Dr Judy-Anne Osborn

Dr Judy-Anne Osborn

Lecturer

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

As a researcher, I am interested in structural and existence problems in applied and pure combinatorics and in mathematics education. Some of my mathematics research work arises out of statistical physics, in which I apply methods from enumerative combinatorics to gain insight into the behaviour of polymers such as DNA. In design theory I am working on understanding the structure of maximal determinant matrices, which have applicability to codes, signal processing and statistical designs. In mathematics education I am interested in the conditions that generate resilience in students engaging in mathematics, and how to effectively engage students with diverse backgrounds, interests and needs.  I am also interested in visualisation of mathematics, and in enabling the general public to access and appreciate mathematics.

My own mathematics education commenced with great teachers in school.  I then went to Melbourne University where I did a Bachelor of Science, Honours, with a major in mathematics, followed by a PhD in mathematics.  I then went to the ANU as a postdoctoral fellow. I completed a Graduate Certificate in Higher Education at ANU.  I then came to the University of Newcastle as a postdoctoral fellow in the CARMA research Centre. I commenced a continuing position as lecturer at Newcastle in 2013.


Qualifications

  • PhD, University of Melbourne
  • Bachelor of Science (Honours)(Mathematics), University of Melbourne
  • Graduate Certificate of Higher Education, Australian National University

Keywords

  • Combinatorics
  • Mathematics Education

Fields of Research

Code Description Percentage
080299 Computation Theory and Mathematics not elsewhere classified 100

Professional Experience

UON Appointment

Title Organisation / Department
Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Chapter (1 outputs)

Year Citation Altmetrics Link
2014 Osborn JH, Badham J, 'Zombies in the City: a Netlogo Model', Mathematical Modelling of Zombies, University of Ottawa Press, Canada (2014)
Co-authors Judy-Anne Osborn

Journal article (12 outputs)

Year Citation Altmetrics Link
2016 Brent RP, Ohtsuka H, Osborn JAH, Prodinger H, 'Some binomial sums involving absolute values', Journal of Integer Sequences, 19 (2016) [C1]

© 2016, University of Waterloo. All Right Reserved.We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, w... [more]

© 2016, University of Waterloo. All Right Reserved.We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form (formula presented) obtaining new results in the cases a = 1, 2. We show that there is a close connection between these double sums in the case a = 1 and the single centered binomial sums considered by Tuenter.

Co-authors Judy-Anne Osborn
2015 Brent RP, Osborn J-AH, Smith WD, 'Note on best possible bounds for determinants of matrices close to the identity matrix', LINEAR ALGEBRA AND ITS APPLICATIONS, 466 21-26 (2015) [C1]
DOI 10.1016/j.laa.2014.09.041
Citations Scopus - 1
Co-authors Judy-Anne Osborn
2015 Prieto-Rodriguez E, Howley P, Holmes K, Osborn J, Roberts M, Kepert A, 'Quality Teaching Rounds in Mathematics Teacher Education', Mathematics Teacher Education and Development (MTED), 17 98-110 (2015) [C1]
Co-authors Judy-Anne Osborn, Andrew Kepert, Peter Howley, Elena Prieto, Malcolm Roberts
2013 Brent RP, Osborn J-AH, 'On minors of maximal determinant matrices', Journal of Integer Sequences, 16 (2013) [C1]
Co-authors Judy-Anne Osborn
2013 Brent RP, Osborn JAH, 'Bounds on minors of binary matrices', Bulletin of the Australian Mathematical Society, 88 280-285 (2013) [C1]

Abstract We prove an upper bound on sums of squares of minors of {+1, -1\}-matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [' (1,-1)-matric... [more]

Abstract We prove an upper bound on sums of squares of minors of {+1, -1\}-matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [' (1,-1)-matrices with near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices. Copyright © 2012 Australian Mathematical Publishing Association Inc.

DOI 10.1017/S000497271200086X
Co-authors Judy-Anne Osborn
2013 Brent RP, Osborn J-AH, 'General lower bounds on maximal determinants of binary matrices', ELECTRONIC JOURNAL OF COMBINATORICS, 20 (2013) [C1]
Co-authors Judy-Anne Osborn
2012 Borwein JM, Osborn J-AH, 'Response to 'Experimental Approaches to Theoretical Thinking: Artefacts and Proofs Proof and Proving in Mathematics Education'', Proof and Proving in Mathematics Education: The 19th ICMI Study, 15 138-143 (2012) [C3]
DOI 10.1007/978-94-007-2129-6
Co-authors Judy-Anne Osborn, Research-Grants
2011 Borwein JM, Osborn J-AH, 'Loving and Hating Mathematics by Reuben Hersh and Vera John-Steiner [Book Review]', The Mathematical Intelligencer, 33 63-69 (2011) [C3]
DOI 10.1007/s00283-011-9260-1.
Co-authors Judy-Anne Osborn, Research-Grants
2010 Osborn J, Prellberg T, 'Forcing adsorption of a tethered polymer by pulling', Journal of Statistical Mechanics: Theory and Experiment, 2010 (2010)

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fix... [more]

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a secondorder thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first order. Strikingly, we find that, if the angle between the pulling force and the surface is below a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a re-entrance transition at constant pulling force for low temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the re-entrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled. © 2010 IOP Publishing Ltd and SISSA.

DOI 10.1088/1742-5468/2010/09/P09018
Citations Scopus - 5Web of Science - 14
Co-authors Judy-Anne Osborn
2010 Osborn J-AH, 'Bi-banded paths, a bijection and the Narayana numbers', Australasian Journal of Combinatorics, 48 243-252 (2010) [C1]
Citations Scopus - 2
Co-authors Judy-Anne Osborn
2009 Brak R, Osborn J, 'Chebyshev type lattice path weight polynomials by a constant term method', Journal of Physics A: Mathematical and Theoretical, 42 (2009)

We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary 'decorated' weights as well as... [more]

We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary 'decorated' weights as well as an arbitrary 'background' weight. Our CT theorem, like Viennot's lattice path theorem from which it is derived primarily by a change of variable lemma, is expressed in terms of orthogonal polynomials which in our applications of interest often turn out to be non-classical. Hence, we also present an efficient method for finding explicit closed-form polynomial expressions for these non-classical orthogonal polynomials. Our method for finding the closed-form polynomial expressions relies on simple combinatorial manipulations of Viennot's diagrammatic representation for orthogonal polynomials. In the course of the paper we also provide a new proof of Viennot's original orthogonal polynomial lattice path theorem. The new proof is of interest because it uses diagonalization of the transfer matrix, but gets around difficulties that have arisen in past attempts to use this approach. In particular we show how to sum over a set of implicitly defined zeros of a given orthogonal polynomial, either by using properties of residues or by using partial fractions. We conclude by applying the method to two lattice path problems important in the study of polymer physics as the models of steric stabilization and sensitized flocculation. © 2009 IOP Publishing Ltd.

DOI 10.1088/1751-8113/42/44/445201
Co-authors Judy-Anne Osborn
2006 Brak R, Essam J, Osborn J, Owczarek AL, Rechnitzer A, 'Lattice Paths and the Constant Term', J Phys Conf Ser, 47-58 (2006)
Co-authors Judy-Anne Osborn
Show 9 more journal articles
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Grants and Funding

Summary

Number of grants 1
Total funding $297,871

Click on a grant title below to expand the full details for that specific grant.


20141 grants / $297,871

Inspiring Mathematics and Science in Teacher Education$297,871

Funding body: Office for Learning and Teaching

Funding body Office for Learning and Teaching
Project Team Doctor Judy-Anne Osborn, Associate Professor Kathryn Holmes, Doctor Elena Prieto-Rodriguez, Doctor Peter Howley, Doctor Andrew Kepert, Doctor Malcolm Roberts
Scheme Commissioned Strategic Projects
Role Lead
Funding Start 2014
Funding Finish 2016
GNo G1301449
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y
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Research Supervision

Number of supervisions

Completed0
Current1

Total current UON EFTSL

Masters0.4

Current Supervision

Commenced Level of Study Research Title / Program / Supervisor Type
2015 Masters Searching For Graphs That Are Close to The Moore Bound
M Philosophy (Mathematics), Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
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News

The Conversation

Tipping the balance towards humanity in World War Z

June 20, 2013

By Judy-Anne Osborn, University of Newcastle

Could a dire new infection sweep the world in a matter of weeks? Might the disease be so strange that it alters the behaviour of people beyond recognition, making them predatory and fearless? Could a great city like Philadelphia be overrun in a matter of hours?

Dr Judy-Anne Osborn

Position

Lecturer
CARMA
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email judy-anne.osborn@newcastle.edu.au
Phone 02 4921 5543
Mobile -
Fax 02 4921 6898

Office

Room V228
Building V - Mathematics
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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