Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Resolving taxonomic uncertainty in vulnerable elasmobranchs: are the Madeira skate (Raja maderensis) and the thornback ray (Raja clavata) distinct species?

Skates and rays constitute the most speciose group of chondrichthyan fishes, yet are characterised by remarkable levels of morphological and ecological conservatism. They can be challenging to identify, which makes monitoring species compositions for fisheries management purposes problematic. Owing to their slow growth and low fecundity, skates are vulnerable to exploitation and species exhibiting endemism or limited ranges are considered to be the most at risk. The Madeira skate Raja maderensis is endemic and classified as ‘Data Deficient’ by the IUCN, yet its taxonomic distinctiveness from the morphologically similar and more wide-ranging thornback ray Raja clavata is unresolved. This study evaluated the sequence divergence of both the variable control region and cytochrome oxidase I ‘DNA barcode’ gene of the mitochondrial genome to elucidate the genetic differentiation of specimens identified as R. maderensis and R. clavata collected across much of their geographic ranges. Genetic evidence was insufficient to support the different species designations. However regardless of putative species identification, individuals occupying waters around the Azores and North African Seamounts represent an evolutionarily significant unit worthy of special consideration for conservation management.

Resolving taxonomic uncertainty in vulnerable elasmobranchs: are the Madeira skate (Raja maderensis) and the thornback ray (Raja clavata) distinct species?

Skates and rays constitute the most speciose group of chondrichthyan fishes, yet are characterised by remarkable levels of morphological and ecological conservatism. They can be challenging to identify, which makes monitoring species compositions for fisheries management purposes problematic. Owing to their slow growth and low fecundity, skates are vulnerable to exploitation and species exhibiting endemism or limited ranges are considered to be the most at risk. The Madeira skate Raja maderensis is endemic and classified as ‘Data Deficient’ by the IUCN, yet its taxonomic distinctiveness from the morphologically similar and more wide-ranging thornback ray Raja clavata is unresolved. This study evaluated the sequence divergence of both the variable control region and cytochrome oxidase I ‘DNA barcode’ gene of the mitochondrial genome to elucidate the genetic differentiation of specimens identified as R. maderensis and R. clavata collected across much of their geographic ranges. Genetic evidence was insufficient to support the different species designations. However regardless of putative species identification, individuals occupying waters around the Azores and North African Seamounts represent an evolutionarily significant unit worthy of special consideration for conservation management.

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

Linking Parametric CAD with Adjoint Surface Sensitivities

The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.

Aerodynamic optimization using Adjoint methods and parametric CAD models

This paper describes an implementation of a method capable of integrating parametric, feature based, CAD models based on commercial software (CATIA) with the SU2 software framework. To exploit the adjoint based methods for aerodynamic optimisation within the SU2, a formulation to obtain geometric sensitivities directly from the commercial CAD parameterisation is introduced, enabling the calculation of gradients with respect to CAD based design variables. To assess the accuracy and efficiency of the alternative approach, two aerodynamic optimisation problems are investigated: an inviscid, 3D, problem with multiple constraints, and a 2D high-lift aerofoil, viscous problem without any constraints. Initial results show the new parameterisation obtaining reliable optimums, with similar levels of performance of the software native parameterisations. In the final paper, details of computing CAD sensitivities will be provided, including accuracy as well as linking geometric sensitivities to aerodynamic objective functions and constraints; the impact in the robustness of the overall method will be assessed and alternative parameterisations will be included.

Effect of web holes on web crippling strength of cold-formed steel channel sections under end-one-flange loading condition - Part II: Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling under end-one-flange (EOF) loading condition is undertaken, using finite element analysis, to investigate the effects of web holes and cross-section sizes. The holes are located either centred above the bearing plates or with a horizontal clear distance to the near edge of the bearing plates. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the depth of the web, the ratio of the length of bearing plates to the flat depth of the web and the location of the holes as defined by the distance of the hole from the edge of the bearing plate divided by the flat depth of web. In this study, design recommendations in the form of web crippling strength reduction factor equations are proposed, which are conservative when compared with the experimental and finite element results.

Testing Wavefunction Collapse Models using Parametric Heating of a Trapped Nanosphere

We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the center-of-mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilising a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoher- ence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show that this approach allows measurements to be made on the timescale of seconds, and that the free parameter λcsl which characterises the model ought to be testable to values as low as 10^{−12} Hz.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

A Two-Stage Online Approach for Collaborative Multi-Agent Planning under Uncertainty

In a team of multiple agents, the pursuance of a common goal is a defining characteristic. Since agents may have different capabilities, and effects of actions may be uncertain, a common goal can generally only be achieved through a careful cooperation between the different agents. In this work, we propose a novel two-stage planner that combines online planning at both team level and individual level through a subgoal delegation scheme. The proposal brings the advantages of online planning approaches to the multi-agent setting. A number of modifications are made to a classical UCT approximate algorithm to (i) adapt it to the application domains considered, (ii) reduce the branching factor in the underlying search process, and (iii) effectively manage uncertain information of action effects by using information fusion mechanisms. The proposed online multi-agent planner reduces the cost of planning and decreases the temporal cost of reaching a goal, while significantly increasing the chance of success of achieving the common goal.