The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Fundamental solutions for linear parabolic systems and matrix processes

University of Technology Sydney. Faculty of Science.In this thesis we use Lie symmetry methods and integral transforms to obtain fundamental matrices for systems of PDEs of the form [Production note: due to software limitations equation can only been found in thesis] for functions (), and ƒ() satisfying some necessary conditions. We also provide the methodology to obtain these matrices for a wider range of systems. We then turn to the Lie symmetry study of the Kolmogorov Backwards equation associated to the process of the eigenvalues of a Wishart process. We focus on 2- dimensional Wishart processes with eigenvalues X > Y ≥ 0 for most of our work. We obtain the cosine transform of the transition density function of the difference X ― Y, as well as some integral expressions for E[X], E[Y]. We also obtain some bounds for the variances of X and Y and the expected values for a wide range of functions of these eigenvalues including, among many others, the expected value for any symmetric polynomia the variables X, Y. These results are all new, to the best of our knowledge

Reversions of QuantiFERON-TB Gold Plus in tuberculosis contact investigation: A prospective multicentre cohort study

Background Interferon-y Release Assays (IGRA) reversions have been reported in different clinical scenarios for the diagnosis of tuberculosis (TB) infection. This study aimed to determine the rate of QuantiFERON-TB Gold Plus (QFT-Plus) reversions during contact investigation as a potential strategy to reduce the number of preventive treatments. Methods Prospective, multicentre cohort study of immunocompetent adult contacts of patients with pulmonary TB tested with QFT-Plus. Contacts with an initial positive QFT-Plus (QFT-i) underwent a second test within 4 weeks (QFT-1), and if negative, underwent a repeat test 4 weeks later (QFT-2). Based on the QFT-2 result, we classified cases as sustained reversion if they remained negative and as temporary reversion if they turned positive. Results We included 415 contacts, of whom 96 (23.1%) had an initial positive test (QFT-i). Following this, 10 had negative QFT-1 results and 4 (4.2%) of these persisted with a negative result in the QFT-2 (sustained reversions). All four sustained reversions occurred in contacts with IFN-γ concentrations between ≥0.35 and ≤0.99 IU•mL-1 in one or both QFT-i tubes. Conclusion In this study, TB contact investigations rarely reveal QFT-Plus reversion. These results do not support retesting cases with an initial positive result to reduce the number of preventive treatments