Novel thiazole and oxazole containing cyclic hexapeptides from a waterbloom of the cyanobacterium Microcystis sp.

Eight novel thiazole and oxazole containing cyclic peptides, microcyclamides GL616, GL582, GL614A, GL614B, GL614C, GL546A, GL546B, and GL628, as well as the known microcyclamide A, were isolated from the hydrophylic extract of a Microcystis sp. water-bloom collected in Gilboa reservoir, Valley of Armageddon, Israel. The planar structure of the compounds was determined by homonuclear and inverse-heteronuclear 2D NMR techniques as well as high-resolution mass spectrometry. The absolute configuration of the asymmetric centers of the amino acids was studied using Marfey's method for HPLC following ozonolysis, hydrolysis and derivatization with Marfey's reagent. This is the first example where acidic and modified amino acids are incorporated in this group of ribosomally biosynthesized metabolites.     

Facile structural elucidation of imidazoles and oxazoles based on NMR spectroscopy and quantum mechanical calculations

The reaction of 1,2,3-tricarbonyl derivatives with hexamethylenetetramine and ammonium acetate in acetic acid provides an unambiguous approach to the synthesis of imidazoles, whereas the Bredereck reaction of α-haloketones in formamide, yields both imidazoles and oxazoles. Herein we describe a facile methodology for distinguishing between these heterocyclic compounds based on a combination of NMR spectroscopy and quantum mechanical calculations. In the NMR data the oxazole C-2 has a chemical shift of ca. 150 ppm whereas in the imidazoles it is found at ca. 135 ppm, with a ¹J_C-H of ca. 250 Hz for the oxazoles and ca. 210 Hz for the imidazoles. ¹J_C-H values can be easily obtained from a gated-decoupled ¹³C spectrum, and even more trivially, from the separation of the H-2 ¹³C satellites in the ¹H spectra. Additionally, the computed NMR data, obtained from density functional theory, are found to be in good agreement with the experimental data and serve as valuable tools in identifying the products of the Bredereck reaction.     

The Graver Complexity of Integer Programming

In this article we establish an exponential lower bound on the Graver complexity of integer programs. This provides new type of evidence supporting the presumable intractability of integer programming. Specifically, we show that the Graver complexity of the incidence matrix of the complete bipartite graph K ₃,m satisfies g(m) = Ω(2 ^m ), with g(m) ≥ 17·2 ^m−3 –7 for every m > 3.     

Dualities and the phase diagram of the p-clock model

A new “bond-algebraic” approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and p-clock models. By combining duality and Peierls arguments, we establish the existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when p?5. This latter symmetry is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for p?5, is critical (massless) with decaying power-law correlations.     

High-multiplicity N-fold IP via configuration LP

Mathematical Programming - N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully...