The quest for rings on bipolar scales

We consider the interval $]{-1},1[$ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t.~$0$ are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conorms and t-norms, and we relate this construction to uninorms. We show that the only way to build a group is to use strict t-norms, and that there is no way to build a ring. Lastly, we show that the main result of this paper is connected to the theory of ordered Abelian groups.

Aggregation on bipolar scales

The paper addresses the problem of extending aggregation operators typically defined on $[0,1]$ to the symmetric interval $[-1,1]$, where the ``0'' value plays a particular role (neutral value). We distinguish the cases where aggregation operators are associative or not. In the former case, the ``0'' value may play the role of neutral or absorbant element, leading to pseudo-addition and pseudo-multiplication. We address also in this category the special case of minimum and maximum defined on some finite ordinal scale. In the latter case, we find that a general class of extended operators can be defined using an interpolation approach, supposing the value of the aggregation to be known for ternary vectors.bipolar scale; bi-capacity; aggregation

Dusty Blue Supergiants: News from High-Angular Resolution Observations

An overview is presented of the recent advances in understanding the B[e] phenomenon among blue supergiant stars in light of high-angular resolution observations and with an emphasis on the results obtained by means of long baseline optical stellar interferometry. The focus of the review is on the circumstellar material and evolutionary phase of B[e] supergiants, but recent results on dust production in regular blue supergiants are also highlighted.Comment: 8 pages, 2 figures. Published in "Advances in Astronomy" by Hindawi Publishing Corporatio

A population study of binocular function.

As part of a genome-wide association study (GWAS) of perceptual traits in healthy adults, we measured stereo acuity, the duration of alternative percepts in binocular rivalry and the extent of dichoptic masking in 1060 participants. We present the distributions of the measures, the correlations between measures, and their relationships to other psychophysical traits. We report sex differences, and correlations with age, interpupillary distance, eye dominance, phorias, visual acuity and personality. The GWAS, using data from 988 participants, yielded one genetic association that passed a permutation test for significance: The variant rs1022907 in the gene VTI1A was associated with self-reported ability to see autostereograms. We list a number of other suggestive genetic associations (p<10(-5)).This work was supported by the Gatsby Charitable Foundation (GAT2903). J.B. was supported by a fellowship from Gonville and Caius College.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.visres.2015.02.01