A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N-fold integer minimization problems for which our approach provides polynomial time solution algorithms.     

Aromatic compounds produced by endophytic fungi isolated from red alga Asparagopsis taxiformis - Falkenbergia stage

Endophytic fungi were isolated from red alga Asparagopsis taxiformis - Falkenbergia stage, collected from the Brazilian coast, and were identified as Annulohypoxylon stygium (AT-03) and A. yungensis (AT-06) based on their macro/micromorphological and molecular features. Bioassay-guided fractionation of the EtOAc extract from laboratory cultures of both strains yielded known compounds pyrogallol from A. stygium, (3R)-scytalone and (3R,4R)-4-hydroxy-scytalone from A. yungensis. Pyrogallol was active against methicillin-resistant Staphylococcus aureus (MRSA) and Escherichia coli strains. An inactive fraction from A. stygium afforded two additional compounds, (3R,4R)-3,4,5-trihydroxy-1-tetralone and tyrosol. Optically active compounds had their stereochemistry determined by circular dichroism (CD) spectroscopy.     

Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A_n has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥₂. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.     

Aromatic interactions impact ligand binding and function at serotonin 5-HT2C G protein-coupled receptors: receptor homology modelling,ligand docking,and molecular dynamics results validated by experimental studies

The serotonin (5-hydroxytryptamine, 5-HT) 5-HT₂ G protein-coupled receptor (GPCR) family consists of types 2A, 2B, and 2C that share ～75% transmembrane (TM) sequence identity. Agonists for 5-HT_2C receptors are under development for psychoses; whereas, at 5-HT_2A receptors, antipsychotic effects are associated with antagonists – in fact, 5-HT_2A agonists can cause hallucinations and 5-HT_2B agonists cause cardiotoxicity. It is known that 5-HT_2A TM6 residues W6.48, F6.51, and F6.52 impact ligand binding and function; however, ligand interactions with these residues at the 5-HT_2C receptor have not been reported. To predict and validate molecular determinants for 5-HT_2C-specific activation, results from receptor homology modelling, ligand docking, and molecular dynamics simulation studies were compared with experimental results for ligand binding and function at wild type and W6.48A, F6.51A, and F6.52A point-mutated 5-HT_2C receptors.     

The optimisation of ultrasonic cleaning procedures for dairy fouled ultrafiltration membranes

Ultrafiltration (UF) of whey is a major membrane based process in the dairy industry. However, commercialization of this application has been limited by membrane fouling, which has a detrimental influence on the permeation rate. There are a number of different chemical and physical cleaning methods currently used for cleaning a fouled membrane. It has been suggested that the cleaning frequency and the severity of such cleaning procedures control the membrane lifetime. The development of an optimal cleaning strategy should therefore have a direct implication on the process economics. Recently, the use of ultrasound has attracted considerable interest as an alternative approach to the conventional methods. In the present study, we have studied the ultrasonic cleaning of polysulfone ultrafiltration membranes fouled with dairy whey solutions. The effects of a number of cleaning process parameters have been examined in the presence of ultrasound and results compared with the conventional operation. Experiments were conducted using a small single sheet membrane unit that was immersed totally within an ultrasonic bath. Results show that ultrasonic cleaning improves the cleaning efficiency under all experimental conditions. The ultrasonic effect is more significant in the absence of surfactant, but is less influenced by temperature and transmembrane pressure. Our results suggest that the ultrasonic energy acts primarily by increasing the turbulence within the cleaning solution.     

Graver basis and proximity techniques for block-structured separable convex integer minimization problems

We consider $N$ -fold $4$ -block decomposable integer programs, which simultaneously generalize $N$ -fold integer programs and two-stage stochastic integer programs with $N$ scenarios. In previous work (Hemmecke et al. in Integer programming and combinatorial optimization. Springer, Berlin, 2010), it was proved that for fixed blocks but variable  $N$ , these integer programs are polynomial-time solvable for any linear objective. We extend this result to the minimization of separable convex objective functions. Our algorithm combines Graver basis techniques with a proximity result (Hochbaum and Shanthikumar in J. ACM 37:843–862,1990), which allows us to use convex continuous optimization as a subroutine.     

An Asymmetric Synthesis of L-694,458, a Human Leukocyte Elastase Inhibitor, via Novel Enzyme Resolution of beta-Lactam Esters

A convergent synthesis of [S-(R,S)]-2-[4-[(4-methylpiperazin-1-yl)carbonyl]phenoxy]-3,3-diethyl-N-[1-[3,4-(methylenedioxy)phenyl]butyl]-4-oxo-1-azetidinecarboxamide (L-694,458, 1), a potent human leukocyte elastase inhibitor, was achieved via chiral synthesis of key intermediates: (S)-3,3-diethyl-4-[4'-[(N-methylpiperazin-1-yl)carbonylphenoxy]-2-azetidinone (2) and (R)-alpha-propylpiperonyl isocyanate (3). Synthesis of beta-lactam 2 was achieved by a novel enantioselective lipase hydrolysis of ester 5 to produce (S)-3,3-diethyl-4-(4'-carboxyphenoxy)-2-azetidinone (6) (60% yield, three cycles, 93% ee) with isolation, epimerization, and recycling of the undesired (R)-ester 5. Isocyanate 3 was prepared by chiral addition of Zn(n-Pr)(2) to piperonal (98% yield, 99.2% ee), azide displacement and reduction to (R)-alpha-propylpiperonylamine (11) (58% yield, 85% ee), crystallization as the D-pyroglutamic acid salt (92% yield, 98.2% ee), and isocyanate formation (98% yield) with phosgene.     

Photocyclization of 2-(naphth-1-yl)-3-(thien-2-yl)propenoic acid and the total assignment of the 1H- and 13C-NMR spectra of the product

Photocyclization of the substituted 2-(naphth-1-yl)-3-(thien-2-yl)propenoic acid ( 3 ) in the presence of iodine and air in a benzene-cyclohexane mixture afforded a separable mixture of three compounds, phenanthro[2,1-b]thiophene-10-carboxylic acid ( 4 ), phenanthro[2,1-b]thiothene ( 5 ), and naphtho[1,8-cde]-thieno[3,2-g][2]benzopyran ( 6 )     

The 1:1 adduct of 4‐aminobenzoic acid with 4‐aminobenzonitrile

The 1:1 adduct of 4‐amino­benzoic acid (PABA) with 4‐am‐inobenzonitrile (PABN), C₇H₇NO₂·C₇H₆N₂, consists of a primary centrosymmetric cyclic hydrogen‐bonded PABA dimer interaction [O?O 2.640 (3) Å] peripherally linked into chains by weaker hydrogen bonds via a head‐to‐tail PABN interaction [N?N 3.179 (4) and N?O 3.062 (4) Å], and is linked between the chains by amine‐N (PABN) to amine‐N (PABA) interactions [N?N 3.233 (5) Å]. No proton transfer occurs.