Computing regular equivalence: practical and theoretical issues

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which group actors are playing equivalent roles. They term these methods positional analysis techniques. The most general definition is regular equivalence which captures the idea that equivalent actors are related in a similar way to equivalent alters. Regular equivalence gives rise to a whole class of partitions on a network. Given a network we have two different computational problems. The first is how to find a particular regular equivalence. An algorithm exists to find the largest regular partition but there are not efficient algorithms to test whether there is a regular k-partition. That is a partition in k groups that is regular. In addition, when dealing with real data, it is unlikely that any regular partitions exist. To overcome this problem relaxations of regular equivalence have been proposed along with optimisation techniques to find nearly regular partitions. In this paper we review the algorithms that have developed to find particular regular equivalences and look at some of the recent theoretical results which give an insight into the complexity of finding regular partitions.

Practical solvent system selection for counter-current separation of pharmaceutical compounds

Counter-current chromatography (CCC) is a technique that shows a lot of potential for large scale purification. Its usefulness in a "research and development" pharmaceutical environment has been investigated, and the conclusions are shown in this article. The use of CCC requires the development of an appropriate solvent system (a parameter of critical importance), a process which can be tedious. This article presents a novel strategy, combining a statistical approach and fast HPLC to generate a three-dimensional partition coefficient map and rapidly predict an optimal solvent system. This screen is performed in half a day and involves 9 experiments per solvent mixture. Test separations were performed using that screen to ensure the validity of the method.