Skip to main content

Research Repository

Advanced Search

Outputs (7)

Generalized surfaces in R^3 (2004)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2004). Generalized surfaces in R^3. Mathematical Proceedings of the Royal Irish Academy, 104A(2), 199-209

Holographic Lithography (2004)
Patent
Purvis, A., McWilliam, R., Seed, N., Williams, G., Ivey, P., Maiden, A., & Johnson, S. (2006). Holographic Lithography. WO2006021818

Method of generating a holographic diffraction pattern and a holographic lithography system are disclosed, the method comprising the steps of: defining at least one geometrical shape; generating at least one line segment to represent the at least one... Read More about Holographic Lithography.

Counting Consistent Phylogenetic Trees is #P-complete (2004)
Journal Article
Bordewich, M., Semple, C., & Talbot, J. (2004). Counting Consistent Phylogenetic Trees is #P-complete. Advances in Mathematics, 33(2), 416-430. https://doi.org/10.1016/j.aam.2003.08.006

Reconstructing phylogenetic trees is a fundamental task in evolutionary biology. Various algorithms exist for this purpose, many of which come under the heading of `supertree methods'. These methods amalgamate a collection Ρ of phylogenetic trees int... Read More about Counting Consistent Phylogenetic Trees is #P-complete.

Approximating the number of acyclic orientations for a class of sparse graphs (2004)
Journal Article
Bordewich, M. (2004). Approximating the number of acyclic orientations for a class of sparse graphs. Combinatorics, Probability and Computing, 13(1), 1-16. https://doi.org/10.1017/s0963548303005844

The Tutte polynomial $T(G;x,y)$ of a graph evaluates to many interesting combinatorial quantities at various points in the $(x,y)$ plane, including the number of spanning trees, number of forests, number of acyclic orientations, the reliability polyn... Read More about Approximating the number of acyclic orientations for a class of sparse graphs.

On the space of oriented affine lines in R^3 (2004)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2004). On the space of oriented affine lines in R^3. Archiv der Mathematik, 82(1), 81 - 84. https://doi.org/10.1007/s00013-003-4861-3

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in, as we illustrate wi... Read More about On the space of oriented affine lines in R^3.