title: Left restriction monoids from left E-completions

authors: Stokes, Tim E.

abstract: Given a monoid S with E any non-empty subset of its idempotents, we present a novel one-sided version of idempotent completion we call left E-completion. In general, the construction yields a one-sided variant of a small category called a constellation by Gould and Hollings. Under certain conditions, this constellation is inductive, meaning that its partial multiplication may be extended to give a left restriction semigroup, a type of unary semigroup whose unary operation models domain. We study the properties of those pairs  for which this happens, and characterise those left restriction semigroups that arise as such left E-completions of their submonoid of elements having domain 1. As first applications, we decompose the left restriction semigroup of partial functions on the set X and the right restriction semigroup of left total partitions on X as left and right E-completions respectively of the transformation semigroup  on X, and decompose the left restriction semigroup of binary relations on X under demonic composition as a left E-completion of the left-total binary relations. In many cases, including these three examples, the construction embeds in a semigroup Zappa-Szép product.

text: Left restriction monoids from left E-completions Given a monoid S with E any non-empty subset of its idempotents, we present a novel one-sided version of idempotent completion we call left E-completion. In general, the construction yields a one-sided variant of a small category called a constellation by Gould and Hollings. Under certain conditions, this constellation is inductive, meaning that its partial multiplication may be extended to give a left restriction semigroup, a type of unary semigroup whose unary operation models domain. We study the properties of those pairs  for which this happens, and characterise those left restriction semigroups that arise as such left E-completions of their submonoid of elements having domain 1. As first applications, we decompose the left restriction semigroup of partial functions on the set X and the right restriction semigroup of left total partitions on X as left and right E-completions respectively of the transformation semigroup  on X, and decompose the left restriction semigroup of binary relations on X under demonic composition as a left E-completion of the left-total binary relations. In many cases, including these three examples, the construction embeds in a semigroup Zappa-Szép product.

year: 2022-05

title: Water requirements for 'Hass' avocado flowering and fruit development in New Zealand

authors: Kaneko, Teruko

subjects: avocado

abstract: The aim of this work was to determine water requirements for Persea americana 'Hass’ avocado trees (mature, ca. 9 years and young, ca. 3 years) from November 2014 to October 2015 in Bay of Plenty, New Zealand. In addition, the effect of water deficit on flowering and early fruit development was investigated in young avocado (ca. 3 years) trees. 

Reference evapotranspiration (ETo) was calculated by the FAO Penman-Monteith equation based on weather information at the orchard. Crop evapotranspiration (ETc) of avocado was measured by sap flow measurements using the compensation heat pulse method (CHPM), and daily crop evapotranspiration was also estimated from a soil water balance (Ewb). Avocado tree water requirements were calculated as crop coefficients (Kc - the ETo/ETc ratio).
•	Monthly cumulative ETo showed a gradual reduction from 145.9 mm in January to 297.7 mm in June. Monthly cumulative ETc for both the mature and young plants was highest at 75 and 41.8 mm in January, and the lowest at 22.4 and 13.53 mm in July, respectively. The results showed a close correlation between ETc and ETo. 
•	Ewb was higher than ETc by 22 % for the mature and 55 % for the young plants, probably caused by drainage which was not measured.
•	In summer, monthly average Kc varied between 0.45-0.60 for the mature and 0.25-0.30 for the young plants. In winter, Kc increased to 0.9-1.0 for the mature and 0.45-0.55 for the young plants.   

To investigate the effect of water deficit on flowering and fruit development, rainout shelters were set up under the young trees from mid-October 2014. During this treatment, the control plants were well irrigated and fertilized, while the drought plants received no irrigation, precipitation, or fertilizers. The rainout shelters were removed in early-May 2015, and monitoring was continued until late-October.
•	During the rainout treatment, at a depth of 0-30 cm, soil water contents of the drought treated plants dropped to 0.13 m3/m3, while that of the control remained above 0.2 m3/m3. However, from March, soil water content of the drought plants was stable at 0.20 m3/m3 at a depth of 31-60 cm and 0.25 m3/m3 at a depth of 61-90 cm. Spatial soil moisture demonstrated the soil was  drier close to the drought treated trees, but wetter near the edge of the rainout shelters. These measurements suggest the drought plants were able to obtain some water from the deeper soil or outside the shelters. 
•	Predawn leaf water potential (PLWP) of the drought plants was lower by 0.06-0.22 MPa than that of the control plants during the flowering season. However, in December, there was no significant difference in stomatal conductance (gs) between the two treatments. The drought leaf water potential (LWP) and stem water potential (SWP) were more negative than the control LWP and SWP. In January and February, the drought LWP and SWP dropped to -0.43 MPa and -0.30 MPa, whereas the control LWP and SWP were around -0.25 MPa and -0.23 MPa, respectively, assuming the rainout shelters caused moderate water stress in the drought-treated plants.
•	Throughout the flowering season, in total, 1382 open female flowers on the control plants and 1515 flowers on the drought plants were marked and their fates monitored. About 21 % of control flowers and 23 % of the drought flowers remained on the tree 16 days after anthesis. 100 days after anthesis, only 4 control and 1 drought fruit from the monitored flowers were retained on the plants. 
•	The two treatments had significant fruit drop in summer, about 70 % of marked fruit dropped in January and February, and a second peak of fruit abscission occurred in winter, caused by frost. At harvest, the retention rate of fruit for the control and drought treatments were 15 % and 5 %, respectively. Moreover, the drought plants had smaller fruit size than fruit of the control plants by 21 % at harvest. The differences in fruit abscission and fruit size were probably caused by the combined effects of water deficit, nutrient deficiency, and crop load. 
•	The control had higher average yield at 36.4 ± 1.1 kg per plant than the drought plants at 27.8 ± 1.0 kg per plant. The dry matter content of the control fruit was 30.4 ± 0.3 %, 7% higher than that of the drought fruit. 

The results can be used to develop irrigation recommendations, and that under the conditions described here the trees were difficult to drought stress in spring and flowering did not appear to be very sensitive to drought stress. However, early fruit growth was very sensitive to water deficits, resulting in a large reduction in fruit size.

text: Water requirements for 'Hass' avocado flowering and fruit development in New Zealand The aim of this work was to determine water requirements for Persea americana 'Hass’ avocado trees (mature, ca. 9 years and young, ca. 3 years) from November 2014 to October 2015 in Bay of Plenty, New Zealand. In addition, the effect of water deficit on flowering and early fruit development was investigated in young avocado (ca. 3 years) trees. 

Reference evapotranspiration (ETo) was calculated by the FAO Penman-Monteith equation based on weather information at the orchard. Crop evapotranspiration (ETc) of avocado was measured by sap flow measurements using the compensation heat pulse method (CHPM), and daily crop evapotranspiration was also estimated from a soil water balance (Ewb). Avocado tree water requirements were calculated as crop coefficients (Kc - the ETo/ETc ratio).
•	Monthly cumulative ETo showed a gradual reduction from 145.9 mm in January to 297.7 mm in June. Monthly cumulative ETc for both the mature and young plants was highest at 75 and 41.8 mm in January, and the lowest at 22.4 and 13.53 mm in July, respectively. The results showed a close correlation between ETc and ETo. 
•	Ewb was higher than ETc by 22 % for the mature and 55 % for the young plants, probably caused by drainage which was not measured.
•	In summer, monthly average Kc varied between 0.45-0.60 for the mature and 0.25-0.30 for the young plants. In winter, Kc increased to 0.9-1.0 for the mature and 0.45-0.55 for the young plants.   

To investigate the effect of water deficit on flowering and fruit development, rainout shelters were set up under the young trees from mid-October 2014. During this treatment, the control plants were well irrigated and fertilized, while the drought plants received no irrigation, precipitation, or fertilizers. The rainout shelters were removed in early-May 2015, and monitoring was continued until late-October.
•	During the rainout treatment, at a depth of 0-30 cm, soil water contents of the drought treated plants dropped to 0.13 m3/m3, while that of the control remained above 0.2 m3/m3. However, from March, soil water content of the drought plants was stable at 0.20 m3/m3 at a depth of 31-60 cm and 0.25 m3/m3 at a depth of 61-90 cm. Spatial soil moisture demonstrated the soil was  drier close to the drought treated trees, but wetter near the edge of the rainout shelters. These measurements suggest the drought plants were able to obtain some water from the deeper soil or outside the shelters. 
•	Predawn leaf water potential (PLWP) of the drought plants was lower by 0.06-0.22 MPa than that of the control plants during the flowering season. However, in December, there was no significant difference in stomatal conductance (gs) between the two treatments. The drought leaf water potential (LWP) and stem water potential (SWP) were more negative than the control LWP and SWP. In January and February, the drought LWP and SWP dropped to -0.43 MPa and -0.30 MPa, whereas the control LWP and SWP were around -0.25 MPa and -0.23 MPa, respectively, assuming the rainout shelters caused moderate water stress in the drought-treated plants.
•	Throughout the flowering season, in total, 1382 open female flowers on the control plants and 1515 flowers on the drought plants were marked and their fates monitored. About 21 % of control flowers and 23 % of the drought flowers remained on the tree 16 days after anthesis. 100 days after anthesis, only 4 control and 1 drought fruit from the monitored flowers were retained on the plants. 
•	The two treatments had significant fruit drop in summer, about 70 % of marked fruit dropped in January and February, and a second peak of fruit abscission occurred in winter, caused by frost. At harvest, the retention rate of fruit for the control and drought treatments were 15 % and 5 %, respectively. Moreover, the drought plants had smaller fruit size than fruit of the control plants by 21 % at harvest. The differences in fruit abscission and fruit size were probably caused by the combined effects of water deficit, nutrient deficiency, and crop load. 
•	The control had higher average yield at 36.4 ± 1.1 kg per plant than the drought plants at 27.8 ± 1.0 kg per plant. The dry matter content of the control fruit was 30.4 ± 0.3 %, 7% higher than that of the drought fruit. 

The results can be used to develop irrigation recommendations, and that under the conditions described here the trees were difficult to drought stress in spring and flowering did not appear to be very sensitive to drought stress. However, early fruit growth was very sensitive to water deficits, resulting in a large reduction in fruit size.

year: 2016

title: Treatment and survival disparities by ethnicity in New Zealand women with stage I-III breast cancer tumour subtypes

authors: Lawrenson, Ross

subjects: Science & Technology

abstract: Purpose
This study aims to look at the distribution of different subtypes of stage I–III breast cancer in Māori and Pacific versus non-Māori/Pacific women, and to examine cancer outcomes by ethnicity within these different subtypes.

Method
This study included 9,015 women diagnosed with stage I–III breast cancer between June 2000 and May 2013, recorded in the combined Waikato and Auckland Breast Cancer Registers, who had complete data on ER, PR and HER2 status. Five ER/PR/HER2 subtypes were defined. Kaplan–Meier method and Cox proportional hazards model were used to examine ethnic disparities in breast cancer-specific survival.

Results
Of the 9,015 women, 891 were Māori, 548 were Pacific and 7,576 others. Both Māori and Pacific women were less likely to have triple negative breast cancer compared to others (8.6, 8.9 vs. 13.0%). Pacific women were more than twice as likely to have ER−, PR− and HER2+ cancer than Māori and others (14.2 vs. 6.0%, 6.7%). After adjustment for age, year of diagnosis, stage, grade and treatment, the hazard ratios of breast cancer-specific mortality for Māori and Pacific women with ER+, PR+ and HER2− were 1.52 (95% CI 1.06–2.18) and 1.55 (95% CI 1.04–2.31) compared to others, respectively. Māori women with HER2+ cancer were twice more likely to die of their cancer than others.

Conclusions
Outcomes for Māori and Pacific women could be improved by better treatment regimens especially for those with HER2+ breast cancer and for women with ER+, PR+ and HER2− breast cancer.

text: Treatment and survival disparities by ethnicity in New Zealand women with stage I-III breast cancer tumour subtypes Purpose
This study aims to look at the distribution of different subtypes of stage I–III breast cancer in Māori and Pacific versus non-Māori/Pacific women, and to examine cancer outcomes by ethnicity within these different subtypes.

Method
This study included 9,015 women diagnosed with stage I–III breast cancer between June 2000 and May 2013, recorded in the combined Waikato and Auckland Breast Cancer Registers, who had complete data on ER, PR and HER2 status. Five ER/PR/HER2 subtypes were defined. Kaplan–Meier method and Cox proportional hazards model were used to examine ethnic disparities in breast cancer-specific survival.

Results
Of the 9,015 women, 891 were Māori, 548 were Pacific and 7,576 others. Both Māori and Pacific women were less likely to have triple negative breast cancer compared to others (8.6, 8.9 vs. 13.0%). Pacific women were more than twice as likely to have ER−, PR− and HER2+ cancer than Māori and others (14.2 vs. 6.0%, 6.7%). After adjustment for age, year of diagnosis, stage, grade and treatment, the hazard ratios of breast cancer-specific mortality for Māori and Pacific women with ER+, PR+ and HER2− were 1.52 (95% CI 1.06–2.18) and 1.55 (95% CI 1.04–2.31) compared to others, respectively. Māori women with HER2+ cancer were twice more likely to die of their cancer than others.

Conclusions
Outcomes for Māori and Pacific women could be improved by better treatment regimens especially for those with HER2+ breast cancer and for women with ER+, PR+ and HER2− breast cancer.

year: 2017