Matching Items (123)
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
Proteins are a fundamental unit in biology. Although proteins have been extensively studied, there is still much to investigate. The mechanism by which proteins fold into their native state, how evolution shapes structural dynamics, and the dynamic mechanisms of many diseases are not well understood. In this thesis, protein folding is explored using a multi-scale modeling method including (i) geometric constraint based simulations that efficiently search for native like topologies and (ii) reservoir replica exchange molecular dynamics, which identify the low free energy structures and refines these structures toward the native conformation. A test set of eight proteins and three ancestral steroid receptor proteins are folded to 2.7Å all-atom RMSD from their experimental crystal structures. Protein evolution and disease associated mutations (DAMs) are most commonly studied by in silico multiple sequence alignment methods. Here, however, the structural dynamics are incorporated to give insight into the evolution of three ancestral proteins and the mechanism of several diseases in human ferritin protein. The differences in conformational dynamics of these evolutionary related, functionally diverged ancestral steroid receptor proteins are investigated by obtaining the most collective motion through essential dynamics. Strikingly, this analysis shows that evolutionary diverged proteins of the same family do not share the same dynamic subspace. Rather, those sharing the same function are simultaneously clustered together and distant from those functionally diverged homologs. This dynamics analysis also identifies 77% of mutations (functional and permissive) necessary to evolve new function. In silico methods for prediction of DAMs rely on differences in evolution rate due to purifying selection and therefore the accuracy of DAM prediction decreases at fast and slow evolvable sites. Here, we investigate structural dynamics through computing the contribution of each residue to the biologically relevant fluctuations and from this define a metric: the dynamic stability index (DSI). Using DSI we study the mechanism for three diseases observed in the human ferritin protein. The T30I and R40G DAMs show a loss of dynamic stability at the C-terminus helix and nearby regulatory loop, agreeing with experimental results implicating the same regulatory loop as a cause in cataracts syndrome.
ContributorsGlembo, Tyler J (Author) / Ozkan, Sefika B (Thesis advisor) / Thorpe, Michael F (Committee member) / Ros, Robert (Committee member) / Kumar, Sudhir (Committee member) / Shumway, John (Committee member) / Arizona State University (Publisher)
Created2011
Description
ABSTRACT Group III-nitride semiconductor materials have been commercially used in fabrication of light-emitting diodes (LEDs) and laser diodes (LDs) covering the spectral range from UV to visible and infrared, and exhibit unique properties suitable for modern optoelectronic applications. Great advances have recently happened in the research and development in high-power and high-efficiency blue-green-white LEDs, blue LDs and other optoelectronic applications. However, there are still many unsolved challenges with these materials. In this dissertation, several issues concerning structural, electronic and optical properties of III-nitrides have been investigated using a combination of transmission electron microscopy (TEM), electron holography (EH) and cathodoluminescence (CL) techniques. First, a trend of indium chemical inhomogeneity has been found as the indium composition increases for the InGaN epitaxial layers grown by hydride vapor phase epitaxy. Second, different mechanisms contributing to the strain relaxation have been studied for non-polar InGaN epitaxial layers grown on zinc oxide (ZnO) substrate. Third, various structural morphologies of non-polar InGaN epitaxial layers grown on free-standing GaN substrate have been investigated. Fourth, the effect of the growth temperature on the performance of GaN lattice-matched InAlN electron blocking layers has been studied. Finally, the electronic and optical properties of GaN nanowires containing a AlN/GaN superlattice structure have been investigated showing relatively small internal electric field and superlattice- and defect-related emissions along the nanowires.
ContributorsSun, Kewei (Author) / Ponce, Fernando (Thesis advisor) / Smith, David (Committee member) / Treacy, Michael (Committee member) / Drucker, Jeffery (Committee member) / Schmidt, Kevin (Committee member) / Arizona State University (Publisher)
Created2011
Description
Multi-task learning (MTL) aims to improve the generalization performance (of the resulting classifiers) by learning multiple related tasks simultaneously. Specifically, MTL exploits the intrinsic task relatedness, based on which the informative domain knowledge from each task can be shared across multiple tasks and thus facilitate the individual task learning. It is particularly desirable to share the domain knowledge (among the tasks) when there are a number of related tasks but only limited training data is available for each task. Modeling the relationship of multiple tasks is critical to the generalization performance of the MTL algorithms. In this dissertation, I propose a series of MTL approaches which assume that multiple tasks are intrinsically related via a shared low-dimensional feature space. The proposed MTL approaches are developed to deal with different scenarios and settings; they are respectively formulated as mathematical optimization problems of minimizing the empirical loss regularized by different structures. For all proposed MTL formulations, I develop the associated optimization algorithms to find their globally optimal solution efficiently. I also conduct theoretical analysis for certain MTL approaches by deriving the globally optimal solution recovery condition and the performance bound. To demonstrate the practical performance, I apply the proposed MTL approaches on different real-world applications: (1) Automated annotation of the Drosophila gene expression pattern images; (2) Categorization of the Yahoo web pages. Our experimental results demonstrate the efficiency and effectiveness of the proposed algorithms.
ContributorsChen, Jianhui (Author) / Ye, Jieping (Thesis advisor) / Kumar, Sudhir (Committee member) / Liu, Huan (Committee member) / Xue, Guoliang (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
In this dissertation, remote plasma interactions with the surfaces of low-k interlayer dielectric (ILD), Cu and Cu adhesion layers are investigated. The first part of the study focuses on the simultaneous plasma treatment of ILD and chemical mechanical polishing (CMP) Cu surfaces using N2/H2 plasma processes. H atoms and radicals in the plasma react with the carbon groups leading to carbon removal for the ILD films. Results indicate that an N2 plasma forms an amide-like layer on the surface which apparently leads to reduced carbon abstraction from an H2 plasma process. In addition, FTIR spectra indicate the formation of hydroxyl (Si-OH) groups following the plasma exposure. Increased temperature (380 °C) processing leads to a reduction of the hydroxyl group formation compared to ambient temperature processes, resulting in reduced changes of the dielectric constant. For CMP Cu surfaces, the carbonate contamination was removed by an H2 plasma process at elevated temperature while the C-C and C-H contamination was removed by an N2 plasma process at elevated temperature. The second part of this study examined oxide stability and cleaning of Ru surfaces as well as consequent Cu film thermal stability with the Ru layers. The ~2 monolayer native Ru oxide was reduced after H-plasma processing. The thermal stability or islanding of the Cu film on the Ru substrate was characterized by in-situ XPS. After plasma cleaning of the Ru adhesion layer, the deposited Cu exhibited full coverage. In contrast, for Cu deposition on the Ru native oxide substrate, Cu islanding was detected and was described in terms of grain boundary grooving and surface and interface energies. The thermal stability of 7 nm Ti, Pt and Ru ii interfacial adhesion layers between a Cu film (10 nm) and a Ta barrier layer (4 nm) have been investigated in the third part. The barrier properties and interfacial stability have been evaluated by Rutherford backscattering spectrometry (RBS). Atomic force microscopy (AFM) was used to measure the surfaces before and after annealing, and all the surfaces are relatively smooth excluding islanding or de-wetting phenomena as a cause of the instability. The RBS showed no discernible diffusion across the adhesion layer/Ta and Ta/Si interfaces which provides a stable underlying layer. For a Ti interfacial layer RBS indicates that during 400 °C annealing Ti interdiffuses through the Cu film and accumulates at the surface. For the Pt/Cu system Pt interdiffuion is detected which is less evident than Ti. Among the three adhesion layer candidates, Ru shows negligible diffusion into the Cu film indicating thermal stability at 400 °C.
ContributorsLiu, Xin (Author) / Nemanich, Robert (Thesis advisor) / Chamberlin, Ralph (Committee member) / Chen, Tingyong (Committee member) / Smith, David (Committee member) / Ponce, Fernando (Committee member) / Arizona State University (Publisher)
Created2012
Description
The energy band gap of a semiconductor material critically influences the operating wavelength of an optoelectronic device. Realization of any desired band gap, or even spatially graded band gaps, is important for applications such as lasers, light-emitting diodes (LEDs), solar cells, and detectors. Compared to thin films, nanowires offer greater flexibility for achieving a variety of alloy compositions. Furthermore, the nanowire geometry permits simultaneous incorporation of a wide range of compositions on a single substrate. Such controllable alloy composition variation can be realized either within an individual nanowire or between distinct nanowires across a substrate. This dissertation explores the control of spatial composition variation in ternary alloy nanowires. Nanowires were grown by the vapor-liquid-solid (VLS) mechanism using chemical vapor deposition (CVD). The gas-phase supersaturation was considered in order to optimize the deposition morphology. Composition and structure were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive x-ray spectroscopy (EDS), and x-ray diffraction (XRD). Optical properties were investigated through photoluminescence (PL) measurements. The chalcogenides selected as alloy endpoints were lead sulfide (PbS), cadmium sulfide (CdS), and cadmium selenide (CdSe). Three growth modes of PbS were identified, which included contributions from spontaneously generated catalyst. The resulting wires were found capable of lasing with wavelengths over 4000 nm, representing the longest known wavelength from a sub-wavelength wire. For CdxPb1-xS nanowires, it was established that the cooling process significantly affects the alloy composition and structure. Quenching was critical to retain metastable alloys with x up to 0.14, representing a new composition in nanowire form. Alternatively, gradual cooling caused phase segregation, which created heterostructures with light emission in both the visible and mid-infrared regimes. The CdSSe alloy system was fully explored for spatial composition variation. CdSxSe1-x nanowires were grown with composition variation across the substrate. Subsequent contact printing preserved the designed composition gradient and led to the demonstration of a variable wavelength photodetector device. CdSSe axial heterostructure nanowires were also achieved. The growth process involved many variables, including a deliberate and controllable change in substrate temperature. As a result, both red and green light emission was detected from single nanowires.
ContributorsNichols, Patricia (Author) / Ning, Cun-Zheng (Thesis advisor) / Carpenter, Ray (Committee member) / Bennett, Peter (Committee member) / Smith, David (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