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.

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.

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.

Parametric Analysis of Concrete Solar Collectors

Concrete solar collectors offer a type of solar collector with structural, aesthetic and economic advantages over current populartechnologies. This study examines the influential parameters of concrete solar collectors. In addition to the external conditions,the performance of a concrete solar collector is influenced by the thermal properties of the concrete matrix, piping network andfluid. Geometric and fluid flow parameters also influence the performance of the concrete solar collector. A literature review ofconcrete solar collectors is conducted in order to define the benchmark parameters from which individual parameters are thencompared. The numerical model consists of a 1D pipe flow network coupled with the heat transfer in a 3D concrete domain. Thispaper is concerned with the physical parameters that define the concrete solar collector, thus a constant surface temperature isused as the exposed surface boundary condition with all other surfaces being insulated. Results show that, of the parametersinvestigated, the pipe spacing, ps, concrete conductivity, kc, and the pipe embedment depth, demb, are among those parameterswhich have greatest effect on the collector’s performance. The optimum balance between these parameters is presented withrespect to the thermal performance and discussed with reference to practical development issues.

Wavelength converters based on four-wave mixing in semiconductor optical amplifiers for advanced modulation formats

Les convertisseurs de longueur d’onde sont essentiels pour la réalisation de réseaux de communications optiques à routage en longueur d’onde. Dans la littérature, les convertisseurs de longueur d’onde basés sur le mélange à quatre ondes dans les amplificateurs optiques à semi-conducteur constituent une solution extrêmement intéressante, et ce, en raison de leurs nombreuses caractéristiques nécessaires à l’implémentation de tels réseaux de communications. Avec l’émergence des systèmes commerciaux de détection cohérente, ainsi qu’avec les récentes avancées dans le domaine du traitement de signal numérique, il est impératif d’évaluer la performance des convertisseurs de longueur d’onde, et ce, dans le contexte des formats de modulation avancés. Les objectifs de cette thèse sont : 1) d’étudier la faisabilité des convertisseurs de longueur d’onde basés sur le mélange à quatre ondes dans les amplificateurs optiques à semi-conducteur pour les formats de modulation avancés et 2) de proposer une technique basée sur le traitement de signal numérique afin d’améliorer leur performance. En premier lieu, une étude expérimentale de la conversion de longueur d’onde de formats de modulation d’amplitude en quadrature (quadrature amplitude modulation - QAM) est réalisée. En particulier, la conversion de longueur d’onde de signaux 16-QAM à 16 Gbaud et 64-QAM à 5 Gbaud dans un amplificateur optique à semi-conducteur commercial est réalisée sur toute la bande C. Les résultats démontrent qu’en raison des distorsions non-linéaires induites sur le signal converti, le point d’opération optimal du convertisseur de longueur d’onde est différent de celui obtenu lors de la conversion de longueur d’onde de formats de modulation en intensité. En effet, dans le contexte des formats de modulation avancés, c’est le compromis entre la puissance du signal converti et les non-linéarités induites qui détermine le point d’opération optimal du convertisseur de longueur d’onde. Les récepteurs cohérents permettent l’utilisation de techniques de traitement de signal numérique afin de compenser la détérioration du signal transmis suite à sa détection. Afin de mettre à profit les nouvelles possibilités offertes par le traitement de signal numérique, une technique numérique de post-compensation des distorsions induites sur le signal converti, basée sur une analyse petit-signal des équations gouvernant la dynamique du gain à l’intérieur des amplificateurs optiques à semi-conducteur, est développée. L’efficacité de cette technique est démontrée à l’aide de simulations numériques et de mesures expérimentales de conversion de longueur d’onde de signaux 16-QAM à 10 Gbaud et 64-QAM à 5 Gbaud. Cette méthode permet d’améliorer de façon significative les performances du convertisseur de longueur d’onde, et ce, principalement pour les formats de modulation avancés d’ordre supérieur tel que 64-QAM. Finalement, une étude expérimentale exhaustive de la technique de post-compensation des distorsions induites sur le signal converti est effectuée pour des signaux 64-QAM. Les résultats démontrent que, même en présence d’un signal à bruité à l’entrée du convertisseur de longueur d’onde, la technique proposée améliore toujours la qualité du signal reçu. De plus, une étude du point d’opération optimal du convertisseur de longueur d’onde est effectuée et démontre que celui-ci varie en fonction des pertes optiques suivant la conversion de longueur d’onde. Dans un réseau de communication optique à routage en longueur d’onde, le signal est susceptible de passer par plusieurs étages de conversion de longueur d’onde. Pour cette raison, l’efficacité de la technique de post-compensation est démontrée, et ce pour la première fois dans la littérature, pour deux étages successifs de conversion de longueur d’onde de signaux 64-QAM à 5 Gbaud. Les résultats de cette thèse montrent que les convertisseurs de longueur d’ondes basés sur le mélange à quatre ondes dans les amplificateurs optiques à semi-conducteur, utilisés en conjonction avec des techniques de traitement de signal numérique, constituent une technologie extrêmement prometteuse pour les réseaux de communications optiques modernes à routage en longueur d’onde.

Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value λ_{∗}>0 such that for all λ> λ_{∗} the problem has least two positive solutions, for λ= λ_{∗} the problem has at least one positive solutions, and no positive solutions exist when λ∈(0,λ_{∗}). Also, we show that for λ≥ λ_{∗} the problem has a smallest positive solution.

Spatially integrated erbium-doped fiber amplifiers enabling space-division multiplexing

L’augmentation exponentielle de la demande de bande passante pour les communications laisse présager une saturation prochaine de la capacité des réseaux de télécommunications qui devrait se matérialiser au cours de la prochaine décennie. En effet, la théorie de l’information prédit que les effets non linéaires dans les fibres monomodes limite la capacité de transmission de celles-ci et peu de gain à ce niveau peut être espéré des techniques traditionnelles de multiplexage développées et utilisées jusqu’à présent dans les systèmes à haut débit. La dimension spatiale du canal optique est proposée comme un nouveau degré de liberté qui peut être utilisé pour augmenter le nombre de canaux de transmission et, par conséquent, résoudre cette menace de «crise de capacité». Ainsi, inspirée par les techniques micro-ondes, la technique émergente appelée multiplexage spatial (SDM) est une technologie prometteuse pour la création de réseaux optiques de prochaine génération. Pour réaliser le SDM dans les liens de fibres optiques, il faut réexaminer tous les dispositifs intégrés, les équipements et les sous-systèmes. Parmi ces éléments, l’amplificateur optique SDM est critique, en particulier pour les systèmes de transmission pour les longues distances. En raison des excellentes caractéristiques de l’amplificateur à fibre dopée à l’erbium (EDFA) utilisé dans les systèmes actuels de pointe, l’EDFA est à nouveau un candidat de choix pour la mise en œuvre des amplificateurs SDM pratiques. Toutefois, étant donné que le SDM introduit une variation spatiale du champ dans le plan transversal de la fibre, les amplificateurs à fibre dopée à l’erbium spatialement intégrés (SIEDFA) nécessitent une conception soignée. Dans cette thèse, nous examinons tout d’abord les progrès récents du SDM, en particulier les amplificateurs optiques SDM. Ensuite, nous identifions et discutons les principaux enjeux des SIEDFA qui exigent un examen scientifique. Suite à cela, la théorie des EDFA est brièvement présentée et une modélisation numérique pouvant être utilisée pour simuler les SIEDFA est proposée. Sur la base d’un outil de simulation fait maison, nous proposons une nouvelle conception des profils de dopage annulaire des fibres à quelques-modes dopées à l’erbium (ED-FMF) et nous évaluons numériquement la performance d’un amplificateur à un étage, avec fibre à dopage annulaire, à ainsi qu’un amplificateur à double étage pour les communications sur des fibres ne comportant que quelques modes. Par la suite, nous concevons des fibres dopées à l’erbium avec une gaine annulaire et multi-cœurs (ED-MCF). Nous avons évalué numériquement le recouvrement de la pompe avec les multiples cœurs de ces amplificateurs. En plus de la conception, nous fabriquons et caractérisons une fibre multi-cœurs à quelques modes dopées à l’erbium. Nous réalisons la première démonstration des amplificateurs à fibre optique spatialement intégrés incorporant de telles fibres dopées. Enfin, nous présentons les conclusions ainsi que les perspectives de cette recherche. La recherche et le développement des SIEDFA offriront d’énormes avantages non seulement pour les systèmes de transmission future SDM, mais aussi pour les systèmes de transmission monomode sur des fibres standards à un cœur car ils permettent de remplacer plusieurs amplificateurs par un amplificateur intégré.

A parametric study of flip-chip reliability via computer simulation

Abstract not available

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Nonlinear distortion generation mechanisms in Doherty amplifiers

Nowadays, wireless communications systems demand for greater mobility and higher data rates. Moreover, the need for spectral efficiency requires the use of non-constant envelope modulation schemes. Hence, power amplifier designers have to build highly efficient, broadband and linear amplifiers. In order to fulfil these strict requirements, the practical Doherty amplifier seems to be the most promising technique. However, due to its complex operation, its nonlinear distortion generation mechanisms are not yet fully understood. Currently, only heuristic interpretations are being used to justify the observed phenomena. Therefore, the main objective of this work is to provide a model capable of describing the Doherty power amplifier nonlinear distortion generation mechanisms, allowing the optimization of its design according to linearity and efficiency criteria. Besides that, this approach will allow a bridge between two different worlds: power amplifier design and digital pre-distortion since the knowledge gathered from the Doherty operation will serve to select the most suitable pre-distortion models.