Wool follicle development in the New Zealand Romney and N type sheep. I. The relationships of development to age in the New Zealand Romney and N type sheep foetuses and a comparison with results obtained from the Merino

1957 ◽  
Vol 8 (4) ◽  
pp. 371 ◽  
Author(s):  
SK Stephenson
Keyword(s):  
New Zealand ◽  
Least Squares ◽  
Linear Relationship ◽  
Population Studies ◽  
Regression Line ◽  
The Body ◽  
Follicle Development ◽  
Method Of Least Squares ◽  
Rate Of Development ◽  
Wool Follicle

The development of the follicle population in New Zealand Romney and N-type sheep foetuses has been studied by comparing stages of development at different ages, using the method developed by Carter and Hardy (1947) and Hardy and Lyne (1956). Their scale has been altered so as to give a linear relationship with age, and a regression line has been fitted to the data by the method of least squares. Analysis of the N-type and New Zealand Romney mating groups and a comparison with the Merino data given by Carter and Hardy (1947) show that no marked or consistent differences occur in the age at which different stages of follicle development are completed or in the rate of development of the follicle population. Studies of different positions on the body agree with the findings of other workers that development begins first on the head and limbs and later over the trunk. Between positions the correlation between the age at which follicle development begins and the rate of development after initiation is not significant.

Wool follicle development in the New Zealand Romney and N type sheep. V. The pre-natal relationships between growth, skin expansion, and primary follicle number

1959 ◽  
Vol 10 (3) ◽  
pp. 453 ◽  
Author(s):  
SK Stephenson
Keyword(s):  
New Zealand ◽  
Surface Area ◽  
Linear Growth ◽  
The Body ◽  
Follicle Development ◽  
Competition Effect ◽  
Primary Follicle ◽  
Skin Expansion ◽  
Wool Follicle

A method is presented for estimating changes in primary follicle number on different regions of the body of the sheep foetus from linear growth measurements and primary follicle density determinations. The major factor controlling the initiation of new primary follicle anlagen on different regions is shown to be rate of skin expansion, and therefore it appears probable that there is a competition effect between anlagen during this phase of development. After allowance is made for area increases, there are still real differences between regions in the rates of initiation of primary anlagen. There is also evidence that, during the period of primary anlagen initiation, foetuses with a greater surface area have a greater total number of primary anlagen.

Wool follicle development in the New Zealand Romney and N type sheep. II. Follicle population density during foetal development

1958 ◽  
Vol 9 (1) ◽  
pp. 138 ◽  
Author(s):  
SK Stephenson
Keyword(s):  
New Zealand ◽  
Population Density ◽  
Subsequent Development ◽  
The Body ◽  
Limiting Factor ◽  
Follicle Development ◽  
Primary Follicle ◽  
Foetal Development ◽  
Secondary Follicle ◽  
The Face

Quantitative aspects of follicle initiation and development have been studied in a series of N-type and New Zealand Romney foetuses. Density of the follicle population and ratios of secondary to primary follicles were examined on 13 positions of the body which covered the main wool-bearing areas, the face and head, and the limbs. Primary follicle development is initiated first on the head and limbs and throughout subsequent development these regions are most advanced. Primary follicle density reaches a maximum between 75 and 90 days of foetal age, after which it decreases as a result of skin growth. Secondary follicle initiation is more rapid on the wool-bearing areas of the body, and higher ratios of secondary to primary follicles are recorded from these regions. No real differences have been found between N-type and New Zealand Romney foetuses in population density of the different follicle types at any age or in the number of secondary follicles developed per primary follicle. The growth of larger primary fibres and follicles in N-type foetuses is not accompanied by, and does not result from, a lower density of primary follicles. There does not appear to be any marked relation between the decreasing density of primary follicles after 90 days of foetal age and the initiation of secondary follicle anlagen. This fact, and the absence of any differences in the number of secondary anlagen formed per primary follicle in N-types, suggest that crowding in N-types is not a limiting factor in the formation of secondary follicle anlagen.

scholarly journals Application of Robust Estimation Methods for the Analysis of Outlier Measurements / Aplikácia Robustných Odhadovacích Metód Pri Analýze Odľahlých Meraní

2011 ◽  
Vol 57 (3) ◽  
pp. 14-29
Author(s):  
Silvia Gašincová ◽  
Juraj Gašinec ◽  
Gabriel Weiss ◽  
Slavomír Labant
Keyword(s):  
Linear Programming ◽  
Least Squares ◽  
Robust Estimation ◽  
Mathematical Analysis ◽  
Physical Environment ◽  
Regression Line ◽  
Measured Data ◽  
Estimation Methods ◽  
Method Of Least Squares ◽  
The Impact

Abstract The basis of mathematical analysis of geodetic measurements is the method of least squares (LSM), whose bicentenary we celebrated in 2006. In geodetic practice, we quite often encounter the phenomenon when outlier measurements penetrate into the set of measured data as a result of e.g. the impact of physical environment. That fact led to modifications of LSM that have been increasingly published mainly in foreign literature in recent years. The mentioned alternative estimation methods are e.g. robust estimation methods and methods in linear programming. The aim of the present paper is to compare LSM with the robust estimation methods on an example of a regression line.

Wool follicle development in the New Zealand Romney and N type sheep. IV. Pre-natal growth and changes in body proportions

1959 ◽  
Vol 10 (3) ◽  
pp. 433 ◽  
Author(s):  
SK Stephenson
Keyword(s):  
New Zealand ◽  
South African ◽  
The Body ◽  
Least Squares Regression ◽  
Allometric Growth ◽  
Body Proportions ◽  
Linear Measurements ◽  
Relative Growth ◽  
Body Weights ◽  
Wool Follicle

Growth, and the relative growth gradients over the body, have been studied in N-type and normal Kew Zealand Romney foetuses. Body weights, and a series of linear measurements taken between different points over the body, have been obtained from a series of foetuses of known ages. Huxley's allometric growth ratios have been calculated from these measurements by using the least squares regression. There are no significant gromth differences between foetuses belonging to the different AT-genotypes of the New Zealand Ronmey. Foetuses belonging to the New Zealand Romney and some British breeds grow at a faster rate than South African Merino foetuses studied by Malan and Curson (1936a) and Cloete (1939). Relative growth gradients over the body are, in general, similar to those of other mammals, but the results do not support the theory of Cloete (1939), that the relative growth rate of a part of the body is solely a function of the age of the part.

CHOOSING A METHOD FOR ESTIMATING THE PARAMETERS OF LINEAR REGRESSION BASED ON IDENTIFICATION OF ANOMALOUS OBSERVATIONS

2021 ◽  
pp. 24-29
Author(s):  
С.И. Носков
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Robust Estimation ◽  
Regression Models ◽  
Regression Line ◽  
Estimation Method ◽  
Model Parameters ◽  
Method Of Least Squares ◽  
Sharp Drop ◽  
Modulus Method

Описываются свойства методов оценивания параметров регрессионных моделей - наименьших квадратов, модулей, антиробастного, а также их применения для решения конкретных практических проблем. При этом метод наименьших модулей не реагирует на аномальные наблюдения выборки, метод антиробастного оценивания сильно отклоняет линию регрессии в их направлении, метод наименьших квадратов занимает промежуточное положение. Показано, что если целью построения модели является проведение на ее основе многовариантных прогнозных расчетов значений зависимой переменной, то выбор метода численной идентификации параметров модели следует производить на основе анализа характера выбросов. Если есть основания полагать, что подобные им ситуации могут иметь место в будущем, следует выбрать метод антиробастного оценивания, в противном же случае - метод наименьших модулей. Построена регрессионная модель грузооборота Красноярской железной дороги на основе применения всех трех методов оценивания параметров. Проведен анализ причин, имеющих место в 2010 году в ситуации резкого падения величины грузооборота, которая вполне может характеризоваться как аномальное наблюдение в данных. Сделаны рекомендации по выбору метода оценивания параметров в этом случае The article describes the properties of methods for estimating the parameters of regression models - least squares, moduli, anti-robust - as well as their application for solving specific practical problems. At the same time, the method of least modules does not respond to anomalous observations of the sample, the method of anti-robust estimation strongly deviates the regression line in their direction, the method of least squares occupies an intermediate position. I show that if the purpose of constructing a model is to carry out multivariate predictive calculations of the values of the dependent variable on its basis, then the choice of a method for the numerical identification of model parameters should be based on an analysis of the nature of emissions. If there is a reason to believe that similar situations may occur in the future, the anti-robust estimation method should be chosen, otherwise - the least modulus method. I built a regression model of the freight turnover of the Krasnoyarsk railway on the basis of the application of all three methods of parameter estimation. I carried out the analysis of the reasons for the situation of a sharp drop in the value of cargo turnover in 2010, which may well be characterized as anomalous observation in the data. I give recommendations on the choice of the parameter estimation method in this case

scholarly journals Observed surface snowmelt at high elevation in theSouthern Alps of New Zealand

2005 ◽  
Vol 40 ◽  
pp. 163-168 ◽  
Author(s):  
Eryn S. Cutler ◽  
Blair Fitzharris
Keyword(s):  
New Zealand ◽  
Linear Relationship ◽  
Regression Line ◽  
High Elevation ◽  
Southern Alps ◽  
Degree Days ◽  
Summer Period ◽  
Equilibrium Line Altitude ◽  
Degree Day ◽  
Data Points

AbstractSnowmelt is measured over a 34 day summer period at 2440ma.s.l. on Tasman Glacier (>500m above the equilibrium-line altitude) using a tipping-bucket lysimeter and an array of ten ablation stakes. A degree-day factor for snowmelt is calculated using a linear relationship between combined measured melt and the number of degree-days. The slope of the regression line for these data points provides an estimate of the degree-day factor for use in runoff models. Average snowmelt is 17.8 mmd–1, but varies between 0 and 78 mmd–1. Melt occurs in a series of distinct cyclical events or pulses, each of which lasts 5–8 days. These correspond to the eastward passage of anticyclones, then troughs over the Southern Alps. When all days with northwest airflow across the Southern Alps are excluded, the melt factor is 3.4 mm˚C–1 d–1. Northwest days belong to a different population with a much higher average melt factor of 9.1 mm˚C–1 d–1, but more measurements are required to better understand key processes.

Wool follicle development in New Zealand Romney and N-type sheep. 3. Diameters of follicles and fibres

1959 ◽  
Vol 10 (1) ◽  
pp. 108 ◽  
Author(s):  
SK Stephenson
Keyword(s):  
New Zealand ◽  
Pleiotropic Effect ◽  
Primary Effect ◽  
N Gene ◽  
Follicle Development ◽  
Primary Follicle ◽  
Fibre Size ◽  
Wool Follicle ◽  
Follicle Size

The diameters of the primary and secondary follicles hare been measured in N type and New Zealand Romney foetuses. It is shown that the primary effect of the N gene is on the primary follicle papilla and fibre size, not on overall follicle size A secondary pleiotropic effect is on the primary follicles, which Increase in diameter as a result of growing large fibres There do not appear to be any other effects of the dominant N gene up to 126 days after conception, either on the follicle population or on the growth of the foetus.

Pre- and post-natal wool follicle development and density in sheep of five genotypes

1996 ◽  
Vol 126 (3) ◽  
pp. 363-370 ◽  
Author(s):  
J. E. Hocking Edwards ◽  
M. J. Birtles ◽  
P. M. Harris ◽  
A. L. Parry ◽  
E. Paterson ◽  
...  
Keyword(s):  
New Zealand ◽  
Similar Pattern ◽  
Critical Period ◽  
The Other ◽  
Follicle Development ◽  
Physiological Factors ◽  
Factors Affecting ◽  
Wool Follicle ◽  
Follicle Maturation ◽  
Skin Samples

SUMMARYThe pre-natal and post-natal development of wool follicles in sheep of five genotypes with contrasting wool types was examined to provide data on which to base studies of physiological factors affecting wool type via follicle development. This study was conducted following Autumn mating in 1992 at Palmerston North, New Zealand (40° S, 176° E). The rate and timing of follicle development in midside skin samples from Romney, Merino, Merino × Romney (M × R), Drysdale and Wiltshire foetuses and lambs collected at weekly intervals from days 76 to 143 of gestation and 1, 3, 7, 12 and 32 weeks after birth were examined.Primary (P) follicle density had a similar pattern of development in each of the genotypes, although the Merino had a significantly greater density of P follicles than the other genotypes. There was a difference in the rate of P follicle maturation between genotypes with the Drysdale, Wiltshire and M × R completing P follicle maturation before the other two genotypes. However, the majority of P follicles in all genotypes were producing fibres by 111 days of gestation. It was concluded that the small differences in the density and time of development of the P follicles could not cause the differences in wool type between genotypes.The pattern of development of the secondary (S) follicle population was examined by comparing S: P ratios. The initiation of S follicles began at similar ages in the five genotypes, but initiation was completed earlier in the Romney, Drysdale and Wiltshire than in the Merino and M × R, as indicated by a significant genotype by age interaction (P < 0·001). There was no difference between genotypes in S:P ratio from 90 to 104 days of gestation. The S:P ratio of the Romney, Drysdale and Wiltshire did not change significantly from 104 days of gestation until the end of the study, indicating that few S follicles were initiated in these genotypes after 104 days of gestation. The M × R data showed a significant increase in S:P ratio until 119 days of gestation and the Merino S:P ratio increased until 126 days of gestation.The period between days 90 and 125 of gestation was identified as being the critical period for the development of different follicle populations in Merino and non-Merino genotypes and it is this period which should be the focus for studies to determine physiological factors controlling secondary follicle development.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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