An empirical Bayes procedure for the selection of Gaussian graphical models

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered. This prior distribution depends on hyper-parameters. It is well-known that the models's posterior distribution is sensitive to the specification of these hyper-parameters and no completely satisfactory method is registered. In order to avoid this problem, we suggest adopting an empirical Bayes strategy, that is a strategy for which the values of the hyper-parameters are determined using the data. Typically, the hyper-parameters are fixed to their maximum likelihood estimations. In order to calculate these maximum likelihood estimations, we suggest a Markov chain Monte Carlo version of the Stochastic Approximation EM algorithm. Moreover, we introduce a new sampling scheme in the space of graphs that improves the add and delete proposal of Armstrong et al. (2009). We illustrate the efficiency of this new scheme on simulated and real datasets

Creativity Training for Future Engineers: Preliminary Results from an Educative Experience

Due in part to the increased pace of cultural and environmental change, as well as increased competition due to globalization, innovation is become one of the primary concerns of the 21st century. We present an academic course designed to develop cognitive abilities related to creativity within an engineering education context, based on a conceptual framework rooted in cognitive sciences. The course was held at \'Ecole Polytechnique de Montr\'eal (\'EPM), a world renowned engineering school and a pillar in Canada's engineering community. The course was offered twice in the 2014-2015 academic year and more than 30 students from the graduate and undergraduate programs participated. The course incorporated ten pedagogical strategies, including serious games, an observation book, individual and group projects, etc., that were expected to facilitate the development of cognitive abilities related to creativity such as encoding, and associative analytical thinking. The CEDA (Creative Engineering Design Assessment) test was used to measure the students' creativity at the beginning and at the end of the course. Field notes were taken after each of the 15 three-hour sessions to qualitatively document the educative intervention along the semester and students gave anonymous written feedback after completing the last session. Quantitative and qualitative results suggest that an increase in creativity is possible to obtain with a course designed to development cognitive abilities related to creativity. Also, students appreciated the course, found it relevant, and made important, meaningful learnings regarding the creative process, its cognitive mechanism and the approaches available to increase it.Comment: 10 page

A New Course on Creativity in an Engineering Program: Foundations and Issues

The importance of innovation in the world's economy, now undeniable, draws great attention to the need to improve organizations' creative potential. In the last 60 years, hundreds of books have been written on the subject and hundreds of webpages display information on how to be more creative and achieve innovation. Several North American and European universities offer graduated programs in creativity. However, building an effective and validated creativity training program is not without challenges. Because of the nature of their work, engineers are often asked to be innovative. Without aiming for a degree in creativity, could future engineers benefit from training programs in creativity? This article presents the conceptual framework and pedagogical elements of a new course in creativity for engineering students.Comment: 10 pages, Intl Conf on Innovative Design and Manufacturing (pp. 270-275). Aug 13-15, Montreal. IEEE Conference Proceeding

Wavelet analysis of the multivariate fractional Brownian motion

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral density is also considered in a second part. Its existence is proved and its evaluation is performed using a von Bahr-Essen like representation of the function \sign(t) |t|^\alpha. The behavior of the cross-spectral density of the wavelet field at the zero frequency is also developed and confirms the results provided by the asymptotic analysis of the correlation

Impact of nitrogenous fertilizers on carbonate dissolution in small agricultural catchments: Implications for weathering CO2 uptake at regional and global scales

The goal of this study was to highlight the occurrence of an additional proton-promoted weathering pathway of carbonate rocks in agricultural areas where N-fertilizers are extensively spread, and to estimate its consequences on riverine alkalinity and uptake of CO2 by weathering. We surveyed 25 small streams in the calcareous molassic Gascogne area located in the Garonne river basin (south-western France) that drain cultivated or forested catchments for their major element compositions during different hydrologic periods. Among these catchments, the Hay and the Montousse´, two experimental catchments, were monitored on a weekly basis. Studies in the literature from other small carbonate catchments in Europe were dissected in the same way. In areas of intensive agriculture, the molar ratio (Ca + Mg)/HCO3 in surface waters is significantly higher (0.7 on average) than in areas of low anthropogenic pressure (0.5). This corresponds to a decrease in riverine alkalinity, which can reach 80% during storm events. This relative loss of alkalinity correlates well with the NO3 content in surface waters. In cultivated areas, the contribution of atmospheric/soil CO2 to the total riverine alkalinity (CO2 ATM-SOIL/HCO3) is less than 50% (expected value for carbonate basins), and it decreases when the nitrate concentration increases. This loss of alkalinity can be attributed to the substitution of carbonic acid (natural weathering pathway) by protons produced by nitrification of Nfertilizers (anthropogenic weathering pathway) occurring in soils during carbonate dissolution. As a consequence of these processes, the alkalinity over the last 30 years shows a decreasing trend in the Save river (one of the main Garonne river tributaries, draining an agricultural catchment), while the nitrate and calcium plus magnesium contents are increasing. We estimated that the contribution of atmospheric/soil CO2 to riverine alkalinity decreased by about 7–17% on average for all the studied catchments. Using these values, the deficit of CO2 uptake can be estimated as up to 0.22–0.53 and 12–29 Tg1 yr1 CO2 on a country scale (France) and a global scale, respectively. These losses represent up to 5.7–13.4% and only 1.6–3.8% of the total CO2 flux naturally consumed by carbonate dissolution, for France and on a global scale, respectively. Nevertheless, this loss of alkalinity relative to the Ca + Mg content relates to carbonate weathering by protons from N-fertilizers nitrification, which is a net source of CO2 for the atmosphere. This anthropogenic CO2 source is not negligible since it could reach 6–15% of CO2 uptake by natural silicate weathering and could consequently partly counterbalance this natural CO2 sink

(SC)RMI: A (S)emi-(C)lassical (R)elativistic (M)otion (I)integrator, to model the orbits of space probes around the Earth and other planets

Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current approach, with the increase of tracking precision (Ka-Band Doppler, interplanetary lasers) and clock stabilities (atomic fountains) is reaching its limits in terms of complexity, and is furthermore error prone. In the appropriate framework of General Relativity, we study a method to numerically integrate the native relativistic equations of motion for a weak gravitational field, also taking into account small non-gravitational forces. The latter are treated as perturbations, in the sense that we assume that both the local structure of space-time is not modified by these forces, and that the unperturbed satellite motion follows the geodesics of the local space-time. The use of a symplectic integrator to compute the unperturbed geodesic motion insures the constancy of the norm of the proper velocity quadrivector. We further show how this general relativistic framework relates to the classical one.Comment: 13 pages, 5 eps figures, 1 table, accepted in Acta Astronautica, presented at the International Astronautical Congress, Vancouver 2004, reference IAC-04-A.7.0