Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Processes controlling DOC in pore water during simulated drought cycles in six different UK peats

The effect of episodic drought on dissolved organic carbon (DOC) dynamics in peatlands has been the subject of considerable debate, as decomposition and DOC production is thought to increase under aerobic conditions, yet decreased DOC concentrations have been observed during drought periods. Decreased DOC solubility due to drought-induced acidification driven by sulphur (S) redox reactions has been proposed as a causal mechanism; however evidence is based on a limited number of studies carried out at a few sites. To test this hypothesis on a range of different peats, we carried out controlled drought simulation experiments on peat cores collected from six sites across Great Britain. Our data show a concurrent increase in sulphate (SO4) and a decrease in DOC across all sites during simulated water table draw-down, although the magnitude of the relationship between SO4 and DOC differed between sites. Instead, we found a consistent relationship across all sites between DOC decrease and acidification measured by the pore water acid neutralising capacity (ANC). ANC provided a more consistent measure of drought-induced acidification than SO4 alone because it accounts for differences in base cation and acid anions concentrations between sites. Rewetting resulted in rapid DOC increases without a concurrent increase in soil respiration, suggesting DOC changes were primarily controlled by soil acidity not soil biota. These results highlight the need for an integrated analysis of hydrologically driven chemical and biological processes in peatlands to improve our understanding and ability to predict the interaction between atmospheric pollution and changing climatic conditions from plot to regional and global scales.

Developing children and young people’s participation in strategic processes: the experience of the Children’s Fund Initiative

The extent of children’s and young people’s participation activities has increased considerably among statutory, voluntary and community sector organisations across the UK in recent years. The Children’s Fund, a major government initiative launched in 2000, represents a systematic drive towards promoting children and young people’s participation in planning, implementing and evaluating preventative services within all 149 local authority areas in England. Based on research carried out by the National Evaluation of the Children’s Fund, this paper explores the experience of Children’s Fund partnerships of engaging children and young people in strategic processes.

A comparison of reverse osmosis, nanofiltration and ultrafiltration as concentration processes for skim milk prior to drying

Skim milk was concentrated by reverse osmosis (RO), nanofiltration (NF) and ultrafiltration (UF) and the retentates were spray-dried. The resulting powders were reconstituted to 25% TS and sterilised to evaluate their heat stability. Reverse osmosis led to maximum retention of calcium, a fall in pH for its retentate and its reconstituted powder. All RO powders produced a weak gel on heating. Some calcium was lost during NF and a greater amount during UF. Their resulting reconstituted powders had a higher pH than those produced by RO. Powders produced by UF showed poor heat stability. Only one powder produced by NF showed good heat stability. This could be improved by addition of stabilisers at appropriate addition rates.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Ethylene and senescence processes

Senescence is a vitally important sequence of events in the latter phase of the life cycle of a plant that determines yield and reproductive success. In many species, and in different plant organs, ethylene is a key regulator of senescence and an increased understanding of the way the hormone functions will enable the timing and location of senescence to be manipulated in order to improve yield, quality and longevity. This chapter examines the physiological and molecular regulation of senescence in different plant organs and introduces the concept of the ‘senescence window’ in which plant organs are receptive to ethylene-mediated senescence cues. Several studies have attempted to elucidate global patterns of the regulation of senescence, which have enabled the function of ethylene to be placed in the context of the involvement of other, often antagonistic, hormones in the execution of senescence and downstream processes. Finally, we examine the consequences of senescence for post-harvest biology, an area where the control of ethylene action has been actively sought in order to control precisely the timing of senescence and ripening processes so that crop quality can be enhanced and maintained.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Planning for the reuse of redundant defence estate: disposal processes, policy frameworks and development impacts

This paper reviews recent research and other literature concerning the planning and development of redundant defence estate. It concentrates on UK sources but includes reference to material from Europe and the North America were it is relevant for comparative purposes. It introduces the topic by providing a brief review of the recent restructuring of the UK defence estate and then proceeds to examine the various planning policy issues generated by this process; the policy frameworks used to guide it; comparable approaches to surplus land disposal and the appraisal of impacts; and ending the main body of the review with an analyse of the economic, social and environmental impacts of military base closure and redevelopment. It concludes that there is a significant body of work focusing on the reuse and redevelopment of redundant defence estate in the UK and abroad, but that much of this work is based on limited research or on personal experience. One particular weakness of the current literature is that it does not fully reflect the institutional difficulties posed by the disposal process and the day-to-day pressures which MOD personnel have to deal with. In doing this, it also under-emphasises the embedded cultures of individuals and professional groups who are required to operationalise the policies, procedures and practices for planning and redeveloping redundant defence estate.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

A technique for delivering individualised formative problems and examples

Active learning plays a strong role in mathematics and statistics, and formative problems are vital for developing key problem-solving skills. To keep students engaged and help them master the fundamentals before challenging themselves further, we have developed a system for delivering problems tailored to a student‟s current level of understanding. Specifically, by adapting simple methodology from clinical trials, a framework for delivering existing problems and other illustrative material has been developed, making use of macros in Excel. The problems are assigned a level of difficulty (a „dose‟), and problems are presented to the student in an order depending on their ability, i.e. based on their performance so far on other problems. We demonstrate and discuss the application of the approach with formative examples developed for a first year course on plane coordinate geometry, and also for problems centred on the topic of chi-square tests.