Computation of an integral basis of a quartic number field

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Computation of an integral basis of quartic number field

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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.

Some variational problems from image processing

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Generating controlled image sets in cognitive neuroscience research.

The investigation of perceptual and cognitive functions with non-invasive brain imaging methods critically depends on the careful selection of stimuli for use in experiments. For example, it must be verified that any observed effects follow from the parameter of interest (e.g. semantic category) rather than other low-level physical features (e.g. luminance, or spectral properties). Otherwise, interpretation of results is confounded. Often, researchers circumvent this issue by including additional control conditions or tasks, both of which are flawed and also prolong experiments. Here, we present some new approaches for controlling classes of stimuli intended for use in cognitive neuroscience, however these methods can be readily extrapolated to other applications and stimulus modalities. Our approach is comprised of two levels. The first level aims at equalizing individual stimuli in terms of their mean luminance. Each data point in the stimulus is adjusted to a standardized value based on a standard value across the stimulus battery. The second level analyzes two populations of stimuli along their spectral properties (i.e. spatial frequency) using a dissimilarity metric that equals the root mean square of the distance between two populations of objects as a function of spatial frequency along x- and y-dimensions of the image. Randomized permutations are used to obtain a minimal value between the populations to minimize, in a completely data-driven manner, the spectral differences between image sets. While another paper in this issue applies these methods in the case of acoustic stimuli (Aeschlimann et al., Brain Topogr 2008), we illustrate this approach here in detail for complex visual stimuli.

A Survey of Active Learning Algorithms for Supervised Remote Sensing Image Classification

Defining an efficient training set is one of the most delicate phases for the success of remote sensing image classification routines. The complexity of the problem, the limited temporal and financial resources, as well as the high intraclass variance can make an algorithm fail if it is trained with a suboptimal dataset. Active learning aims at building efficient training sets by iteratively improving the model performance through sampling. A user-defined heuristic ranks the unlabeled pixels according to a function of the uncertainty of their class membership and then the user is asked to provide labels for the most uncertain pixels. This paper reviews and tests the main families of active learning algorithms: committee, large margin, and posterior probability-based. For each of them, the most recent advances in the remote sensing community are discussed and some heuristics are detailed and tested. Several challenging remote sensing scenarios are considered, including very high spatial resolution and hyperspectral image classification. Finally, guidelines for choosing the good architecture are provided for new and/or unexperienced user.

MSight: an image analysis software for liquid chromatography-mass spectrometry.

Images obtained from high-throughput mass spectrometry (MS) contain information that remains hidden when looking at a single spectrum at a time. Image processing of liquid chromatography-MS datasets can be extremely useful for quality control, experimental monitoring and knowledge extraction. The importance of imaging in differential analysis of proteomic experiments has already been established through two-dimensional gels and can now be foreseen with MS images. We present MSight, a new software designed to construct and manipulate MS images, as well as to facilitate their analysis and comparison.

L'image de la Suisse à l'étranger

L'image qu'un pays a dans le monde est importante à plusieurs titres. Elle peut soutenir la commercialisation de biens et de services exportés, elle revêt un caractère tout particulier dans le cadre des promotions touristique et économique et elle peut aussi être de nature à contribuer aux relations qu'un pays entretient avec d'autres pays aux niveaux politique, économique ou culturel. L'image de la Suisse a fait l'objet d'études dans de nombreux pays, dont les Etats-Unis, l'Allemagne et la Chine, auprès d'échantillons représentatifs de la population ainsi qu'auprès de groupes de leaders d'opinion et cet ouvrage présente de manière synthétique les principaux résultats de ces études. Après une description de l'image globale de la Suisse auprès des personnes interrogées et une analyse des associations faites à l'évocation de la Suisse, une partie importante est consacrée aux dimensions qui caractérisent l'image du pays en différenciant notamment entre les dimensions liées à la Suisse en tant qu'espace socioculturel et les dimensions liées aux aspects économiques. Pour terminer, un dernier chapitre analyse l'impact de faits ayant marqué l'actualité helvétique, comme le grounding de Swissair, sur l'image de la Suisse dans les pays étudiés.

Underwater Gigamosaicing

El procés de fusió de dues o més imatges de la mateixa escena en una d'única i més gran és conegut com a Image Mosaicing. Un cop finalitzat el procés de construcció d'un mosaic, els límits entre les imatges són habitualment visibles, degut a imprecisions en els registres fotomètric i geomètric. L'Image Blending és l'etapa del procediment de mosaicing a la que aquests artefactes són minimitzats o suprimits. Existeixen diverses metodologies a la literatura que tracten aquests problemes, però la majoria es troben orientades a la creació de panorames terrestres, imatges artístiques d'alta resolució o altres aplicacions a les quals el posicionament de la càmera o l'adquisició de les imatges no són etapes rellevants. El treball amb imatges subaquàtiques presenta desafiaments importants, degut a la presència d'scattering (reflexions de partícules en suspensió) i atenuació de la llum i a condicions físiques extremes a milers de metres de profunditat, amb control limitat dels sistemes d'adquisició i la utilització de tecnologia d'alt cost. Imatges amb il·luminació artificial similar, sense llum global com la oferta pel sol, han de ser unides sense mostrar una unió perceptible. Les imatges adquirides a gran profunditat presenten una qualitat altament depenent de la profunditat, i la seva degradació amb aquest factor és molt rellevant. El principal objectiu del treball és presentar dels principals problemes de la imatge subaquàtica, seleccionar les estratègies més adequades i tractar tota la seqüència adquisició-procesament-visualització del procés. Els resultats obtinguts demostren que la solució desenvolupada, basada en una Estratègia de Selecció de Límit Òptim, Fusió en el Domini del Gradient a les regions comunes i Emfatització Adaptativa d'Imatges amb baix nivell de detall permet obtenir uns resultats amb una alta qualitat. També s'ha proposat una estratègia, amb possibilitat d'implementació paral·lela, que permet processar mosaics de kilòmetres d'extensió amb resolució de centímetres per píxel.

Using a NPWE model observer to assess suitable image quality for a digital mammography quality assurance programme.

A method of objectively determining imaging performance for a mammography quality assurance programme for digital systems was developed. The method is based on the assessment of the visibility of a spherical microcalcification of 0.2 mm using a quasi-ideal observer model. It requires the assessment of the spatial resolution (modulation transfer function) and the noise power spectra of the systems. The contrast is measured using a 0.2-mm thick Al sheet and Polymethylmethacrylate (PMMA) blocks. The minimal image quality was defined as that giving a target contrast-to-noise ratio (CNR) of 5.4. Several evaluations of this objective method for evaluating image quality in mammography quality assurance programmes have been considered on computed radiography (CR) and digital radiography (DR) mammography systems. The measurement gives a threshold CNR necessary to reach the minimum standard image quality required with regards to the visibility of a 0.2-mm microcalcification. This method may replace the CDMAM image evaluation and simplify the threshold contrast visibility test used in mammography quality.