On the top-dimensional ℓ2\ell^2-Betti numbers

The purpose of this note is to introduce a trick which relates the (non)-vanishing of the top-dimensional $\ell$ 2-Betti numbers of actions with that of sub-actions. We provide three different types of applications: we prove that the $\ell$ 2-Betti numbers of Aut($F_n$) and Out($F_n$) (and of their Torelli subgroups) do not vanish in degree equal to their virtual cohomological dimension, we prove that the subgroups of the 3-manifold groups have vanishing $\ell$ 2-Betti numbers in degree 3 and 2 and we prove for instance that $F_2^d \times Z$ has ergodic dimension $d + 1$.Comment: An author added. ''Camille No\^us'' is a scientific consortium created to affirm the collaborative and open nature of knowledge creation and dissemination, under the control of the academic community. This scientific collective, like Bourbaki, Henri Paul de Saint Gervais or Arthur Besse in mathematics, or Isadore Nabi in biology, takes on the identity of a scientific personality who embodies the collective contribution of the academic community. More precisely, Camille No{\^u}s is a collective individual who symbolizes our deep attachment to the values of ethics and probation that are carried by the contradictory debate, she is insensitive to the indicators elaborated by the institutional management of research, she knows what our results owe to collective construction. This is the meaning of the ''No{\^u}s'', bearing a collegial We but referring above all to the concept of ''reason'' (or ''rational'' or ''intellect'') inherited from Greek philosophy.Some comments added. Annales de la Facult{\'e} des Sciences de Toulouse. Math\'ematiques., Universit\'e Paul Sabatier, Cellule Mathdoc In pres

Limited regularity of a specific electronic reduced density matrix for molecules

We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we prove that the (N-1)-particle electronic reduced density matrix is not smooth.Comment: 33 page

Pratiques partenariales depuis l’université : vers des logiques entrepreneuriales ?

A partir d’entretiens (N=146) menés avec des acteurs universitaires de 2013 à 2017, cet article interroge dans quelle mesure l’appartenance universitaire façonne les conditions de possibilité de réalisation de partenariats entre enseignants-chercheurs en Sciences Humaines et Sociales (N=51) et acteurs non académiques, dans une perspective comparative entre l’université de Syracuse (Etats-Unis) et de Paris Nanterre (France). Le statut d’universitaire (titulaire) est souligné comme le principal atout par les enquêté.es en termes de sécurité et d’autonomie de travail. En revanche certaines logiques professionnelles, via une transformation des organisations universitaires (surtout en France) et des normes académiques, sont présentées comme des contraintes fortes, bien que modulées par des effets d’appartenance et de positionnement disciplinaires. Face au renforcement de la place de l’établissement dans la différenciation des conditions de travail et d’accès aux ressources professionnelles (financements, partenaires, reconnaissance), différentes stratégies sont mises en œuvre à l’égard de l’université de rattachement. Celles-ci apparaissent marquées par l’adoption – avec ou sans adhésion d’ailleurs – de logiques entrepreneuriales, comme manière se créer soi-même des conditions favorables aux partenariats. Les logiques de compétition et de rémunération sur fonds propres s’étendent alors aux pratiques des universitaires pour voire par les partenariats afin de les (voire se) financer.Based on interviews (N=146) conducted with academic actors from 2013 to 2017, this article investigates to what extend the academic affiliation shapes the conditions of possibility for partnerships between academics in the Humanities and Social Sciences (N=51) and non-academic actors, in a comparative perspective between Syracuse University (USA) and Paris Nanterre (France). The status of academic (tenured) is underlined as the main asset in terms of security and autonomy of work. On the other hand, some professional logics, driven by important transformation of the university organizations (especially in France) and academic norms, are presented as strong constraints, although modulated by disciplinary effects. Taking into account the growing role of the university of affiliation in the differentiation of working conditions and the access to professional resources (funding, partners, recognition), different strategies are implemented by the academics. These strategies are characterized by the adoption - with or without adhesion - of entrepreneurial logics, as a way of creating by oneself the favorable conditions to develop partnerships. Academics then seek to develop their own funds and become more dependent on private resources or competitive calls for projects, in order to finance their partnership projects, or even to use them to finance their other activities

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Backtracking reference stores

National audienceFrançois Pottier's unionFind library is parameterized over an underlying store of mutable references, and provides the usual references, transactional reference stores (for rolling back some changes in case of higher-level errors), and persistent reference stores. We extend this library with a new implementation of backtracking reference stores, to get a Union-Find implementation that efficiently supports arbitrary backtracking and also subsumes the transactional interface. Our backtracking reference stores are not specific to unionFind, they can be used to build arbitrary backtracking data structures. The natural implementation, using a journal to record all writes, provides amortized-constant-time operations with a space overhead linear in the number of store updates. A refined implementation reduces the memory overhead to be linear in the number of store cells updated, and gives performance that match non-backtracking references in practice

Implicit automata in typed λ\lambda-calculi II: streaming transducers vs categorical semantics

We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions, into our $\lambda$-calculus. For the converse, we consider a categorical framework for defining automata and transducers over words, which allows us to relate register updates in SSTs to the semantics of the linear $\lambda$-calculus in a suitable monoidal closed category. To illustrate the relevance of monoidal closure to automata theory, we also leverage this notion to give abstract generalizations of the arguments showing that copyless SSTs may be determinized and that the composition of two regular functions may be implemented by a copyless SST. Our main result is then generalized from strings to trees using a similar approach. In doing so, we exhibit a connection between a feature of streaming tree transducers and the multiplicative/additive distinction of linear logic. Keywords: MSO transductions, implicit complexity, Dialectica categories, Church encodingsComment: 105 pages, 24 figure