This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse

New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

The Principle of Indifference was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called problem of multiple of partitions. In ‘Evidential symmetry and mushy credence ’ Roger White suggests that we have been too quick to jettison

For a positive integer n, let f(ri) be the number of multiplicative partitions of n. That is, f(n) represents the number of different factorizations of n, where two factorizations are considered the same if they differ only in the order of the factors. For example, /"(12) = 4, since 12 = 6

Let D(s) = P 1 m=1 amm s be the Dirichlet series generated by the innite product

Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.

We describe MUSCLE, a new computer program for creating multiple alignments of protein sequences. Elements of the algorithm include fast distance estimation using kmer counting, progressive alignment using a new profile function we call the logexpectation score, and refinement using tree

,0)+2j(mj+1+ · · ·+mk−1), where mj is the number of parts in n (j). This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the k − 1 ordered partitions and restricted paths is also

Abstract not found

The accuracy of multiple sequence alignment pro-gram MAFFT has been improved. The new version (5.3) of MAFFT offers new iterative refinement opti-ons, H-INS-i, F-INS-i and G-INS-i, in which pairwise alignment information are incorporated into objective function. These new options of MAFFT showed