A machine learning approach to exoplanet spectroscopy

The characterization of exoplanetary atmospheres is the new frontier in the field of exoplanets. Transit and eclipse spectroscopy are invaluable sources of information, as they may reveal the chemical composition, the presence of clouds, and the temperature and pressure profiles of the atmospheres of exoplanets. A photometric precision of about one part in 104 is necessary to make statistically significant inferences. The native calibration of current observatories, except Kepler, is not sufficient to reach this precision. In the past, parametric models have been used extensively by most teams to remove instrumental systematics. This approach has caused many debates regarding the use of different parametric choices for the removal of systematic errors. Parametric models decorrelate the systematic noise with the aid of auxiliary information on the instrument: the so-called optical state vectors (OSVs). Such OSVs can include inter- and intra-pixel position of the star or its spectrum, instrument temperatures and inclinations, and/or other parameters. The choice of the parameters to include in the OSVs is somewhat arbitrary, as is the choice of the functional forms to approximate the dependence of systematic noise on those parameters. The solution to many of the issues deriving from the use of OSVs lies in the use of `blind', non-parametric techniques. Such methods do not require a model for the systematics, and for this reason, they can be applied to any instrument with few changes (if any). In this Thesis, I focus on the Independent Component Analysis (ICA) of multiple time series, which performs a linear transformation of those series into maximally independent components. The use of ICA to detrend instrument systematics in exoplanetary light-curves was first proposed by Waldmann (2012). They experimented with spectroscopic light-curves taken with HST/NICMOS and sequential Kepler observations as input light-curves for the ICA. In this Thesis, I present two novel approaches to detrend single photometric observations in a self-consistent way (pixel-ICA), and scanning-mode spectroscopic observations without mixing the signals at different wavelengths (stripe-ICA). The two techniques that I pioneered extend the applicability of ICA to single observations with different instrument design. Some unsupervised preprocessing steps are also tested. The better performances of these algorithms compared to other ones in the literature are demonstrated over a series of Spitzer and Hubble observations, and synthetic data sets. The (re)analysis of archive and new data with similar techniques will cast new light on the characterization of exoplanets

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

Sliceforms: Deployable structures from interlocking slices

A sliceform is a volumetric, honeycomb-like structure assembled from an array of cross-sectional planar slices that are interlocked via pairs of complementary slots placed along each intersection. If the slices are thin, these slotted intersections function as revolute joints, and the sliceform is foldable if the geometry of the embedded spatial linkage permits it, for example a lattice sliceform (LS) is bi-directionally flat-foldable. This thesis concerns a study of such sliceforms toward the design of novel deployable structures. A sliceform torus, composed of two sets of inclined slices arranged at regular intervals about a central axis of symmetry, has been discovered to exhibit a surprising and intriguing folding action whereby its incomplete form can be collapsed to a flat-folded stack of coplanar slices. On deployment, the assembly expands smoothly about an arc until the slices have rotated to their design inclination, then, without reaching any apparent physical limit, abruptly ‘locks out’. With a full complement of slices, the outermost intersections can be interlocked to complete and rigidify the ring. The torus is an example of a rotational sliceform (RS), and analysis of these structures proceeds by noting that their structural geometry comprises an array of pyramidal cells that is commensurate to a spherical scissor grid. The conditions for flat-foldability are determined by examination of the intrinsic geometry of each cell; the incompatibility of the slices with apparent rigid-folding revealed by assessment of the extrinsic motion of the slices. Investigation of their compliant kinematics reveals the articulation to be a bistable transition admitted by small transverse deflections of the slices. This structural form is generalised by development of a technique for generating sliceforms along a smooth spatial curve – curve sliceforms (CS). Their synthesis is more involved than for an RS, but a range of sliceform ‘tubes’ are generated and manufactured. Each example retains the flat-foldable, deployable characteristic of an RS, despite the apparent intrinsic rigidity of each constituent skew cell. Examination of the small-scale models indicates that deployable motion is achieved via imperfect action of the slots, and a simple model of the articulation of a single cell is constructed to investigate how this proceeds, verifying that motion is kinematically admissible via local deformations

Enacting Inquiry Learning in Mathematics through History

International audienceWe explain how history of mathematics can function as a means for enacting inquiry learning activities in mathematics as a scientific subject. It will be discussed how students develop informed conception about i) the epistemology of mathematics, ii) of how mathematicians produce mathematical knowledge, and iii) what kind of questions that drive mathematical research. We give examples from the mathematics education at Roskilde University and we show how (teacher) students from this program are themselves capable of using history to establish inquiry learning environments in mathematics in high school. The realization is argued for in the context of an explicit-reflective framework in the sense of Abd-El-Khalick (2013) and his work in science education

History of Mathematics in Mathematics Education: Recent devlopments

International audience<p>This is a concise survey on the recent developments (since 2000) concerning research on the relations between History and Pedagogy of Mathematics (the <i>HPM domain</i>). Section 1 explains the rationale of the study and formulates the key issues. Section 2 gives a brief historical account of the development of the <i>HPM domain</i> with focus on the main activities in its context and their outcomes. Section 3 provides a sufficiently comprehensive bibliographical survey of the work done in this area since 2000. Finally, section 4 summarizes the main points of this study.</p

Original Sources in the Mathematical Classroom

International audienceThis discussion group seeks to bring together individuals who are interested in the use of original sources in the mathematics classroom, from the perspective of a classroom teacher or a mathematics education researcher, for a discussion of issues and concerns related to their educational potential and effects. Each of the two sessions will focus on a different theme related to the use of original sources in the mathematics classroom. The two sessions will structured around a common framework but sufficiently independent of each other to allow interested individuals to participate in the second session, even if they did not participate in the first session. Both novice and more experienced users of original sources are strongly encouraged to participate in both sessions