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

Playing with paths: enumerating sets of embellished lattice paths

© 2012 Dr. Paul W. T. FijnThis thesis primarily examines several problems in enumerative combinatorics, particu- larly those related to sets of (binomial) paths on an integer lattice. We present three main results of particular interest: (i) an involution for enumerating osculating lattice paths; (ii) a combinatorial proof of a lemma which enables a purely combinatorial method for enumerating non-intersecting paths; and (iii) a combinatorial proof of another recur- rence which, in addition to the previous lemma, enables combinatorial interpretations of product forms. The result in (i) is the first result for osculating paths which allows an arbitrary number of paths. Previous methods have been found for two or three paths, but none previously known were able to be generalised to the full problem. The method presented here uses an involution on a novel object known as stacks, which are readily enumerable. The fixed points of the involution readily biject to non-trivial sets of osculating lattice paths. A more practical constant term formula is also given, in addition to a summation formula. These results are then applied to various classes of alternating sign matrices. The results in (ii) and (iii) are the first known wholly combinatorial proofs for so-called ‘product forms’. These represent the first step in a combinatorial approach to solving the remainder of this very large class of problems. The work is inspired by a pictorial interpretation of a modified jeu de taquin, and this is also given. Both main proofs are bijections between sets of lattice paths on a triangular geometry, with various markings. Finally, we discuss some more practical uses of combinatorial methods, and apply them to several types of problems in genetics. Two key questions are discussed: the plausibility of theorised structures, and the minimal complexity to satisfy the current data. Only general results are given, although the method admits application to many examples, given sufficient data

Patient and physician predictors of patient receipt of therapies recommended by a computerized decision support system when initially prescribed broad-spectrum antibiotics: a cohort study

Objective Antibiotic computerized decision support systems (CDSSs) were developed to guide antibiotic decisions, yet prescriptions of CDSS-recommended antibiotics have remained low. Our aim was to identify predictors of patients' receipt of empiric antibiotic therapies recommended by a CDSS when the prescribing physician had an initial preference for using broad-spectrum antibiotics. Methods We conducted a prospective cohort study in a 1 500-bed tertiary-care hospital in Singapore. We included all patients admitted from October 1, 2011 through September 30, 2012, who were prescribed piperacillin-tazobactam or carbapenem for empiric therapy and auto-triggered to receive antibiotic recommendations by the in-house antibiotic CDSS. Relevant data on the patient, prescribing and attending physicians were collected via electronic linkages of medical records and administrative databases. To account for clustering, we used multilevel logistic regression models to explore factors associated with receipt of CDSS-recommended antibiotic therapy. Results One-quarter of the 1 886 patients received CDSS-recommended antibiotics. More patients treated for pneumonia (33.2%) than sepsis (12.1%) and urinary tract infections (7.1%) received CDSS-recommended antibiotic therapies. The prescribing physician – but not the attending physician or clinical specialty – accounted for some (13.3%) of the variation. Prior hospitalization (odds ratio [OR] 1.32, 95% CI, 1.01-1.71), presumed pneumonia (OR 6.77, 95% CI, 3.28-13.99), intensive care unit (ICU) admission (OR 0.38, 95% CI, 0.21-0.66), and renal impairment (OR 0.70, 95% CI, 0.52-0.93) were factors associated with patients’ receipt of CDSS-recommended antibiotic therapies. Conclusions We observed that ICU admission and renal impairment were negative predictors of patients’ receipt of CDSS-recommended antibiotic therapies. Patients admitted to ICU and those with renal impairment might have more complex clinical conditions that require a physician's assessment in addition to antibiotic CDSS

Stratospheric ozone depletion: high arctic tundra plant growth on Svalbard is not affected by enhanced UV-B after 7 years of UV-B supplementation in the field.

The response of tundra plants to enhanced UV-B radiation simulating 15 and 30% ozone depletion was studied at two high arctic sites (Isdammen and Adventdalen, 78 degrees N, Svalbard).The set-up of the UV-B supplementation systems is described, consisting of large and small UV lamp arrays, installed in 1996 and 2002. After 7 years of exposure to enhanced UV-B radiation, plant cover, density, morphological (leaf fresh and dry weight, leaf thickness, leaf area, reproductive and ecophysiological parameters leaf UV-B absorbance, leaf phenolic content, leaf water content) were not affected by enhanced UV-B radiation. DNA damage in the leaves was not increased with enhanced UV-B in Salix polaris and Cassiope tetragona. DNA damage in Salix polaris leaves was higher than in leaves of C. tetragona. The length of male gametophyte moss plants of Polytrichum hyperboreum was reduced with elevated UV-B as well as the number of Pedicularis hirsuta plants per plot, but the inflorescence length of Bistorta vivipara was not significantly affected. We discuss the possible causes of tolerance of tundra plants to UV-B (absence of response to enhanced UV-B) in terms of methodology (supplementation versus exclusion), ecophysiological adaptations to UV-B and the biogeographical history of polar plants

Highly pathogenic avian influenza causes mass mortality in Sandwich Tern Thalasseus sandvicensis breeding colonies across north-western Europe

In 2022, highly pathogenic avian influenza (HPAI) A(H5N1) virus clade 2.3.4.4b became enzootic and caused mass mortality in Sandwich TernThalasseus sandvicensis and other seabird species across north-western Europe. We present data on the characteristics of the spread of the virus between and within breeding colonies and the number of dead adult Sandwich Terns recorded at breeding sites throughout north-western Europe. Within two months of the first reported mortalities, 20,531 adult Sandwich Terns were found dead, which is >17% of the total north-western European breeding population. This is probably an under-representation of total mortality, as many carcasses are likely to have gone unnoticed and unreported. Within affected colonies, almost all chicks died. After the peak of the outbreak, in a colony established by late breeders, 25.7% of tested adults showed immunity to HPAI subtype H5. Removal of carcasses was associated with lower levels of mortality at affected colonies. More research on the sources and modes of transmission, incubation times, effective containment, and immunity is urgently needed to combat this major threat for colonial seabirds