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: Pandora’s box down-under: origins and numbers of mustelids transported to New Zealand for biological control of rabbits

authors: King, Carolyn M.

subjects: Invasive species

abstract: This paper describes one of the world’s first large-scale experiments in biological control of a major vertebrate pest of agriculture, which was tried in New Zealand during the second half of the nineteenth century. Starting from the late 1860s, pasture damage in Southland and Otago by European rabbits was causing serious reductions in productivity of sheep (wool clip and lambing percentages) associated with malnutrition of the breeding ewes, and a consequent decline in the value of pastoral land. In response, and despite repeated local and international warnings, ferrets, stoats and weasels (Mustela furo, M. erminea and M. nivalis) were liberated on the worst of the rabbit-infested pastures. They were perceived as the ‘natural enemies of the rabbit’ but (unlike foxes) too small to threaten lambs. Over the 50 years after 1870, upwards of 75,000 ferrets, most imported from Australia or locally bred, were released in the South Island. Over the decade 1883–1892, at least 7838 stoats and weasels arrived from Britain. At least 25 shipments are known, with an average of only 10% mortality per shipment. Of the 3585 animals listed by species, 73% were weasels. The total cost of the ferret programme cannot now be estimated; that of stoats and weasels alone was at least £5441, probably twice that, or >$NZ 1–2 million in today’s money. Mustelids (and cats) killed many young rabbits, which was helpful because rates of change in rabbit populations are sensitive to variations in juvenile mortality, but in the most rabbit-prone semi-arid lands, mustelids could not remove enough rabbits to prevent the continuing damage to sheep pastures. The era of deliberate introductions of mustelids to control rabbits in New Zealand was short, expensive, and unsuccessful.

text: Pandora’s box down-under: origins and numbers of mustelids transported to New Zealand for biological control of rabbits This paper describes one of the world’s first large-scale experiments in biological control of a major vertebrate pest of agriculture, which was tried in New Zealand during the second half of the nineteenth century. Starting from the late 1860s, pasture damage in Southland and Otago by European rabbits was causing serious reductions in productivity of sheep (wool clip and lambing percentages) associated with malnutrition of the breeding ewes, and a consequent decline in the value of pastoral land. In response, and despite repeated local and international warnings, ferrets, stoats and weasels (Mustela furo, M. erminea and M. nivalis) were liberated on the worst of the rabbit-infested pastures. They were perceived as the ‘natural enemies of the rabbit’ but (unlike foxes) too small to threaten lambs. Over the 50 years after 1870, upwards of 75,000 ferrets, most imported from Australia or locally bred, were released in the South Island. Over the decade 1883–1892, at least 7838 stoats and weasels arrived from Britain. At least 25 shipments are known, with an average of only 10% mortality per shipment. Of the 3585 animals listed by species, 73% were weasels. The total cost of the ferret programme cannot now be estimated; that of stoats and weasels alone was at least £5441, probably twice that, or >$NZ 1–2 million in today’s money. Mustelids (and cats) killed many young rabbits, which was helpful because rates of change in rabbit populations are sensitive to variations in juvenile mortality, but in the most rabbit-prone semi-arid lands, mustelids could not remove enough rabbits to prevent the continuing damage to sheep pastures. The era of deliberate introductions of mustelids to control rabbits in New Zealand was short, expensive, and unsuccessful.

year: 2017

title: Hoera Te Mimiha

authors: Hart, Philip

abstract: Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

text: Hoera Te Mimiha Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

year: 2016