Milnor invariants of braids and welded braids up to homotopy

We consider the group of pure welded braids (also known as loop braids) up to (link-)homotopy. The pure welded braid group classically identifies, via the Artin action, with the group of basis-conjugating automorphisms of the free group, also known as the McCool group P $\Sigma$ n. It has been shown recently that its quotient by the homotopy relation identifies with the group hP $\Sigma$ n of basis-conjugating automorphisms of the reduced free group. In the present paper, we describe a decomposition of this quotient as an iterated semi-direct product which allows us to solve the Andreadakis problem for this group, and to give a presentation by generators and relations. The Andreadakis equality can be understood, in this context, as a statement about Milnor invariants; a discussion of this question for classical braids up to homotopy is also included

Reply to K. Amos et al. (nucl-th/0401055)

An expression for the spin-orbit interaction coupling between different levels, which was shown to be aberrant more than thirty years ago persists in the literature without clear indication of what is used. It leads to expressions quite simpler than they should be. After an attempt to warn the community of the nuclear physicists on this strange situation (nucl-th/0312038), the authors of the publication in which the "aberrant" interaction is described and used, try to justify their work (nucl-th/0401055), by a very strange "symmetrization" of something already symmetric. They claim also that their method allows to solve some problem related to the Pauli principle and give some references, among which a book which reports the solution of such problem almost forty years ago, with a very small effect. An examination of their own results shows that their optimism is not completely justified. Nevertheless, any user of ECIS, sensitive to their arguments, is requested to ask their opinion to these five coauthors before publishing.Comment: latex arXiv.tex, 1 file, 8 page

Andoyer construction for Hill and Delaunay variables

Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function.Comment: 8 pages, 2 figures, revised versio

Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin

Lactate concentration gradient from right atrium to pulmonary artery: a commentary

Inadequate myocardial performance is a common complication of severe sepsis. Studies in humans strongly argue against a decrease in coronary blood flow in the pathogenesis of this sepsis-induced cardiac injury. Moreover, regional myocardial ischemia may well be present in sepsis patients with coexistent coronary artery disease. Nevertheless, the diagnosis of myocardial ischemia remains difficult in patients with sepsis, since elevation of troponin in these patients can be the result of a variety of conditions other than acute myocardial ischemia. The use of the right atrium to pulmonary artery lactate gradient could perhaps help the clinician in detecting myocardial ischemia in patients with sepsis