Partitioning Posets

Given a poset P = (X, ≺ ), a partition X ₁, ..., X _k of X is called an ordered partition of P if, whenever x ∈ X _i and y ∈ X _j with x ≺ y, then i ≤ j. In this paper, we show that for every poset P = (X, ≺ ) and every integer k ≥ 2, there exists an ordered partition of P into k parts such that the total number of comparable pairs within the parts is at most (m − 1)/k, where m ≥ 1 is the total number of edges in the comparability graph of P. We show that this bound is best possible for k = 2, but we give an improved bound, , for k ≥ 3, where c(k) is a constant depending only on k. We also show that, given a poset P = (X, ≺ ) and an integer 2 ≤ k ≤ |X|, we can find an ordered partition of P into k parts that minimises the total number of comparable pairs within parts in time polynomial in the size of P. We prove more general, weighted versions of these results. Supported by an EPSRC doctoral training grant.     

Cutting two graphs simultaneously

Consider two graphs, and , on the same vertex set V, with and having edges for . We give a simple algorithm that partitions V into sets A and B such that and . We also show, using a probabilistic method, that if and belong to certain classes of graphs, (for instance, if and both have a density of at least 2/, or if and are both regular of degree at most with n sufficiently large) then we can find a partition of V into sets A and B such that for . © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 19–32, 2008     

Detection of methyl salicylate using polymer-filled chemicapacitors

Methyl salicylate (MeS) is used as a chemical warfare agent simulant to test chemical protective garments and other individual personal protective gear. The accurate and real-time detection of this analyte is advantageous for various testing regimes. This paper reports the results of MeS vapor exposures on polymer-filled capacitance-based sensors at temperatures ranging from 15 °C to 50 °C under dry and humid conditions. Multiple capacitors were arranged in an array on a silicon chip each having a different sorptive polymer. The sensors used parallel-plate electrode geometry to measure the dielectric permittivity changes of each polymer when exposed to water and MeS vapor. Of the four polymers tested against MeS, the optimal polymer displayed near or sub-parts-per-million detection limits at 35 °C (0–80%RH).     

Synthesis of biphenyl anilines using iodo phenylformamides via a one-pot Suzuki coupling reaction

We have developed a novel and economical synthesis of biphenyl anilines via a one-pot Suzuki coupling reaction with iodo phenylformamides. This literature is an unprecedented approach to biphenyl anilines replacing costly aminophenylboronic acids with economical iodo anilines for the preparation of biphenyl anilines. It also provides a viable synthesis toward substituted biphenyl anilines where the required aminophenylboronic acids are not readily available.     

Complexities associated with moisture in foamed polysiloxane composites

An understanding of mechanisms of moisture outgassing from silicones and the impact on material mechanical properties is important for compatibility and life prediction in sealed systems containing these materials. A series of thermomechanical (TMA) stress relaxation experiments have been performed to provide information on the important load bearing properties of these materials as a function of time and temperature. Two different silica reinforced foamed polysiloxane materials were tested, a peroxide cured rubber (M97) and a condensation-cured elastomer (S5370). The M97 foam showed unexpectedly complex stress relaxation profiles at temperatures around 100 °C, whereas the S5370 samples showed the expected smooth stress decay behaviour. Dried M97 foam samples show different stress relaxation behaviour to the non-dried materials. Furthermore, stress relaxation studies performed in controlled humidity environments showed that moisture has a significant accelerating influence on the underlying relaxation process. In dry regimes, a reduced stress relaxation rate was observed, with an increase in the force required to maintain a given amount of compression on the sample. To further develop our understanding of the effects of moisture, we have exposed samples to water enriched to 40% in ¹⁷O and used ¹⁷O nuclear magnetic resonance (NMR) spectroscopy to assess labelled hydrolysis reaction products. Our studies show that Si-¹⁷O-Si hydrolysis products are readily incorporated in the polymer and the degradation is enhanced by the influence of gamma radiation and/or heat. In addition, the polysiloxane foams showed different age related trends in sealed (where moisture is retained) and ventilated (open-to-air) regimes. Our observations have been explained by moisture influencing both physical and chemical degradation processes. Our findings on moisture induced changes in silicone stress relaxation rates are novel and demonstrate the importance of controlling humidity in service applications involving these materials.     

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.     

HPTLC determination of rabeprazole and domperidone in capsules and its validation

This paper describes a validated high-performance thin-layer chromatography (HPTLC) method for simultaneous estimation of rabeprazole (RA) and domperidone (DO) in pure powder and in capsule formulations. An HPTLC method separation is achieved on an aluminum sheet of silica gel 60F(254) using ethyl acetate-methanol-benzene-acetonitrile (30:20:30:20 v/v) as mobile phase. Quantitation is achieved with UV detection at 287 nm over a concentration range of 400-1200 ng/spot and 600-1800 ng/spot with mean recovery of 99.82 +/- 0.74 and 99.43 +/- 0.68 for RA and DO, respectively, in the HPTLC method. This method is simple, precise, and sensitive, and it is applicable for the simultaneous determination of RA and DO in pure powder and in capsule formulation.     

Studies in synthesis of furoflavones possessing anti‐cancer activity

Several new furoflavanones (3a‐3I) have been synthesized from the in‐situ generated chalcones by the reaction of ortho‐hydroxy acetyl benzofuran and aryl aldehyde in presence of piperidine. Ethanolic sodium hydroxide (1%) gave chalcones (2a‐2I) as the exclusive product. Flavindogenides (3‐arylidene flavanones) (5a‐5d) have been isolated as the co‐product along with chalcones and flavanones in cases where excess of aryl aldehyde was used. The stereochemistry of 3‐arylidene flavanones has been established by the preparation of both Z (6) and E (5a‐5d) diastereomers. Single crystal X‐ray diffraction data shows the flavanone ring to exist in quasi chair conformation with phenyl ring equatorial. Furoflavanones were finally dehydrogenated to furoflavones (4a‐4I) using DDQ (2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone). The compounds have been screened for in‐vitro cytotoxicity against human cancer cell lines.     

Multifunctional particles: Magnetic nanocrystals and gold nanorods coated with fluorescent dye-doped silica shells

Multifunctional colloidal core-shell nanoparticles of magnetic nanocrystals (of iron oxide or FePt) or gold nanorods encapsulated in silica shells doped with the fluorescent dye, Tris(2,2′-bipyridyl)dichlororuthenium(II) hexahydrate (Rubpy) were synthesized. The as-prepared magnetic nanocrystals are initially hydrophobic and were coated with silica using a microemulsion approach, while the as-prepared gold nanorods are hydrophilic and were coated with silica using a Stöber type of process. Each approach yielded monodisperse nanoparticles with uniform fluorescent dye-doped silica shells. These colloidal heterostructures have the potential to be used as dual-purpose tags—exhibiting a fluorescent signal that could be combined with either dark-field optical contrast (in the case of the gold nanorods), or enhanced contrast in magnetic resonance images (in the case of magnetic nanocrystal cores). The optical and magnetic properties of the fluorescent silica-coated gold nanorods and magnetic nanocrystals are reported.     

Temperature triggered self-assembly of polypeptides into multivalent spherical micelles

We report herein thermally responsive elastin-like polypeptides (ELPs) in a linear AB diblock architecture with an N-terminal peptide ligand that self-assemble into spherical micelles when heated slightly above body temperature. A series of 10 ELP block copolymers (ELP(BC)'s ) with different molecular weights and hydrophilic-to-hydrophobic block ratios were genetically synthesized by recursive directional ligation. The self-assembly of these polymers from unimers into micelles was investigated by light scattering, fluorescence spectroscopy, and cryo-TEM. These ELP(BC)'s undergo two phase transitions as a function of solution temperature: a unimer-to-spherical micelle transition at an intermediate temperature and a micelle-to-bulk aggregate transition at a higher temperature when the hydrophilic-to-hydrophobic block ratio is between 1:2 and 2:1. The critical micelle temperature is controlled by the length of the hydrophobic block, and the size of the micelle is controlled by both the total ELP(BC) length and hydrophilic-to-hydrophobic block ratio. These polypeptide micelles display a critical micelle concentration in the range 4-8 microM demonstrating the high stability of these structures. These studies have also identified a subset of ELP(BC)'s bearing terminal peptide ligands that are capable of forming multivalent spherical micelles that present multiple copies of the ligand on their corona in the clinically relevant temperature range 37-42 degrees C and target cancer cells. These ELP(BC)'s may be useful for drug targeting by thermally triggered multivalency. More broadly, the design rules uncovered by this study should be applicable to the design of other thermally reversible nanoparticles for diverse applications in medicine and biology.