A Note on the Morozov Principle via Lagrange Duality

Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics.     

Robust network design in telecommunications under polytope demand uncertainty

We consider a model for robust network design in telecommunications, in which we minimize the cost of the maximum mismatch between supply and demand. In the present study, the demand is uncertain and takes its values in a polytope defined by constraints. This problem is hardly tractable, so we limit ourselves to computing lower bounds (by a column-generation mechanism) and upper bounds (using an algorithm due to Falk and Soland for maximizing a separable convex function over a polytope). The experimental gap obtained turns out to be large, and this seems to be mainly due to poor upper bounds. Two possible solutions are suggested for further research aimed at improving them: dc optimization (to minimize the difference of two convex functions) and AARC modeling (affinely adjustable robust counterpart).     

Effect of matrices and additives on phosphorylated and ketodeoxyoctonic acid lipids A analysis by matrix‐assisted laser desorption ionization‐mass spectrometry

Lipid A is a major compound of the outer membrane of gram‐negative bacteria and is a key factor of bacterial virulence. As lipid A's structure differs among bacterial species and varies between strains of the same species, knowing its modifications is essential to understand its implications in the infectious process. To analyze these lipids, matrix‐assisted laser desorption ionization‐mass spectrometry (MALDI‐MS) is a well‐suited method that is fast and efficient. However, there are limitations with the matrix and additives used, such as the suppression of signal or prompt fragmentations that could give a false overview of lipid A composition in biological samples. For a comprehensive analysis of the entire lipid A species present in a sample, we tested 16 matrices and 11 additives on two commercial lipids A. The first commercial one contains single phosphorylation group, and the second contains two phosphorylation and two ketodeoxyoctonic acid (KDO) groups. The lipid A containing KDO groups was essentially detected by the 3‐hydroxypicolinic acid (3‐HPA) matrix, whereas the monophosphorylated lipid A could be detected by 13 matrices out of the 16. We also demonstrated that the signal of diphosphorylated lipid A can be enhanced with the use of additives in the matrix. Our study indicated that the best conditions to obtain a clear signal of both lipids A without prompt fragmentation was the use of 3‐HPA with 10mM trifluoroacetic acid (TFA).     

Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Spectral Convex Functions of Operators and Approximate Intertwining Relationships

We develop theoretical tools for the analysis of convex spectral functions of non-symmetric operators on Hilbert spaces. The obtained results are applied to an optimization problem arising from the theory of inverse problems, which involves the notion of intertwining relationship.     

New Insights into the Reactivity of Cisplatin with Free and Restrained Nucleophiles: Microsolvation Effects and Base Selectivity in Cisplatin–DNA Interactions

The reactivity of cisplatin towards different nucleophiles has been studied by using density functional theory (DFT). Water was considered first to analyze the factors that govern the transformation of cisplatin into more electrophilic aquated species by using an activation‐strain model. It was found that the selectivity and reactivity of cisplatin is a delicate trade‐off between strain and interaction energies and that the second chloride is a worse leaving group than the first. When similar studies were carried out with imidazole, guanine (G), and adenine (A), it was found that in general the second nucleophilic substitution reactions have lower activation barriers than the first ones. Finally, simulations of the structural restrictions imposed by the DNA scaffold in intra‐ and interstrand processes showed that the geometries of the reaction products are nonoptimal with respect to the unrestrained A and G nucleophiles, although the energetic cost is not considerable under physiological conditions, which thus permits nucleophilic substitution reactions that lead to highly distorted DNA.     

Evaluation of the activity of the sponge metabolites avarol and avarone and their synthetic derivatives against fouling micro- and macroorganisms

The sesquiterpene hydroquinone avarol (1) was isolated from the marine sponge Dysidea avara, whereas the corresponding quinone, avarone (2), was obtained by oxidation of avarol, and the significantly more lipophilic compounds [3'-(p-chloro-phenyl)avarone (3), 3',4'-ethylenedithioavarone (4), 4'-isopropylthioavarone (5), 4'-tert-butylthioavarone (6), 4'-propylthioavarone (7), 4'-octylthioavarone (8)] were obtained by nucleophilic addition of thiols or p-chloroaniline to avarone. All these compounds were tested, at concentrations ranging from 0.5 to 50 microg/mL, for their effect on the settlement of the cyprid stage of Balanus amphitrite, for toxicity to both nauplii and cyprids and for their growth inhibitory activity on marine bacteria (Cobetia marina, Marinobacterium stanieri, Vibrio fischeri and Pseudoalteromonas haloplanktis) and marine fungi (Halosphaeriopsis mediosetigera, Asteromyces cruciatus, Lulworthia uniseptata and Monodictys pelagica).     

Analysis of amino acids by combination of carrier ampholyte-free IEF with ITP

The use of carrier ampholyte-free IEF (CAF-IEF) with ITP mobilization and conductivity detection in ITP mode for preconcentration and analysis of amino acids is demonstrated. The analytical procedure consists of three subsequent steps. In the first step, amino acids are continuously dosed from an infinite volume reservoir by electromigration to the column, where a sharp, stationary neutralization reaction boundary (NRB) is created in between acidic and basic primary electrolyte. Here, amino acids are selectively focused (trapped), if their pI falls to the pH difference on both sides of the NRB (pH gap). Amino acids create sharp rectangular zones, arranged according to their pI values. In the second step, focused zones are mobilized. After accumulation of the detectable amount of amino acids, dosing electrolyte in the infinite volume reservoir is changed for the mobilizing electrolyte. The migration mode is changed from CAF-IEF to ITP and substances start to migrate toward the analytical capillary. In the third step, analytes are transferred into the analytical column equipped with a conductivity detector and are detected in the new leading electrolyte in an ITP migration mode. The presented CAF-IEF-ITP-ITP with time-dependent accumulation of the large-volume sample enables to achieve in a reasonable time a 100 times lower c-LOD (here in orders of nmol/L), than can be reached by conventional hyphenated ITP-ITP.     

Transimination: An efficacious reaction for the synthesis of macrocycles

A new family of main-chain liquid crystal polymers containing azomethine units have been synthesized and characterized. Our attention has been focused on their strong tendency to generate macrocyclic dimers (AB)² constituted with two mesogenic rods and siloxane spacers. In favourable conditions (diluted solution, acid catalysis) macrocycles may be rapidly formed and purely obtained by fractionation. Synthetic aspects and main thermotropic properties are discussed. In spite of their large size some macrocycles have been obtained as single crystals and then characterized by X-ray diffraction.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.