Matching Items (112)
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
Surveys have shown that several hundred billion weather forecasts are obtained by the United States public each year, and that weather news is one of the most consumed topics in the media. This indicates that the forecast provides information that is significant to the public, and that the public utilizes details associated with it to inform aspects of their life. Phoenix, Arizona is a dry, desert region that experiences a monsoon season and extreme heat. How then, does the weather forecast influence the way Phoenix residents make decisions? This paper aims to draw connections between the weather forecast, decision making, and people who live in a desert environment. To do this, a ten-minute survey was deployed through Amazon Mechanical Turk (MTurk) in which 379 respondents were targeted. The survey asks 45 multiple choice and ranking questions categorized into four sections: obtainment of the forecast, forecast variables of interest, informed decision making based on unique weather variables, and demographics. This research illuminates how residents in the Phoenix metropolitan area use the local weather forecast for decision-making on daily activities, and the main meteorological factors that drive those decisions.
ContributorsMarturano, Julia (Author) / Middel, Ariane (Thesis director) / Schneider, Florian (Committee member) / School of Geographical Sciences and Urban Planning (Contributor, Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
While there are many elements to consider when determining one's risk of heat or cold stress, acclimation could prove to be an important factor to consider. Individuals who are participating in more strenuous activities, while being at a lower risk, will still feel the impacts of acclimation to an extreme climate. To evaluate acclimation in strenuous conditions, I collected finishing times from six different marathon races: the New York City Marathon (New York City, New York), Equinox Marathon (Fairbanks, Alaska), California International Marathon (Sacramento, California), LIVESTRONG Austin Marathon (Austin, Texas), Cincinnati Flying Pig Marathon (Cincinnati, Ohio), and the Ocala Marathon (Ocala, Florida). Additionally, I collected meteorological variables for each race day and the five days leading up to the race (baseline). I tested these values against the finishing times for the local runners, those from the race state, and visitors, those from other locations. Effects of local acclimation could be evaluated by comparing finishing times of local runners to the change between the race day and baseline weather conditions. Locals experienced a significant impact on finishing times for large changes between race day and the baseline conditions for humidity variables, dew point temperature, vapor pressure, relative humidity, and temperature based variables such as the heat index, temperature and the saturation vapor pressure. Wind speed and pressure values also marked a change in performance, however; pressure was determined to be a larger psychological factor than acclimation factor. The locals also demonstrated an acclimation effect as performance improved when conditions were similar on race day to baseline conditions for the three larger races. Humidity variables had the largest impact on runners when those values increased from training and acclimation values; however increased wind speed appeared to offset increased humidity values. These findings support previous acclimation research stating warm wet conditions are more difficult to acclimate to than warm dry conditions. This research while primarily pertaining to those participating physically demanding activities may also be applied to other large scale events such as festivals, fairs, or concerts.
ContributorsDeBiasse, Kimberly Michelle (Author) / Cerveny, Randall S. (Thesis advisor) / Brazel, Anthony (Committee member) / Selover, Nancy (Committee member) / Arizona State University (Publisher)
Created2011
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
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 thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
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
Alzheimer's Disease (AD) is the most common form of dementia observed in elderly patients and has significant social-economic impact. There are many initiatives which aim to capture leading causes of AD. Several genetic, imaging, and biochemical markers are being explored to monitor progression of AD and explore treatment and detection options. The primary focus of this thesis is to identify key biomarkers to understand the pathogenesis and prognosis of Alzheimer's Disease. Feature selection is the process of finding a subset of relevant features to develop efficient and robust learning models. It is an active research topic in diverse areas such as computer vision, bioinformatics, information retrieval, chemical informatics, and computational finance. In this work, state of the art feature selection algorithms, such as Student's t-test, Relief-F, Information Gain, Gini Index, Chi-Square, Fisher Kernel Score, Kruskal-Wallis, Minimum Redundancy Maximum Relevance, and Sparse Logistic regression with Stability Selection have been extensively exploited to identify informative features for AD using data from Alzheimer's Disease Neuroimaging Initiative (ADNI). An integrative approach which uses blood plasma protein, Magnetic Resonance Imaging, and psychometric assessment scores biomarkers has been explored. This work also analyzes the techniques to handle unbalanced data and evaluate the efficacy of sampling techniques. Performance of feature selection algorithm is evaluated using the relevance of derived features and the predictive power of the algorithm using Random Forest and Support Vector Machine classifiers. Performance metrics such as Accuracy, Sensitivity and Specificity, and area under the Receiver Operating Characteristic curve (AUC) have been used for evaluation. The feature selection algorithms best suited to analyze AD proteomics data have been proposed. The key biomarkers distinguishing healthy and AD patients, Mild Cognitive Impairment (MCI) converters and non-converters, and healthy and MCI patients have been identified.
ContributorsDubey, Rashmi (Author) / Ye, Jieping (Thesis advisor) / Wang, Yalin (Committee member) / Wu, Tong (Committee member) / Arizona State University (Publisher)
Created2012