No abstract

In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics.

No abstract

In this paper, we propose an algorithm for the design of lead generation libraries required in combinatorial drug discovery. This algorithm addresses simultaneously the two key criteria of diversity and representativeness of compounds in the resulting library and is computationally efficient when applied to a large class of lead generation design problems. At the same time, additional constraints on experimental resources are also incorporated in the framework presented in this paper. A computationally efficient scalable algorithm is developed, where the ability of the deterministic annealing algorithm to identify clusters is exploited to truncate computations over the entire data set to computations over individual clusters. An analysis of this algorithm quantifies the tradeoff between the error due to truncation and computational effort. Results applied on test data sets corroborate the analysis and show improvement by factors as large as 10 or more, depending on the data sets.