Mixed radix Reed-Muller expansions

The choice of radix is crucial for multi-valued logic synthesis. Practical examples, however, reveal that it is not always possible to find the optimal radix when taking into consideration actual physical parameters of multi-valued operations. In other words, each radix has its advantages and disadvantages. Our proposal is to synthesise logic in different radices, so it may benefit from their combination. The theory presented in this paper is based on Reed-Muller expansions over Galois field arithmetic. The work aims to firstly estimate the potential of the new approach and to secondly analyse its impact on circuit parameters down to the level of physical gates. The presented theory has been applied to real-life examples focusing on cryptographic circuits where Galois Fields find frequent application. The benchmark results show the approach creates a new dimension for the trade-off between circuit parameters and provides information on how the implemented functions are related to different radices.

Contact, trust and social capital in Northern Ireland: a qualitative study of three mixed communities

In a recent paper, Robert Putnam (2007) challenges the contact hypothesis by arguing that ethnic diversity causes people to ‘hunker down’ and essentially withdraw themselves from society. Drawing on
qualitative data collected from three mixed communities in Northern Ireland, this paper explores the extent and quality of contact experienced by Protestants and Catholics in their everyday lives. Themes emerging from our data are generally consistent with the contact hypothesis. There is also some support for Putnam’s theory that mixed environments can induce ‘hunkering down’ and that inter-group trust may be compromised. However, our data challenge Putnam’s argument that these responses are a consequence of ‘anomie’ or ‘social malaise’. Rather, we find that withdrawal from social activity in the neighbourhoods we observed was a calculated response at times of threat, often aimed at protecting existent positive inter-ethnic relations.

Controlling Assembly of Mixed Thiol Monolayers on Silver Nanoparticles to Tune Their Surface Properties

Modifying the surfaces of metal nanoparticles with self-assembled monolayers of functionalized thiols provides a simple and direct method to alter their surface properties. Mixed self-assembled monolayers can extend this approach since, in principle, the surfaces can be tuned by altering the proportion of each modifier that is adsorbed. However, this works best if the composition and microstructure of the monolayers can be controlled. Here, we have modified preprepared silver colloids with binary mixtures of thiols at varying concentrations and modifier ratios. Surface-enhanced Raman spectroscopy was then used to determine the effect of altering these parameters on the composition of the resulting mixed monolayers. The data could be explained using a new model based on a modified competitive Langmuir approach. It was found that the composition of the mixed monolayer only reflected the ratio of modifiers in the feedstock when the total amount of modifier was sufficient for approximately one monolayer coverage. At higher modifier concentrations the thermodynamically favored modifier dominated, but working at near monolayer concentrations allowed the surface composition to be controlled by changing the ratios of modifiers. Finally, a positively charged porphyrin probe molecule was used to investigate the microstructure of the mixed monolayers, i.e., homogeneous versus domains. In this case the modifier domains were found to be <2 nm.

Chemoenzymatic synthesis of a mixed phosphine-phosphine oxide catalyst and its application to asymmetric allylation of aldehydes and hydrogenation of alkenes

The chemoenzymatic synthesis of a Lewis basic phosphine-phosphine oxide organocatalyst from a cis-dihydrodiol metabolite of bromobenzene proceeds via a palladium-catalysed carbon-phosphorus bond coupling and a novel room temperature Arbuzov [2,3]-sigmatropic rearrangement of an allylic diphenylphosphinite. Allylation of aromatic aldehydes were catalysed by the Lewis basic organocatalyst giving homoallylic alcohols in up to 57% ee. This compound also functioned as a ligand for rhodium-catalysed asymmetric hydrogenation of acetamidoacrylate giving reduction products with ee values of up to 84%.