Animals and plants are intricately adapted to their environments, and much genomic information is needed to construct them. In each generation, genomic information is degraded by mutation, and it is also in some sense restored by selection. It is reasonable to ask how “information from selection” may be defined. Given a suitable definition, we may then ask whether there are limits on how much information can result from selection, and if so what determines the limits? Which types of genetic encoding are most efficient, in the sense that they enable selection to maintain the greatest amount of information in the genome? Do sexual and asexual reproduction have the same informational limits? Does the informational efficiency of a genetic code depend on whether reproduction is sexual or asexual? We define information from selection in a way that is closely related to the concept of “physical information” proposed by [?]. For some simple genetic models, including genetic algorithms, we show how to compute the maximum achievable amount of “physical information” – genomic information that can result from selection. This is new, and the major contribution of this paper. The computations are very simple, using models well known in population genetics, as described in for example [?]. Similar models have been repeatedly proposed in the evolutionary computation and the wider computer science community, for example by [?]. The calculations are simple and very well known: our information-theoretic interpretation of the results of the calculations is new, and it gives a fundamental insight into the types of genetic architecture that can code for complex organisms. The results are striking. We consider the case where we keep the mutation-rate u fixed, and we vary the genome length L, and a finite population size (of order 1/u. It turns out that:

We introduce a novel kernel for comparing two text documents. The kernel is an inner product in the feature space consisting of all subsequences of length k. A subsequence is any ordered se(cid:173) quence of k characters occurring in the text though not necessarily contiguously. The subsequences are weighted by an exponentially decaying factor of their full length in the text, hence emphasising those occurrences which are close to contiguous. A direct compu(cid:173) tation of this feature vector would involve a prohibitive amount of computation even for modest values of k, since the dimension of the feature space grows exponentially with k. The paper describes how despite this fact the inner product can be efficiently evaluated by a dynamic programming technique. A preliminary experimental comparison of the performance of the kernel compared with a stan(cid:173) dard word feature space kernel results. [6] is made showing encouraging