tqDist: a library for computing the quartet and triplet distances between binary or general trees.

Unlabelled: tqDist is a software package for computing the triplet and quartet distances between general rooted or unrooted trees, respectively. The program is based on algorithms with running time [Formula: see text] for the triplet distance calculation and [Formula: see text] for the quartet distance calculation, where n is the number of leaves in the trees and d is the degree of the tree with minimum degree. These are currently the fastest algorithms both in theory and in practice.

zipHMMlib: a highly optimised HMM library exploiting repetitions in the input to speed up the forward algorithm.

Background: Hidden Markov models are widely used for genome analysis as they combine ease of modelling with efficient analysis algorithms. Calculating the likelihood of a model using the forward algorithm has worst case time complexity linear in the length of the sequence and quadratic in the number of states in the model. For genome analysis, however, the length runs to millions or billions of observations, and when maximising the likelihood hundreds of evaluations are often needed.

Hide and seek: placing and finding an optimal tree for thousands of homoplasy-rich sequences.

Finding optimal evolutionary trees from sequence data is typically an intractable problem, and there is usually no way of knowing how close to optimal the best tree from some search truly is. The problem would seem to be particularly acute when we have many taxa and when that data has high levels of homoplasy, in which the individual characters require many changes to fit on the best tree. However, a recent mathematical result has provided a precise tool to generate a short number of high-homoplasy characters for any given tree, so that this tree is provably the optimal tree under the maximum parsimony criterion.

The standard lateral gene transfer model is statistically consistent for pectinate four-taxon trees.

Evolutionary events such as incomplete lineage sorting and lateral gene transfers constitute major problems for inferring species trees from gene trees, as they can sometimes lead to gene trees which conflict with the underlying species tree. One particularly simple and efficient way to infer species trees from gene trees under such conditions is to combine three-taxon analyses for several genes using a majority vote approach. For incomplete lineage sorting this method is known to be statistically consistent; however, for lateral gene transfers it was recently shown that a zone of inconsistency exists for a specific four-taxon tree topology, and it was posed as an open question whether inconsistencies could exist for other four-taxon tree topologies? In this letter we analyze all remaining four-taxon topologies and show that no other inconsistencies exist.

A practical O(n log2 n) time algorithm for computing the triplet distance on binary trees.

The triplet distance is a distance measure that compares two rooted trees on the same set of leaves by enumerating all sub-sets of three leaves and counting how often the induced topologies of the tree are equal or different. We present an algorithm that computes the triplet distance between two rooted binary trees in time O (n log2 n). The algorithm is related to an algorithm for computing the quartet distance between two unrooted binary trees in time O (n log n).

Algorithms for hidden markov models restricted to occurrences of regular expressions.

Hidden Markov Models (HMMs) are widely used probabilistic models, particularly for annotating sequential data with an underlying hidden structure. Patterns in the annotation are often more relevant to study than the hidden structure itself. A typical HMM analysis consists of annotating the observed data using a decoding algorithm and analyzing the annotation to study patterns of interest.

Algorithms for computing the triplet and quartet distances for binary and general trees.

Distance measures between trees are useful for comparing trees in a systematic manner, and several different distance measures have been proposed. The triplet and quartet distances, for rooted and unrooted trees, respectively, are defined as the number of subsets of three or four leaves, respectively, where the topologies of the induced subtrees differ. These distances can trivially be computed by explicitly enumerating all sets of three or four leaves and testing if the topologies are different, but this leads to time complexities at least of the order n3 or n4 just for enumerating the sets.