Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability

Long-lived light bullets fully localized in both space and time can be generated in novel photonic media such as multicore optical fiber or waveguide arrays. In this paper we present detailed theoretical analysis on the existence and stability of the discrete-continuous light bullets using a very generic model that occurs in a number of applications.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels. © 2010 The American Physical Society.

Resonance properties of domain boundaries in quasi-two dimensional antiferromagnets

The so-called "internal modes" localized near the domain boundaries in quasi-two dimensional antiferromagnets are investigated. The possible localized states are classified and their frequency dependences on the system discreteness parameter λ=J/β, which describes the ratio of the magnitudes of the exchange interplane interaction and the magnetic anisotropy, are found. A sudden change in the spectrum of the local internal modes is observed at a critical value of this parameter, λ=λb=3/4, where the domain wall shifts from a collinear to a canted shape. When λ<λb there are one symmetric and two antisymmetric local modes, and when λ>λb the modes are two symmetric, one antisymmetric, and one shear. For discreteness parameters close to the critical value, the frequencies of some of the local modes lie deep inside the gap for the linear AFM magnon spectrum and can be observed experimentally. © 2010 American Institute of Physics.

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Fluorescence-enhanced optical imaging on three-dimensional phantoms using a hand-held probe based frequency-domain intensified charge coupled device (ICCD) optical imager

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5×10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) up to 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (up to 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images, improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

A novel 3-D segmentation algorithm for anatomic liver and tumor volume calculations for liver cancer treatment planning

Three-Dimensional (3-D) imaging is vital in computer-assisted surgical planning including minimal invasive surgery, targeted drug delivery, and tumor resection. Selective Internal Radiation Therapy (SIRT) is a liver directed radiation therapy for the treatment of liver cancer. Accurate calculation of anatomical liver and tumor volumes are essential for the determination of the tumor to normal liver ratio and for the calculation of the dose of Y-90 microspheres that will result in high concentration of the radiation in the tumor region as compared to nearby healthy tissue. Present manual techniques for segmentation of the liver from Computed Tomography (CT) tend to be tedious and greatly dependent on the skill of the technician/doctor performing the task. ^ This dissertation presents the development and implementation of a fully integrated algorithm for 3-D liver and tumor segmentation from tri-phase CT that yield highly accurate estimations of the respective volumes of the liver and tumor(s). The algorithm as designed requires minimal human intervention without compromising the accuracy of the segmentation results. Embedded within this algorithm is an effective method for extracting blood vessels that feed the tumor(s) in order to plan effectively the appropriate treatment. ^ Segmentation of the liver led to an accuracy in excess of 95% in estimating liver volumes in 20 datasets in comparison to the manual gold standard volumes. In a similar comparison, tumor segmentation exhibited an accuracy of 86% in estimating tumor(s) volume(s). Qualitative results of the blood vessel segmentation algorithm demonstrated the effectiveness of the algorithm in extracting and rendering the vasculature structure of the liver. Results of the parallel computing process, using a single workstation, showed a 78% gain. Also, statistical analysis carried out to determine if the manual initialization has any impact on the accuracy showed user initialization independence in the results. ^ The dissertation thus provides a complete 3-D solution towards liver cancer treatment planning with the opportunity to extract, visualize and quantify the needed statistics for liver cancer treatment. Since SIRT requires highly accurate calculation of the liver and tumor volumes, this new method provides an effective and computationally efficient process required of such challenging clinical requirements.^

Responsiveness of voltage-gated calcium channels in SH-SY5Y human neuroblastoma cells on quasi-three-dimensional micropatterns formed with poly (l-lactic acid)

Introduction: In this study, quasi-three-dimensional (3D) microwell patterns were fabricated with poly (l-lactic acid) for the development of cell-based assays, targeting voltage-gated calcium channels (VGCCs). Methods and materials: SH-SY5Y human neuroblastoma cells were interfaced with the microwell patterns and found to grow as two dimensional (2D), 3D, and near two dimensional (N2D), categorized on the basis of the cells’ location in the pattern. The capability of the microwell patterns to support 3D cell growth was evaluated in terms of the percentage of the cells in each growth category. Cell spreading was analyzed in terms of projection areas under light microscopy. SH-SY5Y cells’ VGCC responsiveness was evaluated with confocal microscopy and a calcium fluorescent indicator, Calcium GreenTM-1. The expression of L-type calcium channels was evaluated using immunofluorescence staining with DM-BODIPY. Results: It was found that cells within the microwells, either N2D or 3D, showed more rounded shapes and less projection areas than 2D cells on flat poly (l-lactic acid) substrates. Also, cells in microwells showed a significantly lower VGCC responsiveness than cells on flat substrates, in terms of both response magnitudes and percentages of responsive cells, upon depolarization with 50 mM K+. This lower VGCC responsiveness could not be explained by the difference in L-type calcium channel expression. For the two patterns addressed in this study, N2D cells consistently exhibited an intermediate value of either projection areas or VGCC responsiveness between those for 2D and 3D cells, suggesting a correlative relation between cell morphology and VGCC responsiveness. Conclusion: These results suggest that the pattern structure and therefore the cell growth characteristics were critical factors in determining cell VGCC responsiveness and thus provide an approach for engineering cell functionality in cell-based assay systems and tissue engineering scaffolds.

Investigation of spatial patterns of ground-water exchange with lakes, using a three-dimensional numerical model

Hydrogeologic variables controlling groundwater exchange with inflow and flow-through lakes were simulated using a three-dimensional numerical model (MODFLOW) to investigate and quantify spatial patterns of lake bed seepage and hydraulic head distributions in the porous medium surrounding the lakes. Also, the total annual inflow and outflow were calculated as a percentage of lake volume for flow-through lake simulations. The general exponential decline of seepage rates with distance offshore was best demonstrated at lower anisotropy ratio (i.e., Kh/Kv = 1, 10), with increasing deviation from the exponential pattern as anisotropy was increased to 100 and 1000. 2-D vertical section models constructed for comparison with 3-D models showed that groundwater heads and seepages were higher in 3-D simulations. Addition of low conductivity lake sediments decreased seepage rates nearshore and increased seepage rates offshore in inflow lakes, and increased the area of groundwater inseepage on the beds of flow-through lakes. Introduction of heterogeneity into the medium decreased the water table and seepage ratesnearshore, and increased seepage rates offshore in inflow lakes. A laterally restricted aquifer located at the downgradient side of the flow-through lake increased the area of outseepage. Recharge rate, lake depth and lake bed slope had relatively little effect on the spatial patterns of seepage rates and groundwater exchange with lakes.

Three-dimensional tomographic reconstruction of an exceptionally well preserved ichnological assemblage from the Stainmore Foundation, Carboniferous, UK

This Ph.D. thesis addresses current issues with ichnotaxonomic practice, and characterizes an exceptionally well preserved ichnological assemblage from the Carboniferous Stainmore Formation, Northumberland, United Kingdom. Samples were collected from closely localized float representative of various units throughout the succession, which was deposited in a storm-dominated marine shoreface. Three dominant ichnotaxa were selected for three-dimensional morphological analysis due to their complicated morphology and/or unclear taxonomic status: 1) Dactyloidites jordii isp. nov.; 2) Beaconites capronus, and; 3) Neoeione moniliformis comb. nov. Using serial grinding and photography, these ichnotaxa were ground and modelled in true colour. High-resolution models of three taxa produced in this study are the basis of the first complete three-dimensional consideration of the traces, and forms the basis for refined palaeobiological and ethological analysis of these taxa. Dactyloidites jordii isp. nov. is a stellate to palmate burrow composed of numerous long, narrow rays that exhibit three orders of branching arranged into tiered galleries radiating from a central shaft. It is considered to be the feeding structure produced by a vermiform organism. Beaconites capronus is a winding trace with distinctly chevron-shaped, meniscate backfill demonstrated herein to backfill the vertical shafts associated with its burrows in a comparable fashion to the horizontal portion of the burrow. This lack of a surface connection would result in the trace making organism being exposed to low-oxygen porewater. Coping with this porewater dysoxia could be approached by burrowing organisms in a number of ways: 1) revisiting the sediment-water interface; 2) creating periodic shafts; or 3) employing anaerobic metabolism. Neoeione moniliformis was originally introduced as Eione moniliformis, however, the genus Eione Tate, 1859 is a junior homonym of Eione Rafinesque, 1814. This led to the transfer of Eione moniliformis to Parataenidium. Through careful examination and three-dimensional characterization of topotypes, the transfer to Parataenidium moniliformis is demonstrated herein to be problematic, as Parataenidium refers to primarily horizontal burrows with two distinct layers and Eione moniliformis is composed of one distinct level. As such, the new ichnogenus Neoeione is created to accommodate Neoeione moniliformis.

Development and Optimization of Four-dimensional Magnetic Resonance Imaging (4D-MRI) for Radiation Therapy

A tenet of modern radiotherapy (RT) is to identify the treatment target accurately, following which the high-dose treatment volume may be expanded into the surrounding tissues in order to create the clinical and planning target volumes. Respiratory motion can induce errors in target volume delineation and dose delivery in radiation therapy for thoracic and abdominal cancers. Historically, radiotherapy treatment planning in the thoracic and abdominal regions has used 2D or 3D images acquired under uncoached free-breathing conditions, irrespective of whether the target tumor is moving or not. Once the gross target volume has been delineated, standard margins are commonly added in order to account for motion. However, the generic margins do not usually take the target motion trajectory into consideration. That may lead to under- or over-estimate motion with subsequent risk of missing the target during treatment or irradiating excessive normal tissue. That introduces systematic errors into treatment planning and delivery. In clinical practice, four-dimensional (4D) imaging has been popular in For RT motion management. It provides temporal information about tumor and organ at risk motion, and it permits patient-specific treatment planning. The most common contemporary imaging technique for identifying tumor motion is 4D computed tomography (4D-CT). However, CT has poor soft tissue contrast and it induce ionizing radiation hazard. In the last decade, 4D magnetic resonance imaging (4D-MRI) has become an emerging tool to image respiratory motion, especially in the abdomen, because of the superior soft-tissue contrast. Recently, several 4D-MRI techniques have been proposed, including prospective and retrospective approaches. Nevertheless, 4D-MRI techniques are faced with several challenges: 1) suboptimal and inconsistent tumor contrast with large inter-patient variation; 2) relatively low temporal-spatial resolution; 3) it lacks a reliable respiratory surrogate. In this research work, novel 4D-MRI techniques applying MRI weightings that was not used in existing 4D-MRI techniques, including T2/T1-weighted, T2-weighted and Diffusion-weighted MRI were investigated. A result-driven phase retrospective sorting method was proposed, and it was applied to image space as well as k-space of MR imaging. Novel image-based respiratory surrogates were developed, improved and evaluated.