Componentwise and Cartesian decompositions of linear relations

Let $A$ be a, not necessarily closed, linear relation in a Hilbert space \sH with a multivalued part \mul A. An operator $B$ in \sH with \ran B\perp\mul A^{**} is said to be an operator part of $A$ when A=B \hplus (\{0\}\times \mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for the existence of an operator part are established via the so-called canonical decomposition of $A$. In addition, conditions are developed for the decomposition to be orthogonal (components defined in orthogonal subspaces of the underlying space). Such orthogonal decompositions are shown to be valid for several classes of relations. The relation $A$ is said to have a Cartesian decomposition if A=U+\I V, where $U$ and $V$ are symmetric relations and the sum is operatorwise. The connection between a Cartesian decomposition of $A$ and the real and imaginary parts of $A$ is investigated

Insect abundance in cow dung pats of different farming systems

Cow dung pats in pastures provide suitable (micro) habitats for invertebrates to reproduce and to feed. Therefore, their availability is important for invertebrate diversity in farmland landscapes. We investigated the differences in insect abundance in cowpats between three different farming systems : conventional dairy farms, organic dairy farms and nature conservation areas under grazing managemen

Multi-Objective and Multidisciplinary Design Optimisation of Unmanned Aerial Vehicle Systems using Hierarchical Asynchronous Parallel Multi-Objective Evolutionary Algorithms

The overall objective of this research was to realise the practical application of Hierarchical Asynchronous Parallel Evolutionary Algorithms for Multi-objective and Multidisciplinary Design Optimisation (MDO) of UAV Systems using high fidelity analysis tools. The research looked at the assumed aerodynamics and structures of two production UAV wings and attempted to optimise these wings in isolation to the rest of the vehicle. The project was sponsored by the Asian Office of the Air Force Office of Scientific Research under contract number AOARD-044078. The two vehicles wings which were optimised were based upon assumptions made on the Northrop Grumman Global Hawk (GH), a High Altitude Long Endurance (HALE) vehicle, and the General Atomics Altair (Altair), Medium Altitude Long Endurance (MALE) vehicle. The optimisations for both vehicles were performed at cruise altitude with MTOW minus 5% fuel and a 2.5g load case. The GH was assumed to use NASA LRN 1015 aerofoil at the root, crank and tip locations with five spars and ten ribs. The Altair was assumed to use the NACA4415 aerofoil at all three locations with two internal spars and ten ribs. Both models used a parabolic variation of spar, rib and wing skin thickness as a function of span, and in the case of the wing skin thickness, also chord. The work was carried out by integrating the current University of Sydney designed Evolutionary Optimiser (HAPMOEA) with Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) tools. The variable values computed by HAPMOEA were subjected to structural and aerodynamic analysis. The aerodynamic analysis computed the pressure loads using a Boeing developed Morino class panel method code named PANAIR. These aerodynamic results were coupled to a FEA code, MSC.Nastran® and the strain and displacement of the wings computed. The fitness of each wing was computed from the outputs of each program. In total, 48 design variables were defined to describe both the structural and aerodynamic properties of the wings subject to several constraints. These variables allowed for the alteration of the three aerofoil sections describing the root, crank and tip sections. They also described the internal structure of the wings allowing for variable flexibility within the wing box structure. These design variables were manipulated by the optimiser such that two fitness functions were minimised. The fitness functions were the overall mass of the simulated wing box structure and the inverse of the lift to drag ratio. Furthermore, six penalty functions were added to further penalise genetically inferior wings and force the optimiser to not pass on their genetic material. The results indicate that given the initial assumptions made on all the aerodynamic and structural properties of the HALE and MALE wings, a reduction in mass and drag is possible through the use of the HAPMOEA code. The code was terminated after 300 evaluations of each hierarchical level due to plateau effects. These evolutionary optimisation results could be further refined through a gradient based optimiser if required. Even though a reduced number of evaluations were performed, weight and drag reductions of between 10 and 20 percent were easy to achieve and indicate that the wings of both vehicles can be optimised

Effects of breeding habitat and field margins on the reproductive performance of Skylarks (Alauda arvensis) on intensive farmland

Field margin management is a common measure employed in Europe to support farmland bird populations. In this study we found and analysed 237 nests of the Skylark Alauda arvensis in the Netherlands over a period of 6 years to determine the effects of arable field margins and breeding crop on nest-level reproductive success. Additionally, the effect of field margins on predation was investigated and food availability in crops and field margins was compared. Neither clutch size, nest survival nor nestling body weight were improved by field margin availability, irrespective of the breeding crop used. However, the choice of breeding crop had important effects. Nestling weight was significantly lower in cereals than in grassland and lucerne, corresponding with the low prey densities present in cereals. Nest survival was lowest in grassland due to frequent silage cutting. Predation rates were highest in cereals but were not affected by field margin proximity. The highest reproductive success was achieved in lucerne, which was mown twice a year and retained a suitable height for breeding throughout the breeding season. We conclude that field margins are not sufficient to maintain a Skylark population in this intensively farmed area. The presumably more subtle effects of increased food availability cannot compensate for the high nest failure rates resulting from agricultural operations and predation. In this and similar areas, the provisioning of safe nesting habitat throughout the breeding season is essential to improve breeding performance. Our research suggests that this can be achieved by reducing the frequency of silage cutting on grassland and by increasing the surface area of lucerne.Conservation Biolog

Shifts in functional plant groups in ditch banks under agri-environment schemes and in nature reserves

Management of ditch banks of agricultural fields is considered to be a promising and multifunctional application of agri-environment schemes (AES) on farmland. Our previous research has shown that in the Netherlands, there is a small increase in the number of target plant species of AES in ditch banks. However, the productivity and Ellenberg indicator value for nitrogen also increased. This suggests a change in species composition towards more competitive species. This is important, because management mainly focuses on restoring disturbance tolerant species that used to be common in meadows, rather than competitive dominants. In this study we use a large scale dataset of target species composition in ditch banks of nature reserves and ditch banks with and without AES over 10 years to monitor results of functional plant species groups under these different management regimes. Our analyses show that plant functional type composition in ditch banks of agricultural fields indeed shifted towards more competitive species over the last 10 years, independent of AES. In nature reserves, a similar increase in competitive species was observed. The shift towards more competitive species was reflected in the increase of the average height of the vegetation and the increase in species with a leafy canopy structure, whereas species with a semi-basal canopy structure were decreasing. We conclude that current AES does not increase the number of targeted disturbance tolerant species and that more disturbance such as more frequent mowing is required to obtain these species

Predictive response-relevant clustering of expression data provides insights into disease processes

This article describes and illustrates a novel method of microarray data analysis that couples model-based clustering and binary classification to form clusters of ;response-relevant' genes; that is, genes that are informative when discriminating between the different values of the response. Predictions are subsequently made using an appropriate statistical summary of each gene cluster, which we call the ;meta-covariate' representation of the cluster, in a probit regression model. We first illustrate this method by analysing a leukaemia expression dataset, before focusing closely on the meta-covariate analysis of a renal gene expression dataset in a rat model of salt-sensitive hypertension. We explore the biological insights provided by our analysis of these data. In particular, we identify a highly influential cluster of 13 genes-including three transcription factors (Arntl, Bhlhe41 and Npas2)-that is implicated as being protective against hypertension in response to increased dietary sodium. Functional and canonical pathway analysis of this cluster using Ingenuity Pathway Analysis implicated transcriptional activation and circadian rhythm signalling, respectively. Although we illustrate our method using only expression data, the method is applicable to any high-dimensional datasets

Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page