Reconstructing fully-resolved trees from triplet cover distances

It is a classical result that any finite tree with positively weighted edges, and without vertices of degree 2, is uniquely determined by the weighted path distance between each pair of leaves. Moreover, it is possible for a (small) strict subset L of leaf pairs to suffice for reconstructing the tree and its edge weights, given just the distances between the leaf pairs in L. It is known that any set L with this property for a tree in which all interior vertices have degree 3 must form a cover for T {that is, for each interior vertex v of T, L must contain a pair of leaves from each pair of the three components of T ̶ v. Here we provide a partial converse of this result by showing that if a set L of leaf pairs forms a cover of a certain type for such a tree T then T and its edge weights can be uniquely determined from the distances between the pairs of leaves in L. Moreover, there is a polynomial-time algorithm for achieving this reconstruction. The result establishes a special case of a recent question concerning `triplet covers', and is relevant to a problem arising in evolutionary genomics

Disability-aware adaptive and personalised learning for students with multiple disabilities

Purpose The purpose of this paper is to address how virtual learning environments (VLEs) can be designed to include the needs of learners with multiple disabilities. Specifically, it employs AI to show how specific learning materials from a huge repository of learning materials can be recommended to learners with various disabilities. This is made possible through employing semantic web technology to model the learner and their needs. Design/methodology/approach The paper reviews personalised learning for students with disabilities, revealing the shortcomings of existing e-learning environments with respect to students with multiple disabilities. It then proceeds to show how the needs of a student with multiple disabilities can be analysed and then simple logical operators and knowledge-based rules used to personalise learning materials in order to meet the needs of such students. Findings It has been acknowledged in literature that designing for cases of multiple disabilities is difficult. This paper shows that existing learning environments do not consider the needs of students with multiple disabilities. As they are not flexibly designed and hence not adaptable, they cannot meet the needs of such students. Nevertheless, it is possible to anticipate that students with multiple disabilities would use learning environments, and then design learning environments to meet their needs. Practical implications This paper, by presenting various combination rules to present specific learning materials to students with multiple disabilities, lays the foundation for the design and development of learning environments that are inclusive of all learners, regardless of their abilities or disabilities. This could potentially stimulate designers of such systems to produce such inclusive environments. Hopefully, future learning environments will be adaptive enough to meet the needs of learners with multiple disabilities. Social implications This paper, by proposing a solution towards developing inclusive learning environments, is a step towards inclusion of students with multiple disabilities in VLEs. When these students are able to access these environments with little or no barrier, they will be included in the learning community and also make valuable contributions. Originality/value So far, no study has proposed a solution to the difficulties faced by students with multiple disabilities in existing learning environments. This study is the first to raise this issue and propose a solution to designing for multiple disabilities. This will hopefully encourage other researchers to delve into researching the educational needs of students with multiple disabilities

Thermal and structural assessments of a ceramic wafer seal in hypersonic engines

The thermal and structural performances of a ceramic wafer seal in a simulated hypersonic engine environment are numerically assessed. The effects of aerodynamic heating, surface contact conductance between the seal and its adjacent surfaces, flow of purge coolant gases, and leakage of hot engine flow path gases on the seal temperature were investigated from the engine inlet back to the entrance region of the combustion chamber. Finite element structural analyses, coupled with Weibull failure analyses, were performed to determine the structural reliability of the wafer seal

Twisted trees and inconsistency of tree estimation when gaps are treated as missing data -- the impact of model mis-specification in distance corrections

Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004) reported some strikingly broad results about the forms of inconsistency in tree estimation that can arise if corrected distances are not proportional to the true distances. They showed that if the corrected distance is a concave function of the true distance, then inconsistency due to long branch attraction will occur. If these functions are convex, then two "long branch repulsion" trees will be preferred over the true tree -- though these two incorrect trees are expected to be tied as the preferred true. Here we extend their results, and demonstrate the existence of a tree shape (which we refer to as a "twisted Farris-zone" tree) for which a single incorrect tree topology will be guaranteed to be preferred if the corrected distance function is convex. We also report that the standard practice of treating gaps in sequence alignments as missing data is sufficient to produce non-linear corrected distance functions if the substitution process is not independent of the insertion/deletion process. Taken together, these results imply inconsistent tree inference under mild conditions. For example, if some positions in a sequence are constrained to be free of substitutions and insertion/deletion events while the remaining sites evolve with independent substitutions and insertion/deletion events, then the distances obtained by treating gaps as missing data can support an incorrect tree topology even given an unlimited amount of data.Comment: 29 pages, 3 figure

A matroid associated with a phylogenetic tree

A (pseudo-)metric D on a finite set X is said to be a `tree metric' if there is a finite tree with leaf set X and non-negative edge weights so that, for all x,y ∈X, D(x,y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is 13; up to canonical isomorphism 13; uniquely determined by D, and one does not even need all of the distances in order to fully (re-)construct the tree's edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (`lasso') these edge weights. In this paper, we use the results of a previous paper to discuss the structure of a matroid that can be associated with an (unweighted) X-tree T defined by the requirement that its bases are exactly the `tight edge-weight lassos' for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T

A New Galaxy in the Local Group: the Antlia Dwarf Galaxy

We report the discovery of new member of the Local Group in the constellation of Antlia. Optically the system appears to be a typical dwarf spheroidal galaxy of type dE3.5 with no apparent young blue stars or unusual features. A color-magnitude diagram in I, V-I shows the tip of the red giant branch, giving a distance modulus of 25.3 +/- 0.2 (1.15 Mpc +/- 0.1) and a metallicity of -1.6 +/- 0.3. Although Antlia is in a relatively isolated part of the Local Group it is only 1.2 degrees away on the sky from the Local Group dwarf NGC3109, and may be an associated system.Comment: AJ in press, 15 pages, 7 figures, figure 2 in b/w for space saving, full postscript version available at http://www.ast.cam.ac.uk/~gkth/antlia-pp.htm