A variable-penalty alternating directions method for convex optimization

We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems. This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF Grants CCR-8907671, CDA-9024618 and CCR-9306807.     

Synthesis of novel PPARα/γ dual agonists as potential drugs for the treatment of the metabolic syndrome and diabetes type II designed using a new de novo design program PROTOBUILD

Peroxisome proliferator activated receptors (PPARs) have been shown to have critical roles in fatty acid oxidation, triglyceride synthesis, and lipid metabolism - making them an important target in drug discovery. Here we describe the in silico design, synthesis and in vitro characterisation of a novel series of 2,5-disubstituted indoles as PPARα/γ dual agonists. PPAR activation assays are performed with known agonists diazabenzene (WY14.643), aminopyridine (BRL49653) and bisaryl (L165.041), as positive controls. All the indole compounds synthesized are found to be active PPARα and PPARγ agonists, with particular efficacy from those with 2-naphthylmethyl substitution. This is a useful demonstration of a new de novo design methodology implemented by the protobuild program and its ability to rapidly produce novel modulators for a well characterized drug target.     

Alternating direction splitting for block Angular parallel optimization

We develop and compare three decomposition algorithms derived from the method of alternating directions. They may be viewed as block Gauss-Seidel variants of augmented Lagrangian approaches that take advantage of block angular structure. From a parallel computation viewpoint, they are ideally suited to a data parallel environment. Numerical results for large-scale multicommodity flow problems are presented to demonstrate the effectiveness of these decomposition algorithmims on the Thinking Machines CM-5 parallel supercomputer relative to the widely-used serial optimization package MINOS 5.4.This material is based on research supported by the Air Force Office of Scientific Research, Grants AFORS-89-0410 and F49620-1-0036, and by NSF Grants CCR-89-07671, CDA-90-24618, and CCR-93-06807. The work of the second author was supported partially by Grant 95.00732.CT01 from the Italian National Research Council (CNR).     

Synthesis,Bioactivity, Pharmacokinetic and Biomimetic Properties of Multi-Substituted Coumarin Derivatives

A series of novel multi-substituted coumarin derivatives were synthesized, spectroscopically characterized, and evaluated for their antioxidant activity, soybean lipoxygenase (LOX) inhibitory ability, their influence on cell viability in immortalized human keratinocytes (HaCaT), and cytotoxicity in adenocarcinomic human alveolar basal epithelial cells (A549) and human melanoma (A375) cells, in vitro. Coumarin analogues 4a–4f, bearing a hydroxyl group at position 5 of the coumarin scaffold and halogen substituents at the 3-phenyl ring, were the most promising ABTS^•+ scavengers. 6,8-Dibromo-3-(4-hydroxyphenyl)-4-methyl-chromen-2-one (4k) and 6-bromo-3-(4,5-diacetyloxyphenyl)-4-methyl-chromen-2-one (3m) exhibited significant lipid peroxidation inhibitory activity (IC₅₀ 36.9 and 37.1 μM). In the DCF-DA assay, the 4′-fluoro-substituted compound 3f (100%), and the 6-bromo substituted compounds 3i (80.9%) and 4i (100%) presented the highest activity. The 3′-fluoro-substituted coumarins 3e and 4e, along with 3-(4-acetyloxyphenyl)-6,8-dibromo-4-methyl-chromen-2-one (3k), were the most potent lipoxygenase (LOX) inhibitors (IC₅₀ 11.4, 4.1, and 8.7 μM, respectively) while displaying remarkable hydroxyl radical scavenging ability, 85.2%, 100%, and 92.9%, respectively. In silico docking studies of compounds 4e and 3k, revealed that they present allosteric interactions with the enzyme. The majority of the analogues (100 μΜ) did not affect the cell viability of HaCaT cells, though several compounds presented over 60% cytotoxicity in A549 or A375 cells. Finally, the human oral absorption (%HOA) and plasma protein binding (%PPB) properties of the synthesized coumarins were also estimated using biomimetic chromatography, and all compounds presented high %HOA (>99%) and %PPB (60–97%) values.     

Diastereoselective one-pot synthesis of novel ABCD-fused chromeno[2,3-d]pyrazolo[3,4-b]pyridines

A new aspect concerning chromone chemistry leading to the one-pot synthesis of functionalized novel ABCD-fused chromenopyrazolopyridines has been described. The synthesis involves a multicomponent reaction of chromone-3-benzoylhydrazones with isocyanides and acetylenedicarboxylates, whereupon novel complex tetracyclic benzopyrone derivatives containing three stereogenic centres were formed. The structure elucidation of the products was accomplished by 1D and 2D NMR experiments and confirmed by X-ray crystallographic analysis. Full assignment of all ¹H and ¹³C NMR chemical shifts has been unambiguously achieved. The reaction mechanism is also discussed. In addition, eight chromenopyrazolopyridine derivatives were tested for possible biological activity (antioxidant and lipid peroxidation inhibition).     

Enhanced Symmetry Analysis of Two-Dimensional Burgers System

We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are comprehensively studied in the optimal way and new Lie invariant solutions are constructed. We prove that this system admits no local conservation laws and then study hidden conservation laws, including potential ones. Various kinds of hidden symmetries (continuous, discrete and potential ones) are considered for this system as well. We exhaustively describe the solution subsets of the Burgers system that are its common solutions with its inviscid counterpart and with the two-dimensional Navier–Stokes equations. Using the method of differential constraints, which is particularly efficient for the Burgers system, we construct a number of wide families of solutions of this system that are expressed in terms of solutions of the (\(1+1\))-dimensional linear heat equation although they are not related to the well-known linearizable solution subset of the Burgers system.

     

Group classification of systems of diffusion equations

Group classification of a class of systems of diffusion equations is carried out. Arbitrary elements that appear in the system depend on two variables. All forms of the arbitrary elements that provide additional Lie symmetries are determined. Equivalence transformations are used to simplify the analysis. Examples of similarity reductions are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis and biological evaluation of benzo[7,8]chromeno[5,6‐b][1,4]oxazin‐3‐ones

The O‐methylmonoximes 2,3 of stenocarpoquinone‐A and β‐lapachone reacted with methyl phenylacetate to give 1,4‐benzoxazine derivatives 8a, 8b and oxazole 11a. Compound 8a was transformed to compounds 13_I , 13_II , 14. Treatment of compound 14 with osmium tetroxide afforded compounds 15 , 16 and esterification of the latter gave the bis‐ and mono‐ esters 17_I , 17_II , 18. All products are strongly fluorescent. Compounds 8a,b , 11a , 13–18 (azabenzo analogues of khellactones) were tested for their ability to interact with DPPH, to compete with dimethylsulfoxide for hydroxyl radicals, to inhibit soybean lipoxygenase and trypsin activities in vitro. Compounds 16 and 17_II were found to compete significantly with dimethylsulfoxide for hydroxyl radicals, whereas compounds 8a , 11a , 14 and 17_I were found to inhibit strongly soybean lipoxygenase.     

Non-steroidal antiinflammatory drug-copper(II) complexes: structure and biological perspectives

Copper(II) complexes with the non-steroidal antiinflammatory drug mefenamic acid in the presence of aqua or nitrogen donor heterocyclic ligands (2,2'-bipyridine, 1,10-phenanthroline, 2,2'-bipyridylamine or pyridine) have been synthesized and characterized. The crystal structures of [(2,2'-bipyridine)bis(mefenamato)copper(II)], 2, [(2,2'-bipyridylamine)bis(mefenamato)copper(II)], 4, and [bis(pyridine)bis(methanol)bis(mefenamato)copper(II)], 5, have been determined by X-ray crystallography. UV study of the interaction of the complexes with calf-thymus DNA (CT DNA) has shown that the complexes can bind to CT DNA and [bis(aqua)tetrakis(mefenamato)dicopper(II)] exhibits the highest binding constant to CT DNA. The cyclic voltammograms of the complexes in the presence of CT DNA solution have shown that the complexes can bind to CT DNA by the intercalative binding mode verified also by DNA solution viscosity measurements. Competitive studies with ethidium bromide (EB) indicate that the complexes can displace the DNA-bound EB suggesting strong competition with EB. Mefenamic acid and its complexes exhibit good binding propensity to human or bovine serum albumin protein having relatively high binding constant values. All the compounds have been tested for their antioxidant and free radical scavenging activity as well as for their in vitro inhibitory activity against soybean lipoxygenase showing significant activity.