Accurate and efficient spin integration for particle accelerators

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.Comment: 43 pages, 17 figure

Quasi-Splines and their moduli

We study what we call quasi-spline sheaves over locally Noetherian schemes. This is done with the intention of considering splines from the point of view of moduli theory. In other words, we study the way in which certain objects that arise in the theory of splines can be made to depend on parameters. In addition to quasi-spline sheaves, we treat ideal difference-conditions, and individual quasi- splines. Under certain hypotheses each of these types of objects admits a fine moduli scheme. The moduli of quasi-spline sheaves is proper, and there is a natural compactification of the moduli of ideal difference-conditions. We include some speculation on the uses of these moduli in the theory of splines and topology, and an appendix with a treatment of the Billera-Rose homogenization in scheme theoretic language

Exploring a search for long-duration transient gravitational waves associated with magnetar bursts

Soft gamma repeaters and anomalous X-ray pulsars are thought to be magnetars, neutron stars with strong magnetic fields of order $\mathord{\sim} 10^{13}$--$10^{15} \, \mathrm{gauss}$. These objects emit intermittent bursts of hard X-rays and soft gamma rays. Quasiperiodic oscillations in the X-ray tails of giant flares imply the existence of neutron star oscillation modes which could emit gravitational waves powered by the magnetar's magnetic energy reservoir. We describe a method to search for transient gravitational-wave signals associated with magnetar bursts with durations of 10s to 1000s of seconds. The sensitivity of this method is estimated by adding simulated waveforms to data from the sixth science run of Laser Interferometer Gravitational-wave Observatory (LIGO). We find a search sensitivity in terms of the root sum square strain amplitude of $h_{\mathrm{rss}} = 1.3 \times 10^{-21} \, \mathrm{Hz}^{-1/2}$ for a half sine-Gaussian waveform with a central frequency $f_0 = 150 \, \mathrm{Hz}$ and a characteristic time $\tau = 400 \, \mathrm{s}$. This corresponds to a gravitational wave energy of $E_{\mathrm{GW}} = 4.3 \times 10^{46} \, \mathrm{erg}$, the same order of magnitude as the 2004 giant flare which had an estimated electromagnetic energy of $E_{\mathrm{EM}} = \mathord{\sim} 1.7 \times 10^{46} (d/ 8.7 \, \mathrm{kpc})^2 \, \mathrm{erg}$, where $d$ is the distance to SGR 1806-20. We present an extrapolation of these results to Advanced LIGO, estimating a sensitivity to a gravitational wave energy of $E_{\mathrm{GW}} = 3.2 \times 10^{43} \, \mathrm{erg}$ for a magnetar at a distance of $1.6 \, \mathrm{kpc}$. These results suggest this search method can probe significantly below the energy budgets for magnetar burst emission mechanisms such as crust cracking and hydrodynamic deformation

Métodos de reconstrucción en dominio temporal para tomografía por transmisión de ultrasonidos

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Atómica, Molecular y Nuclear, leída el 06-06-2017Breast cancer (BC) is the leading cause of cancer-related death for women in Europe, and the second one after lung cancer in the US [World Cancer Report, 2008]. Early detection is very important for the survival rate of BC, because the smaller the local extension of the neoplasia, the better the output of the surgical treatments employed. Besides, early detection increases the possibility of preserving the breast and decreases the probability of needing more invasive treatments [Secretaría de Salud, 2007, Alteri et al., 2011]. Mammography is currently the standard procedure employed for breast screening programs around the world. Nevertheless, its efficiency has been questioned lately because: (i) it generates many abnormal findings not related to cancer, (ii) it requires irradiating the patient and (iii) it has low specificity with dense breasts [Santen and Mansel, 2005]. Consequently, complementary techniques to mammography are being proposed to improve the detection and characterization of BC. Among these techniques, is the Ultrasound Computed Tomography (USCT), in reflection mode (which provides qualitative maps with the concentration of scatterers in the tissue), and transmission mode (which provides quantitative maps of the sound speed (SS) and the acoustic attenuation (AA) of the tissues). The images provided by the transmission modality have been proposed for BC detection as they can improve the detectability of malignancies in the breast [Mast, 2000, Duric et al., 2009]...El cáncer de mama (CM) es el cáncer más mortal entre las mujeres europeas, y el segundo más común en Estados Unidos [World Cancer Report, 2008]. La detección temprana es un factor que condiciona en gran medida la tasa de supervivencia a esta enfermedad, ya que a menor tamaño de la neoplasia detectada, mejores resultados pueden esperarse para los tratamientos quirúrgicos que se realicen. Además, la detección temprana aumenta la posibilidad de conservar la mama después de la cirugía y disminuye la necesidad de emplear otros tratamientos más invasivos[Secretaría de Salud, 2007, Alteri et al., 2011]. La mamografía es actualmente el procedimiento estándar que se emplea para el cribado del CM. Sin embargo, en los últimas años su eficiencia está siendo muy cuestionada por varios factores: (i) alta tasa de falsos positivos, (ii) requiere la irradiación del paciente y (iii) baja especificidad en mamas densas 2. Debido a lo anterior, para mejorar la detección y caracterización del CM se han propuesto varias técnicas complementarias. Entre ellas está la tomografía ultrasónica (TU), que es una técnica en desarrollo que presenta dos modalidades principales: la reflexión (proporciona mapas cualitativos de la concentración de dispersores en el tejido) y la transmisión (proporciona mapas cuantitativos de la velocidad y atenuación del sonido en el tejido). Los mapas del modo transmisión han sido propuestos como una eficiente alternativa, libre de radiación, para la detección del CM, ya que proporcionan alto contraste y especificidad [Mast, 2000, Duric et al., 2009]...Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu

Towards a High Quality Real-Time Graphics Pipeline

Modern graphics hardware pipelines create photorealistic images with high geometric complexity in real time. The quality is constantly improving and advanced techniques from feature film visual effects, such as high dynamic range images and support for higher-order surface primitives, have recently been adopted. Visual effect techniques have large computational costs and significant memory bandwidth usage. In this thesis, we identify three problem areas and propose new algorithms that increase the performance of a set of computer graphics techniques. Our main focus is on efficient algorithms for the real-time graphics pipeline, but parts of our research are equally applicable to offline rendering. Our first focus is texture compression, which is a technique to reduce the memory bandwidth usage. The core idea is to store images in small compressed blocks which are sent over the memory bus and are decompressed on-the-fly when accessed. We present compression algorithms for two types of texture formats. High dynamic range images capture environment lighting with luminance differences over a wide intensity range. Normal maps store perturbation vectors for local surface normals, and give the illusion of high geometric surface detail. Our compression formats are tailored to these texture types and have compression ratios of 6:1, high visual fidelity, and low-cost decompression logic. Our second focus is tessellation culling. Culling is a commonly used technique in computer graphics for removing work that does not contribute to the final image, such as completely hidden geometry. By discarding rendering primitives from further processing, substantial arithmetic computations and memory bandwidth can be saved. Modern graphics processing units include flexible tessellation stages, where rendering primitives are subdivided for increased geometric detail. Images with highly detailed models can be synthesized, but the incurred cost is significant. We have devised a simple remapping technique that allowsfor better tessellation distribution in screen space. Furthermore, we present programmable tessellation culling, where bounding volumes for displaced geometry are computed and used to conservatively test if a primitive can be discarded before tessellation. We introduce a general tessellation culling framework, and an optimized algorithm for rendering of displaced Bézier patches, which is expected to be a common use case for graphics hardware tessellation. Our third and final focus is forward-looking, and relates to efficient algorithms for stochastic rasterization, a rendering technique where camera effects such as depth of field and motion blur can be faithfully simulated. We extend a graphics pipeline with stochastic rasterization in spatio-temporal space and show that stochastic motion blur can be rendered with rather modest pipeline modifications. Furthermore, backface culling algorithms for motion blur and depth of field rendering are presented, which are directly applicable to stochastic rasterization. Hopefully, our work in this field brings us closer to high quality real-time stochastic rendering

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds

For data given on a nonlinear space, like angles, symmetric positive matrices, the sphere, or the hyperbolic space, there is often enough structure to form a Riemannian manifold. We present the Julia package Manifolds.jl, providing a fast and easy to use library of Riemannian manifolds and Lie groups. We introduce a common interface, available in ManifoldsBase.jl, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using B\'ezier splines, an optimization task on manifolds, and a principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms existing packages in Matlab or Python by several orders of magnitude and is about twice as fast as a comparable package implemented in C++

Weak biases emerging from vocal tract anatomy shape the repeated transmission of vowels

Linguistic diversity is affected by multiple factors, but it is usually assumed that variation in the anatomy of our speech organs plays no explanatory role. Here we use realistic computer models of the human speech organs to test whether inter-individual and inter-group variation in the shape of the hard palate (the bony roof of the mouth) affects acoustics of speech sounds. Based on 107 midsagittal MRI scans of the hard palate of human participants, we modelled with high accuracy the articulation of a set of five cross-linguistically representative vowels by agents learning to produce speech sounds. We found that different hard palate shapes result in subtle differences in the acoustics and articulatory strategies of the produced vowels, and that these individual-level speech idiosyncrasies are amplified by the repeated transmission of language across generations. Therefore, we suggest that, besides culture and environment, quantitative biological variation can be amplified, also influencing language