Efficient Markov bases for Z-polytope sampling : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Manawatū, New Zealand

Listen in Dean's List of Exceptional Theses 2022In this thesis we study the use of lattice bases for fibre sampling, with particular attention paid to applications in volume network tomography. We use a geometric interpretation of the fibre as a Z-polytope to provide insight into the connectivity properties of lattice bases. Fibre sampling is used when we are interested in fitting a statistical model to a random process that may only be observed indirectly via the underdetermined linear system y = Ax. We consider the observed data y and random variable of interest x to contain count data. The likelihood function for such models requires a summation over the fibre Fy, the set of all non-negative integer vectors x satisfying this equation for some particular y. This can be computationally infeasible when Fy is large. One approach to addressing this problem involves sampling from Fy using a Markov Chain Monte Carlo algorithm, which amounts to taking a random walk through Fy . This is facilitated by a Markov basis: a set of moves that can be used construct such a walk, which is therefore a subset of the kernel of the configuration matrix A. Algebraic algorithms for finding Markov bases based on the theory of Gröbner bases are available, but these can fail when the configuration matrix is large and the calculations become computationally infeasible. Instead, we propose constructing a sampler based on a type of lattice basis we call a column partition lattice basis, defined by a matrix U. Constructing such a basis is computationally much cheaper than constructing a Gröbner basis. It is known that lattice bases are not necessarily Markov bases. We give a condition on the matrix U that guarantees that it is a Markov basis, and show for a certain class of configuration matrices how a U matrix that is a Markov basis can be constructed. Construction of lattice bases that are Markov bases is facilitated when the configuration matrix is unimodular, or has unimodular partitions. We consider configuration matrices from volume network tomography, and give classes of traffic network that have configuration matrices with these desirable properties. If a Markov basis cannot be found, one alternative is to sample from some larger set that includes Fy . We give some larger sets that can be used, subject to certain conditions

FINANCIAL DEVELOPMENT AND ACCESS TO FUNDING: THE CASE OF SMALL AND MEDIUM-SIZED ENTERPRISES IN VIETNAM

Over the past three decades, Vietnam has transitioned from an agrarian-based, centrally planned economy to a mixed economy with emerging market status. Additionally, projections indicate that Vietnam will be one of the world’s largest economies by 2050 if growth is sustained at present rates. The evolution of the financial sector, which began with the Doi Moi reforms in the mid-1980s, has been central to facilitating this growth. As the economy has expanded, Vietnam has maintained a gradualist approach to developing market-based mechanisms of resource allocation. However, financial markets are still in an embryonic stage and substantial reform is required if the economy is to meet the expected rates of development. Against this backdrop, this dissertation critically evaluates trends and dynamics in Vietnam’s journey of financial development over the past three decades, with a particular emphasis on the experiences of small and medium-sized enterprises (SMEs). Drawing on quantitative analysis, secondary data and interviews conducted with a range of firms and stakeholders, I argue that financial development in Vietnam has had positive effects in terms of increasing access to funding for SMEs. As the financial system has developed, allocative efficiency has improved to the benefit of SMEs. However, some informants criticised the progress made to date, arguing that a funding mismatch still exists. Specifically, weak corporate governance, state-owned enterprises and a lack of derivatives have prevented effective capital market development. Given Vietnam’s high level of political corruption, this paper concludes that policy makers must place more attention on the political-economic structures of Vietnam if achieving middle-income status is to occur. Specifically, a tighter and more controlled effort to dismantle corporate bureaucracy and nepotism would allow better access to funding for Vietnamese SMEs

Groups with many roots

Given a prime $p$, a finite group $G$ and a non-identity element $g$, what is the largest number of \pth roots $g$ can have? We write $\rho_p(G)$, or just $\rho_p$, for the maximum cardinality of the set $\{x \in G: x^p=g\}$, where $g$ ranges over the non-identity elements of $G$. This paper studies groups for which $\rho_p$ is large. If there is an element $g$ of $G$ with more \pth roots than the identity, then we show $\rho_p(G) \leq \rho_p(P)$, where $P$ is any Sylow $p$-subgroup of $G$, meaning that we can often reduce to the case where $G$ is a $p$-group. We show that if $G$ is a regular $p$-group, then $\rho_p(G) \leq \frac{1}{p}$, while if $G$ is a $p$-group of maximal class, then $\rho_p(G) \leq \frac{1}{p} + \frac{1}{p^2}$ (both these bounds are sharp). We classify the groups with high values of $\rho_2$, and give partial results on groups with high values of $\rho_3$

Making an English Voice: Performing National Identity during the English Musical Renaissance

This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/S1478572215000183.AbstractThis article examines constructions of national musical identity in early twentieth-century Britain by exploring and contextualizing hitherto neglected discourses and practices concerning the production of an ‘English’ singing voice. Tracing the origins and development of ideas surrounding native vocal performance and pedagogy, I reconstruct a culture of English singing as a backdrop against which to offer, by way of conclusion, a reading of the ‘English voice’ performed in Ralph Vaughan Williams's song ‘Silent Noon’. By drawing upon perspectives derived from recent studies of song, vocal production, and national and aesthetic identity, I demonstrate that ‘song’ became a place in which the literal and figurative voices of performers and composers were drawn together in the making of a national music. As such, I advance a series of new historical perspectives through which to rethink notions of an English musical renaissance.</jats:p

Prediction of soil Olsen P through mixed pasture leaf tissue biochemical and biophysical properties, topography and farm management in New Zealand hill country : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Agricultural Science at Massey University, Turitea, New Zealand. EMBARGOED until 1 January 2024.

Embargoed until 1 January 2024In New Zealand hill country, soil Olsen Phosphorus (P) is a key piece of information used to decide rates, products and areas to which aerial applications of phosphate fertilisers are made. Laboratory based soil Olsen P measurements are made on bulked soil cores collected along transects, laid out across slope faces. On most hill country farms, aerial fertiliser applications are applied uniformly over large blocks or the whole property. Accurate, detailed soil maps are scarce, but essential for site specific nutrient management. Current soil sampling techniques provide spatially sparse information and attempts to interpolate point measurements of soil properties in hill country, have not been successful. The potential improvement in nutrient use efficiency would lead to increases in pasture production and quality, and an increase in production of meat and wool produced off the same land area. As sheep and beef production is forced from more productive land into more marginal areas by other land uses, managing hill country landscapes efficiently will become critical for the sheep and beef industry. Increases in global food demand, a growing interest in product origins and production practices by the consumer, and tightening of environmental regulations will further put pressure on these systems. Appropriate soil and fertiliser management has suffered from a lack of information to make sound decisions. Maps of soil Olsen P are a first step, with much potential in the applications of hyperspectral imaging yet to be discovered. The objective of this thesis was to develop a model that could be applied to readily available data layers, to make continuous predictions of phosphate availability in the soil (Olsen P) across New Zealand hill country farms. This research was one part of a larger project that firstly aimed to derive estimates of pasture parameters from hyperspectral imagery. This information could then be used in conjunction with ancillary data to determine soil nutrient status. Finally, this information would be used to inform variable rate fertiliser applications through a prescription map loaded into a computer controlled aerial top dressing system. A multi-site, multi-seasonal database from eight commercial hill country farms incorporating a range of leaf tissue nutrient concentrations, pasture biophysical properties, and topographic, soil and farm management information was built up alongside soil chemical properties. Model development was based on in-situ measurements and laboratory analysis of leaf tissue and soil samples collected on 0.5m x 0.5m plots. A total of 3,030 plots were sampled in the autumn and spring.--Shortened abstrac

DOTHEN-ENTERITE, ITS NATURE &Amp; TREATMENT.

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