Systematic ratio normalization of gas chromatography signals for biological sample discrimination and biomarker discovery

The present paper introduces a new gas chromatography data processing procedure dubbed systematic ratio normalization (SRN) enabling to improve both sample set discrimination and biomarker identification. SRN consists in (1) calculating, for each sample, all the log-ratios between abundances of chromatography-analyzed compounds, then (2) selecting the log-ratio(s) that best maximize the discrimination between sample-sets. The relevance of SRN was evaluated on two data sets acquired through gas chromatography–mass spectrometry as part of separate studies designed (i) to discriminate source-origins between vegetable oils analyzed via an analytical system exposed to instrument drift (data set 1) and (ii) to discriminate animal feed between meat samples aged for different durations (data set 2). Applying SRN to raw data made it possible to obtain robust discrimination models for the two data sets by enhancing the contribution to the data variance of the factor-of-interest while stabilizing the contribution of the disturbance factor. The most discriminant log-ratios were shown to employ the most relevant biomarkers presenting relative independence of the factor-of-interest as well as co-behavior of the disturbance effects potentially biasing the discrimination, such as instrument drift or sample biochemical changes. SRN can be run a posteriori on any data set, and might be generalizable to most of separating methods.     

Conformal autosimilarity

We prove that the conformally autosimilar closed subsets of the Euclidean sphere are exactly the limit sets of convex cocompact Kleinian groups. We also prove other similar results.     

Discreteness criterion for subgroups of products of SL(2)

Let G be a finite product of SL(2, K _i )’s for local fields K _i of characteristic zero. We present a discreteness criterion for nonsolvable subgroups of G containing an irreducible lattice of a maximal unipotent subgroup of G. In particular, such a subgroup has to be arithmetic. This extends a previous result of A. Selberg when G is a product of SL₂( \mathbbR \mathbb{R} )’s.     

A local convergence property of primal-dual methods for nonlinear programming

We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the original primal-dual system are perturbed by a parameter driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by applying the fraction to the boundary rule to maintain strict feasibility of the iterates with respect to the nonnegativity constraints. The analysis of the rate of convergence is carried out by considering an arbitrary sequence of perturbation parameters converging to zero. We first show that, once an iterate belongs to a neighbourhood of convergence of the Newton method applied to the original system, then the whole sequence of iterates converges to the solution. In addition, if the perturbation parameters converge to zero with a rate of convergence at most superlinear, then the sequence of iterates becomes asymptotically tangent to the central trajectory in a natural way. We give an example showing that this property can be false when the perturbation parameter goes to zero quadratically.      

Mechanical Modulation of the Solid-State Luminescence of Tricarbonyl Rhenium(I) Complexes through the Interplay between Two Triplet Excited States

Mechanoresponsive luminescence (MRL) materials promise smart devices for sensing, optoelectronics and security. We present here the first report on the MRL activity of two Re^I complexes, opening up new opportunities for applications in these fields. Both complexes exhibit marked solid-state luminescence enhancement (SLE). Furthermore, the pristine microcrystalline powders emit in the yellow-green region, and grinding led to an amorphous phase with concomitant emission redshift and shrinking of the photoluminescence (PL) quantum yields and lifetimes. Quantum chemical calculations revealed the existence of two low-lying triplet excited states with very similar energy levels, that is, ³IL and ³MLCT, having, respectively, almost pure intraligand (IL) and metal-to-ligand charge-transfer (MLCT) character. Transition between these states could be promoted by rotation around the pyridyltriazole−phenylbenzoxazole bond. In the microcrystals, in which rotations are hindered, the ³IL state induces the prominent PL emission at short wavelengths. Upon grinding, rotation is facilitated and the transition to the ³MLCT state results in a larger proportion of long-wavelength PL. FTIR and variable-temperature PL spectroscopy showed that the opening of the vibrational modes favours non-radiative deactivation of the triplet states in the amorphous phase. In solution, PL only arises from the ³MLCT state. The same mechanism accounts for the spectroscopic differences observed when passing from crystals to amorphous powders, and then to solutions, thereby clarifying the link between SLE and MRL for these complexes.     

Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets

The aim of this paper is to study the geometrical and topological structure of the efficient frontier of simply-shaded sets in a three-dimensional Euclidean space with respect to the usual positive cone. Our main result concerns the contractibility of the efficient frontier and refines a recent result of Daniilidis, Hadjisavvas, and Schaible (Ref. 1) regarding the connectedness of the efficient outcome set for three-criteria optimization problems involving continuous semistrictly quasiconcave objective functions.     

Connectedness of the Efficient Set for Strictly Quasiconcave Sets

Given a closed subset X in , we show the connectedness of its efficient points or nondominated points when X is sequentially strictly quasiconcave. In the particular case of a maximization problem with n continuous and strictly quasiconcave objective functions on a compact convex feasible region of , we deduce the connectedness of the efficient frontier of the problem. This work solves the open problem of the efficient frontier for strictly quasiconcave vector maximization problems.