ORCID Profile
0000-0003-4891-3055
Current Organisation
UNSW Sydney
Does something not look right? The information on this page has been harvested from data sources that may not be up to date. We continue to work with information providers to improve coverage and quality. To report an issue, use the Feedback Form.
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Probability Theory | Mathematical Logic, Set Theory, Lattices And Combinatorics | Pure Mathematics | Coding And Information Theory |
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2004
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2009
DOI: 10.1137/080728913
Publisher: The Electronic Journal of Combinatorics
Date: 10-07-2020
DOI: 10.37236/9373
Abstract: A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order $n$ with $n/2$ zeros and $n/2$ ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of $k$-MOFS$(n)$ is a set of $k$ binary frequency squares of order $n$ in which each pair of squares is orthogonal. A set of $k$-MOFS$(n)$ must satisfy $k\\le(n-1)^2$, and any set of MOFS achieving this bound is said to be complete. For any $n$ for which there exists a Hadamard matrix of order $n$ we show that there exists at least $2^{n^2/4-O(n\\log n)}$ isomorphism classes of complete sets of MOFS$(n)$. For $2 n\\equiv2\\pmod4$ we show that there exists a set of $17$-MOFS$(n)$ but no complete set of MOFS$(n)$. A set of $k$-maxMOFS$(n)$ is a set of $k$-MOFS$(n)$ that is not contained in any set of $(k+1)$-MOFS$(n)$. By computer enumeration, we establish that there exists a set of $k$-maxMOFS$(6)$ if and only if $k\\in\\{1,17\\}$ or $5\\le k\\le 15$. We show that up to isomorphism there is a unique $1$-maxMOFS$(n)$ if $n\\equiv2\\pmod4$, whereas no $1$-maxMOFS$(n)$ exists for $n\\equiv0\\pmod4$. We also prove that there exists a set of $5$-maxMOFS$(n)$ for each order $n\\equiv 2\\pmod{4}$ where $n\\geq 6$.
Publisher: Elsevier BV
Date: 04-2003
Publisher: AMPCo
Date: 07-2018
DOI: 10.5694/MJA17.01236
Abstract: To investigate the organisation and characteristics of general practice in Australia by applying novel network analysis methods to national Medicare claims data. We analysed Medicare claims for general practitioner consultations during 1994-2014 for a random 10% s le of Australian residents, and applied hierarchical block modelling to identify provider practice communities (PPCs). About 1.7 million patients per year. Numbers and characteristics of PPCs (including numbers of providers, patients and claims), proportion of bulk-billed claims, continuity of care, patient loyalty, patient sharing. The number of PPCs fluctuated during the 21-year period there were 7747 PPCs in 2014. The proportion of larger PPCs (six or more providers) increased from 32% in 1994 to 43% in 2014, while that of sole provider PPCs declined from 50% to 39%. The median annual number of claims per PPC increased from 5000 (IQR, 40-19 940) in 1994 to 9980 (190-23 800) in 2014 the proportion of PPCs that bulk-billed all patients was lowest in 2004 (21%) and highest in 2014 (29%). Continuity of care and patient loyalty were stable in 2014, 50% of patients saw the same provider and 78% saw a provider in the same PPC for at least 75% of consultations. Density of patient sharing in a PPC was correlated with patient loyalty to that PPC. During 1994-2014, Australian GP practice communities have generally increased in size, but continuity of care and patient loyalty have remained stable. Our novel approach to the analysis of routinely collected data allows continuous monitoring of the characteristics of Australian general practices and their influence on patient care.
Publisher: Wiley
Date: 15-03-2022
DOI: 10.1002/JCD.21830
Abstract: In this paper we provide a 4‐GDD of type , thereby solving the existence question for the last remaining feasible type for a 4‐GDD with no more than 30 points. We then show that 4‐GDDs of type exist for all but a finite specified set of feasible pairs .
Publisher: University of Wyoming Libraries
Date: 2005
Publisher: University of Wyoming Libraries
Date: 2007
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 12-2013
Publisher: Elsevier BV
Date: 10-2008
Publisher: Springer Science and Business Media LLC
Date: 29-05-2011
Publisher: figshare
Date: 2018
Publisher: IEEE
Date: 06-2010
Publisher: Elsevier BV
Date: 04-2023
Publisher: Elsevier BV
Date: 06-2005
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2007
Publisher: Elsevier BV
Date: 03-2022
Publisher: figshare
Date: 2018
Publisher: Elsevier BV
Date: 04-2006
Publisher: Elsevier BV
Date: 08-2007
Publisher: Elsevier BV
Date: 03-2001
Publisher: Elsevier BV
Date: 04-2016
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 09-2010
Publisher: Springer Science and Business Media LLC
Date: 20-11-2019
Publisher: University of Wyoming Libraries
Date: 2004
Publisher: The Electronic Journal of Combinatorics
Date: 22-04-2002
DOI: 10.37236/1636
Abstract: We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the $r$th support weight enumerators of the code. One of our main tools is a generalisation of a decomposition theorem due to Brylawski.
Publisher: The Electronic Journal of Combinatorics
Date: 30-03-2015
DOI: 10.37236/4726
Abstract: We prove that each maximal partial Latin cube must have more than $29.289\\%$ of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders $n$ the numbers $k$ for which there exists a maximal partial Latin cube of order $n$ with exactly $k$ entries. Finally, we prove that maximal partial Latin cubes of order $n$ exist of each size from approximately half-full ($n^3/2$ for even $n\\geq 10$ and $(n^3+n)/2$ for odd $n\\geq 21$) to completely full, except for when either precisely $1$ or $2$ cells are empty.
Publisher: Elsevier BV
Date: 10-2004
Publisher: Elsevier BV
Date: 11-2023
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 02-2014
Publisher: American Mathematical Society (AMS)
Date: 10-02-2021
DOI: 10.1090/BPROC/70
Abstract: For trace class operators A , B ∈ B 1 ( H ) A, B \\in \\mathcal {B}_1(\\mathcal {H}) ( H \\mathcal {H} a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form \\[ det H ( ( I H − A ) ( I H − B ) ) = det H ( I H − A ) det H ( I H − B ) . {\\det }_{\\mathcal {H}} ((I_{\\mathcal {H}} - A) (I_{\\mathcal {H}} - B)) = {\\det }_{\\mathcal {H}} (I_{\\mathcal {H}} - A) {\\det }_{\\mathcal {H}} (I_{\\mathcal {H}} - B). \\] When trace class operators are replaced by Hilbert–Schmidt operators A , B ∈ B 2 ( H ) A, B \\in \\mathcal {B}_2(\\mathcal {H}) and the Fredholm determinant det H ( I H − A ) {\\det }_{\\mathcal {H}}(I_{\\mathcal {H}} - A) , A ∈ B 1 ( H ) A \\in \\mathcal {B}_1(\\mathcal {H}) , by the 2nd regularized Fredholm determinant det H , 2 ( I H − A ) = det H ( ( I H − A ) exp ( A ) ) {\\det }_{\\mathcal {H},2}(I_{\\mathcal {H}} - A) = {\\det }_{\\mathcal {H}} ((I_{\\mathcal {H}} - A) \\exp (A)) , A ∈ B 2 ( H ) A \\in \\mathcal {B}_2(\\mathcal {H}) , the product formula must be replaced by det H , 2 ( ( I H − A ) ( I H − B ) ) a m p = det H , 2 ( I H − A ) det H , 2 ( I H − B ) a m p × exp ( − tr H ( A B ) ) . \\begin{align*} {\\det }_{\\mathcal {H},2} ((I_{\\mathcal {H}} - A) (I_{\\mathcal {H}} - B)) & = {\\det }_{\\mathcal {H},2} (I_{\\mathcal {H}} - A) {\\det }_{\\mathcal {H},2} (I_{\\mathcal {H}} - B) \\\\ & \\quad \\times \\exp (- \\operatorname {tr}_{\\mathcal {H}}(AB)). \\end{align*} The product formula for the case of higher regularized Fredholm determinants det H , k ( I H − A ) {\\det }_{\\mathcal {H},k}(I_{\\mathcal {H}} - A) , A ∈ B k ( H ) A \\in \\mathcal {B}_k(\\mathcal {H}) , k ∈ N k \\in \\mathbb {N} , k ⩾ 2 k \\geqslant 2 , does not seem to be easily accessible and hence this note aims at filling this gap in the literature.
Publisher: Informa UK Limited
Date: 15-09-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2018
DOI: 10.1137/18M1166250
Publisher: Elsevier BV
Date: 11-2015
Publisher: Springer Science and Business Media LLC
Date: 20-11-2008
Publisher: Elsevier BV
Date: 12-2005
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 05-2016
Publisher: Elsevier BV
Date: 11-2001
Publisher: Springer Science and Business Media LLC
Date: 10-11-2015
Start Date: 2007
End Date: 06-2010
Amount: $242,066.00
Funder: Australian Research Council
View Funded Activity