Computation of an integral basis of a quartic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Motion analysis in terms of wireless video capsule endoscopy

El treball presentat suposa una visió general de l'"Endoscopia amb Càpsula de Vídeo Wireless" i la inspecció de sequències de contraccions intestinals amb les últimes tecnologies de visió per computador. Després de la observació preliminar dels fonaments mèdics requerits, la aplicació de visió per computador es presenta en aquestos termes. En essència, aquest treball proveïx una exhaustiva selecció, descripció i avaluació de cert conjunt de mètodes de processament d'imatges respecte a l'anàlisi de moviment, en el entorn de seqüències d'imatges preses amb una càpsula endoscòpica. Finalment, es presenta una aplicació de software per configurar i emprar de forma ràpida i fàcil un entorn experimental.

Computation of an integral basis of quartic number field

"Vegeu el resum a l'inici del document del fitxer ajunt."

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Factors Affecting the Financial Success of Motion Pictures: What is the Role of Star Power?

In the mid-1940s, American film industry was on its way up to its golden era as studios started mass-producing iconic feature films. The escalating increase in popularity of Hollywood stars was actively suggested for its direct links to box office success by academics. Using data collected in 2007, this paper carries out an empirical investigation on how different factors, including star power, affect the revenue of ‘home-run’ movies in Hollywood. Due to the subjective nature of star power, two different approaches were used: (1) number of nominations and wins of Academy Awards by the key players, and (2) average lifetime gross revenue of films involving the key players preceding the sample year. It is found that number of Academy awards nominations and wins was not statistically significant in generating box office revenue, whereas star power based on the second approach was statistically significant. Other significant factors were critics’ reviews, screen coverage and top distributor, while number of Academy awards, MPAA-rating, seasonality, being a sequel and popular genre were not statistically significant.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Intravoxel incoherent motion perfusion imaging in acute stroke: initial clinical experience.

INTRODUCTION: Intravoxel incoherent motion (IVIM) imaging is an MRI perfusion technique that uses a diffusion-weighted sequence with multiple b values and a bi-compartmental signal model to measure the so-called pseudo-diffusion of blood caused by its passage through the microvascular network. The goal of the current study was to assess the feasibility of IVIM perfusion fraction imaging in patients with acute stroke. METHODS: Images were collected in 17 patients with acute stroke. Exclusion criteria were onset of symptoms to imaging >5 days, hemorrhagic transformation, infratentorial lesions, small lesions <0.5 cm in minimal diameter and hemodynamic instability. IVIM imaging was performed at 3 T, using a standard spin-echo Stejskal-Tanner pulsed gradients diffusion-weighted sequence, using 16 b values from 0 to 900 s/mm(2). Image quality was assessed by two radiologists, and quantitative analysis was performed in regions of interest placed in the stroke area, defined by thresholding the apparent diffusion coefficient maps, as well as in the contralateral region. RESULTS: IVIM perfusion fraction maps showed an area of decreased perfusion fraction f in the region of decreased apparent diffusion coefficient. Quantitative analysis showed a statistically significant decrease in both IVIM perfusion fraction f (0.026 ± 0.019 vs. 0.056 ± 0.025, p = 2.2 · 10(-6)) and diffusion coefficient D compared with the contralateral side (3.9 ± 0.79 · 10(-4) vs. 7.5 ± 0.86 · 10(-4) mm(2)/s, p = 1.3 · 10(-20)). CONCLUSION: IVIM perfusion fraction imaging is feasible in acute stroke. IVIM perfusion fraction is significantly reduced in the visible infarct. Further studies should evaluate the potential for IVIM to predict clinical outcome and treatment response.

Motion compensation strategies in magnetic resonance imaging.

Image quality in magnetic resonance imaging (MRI) is considerably affected by motion. Therefore, motion is one of the most common sources of artifacts in contemporary cardiovascular MRI. Such artifacts in turn may easily lead to misinterpretations in the images and a subsequent loss in diagnostic quality. Hence, there is considerable research interest in strategies that help to overcome these limitations at minimal cost in time, spatial resolution, temporal resolution, and signal-to-noise ratio. This review summarizes and discusses the three principal sources of motion: the beating heart, the breathing lungs, and bulk patient movement. This is followed by a comprehensive overview of commonly used compensation strategies for these different types of motion. Finally, a summary and an outlook are provided.

Head motion detection using FID navigators.

This work explores a concept for motion detection in brain MR examinations using high channel-count RF coil arrays. It applies ultrashort (<100 μsec) free induction decay signals, making use of the knowledge that motion induces variations in these signals when compared to a reference free induction decay signal. As a proof-of-concept, the method was implemented in a standard structural MRI sequence. The stability of the free induction decay-signal was verified in phantom experiments. Human experiments demonstrated that the observed variations in the navigator data provide a sensitive measure for detection of relevant and common subject motion patterns. The proposed methodology provides a means to monitor subject motion throughout a MRI scan while causing little or no impact on the sequence timing and image contrast. It could hence complement available motion detection and correction methods, thus further reducing motion sensitivity in MR applications.

Functional mapping of the human visual cortex with intravoxel incoherent motion MRI.

Functional imaging with intravoxel incoherent motion (IVIM) magnetic resonance imaging (MRI) is demonstrated. Images were acquired at 3 Tesla using a standard Stejskal-Tanner diffusion-weighted echo-planar imaging sequence with multiple b-values. Cerebro-spinal fluid signal, which is highly incoherent, was suppressed with an inversion recovery preparation pulse. IVIM microvascular perfusion parameters were calculated according to a two-compartment (vascular and non-vascular) diffusion model. The results obtained in 8 healthy human volunteers during visual stimulation are presented. The IVIM blood flow related parameter fD* increased 170% during stimulation in the visual cortex, and 70% in the underlying white matter.

Quantitative Measurement of Brain Perfusion with Intravoxel Incoherent Motion MR Imaging.

Purpose: To evaluate the sensitivity of the perfusion parameters derived from Intravoxel Incoherent Motion (IVIM) MR imaging to hypercapnia-induced vasodilatation and hyperoxygenation-induced vasoconstriction in the human brain. Materials and Methods: This study was approved by the local ethics committee and informed consent was obtained from all participants. Images were acquired with a standard pulsed-gradient spin-echo sequence (Stejskal-Tanner) in a clinical 3-T system by using 16 b values ranging from 0 to 900 sec/mm(2). Seven healthy volunteers were examined while they inhaled four different gas mixtures known to modify brain perfusion (pure oxygen, ambient air, 5% CO(2) in ambient air, and 8% CO(2) in ambient air). Diffusion coefficient (D), pseudodiffusion coefficient (D*), perfusion fraction (f), and blood flow-related parameter (fD*) maps were calculated on the basis of the IVIM biexponential model, and the parametric maps were compared among the four different gas mixtures. Paired, one-tailed Student t tests were performed to assess for statistically significant differences. Results: Signal decay curves were biexponential in the brain parenchyma of all volunteers. When compared with inhaled ambient air, the IVIM perfusion parameters D*, f, and fD* increased as the concentration of inhaled CO(2) was increased (for the entire brain, P = .01 for f, D*, and fD* for CO(2) 5%; P = .02 for f, and P = .01 for D* and fD* for CO(2) 8%), and a trend toward a reduction was observed when participants inhaled pure oxygen (although P > .05). D remained globally stable. Conclusion: The IVIM perfusion parameters were reactive to hyperoxygenation-induced vasoconstriction and hypercapnia-induced vasodilatation. Accordingly, IVIM imaging was found to be a valid and promising method to quantify brain perfusion in humans. © RSNA, 2012.