ABA triblock copolymers with a ring‐opening metathesis polymerization/macromolecular chain‐transfer agent approach

Block copolymers containing polystyrene and polycyclooctene were synthesized with a ring‐opening metathesis polymerization/chain‐transfer approach. Polystyrene, containing appropriately placed olefins, was prepared by anionic polymerization and served as a macromolecular chain‐transfer agent for the ring‐opening metathesis polymerization of cyclooctene. These unsaturated polymers were subsequently converted to the corresponding saturated triblock copolymers with a simple heterogeneous catalytic hydrogenation step. The molecular and morphological characterization of the block copolymers was consistent with the absence of significant branching in the central polycyclooctene and polyethylene blocks [high melting temperatures (114–127 °C) and levels of crystallinity (17–42%)]. A dramatic improvement in both the long‐range order and the mechanical properties of a microphase‐separated, symmetric polystyrene–polycyclooctene–polystyrene block copolymer sample was observed after fractionation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 361–373, 2007     

Labeling of Polymer Nanostructures for Medical Imaging: Importance of crosslinking extent, spacer length, and charge density

Radiolabeling studies were employed to investigate the influence of structure on the efficiency of surface functionalization for poly(acrylic acid)-coated shell crosslinked nanoparticles (SCKs) with two types of amine-terminated DOTA chelators. An intricate interplay between the chemical and physical properties of both the DOTA derivative and the SCK nanostructures was revealed, demonstrating the importance of structural control.     

Up a gear? The significance of an elevated mutation rate in tumorigenesis

Mutations involved in many cancers have been identified, but with some cancers requiring six or more mutations to take on their fully metastatic forms, the question remains whether all of these mutations can be acquired via a process of successive mutation, at a normal rate, and clonal expansion or whether heightened mutation rates are required. This issue has been debated for decades. Recently there has been much interest in forms of genomic instability such as chromosomal instability and microsatellite instability. It remains to definitively show whether or not these instabilities are very early causal events in tumorigenesis. This article reviews the evidence for and against genomic instability being an early causal event in tumorigenesis and surveys the mathematical modelling literature in this area. The focus is on chromosomal instability and microsatellite instability in colorectal cancer.     

Linear Systems of Cubics Singular at General Points of Projective Space

We present an elementary proof that given a general collection of d points in Pⁿ the linear system of cubics singular on each point has the expected codimension except when n=4 and d=7. In that case the cubic is unique. This, together with previous work of the author, gives a proof of the Alexander–Hirschowitz interpolation theorem.     

Planar lattices are lexicographically shellable

The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by Stanley and others. This paper, using work of Björner, provides a connection between the two bodies of work, by characterizing when planar posets are Cohen-Macaulay. Planar posets are lattices when they contain a greatest and a least element. We show that a finite planar lattice is lexicographically shellable and therefore Cohen-Macaulay iff it is rank-connected.     

On the connection between harmonic maps and the self-dual Yang—Mills and the sine-Gordon equations

This is an algebraic paper which demonstrates some algebraic connections between the Yang—Mills and the sine-Gordon equation.