Combining unsupervised and supervised artificial neural networks to predictaquatic toxicity

Most quantitative structure-activity relationship (QSAR) models are linear relationships and significant for only a limited domain of compounds. Here we propose a data-driven approach with a flexible combination of unsupervised and supervised neural networks able to predict the toxicity of a large set of different chemicals while still respecting the QSAR postulates. Since QSAR is applicable only to similar compounds, which have similar biological and physicochemical properties, large numbers of compounds are clustered before building local models, and local models are ensembled to obtain the final result. The approach has been used to develop models to predict the fish toxicity of Pimephales promelas and Tetrahymena pyriformis, a protozoan.     

An approximation theorem for sections of reflexive sheaves

 We show that, if X is a Stein manifold and D ? X an open set (not necessarily Stein) such that the restriction map has dense image, then, for any reflexive coherent analytic sheaf ℱ on X, the map has dense image, too. We also characterize the reflexivity of a torsion-free coherent sheaf on complex manifolds in terms of absolute gap sheaves or Kontinuit?tssatz. Received: 14 September 2001 / Revised version: 29 January 2002     

Possible transition from rod-like to disc-like behaviour in ortho-metallated imine complexes of palladium(II): crystal and molecular structure of three palladium complexes

Two series of ortho-metallated palladium imine complexes are reported that contain a coordinated β-diketonate group. In one group the chain length of the imine is varied while the β-diketone is unchanged; in the other the imine chains are both fixed as methoxy and the structure of the β-diketonate is varied. The mesomorphism of these new complexes is reported and discussed in relation to the search for materials showing a biaxial nematic phase.     

Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities

In 1956, R. Penrose studied best-approximate solutions of the matrix equation AX = B. He proved that A⁺B (where A⁺ is the Moore-Penrose inverse) is the unique matrix of minimal Frobenius norm among all matrices which minimize the Frobenius norm of AX ? B. In particular, A⁺ is the unique best-approximate solution of AX = I. The vector version of Penrose's result (that is, the fact that the vector A⁺b is the best-approximate solution in the Euclidean norm of the vector equation Ax = b) has long been generalized to infinite dimensional Hilbert spaces.In this paper, an infinite dimensional version of Penrose's full result is given. We show that a straightforward generalization is not possible and provide new extremal characterizations (in terms of the Hermitian order) of A⁺ and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least-squares solutions. For a certain class of operators, we can phrase our characterizations in terms of a whole class of norms (including the Hilbert-Schmidt and the trace norms), thus providing new extremal characterizations even in the matrix case. We treat both operators with closed range and with not necessarily closed range. Finally, we characterize A⁺ as the unique inner inverse of minimal Hilbert-Schmidt norm if ∥A⁺∥₂ < ∞. We give an application of the new extremal characterization to the compensation problem in systems analysis in infinite-dimensional Hilbert spaces.     

A note on the stabilizability of stochastic heat equations with multiplicative noiseSur la stabilisabilité des équations de la chaleur stochastiques avec bruit multiplicatif

We show that a stochastic heat equation with multiplicative noise on a bounded domain $\text{D}$ can be stabilized by a control acting only on a subdomain $\text{O}\text{?}\text{D}$ if $\text{D}\text{?}\text{O}$ is sufficiently ‘thin’. We consider both linear and semilinear stochastic heat equations. To cite this article: V. Barbu et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 311–316.     

On the normal bundle of submanifolds of

Let be a submanifold of dimension of the complex projective space . We prove results of the following type.i) If is irregular and , then the normal bundle is indecomposable. ii) If is irregular, and , then is not the direct sum of two vector bundles of rank . iii) If , and is decomposable, then the natural restriction map is an isomorphism (and, in particular, if is embedded Segre in , then is indecomposable). iv) Let and , and assume that is a direct sum of line bundles; if assume furthermore that is simply connected and is not divisible in . Then is a complete intersection. These results follow from Theorem 2.1 below together with Le Potier's vanishing theorem. The last statement also uses a criterion of Faltings for complete intersection. In the case when this fact was proved by M. Schneider in 1990 in a completely different way.

     

Grauert’s line bundle convexity,reduction and Riemann domains

We consider a convexity notion for complex spaces X with respect to a holomorphic line bundle L over X. This definition has been introduced by Grauert and, when L is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if H⁰(X,L) separates each point of X, then X can be realized as a Riemann domain over the complex projective space Pⁿ, where n is the complex dimension of X and L is the pull-back of O(1).