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Given a topological space X denote by expkX the space of nonempty subsets of X of size at most k, topologised as a quotient of Xk. This space may be regarded as a union over 1 ≤ l ≤ k of configuration spaces of l distinct unordered points in X. In the special case X = S1 we show that: (1) expkS 1 has the homotopy type of an odd dimensional sphere of… (More)

The kth finite subset space of a topological space X is the space expkX of non-empty finite subsets of X of size at most k , topologised as a quotient of X . The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X . We calculate the homology of the finite subset spaces of a connected… (More)

The kth finite subset space of a topological space X is the space expkX of non-empty finite subsets of X of size at most k , topologised as a quotient of X . The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X . We show that the finite subset spaces of a connected 2–complex admit… (More)

- Atheer A. Matroud, Christopher P. Tuffley, Michael D. Hendy
- Journal of Computational Biology
- 2010

An approximate nested tandem repeat (NTR) in a string T is a complex repetitive structure consisting of many approximate copies of two substrings x and X ("motifs") interspersed with one another. NTRs fall into a class of repetitive structures broadly known as subrepeats. NTRs have been found in real DNA sequences and are expected to be important in… (More)

- Atheer A. Matroud, Mike D Hendy, Christopher P. Tuffley
- Nucleic acids research
- 2012

We introduce the software tool NTRFinder to search for a complex repetitive structure in DNA we call a nested tandem repeat (NTR). An NTR is a recurrence of two or more distinct tandem motifs interspersed with each other. We propose that NTRs can be used as phylogenetic and population markers. We have tested our algorithm on both real and simulated data,… (More)

- Christopher P. Tuffley
- Australasian J. Combinatorics
- 2012

We give a direct combinatorial proof of the known fact that the 3-cube has 384 spanning trees, using an “edge slide” operation on spanning trees. This gives an answer in the case n = 3 to a question implicitly raised by Stanley. Our argument also gives a bijective proof of the n = 3 case of a weighted count of the spanning trees of the n-cube due to Martin… (More)

- Christopher P. Tuffley, WI Timothy, Jonathan M White, Michael D. Hendy, David Penny
- Molecular biology and evolution
- 2012

At macroevolutionary time scales, and for a constant mutation rate, there is an expected linear relationship between time and the number of inferred neutral mutations (the "molecular clock"). However, at shorter time scales, a number of recent studies have observed an apparent acceleration in the rate of molecular evolution. We study this apparent… (More)

The k-th finite subset space of a topological space X is the space expkX of nonempty subsets of X of size at most k, topologised as a quotient of X. Using results from our earlier paper on the finite subset spaces of connected graphs we show that the k-th finite subset space of a connected cell complex is (k − 2)-connected, and (k − 1)-connected if in… (More)

The kth finite subset space of a topological space X is the space expkX of non-empty subsets of X of size at most k, topologised as a quotient of X . Using results from our earlier paper on the finite subset spaces of connected graphs we show that if X is a connected cell complex then the homotopy group πi(expkX) vanishes for i ≤ k−2, and that if in… (More)