ORCID Profile
0000-0002-6399-7771
Current Organisations
Flinders University
,
European Commission
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Publisher: Springer Science and Business Media LLC
Date: 11-04-2011
Publisher: Springer Science and Business Media LLC
Date: 11-1981
DOI: 10.1007/BF00147659
Publisher: Springer Science and Business Media LLC
Date: 03-04-2013
Publisher: Elsevier BV
Date: 11-1993
Publisher: Springer Science and Business Media LLC
Date: 1999
Publisher: Elsevier BV
Date: 11-1993
Publisher: Springer Science and Business Media LLC
Date: 11-1995
DOI: 10.1007/BF01388474
Publisher: Cambridge University Press (CUP)
Date: 08-2007
DOI: 10.1017/S0004972700039435
Abstract: A method of embedding n k configurations into projective space of k –1 dimensions is given. It breaks into the easy problem of finding a rooted spanning tree of the associated Levi graph. Also it is shown how to obtain a “complementary” “theorem” about projective space (over a field or skew-field F ) from any n k theorem over F . Some elementary matroid theory is used, but with an explanation suitable for most people. Various ex les are mentioned, including the planar configurations: Fano 7 3 , Pappus 9 3 , Desargues 10 3 (also in 3d-space), Möbius 8 4 (in 3d-space), and the resulting 7 4 in 3d-space, 9 6 in 5d-space, and 10 7 in 6d-space. (The Möbius configuration is self-complementary.) There are some n k configurations that are not embeddable in certain projective spaces, and these will be taken to similarly not embeddable configurations by complementation. Finally, there is a list of open questions.
Publisher: MDPI AG
Date: 16-05-2023
DOI: 10.3390/MATH11102310
Abstract: Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role.
Publisher: MDPI AG
Date: 05-05-2022
DOI: 10.3390/S22093520
Abstract: The invention of smart low-power devices and ubiquitous Internet connectivity have facilitated the shift of many labour-intensive jobs into the digital domain. The shortage of skilled workforce and the growing food demand have led the agriculture sector to adapt to the digital transformation. Smart sensors and systems are used to monitor crops, plants, the environment, water, soil moisture, and diseases. The transformation to digital agriculture would improve the quality and quantity of food for the ever-increasing human population. This paper discusses the security threats and vulnerabilities to digital agriculture, which are overlooked in other published articles. It also provides a comprehensive review of the side-channel attacks (SCA) specific to digital agriculture, which have not been explored previously. The paper also discusses the open research challenges and future directions.
Publisher: Springer Science and Business Media LLC
Date: 19-11-2013
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/100809155
Publisher: Elsevier BV
Date: 08-2006
Publisher: Springer Science and Business Media LLC
Date: 1999
Publisher: Springer Science and Business Media LLC
Date: 2004
Publisher: Springer Science and Business Media LLC
Date: 04-05-2011
Publisher: Hindawi Limited
Date: 17-09-2013
DOI: 10.1155/2013/379074
Abstract: Topology and geometry should be very closely related mathematical subjects dealing with space. However, they deal with different aspects, the first with properties preserved under deformations, and the second with more linear or rigid aspects, properties invariant under translations, rotations, or projections. The present paper shows a way to go between them in an unexpected way that uses graphs on orientable surfaces, which already have widespread applications. In this way infinitely many geometrical properties are found, starting with the most basic such as the bundle and Pappus theorems. An interesting philosophical consequence is that the most general geometry over noncommutative skewfields such as Hamilton's quaternions corresponds to planar graphs, while graphs on surfaces of higher genus are related to geometry over commutative fields such as the real or complex numbers.
Publisher: Elsevier BV
Date: 10-2010
Publisher: Springer Science and Business Media LLC
Date: 1997
Publisher: Springer Science and Business Media LLC
Date: 09-2006
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/110823274
Publisher: Springer Science and Business Media LLC
Date: 08-04-2012
Publisher: MDPI AG
Date: 20-06-2023
DOI: 10.3390/MATH11122774
Abstract: Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k.
Publisher: Springer Science and Business Media LLC
Date: 06-1988
DOI: 10.1007/BF00183019
Publisher: Cambridge University Press (CUP)
Date: 02-2010
DOI: 10.1017/S1446788708080981
Abstract: We discuss n 4 configurations of n points and n planes in three-dimensional projective space. These have four points on each plane, and four planes through each point. When the last of the 4 n incidences between points and planes happens as a consequence of the preceding 4 n −1 the configuration is called a ‘theorem’. Using a graph-theoretic search algorithm we find that there are two 8 4 and one 9 4 ‘theorems’. One of these 8 4 ‘theorems’ was already found by Möbius in 1828, while the 9 4 ‘theorem’ is related to Desargues’ ten-point configuration. We prove these ‘theorems’ by various methods, and connect them with other questions, such as forbidden minors in graph theory, and sets of electrons that are energy minimal.
Publisher: Springer Science and Business Media LLC
Date: 11-1989
DOI: 10.1007/BF00147433
Publisher: Springer Berlin Heidelberg
Date: 1983
DOI: 10.1007/BFB0071521
Publisher: Elsevier BV
Date: 03-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/090773751
Publisher: Springer Science and Business Media LLC
Date: 06-1994
DOI: 10.1007/BF01265322
Publisher: Springer Science and Business Media LLC
Date: 06-1994
DOI: 10.1007/BF01265323
No related grants have been discovered for David Glynn.