Hauteur | EPFL Graph Search

La hauteur mesure l'étendue de quelque chose selon la verticale. La hauteur prend néanmoins diverses significations suivant le domaine où elle est utilisée. Métrologie En métrologie (science des mesures), la hauteur est la distance verticale entre un point (ou un objet assimilé à un point) et un niveau de référence spécifié. Par extension, c'est aussi la dimension d'un objet, prise dans la direction verticale. Voir Système international d'unités. En altimétrie et en géographie, la hauteur est la distance géométrique entre un point et son projeté sur l'ellipsoïde (selon la normale à cette dernière). La notion de hauteur ne doit pas être confondue avec l'altitude (H) d'un point terrestre, qui se calcule à partir du géoïde (équipotentielle du champ de pesanteur proche du niveau moyen des mers) ou d'un quasi-géoïde selon le type d'altitude utilisé (altitude normale, altitude orthométrique...). Mathématiques Géométrie Hauteur (géométrie) La hauteur est

N-removal optimization by various aeration strategies

Simon Taillard

In order to improve the purification capacity of an aerobic granular sludge, two aeration strategies were designed and tested. The goal was to optimize the nitrogen removal performances via various oxygen patterns in the aeration phase of the reactor cycle. The main process driving theses patterns is that a difference between oxygen concentrations in the reactor will modify the size of the anoxic inner zone of a granule. The first aeration was based on a succession of oxygen peaks (50%DO) and semi anoxic valleys (5%DO). The second was based on a short pulse of oxygen followed by the hermetical isolation of the reactor and a continuous recirculation of the pulse. The objective was to get an n-removal superior to 82%, results of a previous article, and if possible better than 88%, results of a previous experiment in the lab. The succession of oxygenated peaks strategy worked well and gave good results, as the n-removal was increasing with the sludge bed height and time. However, due to laboratories problem and to the shortness of the time-slots available to experiment, the system could not have the time to stabilize and no constant removal value could be found. Therefore, the average n-removal was equal to 69% for 40 days of experimentation, with some peak over 80%. The highest value observed was 88% of n-removal. The recirculation strategy gave unsatisfactory results, actually unexplained. The first recirculation led to the disappearance of high nitrification capacity, giving an n-removal percentage of 48%. The second attempt was worse, as the oxygen concentration started to behave incoherently and over-oxygenated the system. This behavior still lacks a proper explanation and only hypotheses can actually be proposed. Besides these mains results, the surveillance of the sludge in the reactors allowed the discovery of a bias in the evaluation of the suspended biomass measurement. It was explained by the fact that heavier granules tend not to mix well, and therefore the system could not be considered homogenous. The bias was created because measurements were made at different height between the two reactors. In order to remove it, a linear transformation was developed and tested. The first results seem to be consistent, but due to the lack of experimenting time, the working hypothesis could not be deepened. Another bias that was spotted is the possible influence of the operator during the aeration cycle measurement. Three of four off-trend points in the first experiment originated from a cycle measurement. The data set was too small to draw strong conclusions upon the bias. An extended survey of the cycle measurement and their supposed off-trend consequences in previous and future experiments could clarify the situation.

2009

Persistent spatial clusters of high body mass index in a Swiss urban population as revealed by the 5-year GeoCoLaus longitudinal study

Murielle Bochud, Joël Chételat, Idris Guessous, Stéphane Joost, Fred Michel Paccaud

OBJECTIVE Body mass index (BMI) may cluster in space among adults and be spatially dependent. Whether and how BMI clusters evolve over time in a population is currently unknown. We aimed to determine the spatial dependence of BMI and its 5-year evolution in a Swiss general adult urban population, taking into account the neighborhood- and individual-level characteristics. DESIGN Cohort study SETTING Swiss general urban population PARTICIPANTS 6,481 geo-referenced individuals from the CoLaus cohort at baseline (age range 35–74 years, period=2003-2006) and 4,460 at follow-up (period=2009-2012). OUTCOME MEASURES Body weight and height were measured by trained health care professionals with participants standing without shoes in light indoor clothing. BMI was calculated as weight (kg) divided by height squared (m2). Participants were geocoded using their postal address (geographic coordinates of the place of residence). Getis-Ord Gi statistic was used to measure the spatial dependence of BMI values at baseline and its evolution at follow-up. RESULTS BMI was not randomly distributed across the city. At baseline and at follow-up, significant clusters of high versus low BMIs were identified and remained stable during the two periods. These clusters were meaningfully attenuated after adjustment for neighborhood-level income but not individual-level characteristics. Similar results were observed among participants who developed obesity. CONCLUSIONS To our knowledge, this is the first study to report longitudinal changes in BMI clusters in adults from a general population. Spatial clusters of high BMI persisted over a 5-year period and were mainly influenced by neighborhood-level income. ARTICLE SUMMARY STRENGTHS AND LIMITATIONS OF THE STUDY • As far as we know, this is the first study to report the persistence of spatial clusters of high BMI values over a 5-year period in adults from a general population • The observed east to west pattern of BMI clustering fits known socio-economic and ethno-cultural differences distinguishing these opposite regions of the city of Lausanne, Switzerland • A consequence of the social policy applied by the city is likely to fix populations with modest income in subsidized housing located in specific areas • While recruitment methods of the CoLaus study aimed at collecting information on a representative sample of the general population, adult participants and non-participants to the CoLaus study may differ and participation bias cannot be excluded • We considered several individual-level covariates but data on individual income was missing. We used instead the median income of the including city statistical sector.

Bmj Publishing Group2016

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial results in this direction.