The Arason invariant of orthogonal involutions of degree 12 and 8, and quaternionic subgroups of the Brauer group

Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to associate to every orthogonal involution with trivial discriminant and trivial Clifford invariant over a central simple algebra of even co-index a cohomology class $f_3$ of degree 3 with $\mu_2$ coefficients. This invariant $f_3$ is the double of any representative of the Arason invariant; it vanishes when the algebra has degree at most 10, and also when there is a quadratic extension of the center that simultaneously splits the algebra and makes the involution hyperbolic. The paper provides a detailed study of both invariants, with particular attention to the degree 12 case, and to the relation with the existence of a quadratic splitting field.Comment: A mistake pointed out by A. Sivatski in Section 5.3 has been corrected in the new version of this preprin

Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties

An orthogonal involution $\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\sigma$ over $\mathcal{F}(A)$, which is uniquely defined up to a scalar factor. Some properties of the involution, such as hyperbolicity, and isotropy up to an odd-degree extension of the base field, are encoded in this quadratic form, meaning that they hold for the involution $\sigma$ if and only if they hold for $q_\sigma$. As opposed to this, we prove that there exists non-totally decomposable orthogonal involutions that become totally decomposable over $\mathcal{F}(A)$, so that the associated form $q_\sigma$ is a Pfister form. We also provide examples of nonisomorphic involutions on an index $2$ algebra that yield similar quadratic forms, thus proving that the form $q_\sigma$ does not determine the isomorphism class of $\sigma$, even when the underlying algebra has index $2$. As a consequence, we show that the $e_3$ invariant for orthogonal involutions is not classifying in degree $12$, and does not detect totally decomposable involutions in degree $16$, as opposed to what happens for quadratic forms

Valorisation stratégique par contextes de valeur : le cas des introductions sur le nouveau marché

Study of the chapter related to firms' activity in the preliminary prospectuses for 50 listed companies in the "Nouveau marché" shows the existence of 5 disclosure policies. Except for the P/E ratio, empirical study confirms the strategic information effect on value explanation, measured by the Market-to-Book, Firm Value-to-Sales revenue, Firm Value-to-EBIT. Finally, Cumulative Abnormal Return over ten and sixty-day periods are positively associated with the disclosure policy of strategic information.L'étude du chapitre lié à l'activité dans le prospectus préliminaire de 50 sociétés candidates à l'introduction sur le Nouveau marché montre l'existence de cinq politiques de communication. À l'exception du multiple du résultat net, PER, le test empirique confirme l'importance de l'information stratégique dans l'explication de la valeur. Enfin, il s'avère que la rentabilité anormale cumulée à dix et soixante jours suivant l'introduction est positivement corrélée à l'effort de révélation de l'information stratégique, mesuré par le nombre de contextes de valeur

Menger and Nöbeling on pointless topology

This paper looks at how the idea of pointless topology itself evolved during its pre-localic phase by analyzing the definitions of the concept of topological space of Menger and Nöbeling. Menger put forward a topology of lumps in order to generalize the definition of the real line. As to Nöbeling, he developed an abstract theory of posets so that a topological space becomes a particular case of topological poset. The analysis emphasizes two points. First, Menger's geometrical perspective was superseded by an algebraic one, a lattice-theoretical one to be precise. Second, Menger's bottom–up approach was replaced by a top–down one

Algebras with involution that become hyperbolic over the fonction field of a conic

We study central simple algebras with involution of the first kind that become hyperbolic over the function field of the conic associated to a given quaternion algebra $Q$. We classify these algebras in degree~$4$ and give an example of such a division algebra with orthogonal involution of degree~$8$ that does not contain $Q$ with its canonical involution, even though it contains $Q$ and is totally decomposable into a tensor product of quaternion algebras with involution

Reliable ABC model choice via random forests

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with random forests and postponing the approximation of the posterior probability of the predicted MAP for a second stage also relying on random forests. Compared with earlier implementations of ABC model choice, the ABC random forest approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least fifty), and (iv) it includes an approximation of the posterior probability of the selected model. The call to random forests will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. The proposed methodologies are implemented in the R package abcrf available on the CRAN.Comment: 39 pages, 15 figures, 6 table

Un risque intrinsèque : l'omniprésence du design dans les principaux modèles productifs du capitalisme moderne

International audienceUne exploration du design située au cœur des principaux modèles productifs montre à travers le récit de F.W. Taylor, de H. Ford et de T. Ohno que le design occupe un rôle stratégique majeur dans le développement, l'essor de ces modèles et l'impact transformationnel qu'ils ont eu sur l'économie. Et que loin d'être circonscrit au produit, le design s'inscrit dans une démarche totale qui va de l'atelier de production à l'outil de travail en passant par le service. A partir de là, il faut considérer différemment le design au sein des entreprises à l'aune du risque intrinsèque que représente son caractère omniprésent au sein des organisations