overall performance. The solution then describes a method for extracting the fluid surface using the Marching Cubes method and the programmable interfaces exposed by the DirectX pipeline. Particularly, this document presents a method for using the Geometry Shader Stage to generate the triangle mesh as defined by the Marching Cubes method. The implementation results show the ability to simulate over 64K particles at a rate of 900 and 400 frames per second, not including the surface reconstruction steps and including the Marching Cubes steps respectively.
ContributorsFigueroa, Gustavo (Author) / Farin, Gerald (Thesis advisor) / Maciejewski, Ross (Committee member) / Wang, Yalin (Committee member) / Arizona State University (Publisher)
Created2012
Description
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
Description
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2012