Smoothness of stabilisers in generic characteristic

Let $R$ be a commutative unital ring. Given a finitely-presented affine $R$-group $G$ acting on a finitely-presented $R$-scheme $X$ of finite type, we show that there is a prime $p_0$ so that for any $R$-algebra $k$ which is a field of characteristic $p > p_0$, the centralisers in $G_k$ of all subsets $U \subseteq X(k)$ are smooth. We prove this using the Lefschetz principle together with careful application of Gr\"{o}bner basis techniques.Comment: 15 page

Smoothed particle magnetohydrodynamic simulations of protostellar outflows with misaligned magnetic field and rotation axes

We have developed a modified form of the equations of smoothed particle magnetohydrodynamics which are stable in the presence of very steep density gradients. Using this formalism, we have performed simulations of the collapse of magnetised molecular cloud cores to form protostars and drive outflows. Our stable formalism allows for smaller sink particles (< 5 AU) than used previously and the investigation of the effect of varying the angle, {\theta}, between the initial field axis and the rotation axis. The nature of the outflows depends strongly on this angle: jet-like outflows are not produced at all when {\theta} > 30{\deg}, and a collimated outflow is not sustained when {\theta} > 10{\deg}. No substantial outflows of any kind are produced when {\theta} > 60{\deg}. This may place constraints on the geometry of the magnetic field in molecular clouds where bipolar outflows are seen.Comment: Accepted for publication in MNRAS, 13 pages, 14 figures. Animations can be found at http://www.astro.ex.ac.uk/people/blewis/research/outflows_misaligned_fields.htm

Monitoring Frequency of Intra‐Fraction Patient Motion Using the ExacTrac System for LINAC‐based SRS Treatments

Purpose: The aim of this study was to investigate the intra‐fractional patient motion using the ExacTrac system in LINAC‐based stereotactic radiosurgery (SRS). Method: A retrospective analysis of 104 SRS patients with kilovoltage image‐guided setup (Brainlab ExacTrac) data was performed. Each patient was imaged pre‐treatment, and at two time points during treatment (1st and 2nd mid‐treatment), and bony anatomy of the skull was used to establish setup error at each time point. The datasets included the translational and rotational setup error, as well as the time period between image acquisitions. After each image acquisition, the patient was repositioned using the calculated shift to correct the setup error. Only translational errors were corrected due to the absence of a 6D treatment table. Setup time and directional shift values were analyzed to determine correlation between shift magnitudes as well as time between acquisitions. Results: The average magnitude translation was 0.64 ± 0.59 mm, 0.79 ± 0.45 mm, and 0.65 ± 0.35 mm for the pre‐treatment, 1st mid‐treatment, and 2nd mid‐treatment imaging time points. The average time from pre‐treatment image acquisition to 1st mid‐treatment image acquisition was 7.98 ± 0.45 min, from 1st to 2nd mid‐treatment image was 4.87 ± 1.96 min. The greatest translation was 3.64 mm, occurring in the pre‐treatment image. No patient had a 1st or 2nd mid‐treatment image with greater than 2 mm magnitude shifts. Conclusion: There was no correlation between patient motion over time, in direction or magnitude, and duration of treatment. The imaging frequency could be reduced to decrease imaging dose and treatment time without significant changes in patient position

Development of the Digital Signal Processing for the Space Weather Probes Version 2 Sensor Using the MATLAB/Simulink Environment

Space Weather Probes (SWP) is an instrument that provides measurements of the plasma environment of the ionosphere. SWP was flown on the Scintillation Prediction Observation Task (SPORT) mission, a joint mission between the United States of America and Brazil. This thesis will develop the digital signal processing (DSP) hardware design for the Space Weather Probes version 2 (SWP2). The data from these instruments will be used to determine the density and temperature of the local plasma, as well as the electric field in the local plasma. This thesis presents the design and testing of the DSP designs for all of the different probes in SWP2. All design and testing was done in the MATLAB/Simulink environment

Molecular Parentage of Radical Species in the Comae of Comets

Understanding the chemical composition of comets is of great interest to the scientific community. In this work, an integral field unit (IFU) spectrograph is used to detect emissions of C2, C3, CH, CN, and NH2. The azimuthal average profile (line integral of the column density as a function of radial distance from the center of the nucleus) is simulated by the Haser model. The Haser model simulates the outgassing and photo-dissociate of molecular species in the coma. In this work, the lifetime of the parent molecule in the photo-dissociation chain is set as a free parameter. The best fit parent lifetimes for observations of comets 4P/Faye, 10P/Tempel 2, and C/2009 P1 Garradd are obtained. The results are compared to parent lifetimes cited in other studies. HCN as a likely dominant parent for CN is eliminated. Constraints on likely parent molecules for C3 and NH2 are discussed

Radiotherapy Response Using Intravoxel Incoherent Motion Magnetic Resonance Imaging in Liver Patients Treated with Stereotactic Body Radiotherapy

Magnetic resonance imaging is utilized as an important tool in radiation oncology for delineation of healthy and cancerous tissues, and evaluating the functionality of those tissues, structures, and organs. Currently, the clinical imaging protocol at Virginia Commonwealth University includes anatomical imaging for tissue and structure delineation, and to observe treatment induced changes. Diffusion weighted imaging (DWI) is also acquired for calculation of apparent diffusion coefficient (ADC) values to provide quantitative information on tissue diffusivity and microstructure. However, anatomical images and ADC values may not display the true extent of changes in tissue. This work seeks to further utilize the capabilities of MRI and expand its role in treatment response monitoring for liver cancer patients treated with stereotactic body radiotherapy (SBRT). To do so, an imaging protocol and image analysis methodology to evaluate treatment changes on pre- and post-treatment image sets was developed. An extension of DWI, termed intravoxel incoherent motion (IVIM) imaging, was utilized to quantitatively assess levels of perfusion and diffusion within the liver and tumor. Acquisition of high-quality diffusion weighted images of the liver necessitated the development of an MR safe respiratory motion management device, which was designed, constructed and evaluated in this work. An imaging protocol was developed providing anatomical and functional images of the liver, acquired under breath hold, utilizing the respiratory motion management device. An IVIM parameter calculation and texture analysis workflow was developed using MATLAB, and applied to acquired data sets from multiple studies, including past clinical cases, investigator, healthy volunteer, and liver cancer patient . Differences in IVIM and texture analysis parameters were investigated for healthy and diseased tissue, and for select dose regions from pre- and post-treatment imaging sessions. Significant differences, at a voxel level, were found between healthy and diseased tissue, and pre- and post-treatment volumes, for multiple parameters, including apparent diffusion coefficient, pure diffusion, and perfusion, as well as for various texture features. Overall, this study showed the potential of IVIM and texture analysis to be used for discriminating between healthy and diseased tissues in the liver, and for indication of treatment response

The World after Fiction:J. M. Coetzee’s The Childhood of Jesus

Opponents of World Literature fear that its advent marks the end of the ‘work of literature’. J. M. Coetzee’s The Childhood of Jesus (2013) presents a world in which the work of literature has indeed been forgotten. Migrants arrive in a new life ‘washed clean’ of the burden of the European tradition. Simón, who dimly recalls the old life, feels that something is missing in the new. He longs for something altogether ‘other’. Might Simón learn from the exceptional child David to perceive the ‘likeness’ in this world? Are we to read Coetzee’s novel like Simón or like David — and with what consequence for our understanding of the work of literature in a time of World Literature