title: Mixed mutually orthogonal frequency squares

authors: Poulose, Jilmy

abstract: A frequency square of type F(n; λ1, λ2, λ3, . . . , λt) is an array n × n filled with symbols ai, where each ai occurs λi times in every row and column, and n = Pt i=1 λi.
Two such frequency squares F1(n; λ1, λ2, λ3, . . . , λt) and F2(n; µ1, µ2, µ3, . . . , µs) are mutually orthogonal, when superimposed, each of the ts possible ordered pairs (i, j), where 1 ≤ i ≤ t and 1 ≤ j ≤ s, occurs exactly λiµj times.
This thesis generalizes the classical theory of mutually orthogonal Latin squares to mixed frequency settings, where symbols may appear with different frequencies. The non-uniform frequencies lead to a wider range of combinatorial structures with new methods of construction. Then, the thesis investigates maximizing the set of mixed mutually orthogonal frequency squares (MMOFS), focusing on theoretical methods rather than computational tools.
The following lemmas and theorems are new results presented in Chapter 3. In Lemma 4.1, we define mappings from two Latin squares to form two MOFS. Then in Theorem 4.7, we apply this to explore the maximum size of the sets of higher-order MMOFS by using mixed orthogonal arrays. Moreover, Section 2.2 gives an original alternative proof of an existing upper bound for sets of MOFS. Furthermore, we identify sets of MMOFS for small orders in the final chapter by using the new results and the previous theories. These new results include Corollary 4.5, Lemma 5.1, Example 22, Corollary 5.6 and Example 24.

text: Mixed mutually orthogonal frequency squares A frequency square of type F(n; λ1, λ2, λ3, . . . , λt) is an array n × n filled with symbols ai, where each ai occurs λi times in every row and column, and n = Pt i=1 λi.
Two such frequency squares F1(n; λ1, λ2, λ3, . . . , λt) and F2(n; µ1, µ2, µ3, . . . , µs) are mutually orthogonal, when superimposed, each of the ts possible ordered pairs (i, j), where 1 ≤ i ≤ t and 1 ≤ j ≤ s, occurs exactly λiµj times.
This thesis generalizes the classical theory of mutually orthogonal Latin squares to mixed frequency settings, where symbols may appear with different frequencies. The non-uniform frequencies lead to a wider range of combinatorial structures with new methods of construction. Then, the thesis investigates maximizing the set of mixed mutually orthogonal frequency squares (MMOFS), focusing on theoretical methods rather than computational tools.
The following lemmas and theorems are new results presented in Chapter 3. In Lemma 4.1, we define mappings from two Latin squares to form two MOFS. Then in Theorem 4.7, we apply this to explore the maximum size of the sets of higher-order MMOFS by using mixed orthogonal arrays. Moreover, Section 2.2 gives an original alternative proof of an existing upper bound for sets of MOFS. Furthermore, we identify sets of MMOFS for small orders in the final chapter by using the new results and the previous theories. These new results include Corollary 4.5, Lemma 5.1, Example 22, Corollary 5.6 and Example 24.

year: 2025

title: Trial-and-error, Googling and talk: Engineering students taking initiative out of class

authors: Khoo, Elaine G.L.

abstract: A review of the science education literature identifies the importance of outreach in raising public awareness of science while providing students with contextually relevant and meaningful science in ways that enhance their school experiences. The National Virtual School of Emerging Sciences (NVSES) provided just such an opportunity. Established throughout 2012-2014, it enabled 429 secondary students from across Australia to engage with the emerging sciences of Astrophysics and Nanotechnology. Creation of 'virtual' science classrooms allowed small groups of students to connect synchronously twice a week under the guidance of subject specialist teachers. To prepare for this context, teachers modified their face-to-face pedagogies to suit the range of technologies readily accessible in the virtual classroom. This chapter discusses how these different pedagogies were utilised by the NVSES teachers to develop lessons that created unique experiences for students within the virtual classroom environment. Data collected from pre and post student surveys, interviews with the NVSES teachers and access to digitally-recorded lessons demonstrate that while NVSES was highly successful, there were challenges for all involved.

text: Trial-and-error, Googling and talk: Engineering students taking initiative out of class A review of the science education literature identifies the importance of outreach in raising public awareness of science while providing students with contextually relevant and meaningful science in ways that enhance their school experiences. The National Virtual School of Emerging Sciences (NVSES) provided just such an opportunity. Established throughout 2012-2014, it enabled 429 secondary students from across Australia to engage with the emerging sciences of Astrophysics and Nanotechnology. Creation of 'virtual' science classrooms allowed small groups of students to connect synchronously twice a week under the guidance of subject specialist teachers. To prepare for this context, teachers modified their face-to-face pedagogies to suit the range of technologies readily accessible in the virtual classroom. This chapter discusses how these different pedagogies were utilised by the NVSES teachers to develop lessons that created unique experiences for students within the virtual classroom environment. Data collected from pre and post student surveys, interviews with the NVSES teachers and access to digitally-recorded lessons demonstrate that while NVSES was highly successful, there were challenges for all involved.

year: 2018

title: Te Pūtahitanga: A Tiriti-led science-policy approach for Aotearoa New Zealand

authors: Kukutai, Tahu

abstract: This paper examines the interface between science and policymaking and calls for a policy approach that is enabled by, and responsive to, Te Tiriti o Waitangi and Mātauranga Māori. For a science sector to have its greatest reach and impact for all citizens, it must demonstrate relevance, accessibility and inclusion. In Aotearoa, there has been concern about the exclusion of Māori and Pacific expertise from science advice and key decision-making roles. Te Tiriti offers a powerful framework for connecting systems and communities of knowledge in ways that are mutually beneficial and future focused.

text: Te Pūtahitanga: A Tiriti-led science-policy approach for Aotearoa New Zealand This paper examines the interface between science and policymaking and calls for a policy approach that is enabled by, and responsive to, Te Tiriti o Waitangi and Mātauranga Māori. For a science sector to have its greatest reach and impact for all citizens, it must demonstrate relevance, accessibility and inclusion. In Aotearoa, there has been concern about the exclusion of Māori and Pacific expertise from science advice and key decision-making roles. Te Tiriti offers a powerful framework for connecting systems and communities of knowledge in ways that are mutually beneficial and future focused.

year: 2021-04-28