The effect of deterministic noise in subgradient methods

In this paper, we study the influence of noise on subgradient methods for convex constrained optimization. The noise may be due to various sources, and is manifested in inexact computation of the subgradients and function values. Assuming that the noise is deterministic and bounded, we discuss the convergence properties for two cases: the case where the constraint set is compact, and the case where this set need not be compact but the objective function has a sharp set of minima (for example the function is polyhedral). In both cases, using several different stepsize rules, we prove convergence to the optimal value within some tolerance that is given explicitly in terms of the errors. In the first case, the tolerance is nonzero, but in the second case, the optimal value can be obtained exactly, provided the size of the error in the subgradient computation is below some threshold. We then extend these results to objective functions that are the sum of a large number of convex functions, in which case an incremental subgradient method can be used.     

Quinobis(imidazolylidene): Synthesis and Study of an Electron‐Configurable Bis(N‐Heterocyclic Carbene) and Its Bimetallic Complexes

Reaction of bromanil with N,N′‐dimesitylformamidine followed by deprotonation with NaN(SiMe₃)₂ afforded 1,1′,3,3′‐tetramesitylquinobis(imidazolylidene) ( 1 ), a bis(N‐heterocyclic carbene) (NHC) with two NHC moieties connected by a redox active p‐quinone residue, in 72 % yield of isolated compound. Bimetallic complexes of 1 were prepared by coupling to FcN₃ ( 2 ) or FcNCS ( 3 ; Fc=ferrocenyl) or coordination to [M(cod)Cl] ( 4 a or 4 b , where M=Rh or Ir, respectively; cod=1,5‐cyclooctadiene). Treatment of 4 a and 4 b with excess CO(g) afforded the corresponding [M(CO)₂Cl] complexes 5 a and 5 b , respectively. Analysis of 2 – 5 by NMR spectroscopy and X‐ray diffraction indicated that the electron‐deficient quinone did not significantly affect the inherent spectral properties or coordination chemistry of the flanking imidazolylidene units, as compared to analogous NHCs. Infrared spectroscopy and cyclic voltammetry revealed that decreasing the electron density at ML_n afforded an increase in the stretching energy and a decrease in the reduction potential of the quinone, indicative of metal–quinone electronic interaction. Differential pulse voltammetry and chronoamperometry of the metal‐centered oxidations in 2 – 4 revealed two single, one‐electron peaks. Thus, the metal atoms bound to 1 are oxidized at indistinguishable potentials and do not appear electronically coupled. However, the metal–quinone interaction was used to increase the electron density at coordinated metal atoms. Infrared spectroelectrochemistry revealed that the average ν_CO values for 5 a and 5 b decreased by 14 and 15 cm^?1, respectively, upon reduction of the quinone embedded within 1 . These shifts correspond to 10 and 12 cm^?1 decreases in the Tolman electronic parameter of this ditopic ligand.     

GC–MS analysis of low-molecular-weight dicarboxylic acids in atmospheric aerosol: comparison between silylation and esterification derivatization procedures

This paper describes methods for the determination of low-molecular-weight (LMW) dicarboxylic acids in atmospheric aerosols as important chemical tracers for source apportionment of aerosol organics and for studying atmospheric processes leading to secondary organic aerosol formation. The two derivatization procedures most widely used in GC analysis of dicarboxylic acids were compared: esterification using BF₃/alcohol reagent and silylation using N,O-bis(trimethylsilyl)-trifluoroacetamide (BSTFA). The advantages and drawbacks of the two methods are investigated and compared in terms of (1) precision and accuracy of the results and (2) sensitivity and detection limit of the procedure. The comparative investigation was performed on standard solutions containing target C₃–C₉ dicarboxylic acids and on experimental particulate matter (PM) samples. Attention was focused on low-volume sampling devices that collect small amounts of sample for organic speciation. The results show that, overall, both the techniques appear suitable for the analysis of LMW dicarboxylic acids in atmospheric aerosols since they provide low detection limits (≤4 ng m⁻³) and satisfactory reproducibility (RSD% ≤ 15%). Between them, BSTFA should be the reagent of choice under the most limiting conditions of PM filters collected by low-volume air samplers: It provides determination of all the target C₃–C₉ dicarboxylic acids with lower detection limits (≤2 ng m⁻³) and higher reproducibility (RSD% ≤ 10%)      

Adapting N‐Heterocyclic Carbene/Azide Coupling Chemistry for Polymer Synthesis: Enabling Access to Aromatic Polytriazenes

A click by any other name : Coupling bis(N‐heterocyclic carbene)s with bis(azide)s afforded a novel class of conjugated polytriazenes. These polymers were rendered electrically conductive upon doping, and fluorene‐containing variants exhibited luminescence. This adaptation of N‐heterocyclic carbene (NHC)/azide coupling chemistry to polymer synthesis reveals the potential of NHCs as building blocks for accessing polymers having useful electronic properties.

     

Multiscale Modeling for the Simulation of Damage Processes at Refractory Materials under Thermal Shock

Refractory materials, for example ceramic materials, initially contain a multitude of defects such as voids, microcracks, grain boundaries etc. The deformation process and failure mechanisms due to thermal shock at high temperatures above 1000°C are going along with the creation of new micro defects as well as the growth and coalescence of cracks. A material damage model based on the theoretical concept of damage mechanics and the mechanics of microcracks is presented in this paper. Cell models are developed as representative volume elements (RVE) including crack initiation and growth as well as microstructural shielding effects. For simple configurations of the microstructure, the relation between stress, strain and temperature is derived from analytical considerations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Riemann–Hilbert formulation for the KdV equation on a finite interval

The initial-boundary value problem for the KdV equation on a finite interval is analyzed in terms of a singular Riemann–Hilbert problem for a matrix-valued function in the complex k-plane which depends explicitly on the space–time variables. For an appropriate set of initial and boundary data, we derive the k-dependent “spectral functions” which guarantee the uniqueness of Riemann–Hilbert problem's solution. The latter determines a solution of the initial-boundary value problem for KdV equation, for which an integral representation is given. To cite this article: I. Hitzazis, D. Tsoubelis, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Metal clusters as ligands. Substitution of fe ions in Fe/Mo/S clusters by thiophilic CuI ions

The reactivity of Fe/S and Fe/Mo/S clusters, similar or analogous to those occurring in biological systems, with thiophilic metal ions has not been explored. In this Communication, we demonstrate that synthesis of heteropolynuclear clusters with different coordination geometries for different metals at different sites is possible by metal substitution or by metal addition reactions. The two clusters we report herein ([(Cl4-cat)2Mo2Cu5Fe4S9(PnPr3)7(SPnPr3)2]PF6 and [(Cl4-cat)2Mo2Cu6Fe4S10(PnPr3)8]) contain Fe, Mo, and Cu, which display pseudotetrahedral, pseudooctahedral, and pseudotrigonal geometries, respectively. The synthesis of these clusters is achieved by the addition of appropriate amounts of [Cu(CH3CN)4]+ to [(Cl4-cat)2Mo2Fe8(PnPr3)6]. The formation of the different products is temperature- and solvent-dependent. The Cu(I) units incorporated into the metal cluster framework, either bind to available lone pairs of the already bridging S ligands or displace the less thiophilic Fe atoms. Among the essential features of these new molecules are recognizable Fe/S fragments including an Fe6S9 core in the first cluster and the pentlandite Fe4Cu4S6 core in the second cluster.     

In silico analysis of the thermodynamic stability changes of psychrophilic and mesophilic alpha-amylases upon exhaustive single-site mutations

Identifying sequence modifications that distinguish psychrophilic from mesophilic proteins is important for designing enzymes with different thermodynamic stabilities and to understand the underlying mechanisms. The PoPMuSiC algorithm is used to introduce, in silico, all the single-site mutations in four mesophilic and one psychrophilic chloride-dependent alpha-amylases and to evaluate the changes in thermodynamic stability. The analysis of the distribution of the sequence positions that could be stabilized upon mutation shows a clear difference between the three domains of psychrophilic and mesophilic alpha-amylases. Most of the mutations stabilizing the psychrophilic enzyme are found in domains B and C, contrary to the mesophilic proteins where they are preferentially situated in the catalytic domain A. Moreover, the calculations show that the environment of some residues responsible for the activity of the psychrophilic protein has evolved to reinforce favorable interactions with these residues. In the second part, these results are exploited to propose rationally designed mutations that are predicted to confer to the psychrophilic enzyme mesophilic-like thermodynamic properties. Interestingly, most of the mutations found in domain C strengthen the interactions with domain A, in agreement with suggestions made on the basis of structural analyses. Although this study focuses on single-site mutations, the thermodynamic effects of the recommended mutations should be additive if the mutated residues are not close in space.     

Development of novel statistical potentials describing cation-pi interactions in proteins and comparison with semiempirical and quantum chemistry approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation-pi and amino-pi interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation-pi and amino-pi systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree-Fock level (HF) and at the second order of the M?ller-Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation-pi statistical potentials suggests their utility in protein structure and stability prediction and in protein design.