Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference

We present different conditions for the existence of a pair of upper semicontinuous functions representing an interval order on a topological space without imposing any restrictive assumptions neither on the topological space nor on the representing functions. The particular case of second countable topological spaces, which is particularly interesting and frequent in economics, is carefully considered. Some final considerations concerning semiorders finish the paper

EXISTENCE OF MAXIMAL ELEMENTS OF SEMICONTINUOUS PREORDERS

We discuss the existence of an upper semicontinuous multi-utility representation of a preorder on a topological space. We then prove that every weakly upper semicontinuous preorder $\precsim$ is extended by an upper semicontinuous preorder and use this fact in order to show that every weakly upper semicontinuous preorder on a compact topological space admits a maximal element

ARCHI: pipeline for light curve extraction of CHEOPS background star

High precision time series photometry from space is being used for a number of scientific cases. In this context, the recently launched CHEOPS (ESA) mission promises to bring 20 ppm precision over an exposure time of 6 hours, when targeting nearby bright stars, having in mind the detailed characterization of exoplanetary systems through transit measurements. However, the official CHEOPS (ESA) mission pipeline only provides photometry for the main target (the central star in the field). In order to explore the potential of CHEOPS photometry for all stars in the field, in this paper we present archi, an additional open-source pipeline module{\dag}to analyse the background stars present in the image. As archi uses the official Data Reduction Pipeline data as input, it is not meant to be used as independent tool to process raw CHEOPS data but, instead, to be used as an add-on to the official pipeline. We test archi using CHEOPS simulated images, and show that photometry of background stars in CHEOPS images is only slightly degraded (by a factor of 2 to 3) with respect to the main target. This opens a potential for the use of CHEOPS to produce photometric time series of several close-by targets at once, as well as to use different stars in the image to calibrate systematic errors. We also show one clear scientific application where the study of the companion light curve can be important for the understanding of the contamination on the main target.Comment: 14 pages, 13 figures, accepted for publication in MNRAS, all code available at https://github.com/Kamuish/arch

Mathematical utility theory and the representability of demand by continuous homogeneous functions

The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first self-contained and elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions

First-principles molecular-dynamics simulations of a hydrous silica melt: Structural properties and hydrogen diffusion mechanism

We use {\it ab initio} molecular dynamics simulations to study a sample of liquid silica containing 3.84 wt.% H$_2$O.We find that, for temperatures of 3000 K and 3500 K,water is almost exclusively dissolved as hydroxyl groups, the silica network is partially broken and static and dynamical properties of the silica network change considerably upon the addition of water.Water molecules or free O-H groups occur only at the highest temperature but are not stable and disintegrate rapidly.Structural properties of this system are compared to those of pure silica and sodium tetrasilicate melts at equivalent temperatures. These comparisons confirm the picture of a partially broken tetrahedral network in the hydrous liquid and suggest that the structure of the matrix is as much changed by the addition of water than it is by the addition of the same amount (in mole %) of sodium oxide. On larger length scales, correlations are qualitatively similar but seem to be more pronounced in the hydrous silica liquid. Finally, we study the diffusion mechanisms of the hydrogen atoms in the melt. It turns out that HOSi$_2$ triclusters and SiO dangling bonds play a decisive role as intermediate states for the hydrogen diffusion.Comment: 25 pages, 18 figures. submitte

Isotonies on ordered cones throught the concept of a decreasing scale

Using techniques based on decreasing scales, necessary and sufficient conditions are presented for the existence of a continuous and homogeneous of degree one real-valued function representing a (not necessarily complete) preorder defined on a cone of a real vector space. Applications to measure theory and expected utility are given as consequences

Confinement-Induced Transition between Wavelike Collective Cell Migration Modes

International audienceThe structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of longrange mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell mono-layers to quasi-one dimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multi-nodal wave, controlled by the confinement size. We conrm experimentally the existence of such a phasetransition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level