On the exterior algebra method applied to restricted set addition

In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A$A$ of the p$p$-element group Z/pZ$\mathbb{Z}/p\mathbb{Z}$ (where p$p$ is a prime), at least min{p,m|A|−m²+1}$min\{p,m\left|A\right|-m^2+1\}$ different elements of the group can be written as the sum of m$m$ different elements of A$A$. In this note we present an easily accessible simplified version of their proof for the case m=2$m=2$, and explain how the method can be applied to obtain the corresponding inverse theorem.     

Subdiffraction resolution in total internal reflection fluorescence microscopy with a grating substrate

We propose a fluorescence surface imaging system that presents a power of resolution beyond that of the diffraction limit without resorting to saturation effects or probe scanning. This is achieved by depositing the sample on an optimized periodically nanostructured substrate in a standard total internal reflection fluorescence microscope. The grating generates a high-spatial-frequency light grid that can be moved throughout the sample by changing the incident angle. An appropriate reconstruction procedure permits one to recover the fluorescence amplitude from the images obtained for various incidences. Simulations of this imaging system show that the resolution is not limited by diffraction but by the period of the grating.     

Standardless identification of selenocystathionine and its gamma-glutamyl derivatives in monkeypot nuts by 3D liquid chromatography with ICP-MS detection followed by nanoHPLC-Q-TOF-MS/MS

A three-step chromatographic procedure using orthogonal separation mechanisms (size-exclusion, cation-exchange and ion-pairing reversed phase) was developed to purify three low molecular weight selenospecies, including the major compound, from the aqueous extract of monkeypot (Lecythis minor) nuts. The following reversed-phase nanoHPLC-electrospray Q-TOF-MS/MS allowed the formal standardless identification of selenocystathionine and two isoforms of gamma-glutamyl-selenocystathionine. This is the first MS and MS/MS-based formal evidence of the presence of these compounds in a biological sample.     

Structure-activity-based design of a synthetic malaria peptide eliciting sporozoite inhibitory antibodies in a virosomal formulation

The circumsporozoite protein (CSP) of Plasmodium falciparum is a leading candidate antigen for inclusion in a malaria subunit vaccine. We describe here the design of a conformationally constrained synthetic peptide, designated UK-39, which has structural and antigenic similarity to the NPNA-repeat region of native CSP. NMR studies on the antigen support the presence of helical turn-like structures within consecutive NPNA motifs in aqueous solution. Intramuscular delivery of UK-39 to mice and rabbits on the surface of reconstituted influenza virosomes elicited high titers of sporozoite crossreactive antibodies. Influenza virus proteins were crucially important for the immunostimulatory activity of the virosome-based antigen delivery system, as a liposomal formulation of UK-39 was not immunogenic. IgG antibodies elicited by UK-39 inhibited invasion of hepatocytes by P. falciparum sporozoites, but not by antigenically distinct P. yoelii sporozoites. Our approach to optimized virosome-formulated synthetic peptide vaccines should be generally applicable for other infectious and noninfectious diseases.     

The 0-1 Knapsack problem with a single continuous variable

Specifically we investigate the polyhedral structure of the knapsack problem with a single continuous variable, called the mixed 0-1 knapsack problem. First different classes of facet-defining inequalities are derived based on restriction and lifting. The order of lifting, particularly of the continuous variable, plays an important role. Secondly we show that the flow cover inequalities derived for the single node flow set, consisting of arc flows into and out of a single node with binary variable lower and upper bounds on each arc, can be obtained from valid inequalities for the mixed 0-1 knapsack problem. Thus the separation heuristic we derive for mixed knapsack sets can also be used to derive cuts for more general mixed 0-1 constraints. Initial computational results on a variety of problems are presented. Received May 22, 1997 / Revised version received December 22, 1997 Published online November 24, 1998     

Renormalization Group for Strongly Coupled Maps

Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular class of configurations nor to some vanishingly small region of parameter space. After defining the strong-coupling limit in which the RG applies to almost all asymptotic solutions, we first present the simple case of coupled tent maps. We then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties, extending the formal approach developed by Collet and Eckmann for single maps. We finally discuss and illustrate the general consequences of the RG: CMLs are shown to share universal properties in the space-continuous limit which emerges naturally as the group is iterated. We prove that the scaling properly ties of the local map carry to the coupled systems, with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems. This explains various scaling laws and self-similar features previously observed numerically.     

Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised Lorenz system; then using the new system a new complex no equilibrium point hyperchaotic system is reported. Both the new systems have hidden chaotic attractors. Various dynamical behaviours are observed in the new systems like chaotic, periodic, quasi-periodic and hyperchaotic. Both the systems have inverse crisis route to chaos with the variation of parameter a and crisis route to chaos with the variation of parameters \(b,\ c\) and d. These phenomena along with hidden attractors in a complex hyperchaotic system are not seen in the literature. Synchronisation between the identical new hyperchaotic systems is achieved using the contraction theory. Further the synchronisation between the identical new complex hyperchaotic systems is achieved using adaptive contraction theory. The proposed synchronisation strategies are validated using the MATLAB simulation and circuit implementation results. Further, an application of the proposed system is shown by transmitting and receiving an audio signal.     

5-Aminooxazole as an internal traceless activator of C-terminal carboxylic acid: rapid access to diversely functionalized cyclodepsipeptides

A conceptually novel macrolactonization protocol has been developed. It is a domino process involving a sequence of: 1) protonation of 5-aminooxazole leading to the electrophilic iminium salt; 2) trapping of the iminium species by the neighboring C-terminal carboxylic acid leading to a putative spirolactone; and 3) intramolecular nucleophilic addition of the tethered alcohol to the spirolactone followed by fragmentation. The strategically incorporated 5-aminooxazole serves as an internal traceless activator of the neighboring C-terminal carboxylic acid, since it became an integral part of the peptide backbone after cyclization. No coupling reagent is required and the entire sequence is triggered by just a few equivalents of trifluoroacetic acid under very mild conditions (MeCN as the solvent at room temperature). The spirolactone as an activated form of the carboxylic acid has been evidenced by a sulfur-migration experiment. By combining with a three-component synthesis of 5-aminooxazole, a two-step synthesis of structurally complex cyclodepsipeptides from readily accessible starting materials was developed.     

Simultaneous determination of monomethylmercury, monobutyltin, dibutyltin and tributyltin in environmental samples by multi-elemental-species-specific isotope dilution analysis using electron ionisation GC-MS

In this work, the simultaneous determination of four organometallic species (monomethylmercury, monobutyltin, dibutyltin and tributyltin) in environmental samples by using a GC-MS system with electron ionisation has been established. The measurement of isotope ratios in each species was accomplished by selecting the most adequate molecular cluster, and simple mathematical equations were applied to correct the contributions of 13C from the organic groups attached to the tin and mercury atoms. The influence of different parameters such as dwell time on the precision and accuracy of the measured isotope ratios in each target species has also been studied. The determination and the sample preparation procedures presented in this work were first individually validated by analysing several certified reference materials for butyltin compounds (mussel tissue CRM-477 and marine sediment SOPH-1) and for monomethylmercury (tuna fish CRM-464) using an innovative focused microwave technology for the extraction of the species from the solid samples. Additionally, the simultaneous determination of the four species was successfully validated by obtaining quantitative recoveries in spiked natural waters and by analysing the certified reference material BCR-710 (certified in tributyltin and monomethylmercury). The values obtained in such certified tissue were fully in agreement not only with the certified mass fractions but also with the proposed indicative values for mono- and dibutyltin.