Unifying Practical Uncertainty Representations: II. Clouds

There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models . This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expanded section concerning clouds and probability intervals

The rise and fall of stellar discs across the peak of cosmic star formation history: mergers versus smooth accretion

Building galaxy merger trees from a state-of-the-art cosmological hydrodynamics simulation, Horizon-AGN, we perform a statistical study of how mergers and smooth accretion drive galaxy morphologic properties above $z > 1$. More specifically, we investigate how stellar densities, effective radii and shape parameters derived from the inertia tensor depend on mergers of different mass ratios. We find strong evidence that smooth accretion tends to flatten small galaxies over cosmic time, leading to the formation of disks. On the other hand, mergers, and not only the major ones, exhibit a propensity to puff up and destroy stellar disks, confirming the origin of elliptical galaxies. We also find that elliptical galaxies are more susceptible to grow in size through mergers than disc galaxies with a size-mass evolution r \prop M^{1.2} instead of r \prop M^{-0.5} - M^{0.5} depending on the merger mass ratio. The gas content drive the size-mass evolution due to merger with a faster size growth for gas-poor galaxies r \prop M^2 than for gas-rich galaxies r \prop M.Comment: 16 pages, 19 figures, submitted to MNRA

Computing Expectations with Continuous P-Boxes: Univariate Case

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis, tractable methods to compute them are crucial in many applications involving imprecise probabilistic models. We concentrate on p-boxes (a simple and popular model), and on the computation of lower expectations of non-monotone functions. This paper is devoted to the univariate case, that is where only one variable has uncertainty. We propose and compare two approaches : the first using general linear programming, and the second using the fact that p-boxes are special cases of random sets. We underline the complementarity of both approaches, as well as the differences.Comment: 31 pages, 6 figures, constitute an extended version of a small paper accepted in ISIPTA conference, and a preprint version of a paper accepted in IJA

Swirling around filaments: are large-scale structure vortices spinning up dark halos?

The kinematic analysis of dark matter and hydrodynamical simulations suggests that the vorticity in large-scale structure is mostly confined to, and predominantly aligned with their filaments, with an excess of probability of 20 per cent to have the angle between vorticity and filaments direction lower than 60 degrees relative to random orientations. The cross sections of these filaments are typically partitioned into four quadrants with opposite vorticity sign, arising from multiple flows, originating from neighbouring walls. The spins of halos embedded within these filaments are consistently aligned with this vorticity for any halo mass, with a stronger alignment for the most massive structures up to an excess of probability of 165 per cent. On large scales, adiabatic/cooling hydrodynamical simulations display the same vorticity in the gas as in the dark matter. The global geometry of the flow within the cosmic web is therefore qualitatively consistent with a spin acquisition for smaller halos induced by this large-scale coherence, as argued in Codis et al. (2012). In effect, secondary anisotropic infall (originating from the vortex-rich filament within which these lower-mass halos form) dominates the angular momentum budget of these halos. The transition mass from alignment to orthogonality is related to the size of a given multi-flow region with a given polarity. This transition may be reconciled with the standard tidal torque theory if the latter is augmented so as to account for the larger scale anisotropic environment of walls and filaments.Comment: 17 pages, 19 figures, 3 tables. accepted for publication in MNRA

A global approach to manage the performance of the problem solving process in innovative design

This article focuses on the problem solving process in design. Today, enterprises face an important need of innovation, as they have to regularly propose new products or new services. Design is one of the key activities of enterprises in order to be innovative, but it is also one whose performances are hard to assess and activities difficult to manage. Studies on performance of the design process are quite few. Despite there exists many tools to evaluate and manage performance in a variety of fields, few tools are proposed Please check and confirm the author names and initials. Amend if necessary.or customized for the design activity. Some parts of this activity are more or less manageable, but one remains hardly controllable: the problem solving process. Three main topics are tackled in this article. Firstly, the article defines the performance, the enterprise organization, the design activity and the role of problem solving in this activity. Then the focus will be done on the ways to measure and manage the performance of problem solving in design; criteria to evaluate it and a set of indicators that impact it are proposed. In last, the use of this set of indicators will be proposed and a link between the indicators and a strategic choice will be established in order to build the problem solving process in accordance with this strategic position