A simple linear time algorithm for the locally connected spanning tree problem on maximal planar chordal graphs

A locally connected spanning tree (LCST) T of a graph G is a spanning tree of G such that, for each node, its neighborhood in T induces a connected sub- graph in G. The problem of determining whether a graph contains an LCST or not has been proved to be NP-complete, even if the graph is planar or chordal. The main result of this paper is a simple linear time algorithm that, given a maximal planar chordal graph, determines in linear time whether it contains an LCST or not, and produces one if it exists. We give an anal- ogous result for the case when the input graph is a maximal outerplanar graph

Controlled surface initiated polymerization of N-isopropylacrylamide from polycaprolactone substrates for regulating cell attachment and detachment

Poly(ε-caprolactone) (PCL) substrates were modified with thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) brushes to direct and control cellular attachment and detachment. Prior to brush growth, the surface of PCL was activated by a diamine to allow for initiator coupling. Infrared spectra taken before and after cell culturing demonstrated the covalently attached nature of the PNIPAM brushes. PCL is a biocompatible polymer and to prove that the modifications described above did not change this characteristic property, a cell attachment/detachment study was carried out. The modified substrates showed a lower cell attachment when compared to PCL alone and to PCL films modified with the initiator. The possibility to detach the cells in the form of a sheet was proved using PNIPAM-modified PCL films by lowering the temperature to 25 °C. No relevant detachment was shown by the unmodified or by the initiator modified surfaces. This confirmed that the detachment was temperature dependent and not connected to other factors such as polymer swelling. These functionalized polymeric films can find applications as smart cell culture systems in regenerative medicine applications

On the Molecular Origin of the Cooperative Coil-to-globule Transition of Poly(N-isopropylacrylamide) in Water

By means of atomistic molecular dynamics simulations we investigate the behaviour of poly(N-isopropylacrylamide), PNIPAM, in water at temperatures below and above the lower critical solution temperature (LCST), including the undercooled regime. The transition between water soluble and insoluble states at the LCST is described as a cooperative process involving an intramolecular coil-to-globule transition preceding the aggregation of chains and the polymer precipitation. In this work we investigate the molecular origin of such cooperativity and the evolution of the hydration pattern in the undercooled polymer solution. The solution behaviour of an atactic 30-mer at high dilution is studied in the temperature interval from 243 to 323 K with a favourable comparison to available experimental data. In the PNIPAM water soluble states we detect a correlation between polymer segmental dynamics and diffusion motion of bound water, occurring with the same activation energy. Simulation results show that below the coil-to-globule transition temperature PNIPAM is surrounded by a network of hydrogen bonded water molecules and that the cooperativity arises from the structuring of water clusters in proximity to hydrophobic groups. Differently, the perturbation of the hydrogen bond pattern involving water and amide groups occurs above the transition temperature. Altogether these findings reveal that even above the LCST PNIPAM remains largely hydrated and that the coil-to-globule transition is related with a significant rearrangement of the solvent in proximity of the surface of the polymer. The comparison between the hydrogen bonding of water in the surrounding of PNIPAM isopropyl groups and in bulk displays a decreased structuring of solvent at the hydrophobic polymer-water interface across the transition temperature, as expected because of the topological extension along the chain of such interface

Surface Transitions for Confined Associating Mixtures

Thin films of binary mixtures that interact through isotropic forces and directionally specific "hydrogen bonding" are considered through Monte Carlo simulations. We show, in good agreement with experiment, that the single phase of these mixtures can be stabilized or destabilized on confinement. These results resolve a long standing controversy, since previous theories suggest that confinement only stabilizes the single phase of fluid mixtures.Comment: LaTeX document, documentstyle[aps,preprint]{revtex}, psfig.sty, bibtex, 13 pages, 4 figure