Diallel analysis of varying late season night temperatures on the development of a range of fluecured tobacco (Nicotiana tabacum l.) genotypes : a thesis presented in partial fulfillment of the requirements for the degree of Masterate of Agricultural Science in Plant Science at Massey University

Pg 62 not in original - misnumberedA study was conducted in the climate room facilities, at D.S.I.R. Plant Physiology Division, Palmerston North, on the effect of varying late season night temperatures on the development of a range of flue-cured tobacco genotypes. The study involved imposing three night temperatures, 10°C, 15°C and 20°C, when the plants came into flower. Ten F1 genotypes of a five parent diallel cross (no parents, no reciprocals) were grown at each night temperature with three replications per temperature. Fourteen morphological, physical and chemical characters were measured. The effect of late season night temperature was negligible but there was some evidence of genotype environment interaction for some of the characters. The experiment was conducted using single plants as plots and the statistical analysis showed acceptable coefficients of variation for biological studies. The genetic analysis of the diallel showed that general combining ability variance is the most important type of genetic variance in the characters examined. This agrees with the majority of other tobacco diallel studies. As general combining ability variance is largely a measure of additive genetic variance, breeding homozygous lines from a heterozygous base population should be the best approach to follow. Heritability values were of sufficient size for several of the commercially important characters to indicate that improvement through selection was possible. General combining ability and phenotypic simple correlations between pairs of characters were generally in good agreement, demonstrating that phenotypic selection will result in altering the genotypes in the desired direction for the characters in question. The experiment showed a large negative correlation between the two economically important characters, yield and total nicotine alkaloids. This result is in agreement with similar studies carried out by other workers in this field. The experiment revealed a number of improvements which could be useful in the conduct of future tobacco climate room studies

Becoming a three tikanga church : the Bi-cultural Commission on the Revision of the Constitution 1986-1992 : a thesis presented in partial fulfillment of the requirements for the degree of Master of Arts in History at Massey University

Text in Maori from pages 136 onwardsIn 1984 the General Synod of the Church of the Province of New Zealand established a Bi-cultural Commission on the Treaty of Waitangi. The Commission was required to study the Treaty and consider whether any principles of partnership and bi-cultural development were implied, and if so, how those principles could be embodied in the life of the Church. The Commission of three Maori and three Pakeha members consulted widely throughout the Church in both Maori and Pakeha settings, reporting back to General Synod in 1986 with 18 recommendations covering a wide range of issues, including land and the Maori language. The most significant of the recommendations established a further Bi-cultural Commission to revise the Church's constitution. The Commission's task was to be the revision of the constitution to ensure: that the preamble reflected the growth of the Church in New Zealand from 1814 to the present day; that the principles of partnership and bi-cultural development were expressed and entrenched; that the provisions of the Church of England Empowering Act 1928 were incorporated; and that Te Pihopa o Aotearoa and Te Runanga o Te Pihopatanga o Aotearoa had equal status with Diocesan Bishops and Synods. The Commission was, 'to have regard to the Report and Recommendations of the Bi-cultural Commission on the Treaty of Waitangi; and in particular to consider the Commission's response to the submission from Te Runanga [o Te Pihopatanga].' 1 Bi-cultural Commission of the Anglican Church on the Treaty of Waitangi, Report of the Bi-Cultural Commission of the Anglican Church on the Treaty of Waitangi, te Kaupapa Tikanga Rua. [Christchurch]: Provincial Secretary of the Church of the Province of New Zealand,1986, p.26. Crucial factors in the development of the constitution were the Commission on the Treaty of Waitangi's definition of the terms partnership and bi-cultural development, and the structural model proposed to the Commission by Te Runanga o Te Pihopatanga

Efficient Optimization of Loops and Limits with Randomized Telescoping Sums

We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the solutions to differential equations are all examples of optimization problems with this character. In such problems, it can be expensive to compute the objective function value and its gradient, but truncating the loop or using less accurate approximations can induce biases that damage the overall solution. We propose randomized telescope (RT) gradient estimators, which represent the objective as the sum of a telescoping series and sample linear combinations of terms to provide cheap unbiased gradient estimates. We identify conditions under which RT estimators achieve optimization convergence rates independent of the length of the loop or the required accuracy of the approximation. We also derive a method for tuning RT estimators online to maximize a lower bound on the expected decrease in loss per unit of computation. We evaluate our adaptive RT estimators on a range of applications including meta-optimization of learning rates, variational inference of ODE parameters, and training an LSTM to model long sequences

Thinplate Splines on the Sphere

In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations

One-Step Recurrences for Stationary Random Fields on the Sphere

Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$