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Andrews and Sellers recently initiated the study of arithmetic properties of Fishburn numbers. In this paper, we prove prime power congruences for generalized Fishburn numbers. These numbers are the coefficients in the $1-q$ expansion of the Kontsevich-Zagier series $\mathscr{F}_{t}(q)$ for the torus knots $T(3,2^t)$, $t \geq 2$. The proof uses a strong divisibility result of Ahlgren, Kim and Lovejoy and a new "strange identity" for $\mathscr{F}_{t}(q)$., 13 pages, to appear in the Journal of Combinatorial Theory, Series A

The contribution of this paper is to develop and analyze a new wavelet-based regularized restoration method for noise removal in photon limited imagery. This new framework presents the two main following advantages: (1) it assigns a new value to the non-significant wavelet coefficients which reduces artifacts and enables the incorporation of realistic prior information into the estimation process and (2) it is based on a local detection process with a measure of the significance of the detected structures. Its potential to improve nuclear medicine imaging is examined.

In this short communication a non-linear Wiener filtering is obtained from a Bayesian approach of the probability density function modelled as a Gaussian mixture. Its application on the wavelet denoising leads to excellent results.

We determine in this paper the general expression of the probability density function of the wavelet coefficient for a Poisson noise. We then examine the special case of the Haar wavelet for which we give threshold tables enabling the reader to process his own data.

Smoking habits did not influence either the risk of any form of endometriosis (superficial peritoneal endometriosis, ovarian endometriomas, and deep infiltrating endometriosis) and did not correlate with the revised American Fertility Society stages or scores.

A review of methods used for deriving seafloor reflectance and water diffuse attenuation form remotely sensed data is conducted. Emphasis is made on inverse methods applied to remote sensing of ocean properties. Then an inverse scheme for the retrieval of optically active components in coastal shallow waters is described and validated through simulation. The proposed method is based on a synthetic reflectance database and an optimization scheme. A sensitivity analysis is performed. It shows that the method is robust, even when applied to extreme environmental conditions, given that the database covers the optical properties of the water body under consideration.

A collaboration between the Observatoire de la Cote d'Azur (OCA) and the Centre National d'Etudes Spatiales (CNES) started in 1996 for detecting optically faint sources close to the geostationary ring using the OCA Schmidt camera. After a first approach based on photographic films we have installed a 2048 × 2048 CCD camera at the focus of the telescope. An automated analysis method was developed. After identifying all stellar trails on the CCD frames we substract them after a suitable modelization. The detection of the remaining objects takes into account the noise variations due to the model defects. For each CCD frame about two hundred point-like objects are identified. The detection of possible space objects is achieved by matching the lists of candidates obtained on three or more successive images. Few objects are observed at a limiting magnitude around 20. We determine their approximate orbits in order to allow follow up observations for each object. A software allowing the user to process the images just after the acquisition has been developed. A one year observational campaign is foreseen in the near future.

Image fusion techniques are increasingly applied to astronomical images in order to improve sensitivity or to compare images. We discuss in this paper the ability of multiscale transforms for many applications: geometrical and photometrical registrations, co-addition and compression. A strategy for multiscale image fusion is derived.

We have implemented a multiscale vision model based on the wavelet transform to analyse field astronomical images. The discrete transform is performed by the a trous algorithm. The vision model is based on the notion of the significant structures. We identify the pixels of the wavelet transform space (WTS) associated with the objects. At each scale a region labelling is carried out. An interscale connectivity graph is then established. In accordance with some rules that permit false detections to be removed, the objects and their sub-objects are identified. They define respectively trees and sub-trees in the graph. So, the identification of the WTS pixels of the tree related to a given object leads to the reconstruction of its image by the conjugate gradient method. The model has been tested successfully on astronomical images which shows that complex structures are better analysed than using usual astronomical vision models.

A wide-fleld astronomical image is often considered as a set of quasi point-like sources spread on a slow-varying backgound. With this model, the image is described as a set of connected flelds. We have to code the fleld positions, the fleld boundaries and their pixel values. It exists difierent methods for coding this information, they are mainly connected to the Mathematical Morphology. The flelds may be coded from their contours, their binary skeletons or the grey-tone ones. On difierent examples, we show that the morphological skeleton transformation in general gives us the best results. The H-transform is a two-dimensional generalization of the Haar transform, a typical wavelet transform. It is to-day often used for compressing astronomical images. Blocking efiects appear in the restored image. The quality of the restoration is improved by introducing in the inverse H-transform scheme an a priori knowledge on the solution which consists to choose the smoothest image at each scale. These two difierent approaches lead to high compression rates on classical astronomical images. In fact, the images are very difierently described. With the morphological methods, the highest compression rates are obtained if the images is composed only of small point-like sources, while the wavelet transform is well adapted to the compression of images with information at difierent scales. So the best compression technique is directly connected to the image modelling. The use of compression methods depends also of the further application. A perfect solution does not exist for image compression, we must take into account the image texture and the futur use.

The analysis of the sky shows many kinds of hierarchically distributed objects. We have introduced a multiscale vision model based on the wavelet transform. The discrete transform is performed by the a trous algorithm which furnishes an isotropic vision, with a unique wavelet function. The vision model is based on the notion of the significant structures. We identify the pixels of the wavelet transform space (WTS) we can attribute to the objects. At each scale a region labelling is done. An interscale connectivity graph is then established. Connected trees are identified from the preceding graph. An object is generally associated to a subtree built from this graph. The identification of WTS pixels related to a given object leads to reconstructing an image by partial restoration algorithms. The object properties are extracted from the restored image. The main difficulty lies in the object reconstruction knowing the wavelet coefficients in the volume where the object is defined. It is a classical inverse problem. We choose to solve it using iterative algorithms. These algorithms give correct restored images, as we show on different examples, without or with adding a Gaussian noise. The influence of close objects can be partially removed.

The notion of a multiresolution support is introduced. This is a sequence of Boolean images related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. Algorithmic details, and a range of practical examples, illustrate this approach.

Introduction et objectifs Cancers Pro Doc et Cancers Pro Actu sont deux outils documentaires sur la prevention des cancers professionnels, mis en place en 2013 par l’Institut national du cancer (INCa) et ses partenaires, et qui comptent, fin 2015, plus de 1200 abonnes. Apres ces trois ans d’existence, le comite editorial a souhaite realiser une enquete aupres des abonnes pour evaluer la pertinence et l’utilisation de ces deux outils et permettre d’identifier des pistes d’amelioration. Ces deux outils ont pour objectif de faciliter la recherche documentaire de l’ensemble des professionnels de la sante au travail et de contribuer a une diffusion plus large des informations parues dans ce domaine. Cancers Pro Actu, bulletin de veille trimestriel, presente une selection d’outils et de supports d’aide a la pratique recemment parus et accessibles gratuitement sur Internet. Cancers Pro Doc est une base de ressources documentaires qui repertorie les documents perennes de Cancers Pro Actu et dispose d’un moteur de recherche avancee. Methode et resultats attendus La communication presentera les premiers enseignements d’une enquete de satisfaction qui sera realisee durant le premier semestre 2016 aupres des abonnes de Cancers Pro Actu et des utilisateurs de Cancers Pro Doc. L’enquete s’appuiera sur un questionnaire en ligne, puis sur des entretiens plus approfondis avec des professionnels volontaires. Par ailleurs, les donnees de consultation du bulletin de veille et du site internet seront analysees. Nous disposerons ainsi de donnees concernant les habitudes de lecture des utilisateurs, leurs pratiques en matiere de recherches documentaires et leurs perceptions vis-a-vis des outils mis a disposition. Conclusion L’ensemble des resultats collectes permettra d’identifier les evolutions necessaires pour ameliorer Cancers Pro Doc et Cancers Pro Actu et repondre au mieux aux attentes des abonnes et des lecteurs potentiels. Cette demarche s’integre dans une reflexion initiee en 2010 par l’INCa et un ensemble d’acteurs de la sante au travail sur la circulation de l’information sur la prevention des cancers professionnels et les possibilites de l’ameliorer.

We present a parallel algorithm which allows to recognize rapidly structures in a 3-dimensional set of discrete data points resulting from numerical experiments, and to study their morphological properties. The algorithm consists of two main steps: (1) wavelet analysis in order to separate those data points which belong to structures from uniformly distributed background points, and (2) segmentation analysis in order to label individual structures and their corresponding data points. Parameters which characterize the morphology of these structures may then be extracted easily. The fast parallel implementation on a Connection Machine CM-200 makes the algorithm interesting for other areas in computational physics which require a method for morphological comparisons. The algorithm is illustrated by an example in the field of cosmology for studying the formation of the Large Scale Structure in the Universe. This analysis allows to distinguish clearly qualitatively as well as quantitatively between two models which respectively favour filamentary or clustered structures.

The wavelet transform gives information in both spatial and frequency domains and is a very useful tool for describing the hierarchical structures. A new approach for filtering based on the wavelet transform is presented in this paper, and several algorithms are proposed. A criterion of quality, which takes into account the resolution, is used to compare these algorithms. We show that deconvolution can be done using filtered wavelet coefficients. By computing the wavelet from the point spread function, we find a new transform algorithm and a reconstruction method related to it.

Extended astronomical objects are irregular structures for which models can not be easily derived from analytical functions. The fractal and multifractal sets furnish a conceptual framework to this kind of objects. Studies of fractal sets led to the use of the Wavelet Transform which allows us to analyse a function both in the spatial and in the frequential spaces. We applied this analyzing method on catalogues of galaxies, in order to get some new information on the heterogeneity of the Universe. We found that the distribution of galaxies shows hierarchical clustering along the whole range of scales. In fact, all the celestial extended objects, nebulae, planetary nebulae, galaxies, etc. show hierachized structures. The wavelet transform leads to introduce the concept of Hierarchical Statistical Models . After a definition of the continuous wavelet transform, the algorithms which furnish the discrete transform are described. We specify their links with the concept of hierarchical models. Some applications to classical image analysis problems are given: filtering, restoration, matching, detection etc., In conclusion we discuss on how this new vision model could improve our approach of the description of astronomical sources, and especially the Universe.

Huang, L. and A. Bijaoui. An efficient image compression algorithm without distortion, Pattern Recognition Letters 12 (1991) 69–72. We present in this paper an efficient image compression algorithm without distortion. It is based on a special iterative central prediction method with a hierarchic 4-bit code. By applying this method to some hydrodynamic simulation images, high compression ratios have been obtained.

Objectif L’objectif de notre etude est d’evaluer le retentissement des injections sous-tenoniennes d’acetonide de triamcinolone sur la pression intra-oculaire. Materiels et Methodes Il s’agit d’une etude prospective – retrospective. Tous les patients ayant beneficie d’une injection sous-tenonienne de 40 mg d’acetonide de triamcinolone entre le 3 decembre 2004 et le 2 decembre 2005, ont ete inclus. Les donnees analysees etaient l’âge du patient, le sexe, l’indication, les antecedents d’hypertonie oculaire ou de glaucome, le nombre d’injections realisees, la mesure de la pression intra-oculaire aux deux yeux avant injection, puis a J8, M1, M3 et M6. La presence d’un reflux lors de l’injection et l’utilisation d’un traitement hypotonisant au cours de la periode analysee ont ete notees. Resultats Cent vingt-sept patients ont ete inclus. La pression intra-oculaire moyenne du cote injecte a augmente au cours des trois mois suivant l’injection, puis diminue a 6 mois. 40,16 % des patients ont presente une elevation de pression intra-oculaire superieure ou egale a 5 mmHg et 11 % une elevation de la pression intra-oculaire superieure ou egale a 10 mmHg. 52,76 % des patients ont presente un reflux lors de l’injection et ces patients avaient plus frequemment une hypertonie oculaire. En cas d’hypertonie, une reponse au traitement par collyre topique a tou-jours ete obtenue. Discussion Une hypertonie oculaire moderee et facile a gerer est frequente apres injection sous-tenonienne d’acetonide de triamcinolone (40,16 %). La presence d’un reflux semble etre un facteur favorisant cette hypertonie oculaire, probablement en « baignant » abondamment le segment anterieur et le trabeculum de corticoide par diffusion sous conjonctivale. Cette complication frequente (52,76 %) est tres genante car en plus du risque de survenue d’une hypertonie elle ne permet pas d’administrer la dose de produit souhaitee. Conclusion La voie d’injection sous-tenonienne d’acetonide de triamcinolone entraine frequemment une hypertonie oculaire moderee. C’est une voie d’administration facile et denuee d’effets secondaires graves. Elle necessite cependant d’etre amelioree afin d’eviter le reflux et permettre un meilleur rapport benefice (dose)/risque (HTO).

Introduction Etude prospective visant a comparer les resultats visuels fonctionnels et la qualite de vision de deux types d’implants multifocaux : l’implant en acrylique hydrophobe refractif multi zones, et l’implant en acrylique hydrophobe refractif et diffractif apodise. Objectifs et Methodes 36 patients ont ete operes d’une cataracte unilaterale ou bilaterale par phacoemulsification et ont ete implantes de facon aleatoire avec un implant en acrylique hydrophobe refractif multi zones ou avec un implant en acrylique hydrophobe refractif et diffractif apodise. Chaque patient a beneficie pour les deux yeux du meme type d’implant. L’absence de pathologie oculaire et d’astigmatisme corneen superieur a 1 dioptrie a ete verifiee par un examen clinique preoperatoire complet. Le resultat visuel a ete evalue dans les deux groupes (groupe 1 : implant en acrylique hydrophobe refractif multi zones ; groupe 2 : implant en acrylique hydrophobe refractif et diffractif apodise) entre 1 et 3 mois apres l’implantation. La qualite de vision a ete exploree par un questionnaire centre sur l’index de satisfaction des patients, l’existence de halos et d’eblouissement en vision nocturne. Resultats 36 patients (18 du groupe 1 et 18 du groupe 2) âges de 32 a 85 ans avec une moyenne de 66 ans pour le groupe 1 et 69 ans pour le groupe 2, ont participe a notre etude. 65 % des patients du groupe 1 ont recupere une acuite visuelle de loin sans correction d’au moins 9/10 contre 85 % pour ceux du groupe 2. 81 % des patients du groupe 1 ont recupere une acuite visuelle de pres sans correction d’au moins Parinaud 3 contre 84 % pour ceux du groupe 2. L’implant en acrylique hydrophobe refractif multi zones s’est montre legerement plus inducteur d’eblouissements et de halos que l’implant en acrylique hydrophobe refractif et diffractif apodise, sans pour autant que les patients ne signalent un reel inconfort avec ces effets secondaires (20 % de plaintes dans le groupe 1, 11 % dans le groupe 2). 100 % des patients du groupe 1 et 2 ont ete satisfaits du resultat global. Discussion En raison de ces effets secondaires, une information eclairee aux patients candidats est indispensable. Les meilleurs candidats pour ce type de chirurgie sont les emmetropes et les petits hypermetropes. Il serait interessant d’evaluer ces implants dans des conditions extremes (grandes ametropies, astigmatismes corneens superieurs a 1 dioptrie). Conclusion La multifocalite dans le traitement chirurgical de la cataracte est un nouveau concept en phase d’expansion et seduisant en termes de satisfaction des patients, mais il faut en preciser les avantages et les limites.

Introduction Nous presentons un cas clinique de diplopie verticale et oblique binoculaire secondaire a une atteinte ischemique du tronc cerebral. L’origine traumatique est discutee. Objectifs et Methodes nous presentons un cas clinique avec une revue de la litterature Observation Il s’agit d’une patiente de 34 ans qui a presente un an auparavant un traumatisme cervical mineur. Dans la suite de celui-ci, une dissection bilaterale des arteres vertebrales a ete decouverte. Cette observation s’exprimait cliniquement au niveau neurologique par un syndrome de Wallenberg associe a une instabilite chronique emaillee de vertige rotatoire. Sur le plan ophtalmologique elle presentait un down shoot gauche et une limitation secondaire a une atteinte du petit oblique et du droit externe gauche sequellaire d’une atteinte mesencephalique et pontique (respectivement siege de l’origine nucleaire du nerf oculomoteur commun et du nerf abducens). Discussion Cette observation de dissection vertebrale bilaterale chez une jeune femme amene a discuter les etiologies autres que traumatique. En effet, cette patiente presente des antecedents de migraines avec aura visuelle repondant aux criteres de l’Internal Society of Headache, qui doivent faire discuter d’autres causes vasculaires (particulierement emboliques). Ces etiologies sont d’autant plus probables qu’il s’agit d’une femme jeune sous contraceptif oral et presentant des migraines avec auras visuelles frequentes (revue de la litterature). L’origine traumatique evoquee initialement est en effet non prouvee et sans facteur traumatique direct. Les signes cliniques sont d’ailleurs survenus au decours de migraines avec auras visuelles similaires aux episodes migraineux anciens et seulement atypiques par leur duree et les signes associes. Conclusion Nous rappelons l’interet des cephalees sentinelles chez une migraineuse connue avec auras visuelles et sous contraception orale dans le diagnostic des accidents vasculaires ischemiques de la femme jeune.