Differential calculus over double Lie algebroids

The notion of double Lie algebroid was defined by M. Van den Bergh and was illustrated by the double quasi Poisson case. We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative de Rham complex and the double Poisson-Lichnerowicz cohomology (Pichereau-vanWeyer) as particular cases of our construction.Comment: 18 page

Relative polynomial closure and monadically Krull monoids of integer-valued polynomials

Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N_0,+). This implies that [f] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset. The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S doesn't have isolated points in v-adic topology.Comment: 12 pages; v.2 contains corrections, in that some necessary conditions on those subsets S, for which we consider integer-valued polynomials on subsets, are impose

Implementing the Agenda for Global Action on human resources for health : Analysis from an international tracking survey

Peer reviewedPublisher PD

Living with water scarcity. A tale from Africa

Sophie Salffner has spent six months in Nigeria doing linguistic fieldwork. She never lived a day without water, but learnt how to manage it in a different way. In this short article, Sophie describes her experience in the world of water scarcity, far away from home and far away from the luxurious daily showers and running tap water of her home country Germany

The Challenges of collaboration and democratic participation in turbulent and unsettled times

This paper proposes new key ways to thinking about self-organisation in cities in what, I suggest, are increasingly unsettled and turbulent times. The importance of thinking about self-organisation in cities is all the more salient in the current economic and social context where in many parts of the world there is a withdrawal by the state from public involvement and expenditure, which is impacting on urban citizens, particularly those who are vulnerable, in increasing negative ways. Self-organisation is thus an important and key direction for the future, if cities are to remain inclusive, just and responsive to local needs. Yet such self-organisation can only be truly meaningful and effective if it is conducted collaboratively and democratically, involving as many people as possible, particularly those whose voices are not often heard. In so doing, it is also important to recognise that such involvement and democratic participation are not always consensual; rather conflict is inevitable and potentially positive, as people learnt to recognise their differences, which are often implicated in power, and to negotiate solutions together

An empirical central limit theorem in L^1 for stationary sequences

In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems and causal linear processes. To prove our main result, we give a Central Limit Theorem for ergodic stationary sequences of random variables with values in L^1. The conditions obtained are expressed in terms of projective-type conditions. The main tools are martingale approximations.Comment: 20 page

Review of 13th: A Beautiful and Powerful Wake Up Call

This film review of 13th is featured in the journal Tapestries: Interwoven voices of local and global identities, volume 6

Approximability of the Multiple Stack TSP

STSP seeks a pair of pickup and delivery tours in two distinct networks, where the two tours are related by LIFO contraints. We address here the problem approximability. We notably establish that asymmetric MaxSTSP and MinSTSP12 are APX, and propose a heuristic that yields to a 1/2, 3/4 and 3/2 standard approximation for respectively Max2STSP, Max2STSP12 and Min2STSP12