ORCID Profile
0000-0002-7263-8340
Current Organisations
RMIT University
,
Monash University
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Publisher: Wiley
Date: 09-2012
DOI: 10.1112/S1461157012001106
Abstract: Given an elliptic curve E over a field of positive characteristic p , we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs. This yields a simple algorithm that, given E and a suitable non-residue in đť”˝ p 2 , determines the supersingularity of E in O ( n 3 log 2 n ) time and O ( n ) space, where n = O (log p ) . Both these complexity bounds are significant improvements over existing methods, as we demonstrate with some practical computations.
Publisher: Elsevier BV
Date: 02-2017
Publisher: Elsevier BV
Date: 11-2022
DOI: 10.1016/J.NEUROIMAGE.2022.119659
Abstract: The human brain is a complex network that seamlessly manifests behaviour and cognition. This network comprises neurons that directly, or indirectly mediate communication between brain regions. Here, we show how multilayer/multiplex network analysis provides a suitable framework to uncover the throughput of structural connectivity (SC) to mediate information transfer-giving rise to functional connectivity (FC). We implemented a novel method to reconcile SC and FC using diffusion and resting-state functional MRI connectivity data from 484 subjects (272 females, 212 males age = 29.15 ± 3.47) from the Human Connectome Project. First, we counted the number of direct and indirect structural paths that mediate FC. FC nodes with indirect SC paths were then weighted according to their least restrictive SC path. We refer to this as SC-FC Bandwidth. We then mapped paths with the highest SC-FC Bandwidth across 7 canonical resting-state networks. We found that most pairs of FC nodes were connected by SC paths of length two and three (SC paths of length >5 were virtually non-existent). Direct SC-FC connections accounted for only 10% of all SC-FC connections. The majority of FC nodes without a direct SC path were mediated by a proportion of two (44%) or three SC path lengths (39%). Only a small proportion of FC nodes were mediated by SC path lengths of four (5%). We found high-bandwidth direct SC-FC connections show dense intra- and sparse inter-network connectivity, with a bilateral, anteroposterior distribution. High bandwidth SC-FC triangles have a right superomedial distribution within the somatomotor network. High-bandwidth SC-FC quads have a superoposterior distribution within the default mode network. Our method allows the measurement of indirect SC-FC using undirected, weighted graphs derived from multimodal MRI data in order to map the location and throughput of SC to mediate FC. An extension of this work may be to explore how SC-FC Bandwidth changes over time, relates to cognition/behavior, and if this measure reflects a marker of neurological injury or psychiatric disorders.
Publisher: Elsevier BV
Date: 03-2019
Publisher: Journal of Graph Algorithms and Applications
Date: 2019
DOI: 10.7155/JGAA.00490
Publisher: Springer Science and Business Media LLC
Date: 09-07-2022
DOI: 10.1007/S10479-022-04860-8
Abstract: We investigate an important research question for solving the car sequencing problem, that is, which characteristics make an instance hard to solve? To do so, we carry out an instance space analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance. In order to visualize the instance space, the feature vectors are projected onto a 2-D space using dimensionality reduction techniques. The resulting 2-D visualizations provide new insights into the characteristics of the instances used for testing and how these characteristics influence the behaviours of an optimization algorithm. This analysis guides us in constructing a new set of benchmark instances with a range of instance properties. We demonstrate that these new instances are more erse than the previous benchmarks, including some instances that are significantly more difficult to solve. We introduce two new algorithms for solving the car sequencing problem and compare them with four existing methods from the literature. Our new algorithms are shown to perform competitively for this problem but no single algorithm can outperform all others over all instances. This observation motivates us to build an algorithm selection model based on machine learning, to identify the niche in the instance space that an algorithm is expected to perform well on. Our analysis helps to understand problem hardness and select an appropriate algorithm for solving a given car sequencing problem instance.
Publisher: Elsevier BV
Date: 03-2019
Publisher: Informa UK Limited
Date: 24-06-2020
Publisher: ACM
Date: 31-01-2017
Publisher: Springer Science and Business Media LLC
Date: 10-2010
Publisher: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
Date: 2020
Publisher: Elsevier BV
Date: 03-2012
Publisher: Elsevier BV
Date: 2021
Publisher: Wiley
Date: 09-2012
DOI: 10.1112/S1461157012001052
Abstract: The chromatic polynomial P ( G , λ ) gives the number of ways a graph G can be properly coloured in at most λ colours. This polynomial has been extensively studied in both combinatorics and statistical physics, but there has been little work on its algebraic properties. This paper reports a systematic study of the Galois groups of chromatic polynomials. We give a summary of the Galois groups of all chromatic polynomials of strongly non-clique-separable graphs of order at most 10 and all chromatic polynomials of non-clique-separable θ -graphs of order at most 19. Most of these chromatic polynomials have symmetric Galois groups. We give five infinite families of graphs: one of these families has chromatic polynomials with a dihedral Galois group and two of these families have chromatic polynomials with cyclic Galois groups. This includes the first known infinite family of graphs that have chromatic polynomials with the cyclic Galois group of order 3.
Publisher: Springer Science and Business Media LLC
Date: 21-06-2021
Publisher: Springer Science and Business Media LLC
Date: 27-08-2020
Publisher: MDPI AG
Date: 21-07-2021
DOI: 10.3390/A14080219
Abstract: The increasing demand for work-ready students has heightened the need for universities to provide work integrated learning programs to enhance and reinforce students’ learning experiences. Students benefit most when placements meet their academic requirements and graduate aspirations. Businesses and community partners are more engaged when they are allocated students that meet their industry requirements. In this paper, both an integer programming model and an ant colony optimisation heuristic are proposed, with the aim of automating the allocation of students to industry placements. The emphasis is on maximising student engagement and industry partner satisfaction. As part of the objectives, these methods incorporate ersity in industry sectors for students undertaking multiple placements, gender equity across placement providers, and the provision for partners to rank student selections. The experimental analysis is in two parts: (a) we investigate how the integer programming model performs against manual allocations and (b) the scalability of the IP model is examined. The results show that the IP model easily outperforms the previous manual allocations. Additionally, an artificial dataset is generated which has similar properties to the original data but also includes greater numbers of students and placements to test the scalability of the algorithms. The results show that integer programming is the best option for problem instances consisting of less than 3000 students. When the problem becomes larger, significantly increasing the time required for an IP solution, ant colony optimisation provides a useful alternative as it is always able to find good feasible solutions within short time-frames.
Publisher: Elsevier BV
Date: 03-2021
Publisher: IEEE
Date: 03-2014
No related grants have been discovered for Kerri Morgan.