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A central limit theorem for parsimony length of trees
(University of Canterbury. Dept. of Mathematics, 1994)In phylogenetic analysis it is useful to study the distribution of parsimony length of a tree, under the null model by which the leaves are independently assigned letters according to prescribed probabilities. Except in ... 
Classifying and counting linear phylogenetic invariants for the Jukes Cantor model
(University of Canterbury. Dept. of Mathematics, 1994)Linear invariants are useful tools for testing phylogenetic hypotheses from aligned DNA/RNA sequences, particularly when the sites evolve at different rates. Here we give a simple, graph theoretic classification, for ... 
Comparing forensic hypotheses from PCR results in cases involving mixtures of body fluids
(University of Canterbury. Dept. of Mathematics, 1995)Likelihood ratios provide a convenient and widelyused measure for assessing the relative support for forensic hypotheses given certain evidence. We extend earlier work to provide techniques for computing these ratios ... 
The number of nucleotide sites needed to accurately reconstruct large evolutionary trees
(University of Canterbury. Dept. of Mathematics, 1996)Biologists seek to reconstruct evolutionary trees for increasing number of species, n, from aligned genetic sequences. How fast the sequence length N must grow, as a function of n, in order to accurately recover the ... 
Reconstructing trees when sequence sites evolve at variable rates
(University of Canterbury. Dept. of Mathematics, 1994)For a sequence of colors independently evolving on a tree under a simple Markov model, we consider conditions under which the tree can be uniquely recovered from the "sequence spectrum"  the expected frequencies of the ... 
On 4dimensional elation Laguerre planes admitting simple lie groups of automorphisms
(University of Canterbury. Dept. of Mathematics, 1997)This paper concerns 4dimensional ( topological locally compact connected) elation Laguerre planes that admit large automorphism groups. In particular, it is shown that such a plane is classical if its automorphism group ... 
Semiclassical projective planes over halfordered fields
(University of Canterbury. Dept. of Mathematics, 1995)T his paper concerns a generalization of Moulton planes constructed by J. Jakóbowski [2]. We consider those planes over ordered fields and solve the isomorphism and collineation problem posed in [2]. 
On the continuity of the geometric operations in Minkowski planes with parallel classes S2
(University of Canterbury. Dept. of Mathematics, 1993)In a Minkowski plane M with parallel classes S ² conditions are investigated that simplify the verification of the continuity of the geometric operations in order to show that M is a topological Minkowski plane. The point ... 
Elation Laguerre planes of order p2 that admit an automorphism group of order p2 in the elation complement
(University of Canterbury. Dept. of Mathematics, 1993)Following the program for finite translation planes to construct such planes from collineation groups in the translation complement a search for nonMiquelian Laguerre planes of odd order is initiated. In this note finite ... 
A classification of Minkowski planes over halfordered fields
(University of Canterbury. Dept. of Mathematics, 1999)This paper concerns a construction of Minkowski planes over halfordered fields [5] and [20]. Solving various functional equations the KleinKroll types of these Minkowski planes are determined with respect to G and ... 
Reconstructing phylogenies from nucleotide pattern probabilities : a survey and some new result
(University of Canterbury. Dept. of Mathematics, 1997)The variations between homologous nucleotide sequences representative of various species are, in part, a consequence of the evolutionary history of these species. Determining the evolutionary tree from patterns in the ... 
Distributions of cherries for two models of trees
(University of Canterbury. Dept. of Mathematics, 1999)Null models for generating binary phylogenetic trees are useful for testing evolutionary hypotheses and reconstructing phylogenies. We consider two such null models  the Yule and uniform models  and in particular the ... 
On some matrix trace inequalities
(University of Canterbury. Dept. of Mathematics, 1998)A number of authors have recently considered matrix trace inequalities of CauchySchwartz type. We extend some of these results and look at some other classical inequalities which can be reformulated as more general trace ... 
A family of Minkowski planes over halfordered fields
(University of Canterbury. Dept. of Mathematics, 1996)This paper concerns a construction of J. Jakóbowski [7] of Minkowski planes over halfordered fields. A more group theoretic definition of such planes is given. Isomorphisms between and automorphisms of these Minkowski ... 
Scale invariant means and the first digit problem
(University of Canterbury. Dept. of Mathematics, 1998)It is a well established fact that in some circumstances, lists of what appear to be random numbers, show a striking nonuniform distribution of digits. In many instances, these numbers arise relative to a system of ... 
On the existence of topological ovals in flat projective planes
(University of Canterbury. Dept. of Mathematics, 1996)We show that every flat projective plane contains topological ovals. This is achieved by completing certain closed partial ovals, the socalled quasiovals, to topological ovals. 
Determinantal identities for modular Schur symmetric functions
(University of Canterbury. Dept. of Mathematics, 1995)Modular symmetric functions are a new class of symmetric functions which depend both on a partition ⋋ and an integer modulus p > 2. For p prime, these functions have representation theoretic significance as the irreducible ... 
Finite Möbius nearplanes
(University of Canterbury. Dept. of Mathematics, 1998)We introduce finite Möbius nearplanes of order n and show that these planes uniquely extend to Möbius planes of the same order if n ≥ 5. Furthermore, Mobius nearplanes of order n ≤ 4 are discussed and the situation for ... 
Laguerre nearplanes of order four
(University of Canterbury. Dept. of Mathematics, 1999)We investigate Laguerre nearplanes of order 4 and classify all such planes. We further develop various descriptions of these planes and characterise those Laguerre nearplanes that can be extended to the Miquelian ... 
Short wave groups in deep water
(University of Canterbury. Dept. of Mathematics, 1981)Waves on the water surface propagate typically in wave groups, each group consisting of a small number of waves. The envelopes of the wave groups change, in general, as the groups propagate. Particular envelope ...