In this paper we define Courant algebroids in a purely algebraic way and study their deformation theory by using two different but equivalent graded Poisson algebras of degree −2.

We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin–Courant, as the only rules in certain in...

Kuznetsov’s condition says that variables X and Y are independent when any product of bounded functions f X and g Y behaves in a certain way: the interval of expected values f X g Y must be equal to the interval product f X g Y . The main result of this paper shows how to compute lower expectations using Kuznetsov’s condition. We also generalize Kuznetsov’s condition to conditional expectation ...

Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-$k$-counting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and $k$-Approval Chamberlin--Courant as the ...

We show that quasi-Poisson structures can be identified with Dirac structures in suitable Courant algebroids. This provides a geometric way to construct Lie algebroids associated with quasi-Poisson spaces.

We show that the Manin triple characterization of Lie bialgebras in terms of the Drinfel’d double may be extended to arbitrary Poisson manifolds and indeed Lie bialgebroids by using double cotangent bundles, rather than the direct sum structures (Courant algebroids) utilized for similar purposes by Liu, Weinstein and Xu. This is achieved in terms of an abstract notion of double Lie algebroid (w...

Résumé. Il est aujourd’hui courant d’utiliser une approche «orientée service» pour définir des applications complexes. Dans ce cadre, les services constituent les unités de base, assemblés par des mécanismes de plus haut niveau comme les orchestrations. Nous présentons ici un atelier logiciel construit dans une démarche dirigée par les modèles permettant la composition d’orchestrations de servi...

We prove two discrete analogues of Courant’s Nodal Domain Theorem.

We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal, Whitney sum E⊕C where E is a given Courant algebroid and C is a flat, pseudo-Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive Courant algebroid, that is, a Courant algebroid with a surjective anchor, and describ...