The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Platanus acerifolia’s buds: additional non-polar metabolites and structure revision of two previous dihydrochalcone-like metabolites

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the n-hexane extract of the fresh unripe buds resulted in the isolation of 11 metabolites. Besides six common wax constituents, the n-hexane portion led to the isolation of four gem-dimethylpyrano flavanones. They corresponded to two pairs of angular and linear isomers derived only from pinocembrin (5,7-dihydroxyflavanone). Additionally, a novel β-decadione was split into the major keto-enol tautomer as shown by the detailed NMR and EIMS analyses. Moreover, the structures of grenoblone and 4-hydroxygrenoblone, two previously reported dihydrochalcone-like metabolites, were revised according to the EIMS spectra.     

One-Dimensional Particle Processes with Acceleration/Braking Asymmetry

The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental Diagram of traffic and to be associated to hysteresis effects of traffic flow. We study this question in the context of exclusion and queueing processes, by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t. the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability are observed, depending on the level of the aforementioned asymmetry. In addition, we provide a large deviation formulation of the fundamental diagram which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Optical microscopy to study single nanoparticles electrochemistry: From reaction to motion

Nanoparticles (NPs)-based electrochemical devices are generating a growing interest and optical microscopy has recently proven to be a powerful tool to apprehend their electrochemical behavior. Through several striking examples, this review demonstrates how label-free optical imaging coupled to an electrochemical actuation can be used to probe operando the physical and electrochemical properties of single NPs, with high resolution and sensitivity and without additional emitters. Such an approach can be particularly relevant to establish clear structure-motion/reactivity relationships required to optimize NPs exploited as electrode materials.     

MS Analysis and Molecular Characterization of Botrytis cinerea Protease Prot-2. Use in Bioactive Peptides Production

Prot-2 protease previously purified to homogeneity from Botrytis cinerea showed potentiality to be used in detergency and for production of bioactive peptides. To extend the characterization of Prot-2 protease, antifungal and antibacterial assays were performed in vitro using protein hydrolysates prepared from muscle of mackerel (Scomber scomborus) treated with this enzyme. The most active hydrolysate (degree of hydrolysis of 8 %) exhibited inhibition effect towards bacteria and phytopathogenic fungi, demonstrating that Prot-2 proteolysis generated bioactive peptides. Biochemical and molecular characterization of the purified Prot-2, by SDS-PAGE/Tryptic in gel-digestion and LC-MS/MS analysis, was investigated. The peptide amino acid sequence alignment search in database revealed a moderate homology between the determined amino acid sequence of Prot-2 protease and the known fungal trypsin/chymotrypsin in particular from Glomerella, Metarhizium and Streptomyces. From peptide sequence data obtained by mass spectrometry and sequences homologies, primers were defined and a cDNA fragment of 786 bp was amplified by RT-PCR. The cDNA nucleotide sequence analysis revealed an open reading frame coding for 262 amino acid residues. The deduced amino acid sequence of Prot-2 showed moderate identity with trypsin of Glomerella graminicola (74 %) and with chymotrypsin from Metarhizium anisopliae (71 %). Prot-2 exhibited a Ser protease homology and showed in addition the specific His motif of trypsin/chymotrypsin family.     

Biselective refocusing pulses and the SERF experiment

The SERF experiment is a variant of the homonuclear J-resolved experiment, in which a single coupling constant is measured. It consists of a single chemical shift selective excitation that is followed by a biselective spin echo. Recent articles mention the existence of artefacts in SERF spectra that are supposedly related to pulse imperfections. This article presents a detailed study of the biselective refocusing pulses. It also reports a method for predicting the position and amplitude of the expected and unexpected 2D spectral peaks in SERF spectra. Artefacts can be partially eliminated by phase cycling or by the introduction of static field gradient pulses in the acquisition sequence. A procedure to obtain of pure absorption peaks in SERF spectra is proposed.