title: Defining sets and critical sets in (0,1)-matrices.

authors: Cavenagh, Nicholas J.

subjects: (0,1)-matrix

abstract: If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. If the removal of any entry of D destroys this property (i.e. at least two completions become possible), we say that D is a critical set for M. In this note, we show that the complement of a critical set for a (0, 1)-matrix M is a defining set for M. We also study the possible sizes (number of filled-in cells) of defining sets for square matrices M with uniform row and column sums, which are also frequency squares. In particular, we show that when the matrix is of even order 2m and the row and column sums are all equal to m, the smallest possible size of a critical set is precisely m². We give the exact structure of critical sets with this property.

text: Defining sets and critical sets in (0,1)-matrices. If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. If the removal of any entry of D destroys this property (i.e. at least two completions become possible), we say that D is a critical set for M. In this note, we show that the complement of a critical set for a (0, 1)-matrix M is a defining set for M. We also study the possible sizes (number of filled-in cells) of defining sets for square matrices M with uniform row and column sums, which are also frequency squares. In particular, we show that when the matrix is of even order 2m and the row and column sums are all equal to m, the smallest possible size of a critical set is precisely m². We give the exact structure of critical sets with this property.

year: 2013

title: A bioenergetic assessment of the influence of stocking practices on rainbow trout (Oncorhynchus mykiss) growth and consumption in a New Zealand lake

authors: Blair, Jennifer Marie

subjects: density dependence

abstract: To investigate the carrying capacity and factors affecting growth of rainbow trout in Lake Rotoiti, we employed a bioenergetics model to assess the influence of stocking rates, timing of releases and prey abundance on growth and prey consumption. We hypothesised that stocking rates and prey abundance would affect growth and prey consumption by influencing per-capita prey availability, and that the environmental conditions encountered by fish at the time of stocking would affect growth and consumption.
Prey consumption of stocked rainbow trout was calculated with the Wisconsin bioenergetics model. We calculated growth trajectories of released trout based on data from stocked trout that were released in spring and autumn from 1993 to 2009 and then re-captured by anglers. Diet, prey energy density, body mass lost during spawning and lake temperature were measured locally.
Stocking timing had no effect on return rates to anglers or length or weight of caught fish. Although trout released in autumn were smaller than those released in spring, autumn-released trout grew at a faster rate and had similar lengths and weights to spring cohorts after 2 years of growth in the lake. Modelled consumption parameters were negatively correlated with trout population size, suggesting that stocking rates (347–809 fish ha−1 year−1) caused density-dependent effects on growth. Although common smelt (Retropinna retropinna) accounted for 85% of total prey consumption, no significant relationship was found between prey consumption by individual trout and adult smelt abundance, possibly because trout are targeting smaller smelt that our abundance estimate did not account for.
Releasing trout in autumn appears to be advantageous for growth, possibly because (i) temperature is more suitable for growth in autumn–winter than in spring–summer and (ii) prey for small trout is abundant in autumn. Mild winter conditions appear to enhance overwinter survival and growth of rainbow trout in warm-temperate lakes compared to higher latitudes. This implies that moderately productive warm-temperate lake ecosystems are highly suitable for trout growth in winter, but less so in summer, when lake stratification and high nutrient levels may create conditions suitable for algal blooms and hypolimnetic deoxygenation. High growth rates of trout in warm-temperate lakes can therefore be supported by timing releases to coincide with favourable winter conditions.

text: A bioenergetic assessment of the influence of stocking practices on rainbow trout (Oncorhynchus mykiss) growth and consumption in a New Zealand lake To investigate the carrying capacity and factors affecting growth of rainbow trout in Lake Rotoiti, we employed a bioenergetics model to assess the influence of stocking rates, timing of releases and prey abundance on growth and prey consumption. We hypothesised that stocking rates and prey abundance would affect growth and prey consumption by influencing per-capita prey availability, and that the environmental conditions encountered by fish at the time of stocking would affect growth and consumption.
Prey consumption of stocked rainbow trout was calculated with the Wisconsin bioenergetics model. We calculated growth trajectories of released trout based on data from stocked trout that were released in spring and autumn from 1993 to 2009 and then re-captured by anglers. Diet, prey energy density, body mass lost during spawning and lake temperature were measured locally.
Stocking timing had no effect on return rates to anglers or length or weight of caught fish. Although trout released in autumn were smaller than those released in spring, autumn-released trout grew at a faster rate and had similar lengths and weights to spring cohorts after 2 years of growth in the lake. Modelled consumption parameters were negatively correlated with trout population size, suggesting that stocking rates (347–809 fish ha−1 year−1) caused density-dependent effects on growth. Although common smelt (Retropinna retropinna) accounted for 85% of total prey consumption, no significant relationship was found between prey consumption by individual trout and adult smelt abundance, possibly because trout are targeting smaller smelt that our abundance estimate did not account for.
Releasing trout in autumn appears to be advantageous for growth, possibly because (i) temperature is more suitable for growth in autumn–winter than in spring–summer and (ii) prey for small trout is abundant in autumn. Mild winter conditions appear to enhance overwinter survival and growth of rainbow trout in warm-temperate lakes compared to higher latitudes. This implies that moderately productive warm-temperate lake ecosystems are highly suitable for trout growth in winter, but less so in summer, when lake stratification and high nutrient levels may create conditions suitable for algal blooms and hypolimnetic deoxygenation. High growth rates of trout in warm-temperate lakes can therefore be supported by timing releases to coincide with favourable winter conditions.

year: 2013

title: Section 2: Native disruption: Maori and the precariat: Introduction

authors: Masters-Awatere, Bridgette

abstract: Within this section, the authors encourage the reader to look back into history and then consider the future. We are invited to re-examine deeds from this country’s past. To immerse ourselves in a narrative that may be different to the one we have been taught in school, or heard among our friends and family. Through their stories we can see multiple narratives. Readers are invited to understand, embrace and own the past. By recognising and accepting the past — our collective histories — we can determine our collective present and future.

text: Section 2: Native disruption: Maori and the precariat: Introduction Within this section, the authors encourage the reader to look back into history and then consider the future. We are invited to re-examine deeds from this country’s past. To immerse ourselves in a narrative that may be different to the one we have been taught in school, or heard among our friends and family. Through their stories we can see multiple narratives. Readers are invited to understand, embrace and own the past. By recognising and accepting the past — our collective histories — we can determine our collective present and future.

year: 2017