An Upper Bound on the Complexity of Recognizable Tree Languages

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\bf\Delta}^1\_2$

The multigraded Nijenhuis-Richardson Algebra, its universal property and application

We define two $(n+1)$ graded Lie brackets on spaces of multilinear mappings. The first one is able to recognize $n$-graded associative algebras and their modules and gives immediately the correct differential for Hochschild cohomology. The second one recognizes $n$-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology

Toward scalable information processing with ultracold polar molecules in an electric field: a numerical investigation

We numerically investigate the possibilities of driving quantum algorithms with laser pulses in a register of ultracold NaCs polar molecules in a static electric field. We focuse on the possibilities of performing scalable logical operations by considering circuits that involve intermolecular gates (implemented on adjacent interacting molecules) to enable the transfer of information from one molecule to another during conditional laser-driven population inversions. We study the implementation of an arithmetic operation (the addition of 0 or 1 on a binary digit and a carry in) which requires population inversions only and the Deutsch-Josza algorithm which requires a control of the phases. Under typical experimental conditions, our simulations show that high fidelity logical operations involving several qubits can be performed in a time scale of a few hundred of microseconds, opening promising perspectives for the manipulation of a large number of qubits in these systems

Depinning of domain walls with an internal degree of freedom

Taking into account the coupling between the position of the wall and an internal degree of freedom, namely its phase $\phi$, we examine, in the rigid wall approximation, the dynamics of a magnetic domain wall subject to a weak pinning potential. We determine the corresponding force-velocity characteristics, which display several unusual features when compared to standard depinning laws. At zero temperature, there exists a bistable regime for low forces, with a logarithmic behavior close to the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different topological modes of the phase evolution. At finite temperature, the force-velocity characteristics become non-monotonous. We compare our results to recent experiments on permalloy nanowires

Alternated Hochschild Cohomology

23 pagesIn this paper we construct a graded Lie algebra on the space of cochains on a \mathbbZ_2-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial) skew-symmetrization; the coboundary operator is a skew-symmetrized version of the Hochschild differential. We show that an order-one element $m$ satisfying the zero-square condition $[m,m]=0$ defines an algebraic structure called ''Lie antialgebra''. The cohomology (and deformation) theory of these algebras is then defined. We present two examples of non-trivial cohomology classes which are similar to the celebrated Gelfand-Fuchs and Godbillon-Vey classes

Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model

Cancer is a proliferation disease affecting a genetically unstable cell population, in which molecular alterations can be somatically inherited by genetic, epigenetic or extragenetic transmission processes, leading to a cooperation of neoplastic cells within tumoral tissue. The efflux protein P-glycoprotein (P gp) is overexpressed in many cancer cells and has known capacity to confer multidrug resistance to cytotoxic therapies. Recently, cell-to-cell P-gp transfers have been shown. Herein, we combine experimental evidence and a mathematical model to examine the consequences of an intercellular P-gp trafficking in the extragenetic transfer of multidrug resistance from resistant to sensitive cell subpopulations. We report cell-to-cell transfers of functional P-gp in co-cultures of a P-gp overexpressing human breast cancer MCF-7 cell variant, selected for its resistance towards doxorubicin, with the parental sensitive cell line. We found that P-gp as well as efflux activity distribution are progressively reorganized over time in co-cultures analyzed by flow cytometry. A mathematical model based on a Boltzmann type integro-partial differential equation structured by a continuum variable corresponding to P-gp activity describes the cell populations in co-culture. The mathematical model elucidates the population elements in the experimental data, specifically, the initial proportions, the proliferative growth rates, and the transfer rates of P-gp in the sensitive and resistant subpopulations. We confirmed cell-to-cell transfer of functional P-gp. The transfer process depends on the gradient of P-gp expression in the donor-recipient cell interactions, as they evolve over time. Extragenetically acquired drug resistance is an additional aptitude of neoplastic cells which has implications in the diagnostic value of P-gp expression and in the design of chemotherapy regimensComment: 13 pages, 8 figures, 1 tabl

The maison europeenne des procedes innovants (MEPI),an example of piloting and industrial demonstration facility for the green process engineering

Abstract. Economical, energy savings and environmental challenges require an actual technological breakthrough in process engineering, aiming with productivity, product quality, safety and reliability objectives. This explains the present growth of interest in innovative technologies (intensified devices for reaction, mixing and separation) and methods (multifunctionality, hybrid separation, batch to continuous methodology, new media …), the whole being recognized as Process Intensification. Up to now, a few of innovations has been successfully industrialized, probably due to the lack of experience and retrofitting in front of a breakthrough that always represents a technical and financial risk. There is now clearly a need for industrial demonstrations of successful PI experiments avoiding the questions of confidentiality. Consequently, a piloting and demonstration facility has been created in Toulouse in order to accelerate the implementation of PI technology in industry and the development of the Green Process Engineering. The idea is to build a data bank of success stories. The principle of this industrial technical platform lies on the association of 3 types of partners: university, equipment providers and industrial end-users

Are emerging deep eutectic solvents (DES) relevant for lipase-catalyzed lipophilizations?

With the recent interest on green chemistry, the scientists have focused on developing new and more efficiient solvents to carry out enzymatic-catalyzed reactions with emphasis on reduced costs, risks and toxicity while improving biodegradability. Among the new available solvents, the multimolecular-based liquids (such as ionic liquids and eutectic solvents) have been the subject of most recent studies. Currently, and mainly due to its environmental and economic features, DES are arousing much interest and curiosity. Regarding the biotransformations with lipases, the so-called “lipophilization” reactions are of major interest. However, they are complex to implement mainly because it is difficult to find a suitable reaction medium. Thus, this review aimed at providing a presentation of these multimolecular- based solvents with general overview of the recent studies dealing with lipase-catalyzed reactions in DES. In addition, emphasis was placed on their strengths and weaknesses, especially with the perspective to be use as efficient and green medium to implement complex and valuable biotransformation such as lipase-catalyzed lipophilizations. (Résumé d'auteur