title: Override and restricted union for partial functions

authors: Stokes, Tim

abstract: The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

text: Override and restricted union for partial functions The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

year: 2024-08-12

title: Modelling post-earthquake building recovery under human resource constraints

authors: Li, Lianyan

abstract: Demand surge phenomenon as a result of shortages of human resources needed for post-disaster recovery and reconstruction can be detrimental to recovery outcomes. To quantify the impact of human resource constraints on the recovery of an urban environment, this research introduces a novel Dynamic Stochastic Queuing (DSQ) model, revealing such dynamic interplays over time. Central to this model is the incorporation of a spectrum of socioeconomic factors to formulate optimal recovery strategies under different dynamic resource mobilisation patterns. A recovery efficiency index is defined and employed as a proxy to facilitate comparisons across diverse recovery strategies. A case study is presented to illustrate the application of the model by simulating the building recovery of a portfolio of residential buildings in New Zealand following the 2010–2011 Canterbury Earthquake Sequence (CES). The findings indicate that proactive resource mobilisation strategies can significantly enhance both recovery efficiency and speed. It becomes possible to shorten the post-disaster recovery time significantly by strategically sequencing repairs of damaged structures while taking into account resource mobilisation strategies.

text: Modelling post-earthquake building recovery under human resource constraints Demand surge phenomenon as a result of shortages of human resources needed for post-disaster recovery and reconstruction can be detrimental to recovery outcomes. To quantify the impact of human resource constraints on the recovery of an urban environment, this research introduces a novel Dynamic Stochastic Queuing (DSQ) model, revealing such dynamic interplays over time. Central to this model is the incorporation of a spectrum of socioeconomic factors to formulate optimal recovery strategies under different dynamic resource mobilisation patterns. A recovery efficiency index is defined and employed as a proxy to facilitate comparisons across diverse recovery strategies. A case study is presented to illustrate the application of the model by simulating the building recovery of a portfolio of residential buildings in New Zealand following the 2010–2011 Canterbury Earthquake Sequence (CES). The findings indicate that proactive resource mobilisation strategies can significantly enhance both recovery efficiency and speed. It becomes possible to shorten the post-disaster recovery time significantly by strategically sequencing repairs of damaged structures while taking into account resource mobilisation strategies.

year: 2025

title: Biculturalism in practice, ‘Te Pounamu’: Integration of a Māori model with traditional clinical assessment processes

authors: Manna, Leona

subjects: Maori

abstract: Traditional clinical psychological assessment follows a western paradigm of interaction, which relies heavily on verbalisations of internal and external symptoms. This process relies upon the assumption of and acceptance that tangata whaiora (consumer/s) are able to do this. Training encourages a clinical psychologist to take into account differences which may or may not be obvious, e.g., differences in religious beliefs, gender, hearing, or sight. However, as clinicians we often neglect to assess tangata whaiora abilities to verbalise such information. Te Pounamu, as a Māori model demonstrates the underlying principles of Te Tiriti O Waitangi. Providing the best treatment outcomes is about acknowledging all aspects of one’s wellbeing: physical, mental, spiritual, and whānau. Te Pounamu provides a process that acknowledges such aspects in a way of knowing that is healing. From clinical experience, the interactive mode that Te Pounamu utilises has been found efficacious in assisting tangata whaiora to understand how such factors contribute to poor mental health.

text: Biculturalism in practice, ‘Te Pounamu’: Integration of a Māori model with traditional clinical assessment processes Traditional clinical psychological assessment follows a western paradigm of interaction, which relies heavily on verbalisations of internal and external symptoms. This process relies upon the assumption of and acceptance that tangata whaiora (consumer/s) are able to do this. Training encourages a clinical psychologist to take into account differences which may or may not be obvious, e.g., differences in religious beliefs, gender, hearing, or sight. However, as clinicians we often neglect to assess tangata whaiora abilities to verbalise such information. Te Pounamu, as a Māori model demonstrates the underlying principles of Te Tiriti O Waitangi. Providing the best treatment outcomes is about acknowledging all aspects of one’s wellbeing: physical, mental, spiritual, and whānau. Te Pounamu provides a process that acknowledges such aspects in a way of knowing that is healing. From clinical experience, the interactive mode that Te Pounamu utilises has been found efficacious in assisting tangata whaiora to understand how such factors contribute to poor mental health.

year: 2003