On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

On the writer identification in old handwritten music scores

Report for the scientific sojourn at the University of Bern, Swiss, from Mars until June 2008. Writer identification consists in determining the writer of a piece of handwriting from a set of writers. Even though an important amount of compositions contains handwritten text in the music scores, the aim of the work is to use only music notation to determine the author. It’s been developed two approaches for writer identification in old handwritten music scores. The methods proposed extract features from every music line, and also features from a texture image of music symbols. First of all, the music sheet is first preprocessed for obtaining a binarized music score without the staff lines. The classification is performed using a k-NN classifier based on Euclidean distance. The proposed method has been tested on a database of old music scores from the 17th to 19th centuries, achieving encouraging identification rates.

Aerotropolis: an aviation-linked space

This paper examines the conditions allowing the formation of aeropolitan areas as large industrial areas with a high concentration of commercial activities in the proximity of selected airports. We assume that firms deliver their production by plane and land competition takes place among service operators, firms and farmers. Service operators supply facilities that firms can absorb. Our framework identifies a unique land equilibrium characterized by the spatial sequence Airport - Industrial park - Rural area (A-I-R). Aerotropolis-type configurations are associated with the level of transport costs and the degree of intensity of facilities. Keywords: aerotropolis; facilities; bid-rent function. JEL Classification Numbers: L29; L90; R14.

Caracterización de materiales en banda W

Para medir los coeficientes de transmisión y reflexión, S21 y S11, de diferentes materiales o muestras planas, se usa un sistema de toma de medidas en espacio libre operando banda W (75 – 110 GHz). Usando estos parámetros, S21 y S11, podemos calcular la permitividad dieléctrica relativa compleja (Er ) y la permeabilidad magnética relativa compleja (μr) mediante un proceso llamado NRW (Nicolson-Ross-Weir). El sistema para medir consiste en dos antenas de bocina, una transmisora y otra receptora, dos espejos con los que obtenemos una onda plana para medir las propiedades del material y un ordenador o dispositivo que calcula los resultados. Este dispositivo requiere de calibración para la obtención de resultados óptimos. Dicho sistema se puede simular de manera ideal con un software llamado ADS (Assistance Design System) para el estudio y comparación de grosores, permitividades dieléctricas relativas y permeabilidades magnéticas relativas de los materiales en función de la frecuencia.

Prefabrication of composite grafts for long-segment tracheal reconstruction.

OBJECTIVE: To investigate the prefabrication of vascularized mucosa-lined composite grafts intended to replace circumferential tracheal defects. DESIGN: Plane grafts composed of ear cartilage and full-thickness oral mucosa were revascularized by the laterothoracic fascia. The use of meshed vs nonmeshed mucosa to improve the epithelial coverage was examined. We also investigated the creation of a vascular bed over the cartilage and the subsequent application of meshed mucosa. Macroscopic aspects, viability, and degree of mucosal lining were analyzed. SUBJECTS: Twenty male New Zealand white rabbits. INTERVENTIONS: Ten animals underwent placement of auricular cartilage under the laterothoracic fascia. Intact (group 1) or meshed mucosa (group 2) was applied over the fascia and protected by a silicone sheet. After 3 weeks, prefabricated grafts were removed for comparison. In 10 other animals, a sheet of perforated cartilage was placed under the laterothoracic fascia. Two weeks later, 5 grafts (group 3) were harvested. The remaining 5 grafts were reopened for mucosal application over the cartilage and revascularized for 3 additional weeks (group 4). RESULTS: Vascularized plane grafts were obtained in all groups. Mucosal lining increased significantly with meshed mucosa (14%-68%; mean, 40%) compared with nonmeshed mucosa (3%-15%; mean, 10%) (P = .008). Induction of a vascular bed over perforated cartilage was achieved, but survival of secondary implanted mucosa was variable. CONCLUSIONS: A reliable technique to prefabricate composite grafts with cartilaginous support and mucosal lining is presented. The use of meshed mucosa significantly improves epithelial coverage.

The feasibility of 350 μm spatial resolution coronary magnetic resonance angiography at 3 T in humans.

PURPOSE: The purposes of this study were to (1) develop a high-resolution 3-T magnetic resonance angiography (MRA) technique with an in-plane resolution approximate to that of multidetector coronary computed tomography (MDCT) and a voxel size of 0.35 × 0.35 × 1.5 mm³ and to (2) investigate the image quality of this technique in healthy participants and preliminarily in patients with known coronary artery disease (CAD). MATERIALS AND METHODS: A 3-T coronary MRA technique optimized for an image acquisition voxel as small as 0.35 × 0.35 × 1.5 mm³ (high-resolution coronary MRA [HRC]) was implemented and the coronary arteries of 22 participants were imaged. These included 11 healthy participants (average age, 28.5 years; 5 men) and 11 participants with CAD (average age, 52.9 years; 5 women) as identified on MDCT. In addition, the 11 healthy participants were imaged using a method with a more common spatial resolution of 0.7 × 1 × 3 mm³ (regular-resolution coronary MRA [RRC]). Qualitative and quantitative comparisons were made between the 2 MRA techniques. RESULTS: Normal vessels and CAD lesions were successfully depicted at 350 × 350 μm² in-plane resolution with adequate signal-to-noise ratio (SNR) and contrast-to-noise ratio. The CAD findings were consistent among MDCT and HRC. The HRC showed a 47% improvement in sharpness despite a reduction in SNR (by 72%) and in contrast-to-noise ratio (by 86%) compared with the regular-resolution coronary MRA. CONCLUSION: This study, as a first step toward substantial improvement in the resolution of coronary MRA, demonstrates the feasibility of obtaining at 3 T a spatial resolution that approximates that of MDCT. The acquisition in-plane pixel dimensions are as small as 350 × 350 μm² with a 1.5-mm slice thickness. Although SNR is lower, the images have improved sharpness, resulting in image quality that allows qualitative identification of disease sites on MRA consistent with MDCT.

Cardiac rotation and relaxation after anterolateral myocardial infarction.

BACKGROUND: Both systolic and diastolic dysfunction have been observed in patients with anterolateral myocardial infarction. Diastolic dysfunction is related to disturbances in relaxation and diastolic filling. OBJECTIVE: To analyse cardiac rotation, regional shortening and diastolic relaxation in patients with anterolateral infarction. METHODS: Cardiac rotation and relaxation in controls and patients with chronic anterolateral infarction were assessed by myocardial tagging. Myocardial tagging is based on magnetic resonance imaging and allows us to label specific myocardial regions for imaging cardiac motion (rotation, translation and radial displacement). A rectangular grid was placed on the myocardium (basal, equatorial and apical short-axis plane) of each of 18 patients with chronic anterolateral infarction and 13 controls. Cardiac rotation, change in area and shortening of circumference were determined in each case. RESULTS: The left ventricle in controls performs a systolic wringing motion with a clockwise rotation at the base and a counterclockwise rotation at the apex when viewed from the apex. During relaxation a rotational motion in the opposite direction (namely untwisting) can be observed. In patients with anterolateral infarction, there is less systolic rotation at the apex and diastolic untwisting is delayed and prolonged in comparison with controls. In the presence of a left ventricular aneurysm (n = 4) apical rotation is completely lost. There is less shortening of circumference in infarcted and remote regions. CONCLUSIONS: The wringing motion of the myocardium might be an important mechanism involved in maintaining normal cardiac function with minimal expenditure of energy. This mechanism no longer operates in patients with left ventricular aneurysms and operates significantly less than normal in those with anterolateral hypokinaesia. Diastolic untwisting is significantly delayed and prolonged in patients with anterolateral infarction, which could explain the occurrence of diastolic dysfunction in these patients.

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.

Ascending aorta measurements as assessed by ECG-gated multi-detector computed tomography : a pilot study to etablish normative values for transcatheters therapies

Rapport de synthèse : Mesures de l'aorte ascendante par scanner synchronisé au rythme cardiaque: une étude pilote pour établir des valeurs normatives dans le cadre des futures thérapies par transcathéter. Objectif : L'objectif de cette étude est d'établir les valeurs morphométriques normatives de l'aorte ascendante à l'aide de l'angiographie par scanner synchronisé au rythme cardiaque, afin d'aider au développement des futurs traitements par transcathéter. Matériels et méthodes : Chez soixante-dix-sept patients (âgé de 22 à 83 ans, âge moyen: 54,7 ans), une angiographie par scanner synchronisé au rythme cardiaque a été réalisée pour évaluation des vaisseaux coronaires. Les examens ont été revus afin d'étudier l'anatomie de la chambre de chasse du ventricule gauche jusqu'au tronc brachio-céphalique droit. A l'aide de programmes de reconstructions multiplanaires et de segmentation automatique, différents diamètres et longueurs considérés comme importants pour les futurs traitements par transcathéter ont été mesurés. Les valeurs sont exprimées en moyennes, médianes, maximums, minimums, écart-types et en coefficients de variation. Les variations de diamètre de l'aorte ascendante durant le cycle cardiaque ont été aussi considérées. Résultats : Le diamètre moyen de la chambre de chasse du ventricule gauche était de 20.3+/-3.4 mm. Au niveau du sinus coronaire de l'aorte, il était de 34.2+/-4.1 mm et au niveau de la jonction sinotubulaire il était de 29.7+/-3.4 mm. Le diamètre moyen de l'aorte ascendante était de 32.7+/-3.8 mm. Le coefficient de variation de ces mesures variait de 12 à 17%. La distance moyenne entre l'insertion proximale des valvules aortiques et le départ du tronc brachio-céphalique droit était de 92.6+/-11.8 mm. La distance moyenne entre l'insertion proximale des valvules aortiques et l'origine de l'artère coronaire proximale était de 12.1+/-3.7 mm avec un coefficient de variation de 31%. La distance moyenne entre les deux ostia coronaires était de 7.2+/-3.1 mm avec un coefficient de variation de 43%. La longueur moyenne du petit arc de l'aorte ascendante entre l'artère coronaire gauche et le tronc brachio-céphalique droit était de 52.9+/-9.5 mm. La longueur moyenne de la continuité fibreuse entre la valve aortique et la valvule mitrale antérieure était de 14.6+/-3.3 mm avec un coefficient de variation de 23%. L'aire moyenne de la valve aortique était de 582.0+/-131.9 mm2. La variation du diamètre antéro-postérieur et transverse de l'aorte ascendante était respectivement de 8.4% et de 7.3%. Conclusion Il existe d'importantes variations inter-individuelles dans les mesures de l'aorte ascendante avec cependant des variations intra-individuelles faibles durant le cycle cardiaque. De ce fait, une approche personnalisée pour chaque patient est recommandée dans la confection des futures endoprothèses de l'aorte ascendante. Le scanner synchronisé au rythme cardiaque jouera un rôle prépondérant dans le bilan préthérapeutique. Abstract : The aim of this study was to provide an insight into normative values of the ascending aorta in regards to novel endovascular procedures using ECG-gated multi-detector CT angiography. Seventy-seven adult patients without ascending aortic abnormalities were evaluated. Measurements at relevant levels of the aortic root and ascending aorta were obtained. Diameter variations of the ascending aorta during cardiac cycle were also considered. Mean diameters (mm) were as follows: LV outflow tract 20.3+/-3.4, coronary sinus 34.2+/-4.1, sinotubular junction 29.7+-3.4 and mid ascending aorta 32.7+/-3.8 with coefficients of variation (CV) ranging from 12 to 17%. Mean distances (mm) were: from the plane passing through the proximal insertions of the aortic valve cusps to the right brachio-cephalic artery (BCA) 92.6111.8, from the plane passing through the proximal insertions of the aortic valve cusps to the proximal coronary ostium 12.1+/-3.7, and between both coronary ostia 7.2+/-3.1, minimal arc of the ascending aorta from left coronary ostium to right BCA 52.9 X9.5, and the fibrous continuity between the aortic valve and the anterior leaflet of the mitral valve 14.óf3.3, CV 13-43%. Mean aortic valve area was 582+-131.9 mm2. The variations of the antero-posterior and transverse diameters of the ascending aorta during the cardiac cycle were 8.4% and 7.3%, respectively. Results showed large inter-individual variations in diameters and distances but with limited intra-individual variations during the cardiac cycle. A personalized approach for planning endovascular devices must be considered.

Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariableswith some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependenceof a composition with a categorical variable, a colored set of ternary diagrams mightbe a good idea for a first look at the data, but it will fast hide important aspects ifthe composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if theconventional, black-box ilr is used.Thinking on terms of the Euclidean structure of the simplex, we suggest to set upappropriate projections, which on one side show the compositional geometry and on theother side are still comprehensible by a non-expert analyst, readable for all locations andscales of the data. This is e.g. done by defining special balance displays with carefully-selected axes. Following this idea, we need to systematically ask how to display, explore,describe, and test the relation to complementary or explanatory data of categorical, real,ratio or again compositional scales.This contribution shows that it is sufficient to use some basic concepts and very fewadvanced tools from multivariate statistics (principal covariances, multivariate linearmodels, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariateanalysis

Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Relacions estructura-propietat per un conjunt d'hidrocarburs a partir de nous descriptors tridimensionals derivats de la semblança molecular quàntica

En aquest article es defineixen uns nous índexs tridimensionals per a la descripció de les molècules a partir de paràmetres derivats de la Teoria de la Semblança Molecular i de les distàncies euclidianes entre els àtoms i les càrregues atòmiques efectives. Aquests indexs,anomenats 3D, s'han aplicat a l'estudi de les relacions estructura-propietat d'una família d'hidrocarburs, i han demostrat una capacitat de descripció de tres propietats de la família (temperatura d'ebullició, temperatura de fusió i densitat) molt més acurada que quan s'utilitzen els indexs 2D clàssics

Statistical modeling on (α, +∞)

Observations in daily practice are sometimes registered as positive values larger then a given threshold α. The sample space is in this case the interval (α,+∞), α & 0, which can be structured as a real Euclidean space in different ways. This fact opens the door to alternative statistical models depending not only on the assumed distribution function, but also on the metric which is considered as appropriate, i.e. the way differences are measured, and thus variability

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Distributions on the simplex

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties