FRACTOP: A Geometric Partitioning Metaheuristic for Global Optimization

We propose a new metaheuristic, FRACTOP, for global optimization. FRACTOP is based on the geometric partitioning of the feasible region so that search metaheuristics such as Simulated Annealing (SA), or Genetic Algorithms (GA) which are activated in smaller subregions, have increased reliability in locating the global optimum. FRACTOP is able to incorporate any search heuristic devised for global optimization. The main contribution of FRACTOP is that it provides an intelligent guidance (through fuzzy measures) in locating the subregion containing the global optimum solution for the search heuristics imbedded in it. By executing the search in nonoverlapping subregions, FRACTOP eliminates the repetitive visits of the search heuristics to the same local area and furthermore, it becomes amenable for parallel processing. As FRACTOP conducts the search deeper into smaller subregions, many unpromising subregions are discarded from the feasible region. Thus, the initial feasible region gains a fractal structure with many space gaps which economizes on computation time. Computational experiments with FRACTOP indicate that the metaheuristic improves significantly the results obtained by random search (RS), SA and GA.     

Poly(cyclohexene oxide)/clay nanocomposites by photoinitiated cationic polymerization via activated monomer mechanism

Poly(cyclohexene oxide) (PCHO)/clay nanocomposites were prepared by in situ photoinitiated activated monomer cationic polymerization. The polymerization of cyclohexene oxide through the interlayer galleries of the clay can provide distribution of the clay layers in the polymer matrix homogenously and results in the formation of PCHO/clay nanocomposites. The exfoliated structures were characterized by X‐ray diffraction spectroscopy, thermogravimetric analysis, transmission electron microscopy, and atomic force microscopy. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5328–5335, 2009     

Clustering via minimum volume ellipsoids

We propose minimum volume ellipsoids (MVE) clustering as an alternative clustering technique to k-means for data clusters with ellipsoidal shapes and explore its value and practicality. MVE clustering allocates data points into clusters in a way that minimizes the geometric mean of the volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of “ellipsoidal” distributions and compare its performance with the k-means clustering algorithm as well as the MCLUST algorithm (which is based on a maximum likelihood EM algorithm) available in the statistical package R. Research of the first author was supported in part by a Discovery Grant from NSERC and a research grant from Faculty of Mathematics, University of Waterloo. Research of the second author was supported in part by a Discovery Grant from NSERC and a PREA from Ontario, Canada.     

Fabrication and characterization of calix[4]arene Langmuir–Blodgett thin film for gas sensing applications

Microwave irradiation has been found to be a highly efficient method for etherification of p-tert-butylcalix[4]arene with alkyl bromides or ditosylate. The corresponding products were obtained as a pure form in modest yield within short reaction time when the reactions were performed under microwave irradiation.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

Determination of nitrogen mustard hydrolysis products in rat urine samples using GC-MS

A gas chromatographic-mass spectrometric method was developed, validated and demonstrated by measuring the levels of nitrogen mustard hydrolysis products in the urine collected from dosed rats. The recovery values for trimethylsilyl derivatives of EDEA and MDEA are between 82-95% and 88-112%, respectively. In vivo studies performed by using three different doses (0.5 mg/kg, 1.0 mg/kg, and 2.0 mg/kg) of HN2 base of nitrogen mustard. MDEA concentrations were between 43.1-232.2 ng/mL. The limit of detection (S/N = 3) values are 2.5 ng/mL and 1.6 ng/mL for EDEA and MDEA, respectively, and the precision of the method in terms of RSD is between 5-8%.     

Effect of structural isomerism and polymer end group on the pH-stability of hydrogen-bonded multilayers

Association of tannic acid (TA) with structurally isomeric poly(N-isopropylacrylamide) (PNIPAM) and poly(2-isopropyl-2-oxazoline) (PIPOX) has been examined at surfaces to understand the effect of different molecular arrangements in a polymer repeating unit of structural isomers on the construction and pH-stability of hydrogen-bonded multilayers. Films were fabricated using layer-by-layer (LbL) technique through hydrogen-bonding interactions primarily between carbonyl groups of neutral polymers and hydroxyl groups of TA molecules at pH 2. PIPOX and TA formed thinner and more stable films in the pH scale with a critical dissolution pH of 9 when compared to films of PNIPAM and TA with a critical pH of 8. The differences in the thickness and pH-stability were due to different conformational behavior of PNIPAM and PIPOX in water which affects the accessibility of carbonyl groups for participation in the hydrogen bonding and the number of binding sites between the polymer pairs. Addition of electrostatic interactions by introducing amino groups only at the PIPOX chain end shifted the critical dissolution pH to higher values and resulted in gradual dissolution of the films in a wide pH range of 9-12. Such films hold promise for use in biomedical field due to biocompatibility and lower critical solution temperature (LCST) behavior at near physiological temperature of PNIPAM and PIPOX together with the pH-response of the hydrogen-bonded films.     

Rhodium- and palladium-catalyzed 1,5-substitution reactions of 2-en-4-yne acetates and carbonates with organoboronic acids

Two methods involving the rhodium-catalyzed reaction of 2-en-4-yne acetates and the palladium-catalyzed reaction of 2-en-4-yne carbonates with organoboronic acids were investigated; both afforded exclusively the (E)-configured vinylallenes. The coordinative interaction of the rhodium with the acetate group promoted the δ-elimination of Rh(I)-OAc from the alkenylrhodium intermediate II in both syn and anti modes, with the syn-elimination being the major path. DFT calculations revealed that a conformer of this intermediate (II), which can lead to the (E)-configured vinylallene product via the syn-elimination mode, is energetically the most favorable conformer. The rhodium-catalyzed procedure is not applicable to reactions involving (E)-configured enyne acetates, because the geometry of the alkenylrhodium intermediate that is derived from the corresponding (E)-enyne acetate would not allow such coordinative interaction to occur. The palladium-catalyzed method, which proceeds through formation of the σ-vinylallenylpalladium intermediate, B, is suitable for both the (E)- and (Z)-configured enyne carbonates and appears to have a wider scope for both organoboronic acids and enyne substrates. The palladium-catalyzed reaction of an enantiomerically enriched enyne carbonate proceeded with racemization.     

A 'microfluidic pinball' for on-chip generation of Layer-by-Layer polyelectrolyte microcapsules

Inspired by the game of "pinball" where rolling metal balls are guided by obstacles, here we describe a novel microfluidic technique which utilizes micropillars in a flow channel to continuously generate, encapsulate and guide Layer-by-Layer (LbL) polyelectrolyte microcapsules. Droplet-based microfluidic techniques were exploited to generate oil droplets which were smoothly guided along a row of micropillars to repeatedly travel through three parallel laminar streams consisting of two polymers and a washing solution. Devices were prototyped in PDMS and generated highly monodisperse and stable 45±2 μm sized polyelectrolyte microcapsules. A total of six layers of hydrogen bonded polyelectrolytes (3 bi-layers) were adsorbed on each droplet within <3 minutes and a fluorescent intensity measurement confirmed polymer film deposition. AFM analysis revealed the thickness of each polymer layer to be approx. 2.8 nm. Our design approach not only provides a faster and more efficient alternative to conventional LbL deposition techniques, but also achieves the highest number of polyelectrolyte multilayers (PEMs) reported thus far using microfluidics. Additionally, with our design, a larger number of PEMs can be deposited without adding any extra operational or interfacial complexities (e.g. syringe pumps) which are a necessity in most other designs. Based on the aforementioned advantages of our device, it may be developed into a great tool for drug encapsulation, or to create capsules for biosensing where deposition of thin nanofilms with controlled interfacial properties is highly required.