title: On the Distances between Latin Squares and the Smallest Defining Set Size

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: In this note, we show that for each Latin square L of order n≥2 , there exists a Latin square L’≠L of order n such that L and L’ differ in at most 8√n  cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n. We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).

text: On the Distances between Latin Squares and the Smallest Defining Set Size In this note, we show that for each Latin square L of order n≥2 , there exists a Latin square L’≠L of order n such that L and L’ differ in at most 8√n  cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n. We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).

year: 2017

title: Twardowski, rationality, and post-truth

authors: Ulatowski, Joseph W.

subjects: Kazimierz Twardowski

abstract: If Twardowski is correct about rationality, then truth comes in degrees. If truth comes in degrees, then we must replace a classical conception of truth with a nearby alternative. Post-truth accepts that statements need not be true or false but may be scalar. Thus, Twardowski's own vision of rationality (logistic anti-irrationalism) would have to accept that truth comes in degrees.

text: Twardowski, rationality, and post-truth If Twardowski is correct about rationality, then truth comes in degrees. If truth comes in degrees, then we must replace a classical conception of truth with a nearby alternative. Post-truth accepts that statements need not be true or false but may be scalar. Thus, Twardowski's own vision of rationality (logistic anti-irrationalism) would have to accept that truth comes in degrees.

year: 2026

title: Haumanu Hauora: refining public health institution policy to include Māori and climate change

authors: Masters-Awatere, Bridgette

abstract: The deepening climate crisis generates specific impacts that will exacerbate the already disproportionately negative health outcomes experienced by Indigenous people. Disparate health outcomes have not spontaneously emerged, but rather have been foreshadowed by existing inequities. This article summarizes a sample of the work from a two-year research project in Aotearoa New Zealand to understand existing policy processes and ascertain the extent to which health institutions give serious consideration to climate change impacts on Māori (Indigenous people) with health vulnerabilities. Speaking to tāngata whenua (Indigenous Māori), District Health Board (DHB) employees, and subject matter experts (SMEs), it was clear that policy processes were ad hoc and problematically silenced consistent Māori input. While research participants expressed their experiences of, and aspirations for, dealing with climate change, their voices were not evident in DHB policy development processes. The deficit within existing policy process reflects a lack of preparedness in the face of climate change. Despite clear resilience and adaptation strategies, structural change is needed to address identified disadvantages. Through a co-designed policy framework (“Haumanu Hauora”), we guide policy formation to mitigate climate change risk to Māori (and others). Central to the revised policy framework is the creation of space for both internal and external Māori voices to ensure consistent Māori input throughout the policy process. We also introduce a commissioning, refining, and monitoring stage (that includes evaluation). Haumanu Hauora considers whānau-centered healthcare knowledge, needs, resources, and aspirations, to contribute to a transformed and responsive health system. Above all, we believe that strengthening health institution responsiveness to Māori health needs is essential.

text: Haumanu Hauora: refining public health institution policy to include Māori and climate change The deepening climate crisis generates specific impacts that will exacerbate the already disproportionately negative health outcomes experienced by Indigenous people. Disparate health outcomes have not spontaneously emerged, but rather have been foreshadowed by existing inequities. This article summarizes a sample of the work from a two-year research project in Aotearoa New Zealand to understand existing policy processes and ascertain the extent to which health institutions give serious consideration to climate change impacts on Māori (Indigenous people) with health vulnerabilities. Speaking to tāngata whenua (Indigenous Māori), District Health Board (DHB) employees, and subject matter experts (SMEs), it was clear that policy processes were ad hoc and problematically silenced consistent Māori input. While research participants expressed their experiences of, and aspirations for, dealing with climate change, their voices were not evident in DHB policy development processes. The deficit within existing policy process reflects a lack of preparedness in the face of climate change. Despite clear resilience and adaptation strategies, structural change is needed to address identified disadvantages. Through a co-designed policy framework (“Haumanu Hauora”), we guide policy formation to mitigate climate change risk to Māori (and others). Central to the revised policy framework is the creation of space for both internal and external Māori voices to ensure consistent Māori input throughout the policy process. We also introduce a commissioning, refining, and monitoring stage (that includes evaluation). Haumanu Hauora considers whānau-centered healthcare knowledge, needs, resources, and aspirations, to contribute to a transformed and responsive health system. Above all, we believe that strengthening health institution responsiveness to Māori health needs is essential.

year: 2023-05-05