The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

On the Stereochemistry of Natural Irones,Dihydroirones, and their Precursors

Natural irones from the essential oil of Iris rhizomes develop by oxidative degradation of C₃₁-triterpenoids produced by the plant. Two enantiomeric forms of irones are found in Iris, oils of different origin. The optical properties and CD spectra of irones, dihydroirones and their C₃₁-precursors are reported and their absolute stereochemistry is determined.     

Foreword

Foundations of Computational Mathematics -     

Ascospiroketals A and B, unprecedented cycloethers from the marine-derived fungus Ascochyta salicorniae

Chemical investigation of the marine-derived fungus Ascochyta salicorniae led to the isolation of two novel natural products, ascospiroketals A (1) and B (2). From a biosynthetic standpoint, the compounds possess new ring systems. [structure: see text].     

Characterization of ethyl chloroformate derivative of <Emphasis Type="Italic">β</Emphasis>-methylamino-<Emphasis Type="SmallCaps">l</Emphasis>-alanine

Beta-methylamino-L-alanine (BMAA) is a neurotoxic amino acid that can be produced by cyanobacteria in aqueous environments. To analyze this compound by gas chromatography/mass spectrometry (GC/MS), BMAA must be derivatized to a nonpolar, volatile compound. This can be accomplished by reacting BMAA with ethyl chloroformate. While carrying out electron ionization (EI) mass spectrometric analysis on the (13)C-labeled derivative, it was discovered that the formation of an ion with a peak at m/z 245.12 is the result of [CH(3)CH(2)O.] loss from the amino groups resulting from alpha-cleavage. This differs from previous reports that attributed this peak to alpha-cleavage of the carboxylic ester portion of the BMAA derivative. This finding is important for understanding BMAA derivative mass spectrometric fragmentation patterns and ultimately to properly identifying and quantifying BMAA. Fragmentation pathways for the formation of other major peaks observed in the EI mass spectra are also proposed.     

Newton–Hensel Interpolation Lifting

The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power p^k for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤ_p. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].     

Polyketides from the marine-derived fungus Ascochyta salicorniae and their potential to inhibit protein phosphatases

Chemical investigation of the marine fungus Ascochyta salicorniae led to the isolation of two new epimeric compounds, ascolactones A (1) and B (2), in addition to the structurally-related polyketides hyalopyrone (3), ascochitine (4), ascochital (5) and ascosalipyrone (6). The absolute configurations of the epimeric compounds 1 and 2 were assigned as (1R,9R) and (1S,9R), respectively, through simulation of the chiroptical properties using quantum-chemical CD calculations, and chiral GC-MS subsequent to oxidative cleavage (Baeyer-Villiger oxidation) of the side chain. In silico screening using the PASS software identified some of the A. salicorniae compounds (1-6) as potential inhibitors of protein phosphatases. Compound was found to inhibit the enzymatic activity of MPtpB with an IC(50) value of 11.5 microM.     

Electron Transfer in a Supramolecular Associate of a Fullerene Fragment

Herein, we investigate the association of a fullerene fragment, hemifullerene C₃₀H₁₂, with an electron‐donating bowl‐shaped tetrathiafulvalene derivative (truxTTF). UV/Vis titrations and DFT calculations support formation of the supramolecular complex, for which an association constant of log K_a=3.6±0.3 in CHCl₃ at room temperature is calculated. Remarkably, electron transfer from truxTTF to C₃₀H₁₂ to form the fully charge‐separated species takes place upon irradiation of the associate with light, constituting the first example in which a fullerene fragment mimics the electron‐accepting behavior of fullerenes within a supramolecular complex.