Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

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

Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold

Let $M$ be a manifold and $T^*M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\infty} (T^*M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.Comment: arxiv version is already officia

A hermeneutic inquiry into user-created personas in different Namibian locales

Persona is a tool broadly used in technology design to support communicational interactions between designers and users. Different Persona types and methods have evolved mostly in the Global North, and been partially deployed in the Global South every so often in its original User-Centred Design methodology. We postulate persona conceptualizations are expected to differ across cultures. We demonstrate this with an exploratory-case study on user-created persona co-designed with four Namibian ethnic groups: ovaHerero, Ovambo, ovaHimba and Khoisan. We follow a hermeneutic inquiry approach to discern cultural nuances from diverse human conducts. Findings reveal diverse self-representations whereby for each ethnic group results emerge in unalike fashions, viewpoints, recounts and storylines. This paper ultimately argues User-Created Persona as a potentially valid approach for pursuing cross-cultural depictions of personas that communicate cultural features and user experiences paramount to designing acceptable and gratifying technologies in dissimilar locales

A numerical approach to large deviations in continuous-time

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.Comment: Submitted to J. Stat. Mec

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Microscopic energy flows in disordered Ising spin systems

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "mean-field approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure

Chaotic properties of systems with Markov dynamics

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.Comment: 4 pages, to appear in the Physical Review Letter

Intracellular mechanism of the action of inhibin on the secretion of follicular stimulating hormone and of luteinizing hormone induced by LH-RH in vitro

The FSH secretion-inhibiting action of inhibin in vitro under basal conditions and also in the presence of LH-RH is suppressed by the addition of MIX, a phosphodiesterase inhibitor. In the presence of LH-RH, inhibin reduces significantly the intracellular level of cAMP in isolated pituitary cells. In contrast, the simultaneous addition of MIX and inhibin raises the cAMP level, and this stimulation is comparable to the increase observed when MIX is added alone. These observations suggest that one mode of action of inhibin could be mediated by a reduction in cAMP within the pituitary gonadotropic cell