82. A Further Note on Magic.

A Further Note on Runs in Independent Sequences

Given a sequence of letters generated independently from a finite alphabet, we consider the case when more than one, but not all, letters are generated with the highest probability. The length of the longest run of any of these letters is shown to be one greater than the length of the longest run in a particular state of an associated Markov chain. Using results of Foulser and Karlin (19...

A note on higher-dimensional magic matrices

We provide exact and asymptotic formulae for the number of unrestricted, respectively indecomposable, d-dimensional matrices where the sum of all matrix entries with one coordinate fixed equals 2.

A Further Note on Alternatives to Bpref

This paper compares the robustness of information retrieval (IR) metrics to incomplete relevance assessments, using four different sets of graded-relevance test collections with submitted runs – two from TREC and two from NTCIR. We investigate the effect of reducing the original relevance data on discriminative power (i.e., how often statistical significance can be detected given the probabilit...

A further note on mongolism in twins.

A Further Note on Inductive Generalization

In this paper, we develop the algorithm, given in Plotkin (1970), for finding the least generalization of two clauses, into a theory of inductive generalization. The types of hypothesis which can be formed are very simple. They all have the form: (x)Pxm Qx. We have been guided by ideas from the philosophy of science, following Buchanan (1966). There is no search for infallible methods of genera...