Non-linear hierarchical visualisation

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. High Throughput Screening (HTS) is an important tool in the pharmaceutical industry for discovering leads which can be optimised and further developed into candidate drugs. Since the development of new robotic technologies, the ability to test the activities of compounds has considerably increased in recent years. Traditional methods, looking at tables and graphical plots for analysing relationships between measured activities and the structure of compounds, have not been feasible when facing a large HTS dataset. Instead, data visualisation provides a method for analysing such large datasets, especially with high dimensions. So far, a few visualisation techniques for drug design have been developed, but most of them just cope with several properties of compounds at one time. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine the distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of t.he hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E- and M-step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model. In this thesis we also demonstrate the applicability of the hierarchy of latent trait models in the field of document data mining.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Microbial community composition and bacterioplankton at time series station Helgoland Roads, North Sea

A process of global importance in carbon cycling is the remineralization of algae biomass by heterotrophic bacteria, most notably during massive marine algae blooms. Such blooms can trigger secondary blooms of planktonic bacteria that consist of swift successions of distinct bacterial clades, most prominently members of the Flavobacteriia, Gammaproteobacteria and the alphaproteobacterial Roseobacter clade. This study explores such successions during spring phytoplankton blooms in the southern North Sea (German Bight) for four consecutive years. The surface water samples were taken at Helgoland Island about 40 km offshore in the southeastern North Sea in the German Bight at the station 'Kabeltonne' (54° 11.3' N, 7° 54.0' E) between the main island and the minor island, Düne (German for 'dune') using small research vessels (http://www.awi.de/en/expedition/ships/more-ships.html). Water depths at this site fluctuate from 6 to 10 m over the tidal cycle. Samples were processed as described previously (Teeling et al., 2012; doi:10.7554/eLife.11888.001) in the laboratory of the Biological Station Helgoland within less than two hours after sampling. Assessment of absolute cell numbers and bacterioplankton community composition was carried out as described previously (Thiele et al., 2011; doi:10.1016/B978-0-444-53199-5.00056-7). To obtain total cell numbers, DNA of formaldehyde fixed cells filtered on 0.2 mm pore sized filters was stained with 4',6-diamidino-2-phenylindole (DAPI). Fluorescently labeled cells were subsequently counted on filter sections using an epifluores-cence microscope. Likewise, bacterioplankton community composition was assessed by catalyzedreporter deposition fluorescence in situ hybridization (CARD-FISH) of formaldehyde fixed cells on 0.2 mm pore sized filters.

Collection of vegetation and soil surface cover in the Jena Experiment (time series since 2002)

This collection contains measurements of vegetation and soil surface cover measured on the plots of the different sub-experiments at the field site of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. The following series of datasets are contained in this collection: 1. Measurements of vegetation cover, i.e. the proportion of soil surface area that is covered by different categories of plants per estimated plot area. Data was collected on the plant community level (sown plant community, weed plant community, dead plant material, and bare ground) and on the level of individual plant species in case of the species that have been sown into the plots to create the gradient of plant diversity.

Imputing accelerometer non-wear time when assessing children's moderate-to-vigorous physical activity

BACKGROUND: Moderate-to-vigorous physical activity (MVPA) is an important determinant of children’s physical health, and is commonly measured using accelerometers. A major limitation of accelerometers is non-wear time, which is the time the participant did not wear their device. Given that non-wear time is traditionally discarded from the dataset prior to estimating MVPA, final estimates of MVPA may be biased. Therefore, alternate approaches should be explored. OBJECTIVES: The objectives of this thesis were to 1) develop and describe an imputation approach that uses the socio-demographic, time, health, and behavioural data from participants to replace non-wear time accelerometer data, 2) determine the extent to which imputation of non-wear time data influences estimates of MVPA, and 3) determine if imputation of non-wear time data influences the associations between MVPA, body mass index (BMI), and systolic blood pressure (SBP). METHODS: Seven days of accelerometer data were collected using Actical accelerometers from 332 children aged 10-13. Three methods for handling missing accelerometer data were compared: 1) the “non-imputed” method wherein non-wear time was deleted from the dataset, 2) imputation dataset I, wherein the imputation of MVPA during non-wear time was based upon socio-demographic factors of the participant (e.g., age), health information (e.g., BMI), and time characteristics of the non-wear period (e.g., season), and 3) imputation dataset II wherein the imputation of MVPA was based upon the same variables as imputation dataset I, plus organized sport information. Associations between MVPA and health outcomes in each method were assessed using linear regression. RESULTS: Non-wear time accounted for 7.5% of epochs during waking hours. The average minutes/day of MVPA was 56.8 (95% CI: 54.2, 59.5) in the non-imputed dataset, 58.4 (95% CI: 55.8, 61.0) in imputed dataset I, and 59.0 (95% CI: 56.3, 61.5) in imputed dataset II. Estimates between datasets were not significantly different. The strength of the relationship between MVPA with BMI and SBP were comparable between all three datasets. CONCLUSION: These findings suggest that studies that achieve high accelerometer compliance with unsystematic patterns of missing data can use the traditional approach of deleting non-wear time from the dataset to obtain MVPA measures without substantial bias.

Oceans of energy? The non-linear trajectory of the emerging wave energy technology

This paper addresses the construction and structuring of a technological niche – i.e. a protected space where promising but still underperforming technologies are stabilized and articulated with societal needs – and discusses the processes that influence niche development and may enable niche breakout. In theoretical terms the paper is grounded on the multi-level approach to sustainability transitions, and particularly on the niche literature. But it also attempts to address the limitations of this literature in what concerns the spatial dimension of niche development. It is argued that technological niches can transcend the narrow territorial boundaries to which they are often confined, and encompass communities and actions that span several spatial levels, without losing some territorial embeddedness. It is further proposed that these features shape the niche trajectory and, therefore, need to be explicitly considered by the niche theoretical framework. To address this problem the paper builds on and extends the socio-cognitive perspective to technology development, introducing a further dimension – space – which broadens the concept of technological niche and permits to better capture the complexity of niche behaviour. This extended framework is applied to the case of an emerging renewable energy technology – wave energy - which exhibits a particularly slow and non-linear development trajectory. The empirical analysis starts by examining how an “overall niche space” in wave energy was spatially constructed over time. Then it investigates in greater detail the niche development processes that took place in Portugal, a country that was among the pioneers in the field, and whose actors have been, from very early stages, engaged in the activities conducted at various spatial levels. Through this combined analysis, the paper seeks to understand whether and how niche development is shaped by processes taking place at different spatial levels. More specifically it investigates the interplay between territorial and relational elements in niche development, and how these different dynamics influence the performance of the niche processes and impact on the overall niche trajectory. The results confirm the niche multi-spatial dynamics, showing that it is shaped by the interplay between a niche relational space constructed by actors’ actions and interactions on/across levels, and the territorial effects introduced by these actors’ embeddedness in particular geographical and institutional settings. They contribute to a more precise understanding of the processes that can accelerate or slow down the trajectory of a technological niche. In addition, the results shed some light into the niche activities conducted in/originating from a specific territorial setting - Portugal - offering some insights into the behaviour of key actors and its implications for the positioning of the country in the emerging field, which can be relevant for the formulation of strategies and policies for this area.

Characterization of Non-linear Polymer Properties to Predict Process Induced Warpage and Residual Stress of Electronic Packages

Nonlinear thermo-mechanical properties of advanced polymers are crucial to accurate prediction of the process induced warpage and residual stress of electronics packages. The Fiber Bragg grating (FBG) sensor based method is advanced and implemented to determine temperature and time dependent nonlinear properties. The FBG sensor is embedded in the center of the cylindrical specimen, which deforms together with the specimen. The strains of the specimen at different loading conditions are monitored by the FBG sensor. Two main sources of the warpage are considered: curing induced warpage and coefficient of thermal expansion (CTE) mismatch induced warpage. The effective chemical shrinkage and the equilibrium modulus are needed for the curing induced warpage prediction. Considering various polymeric materials used in microelectronic packages, unique curing setups and procedures are developed for elastomers (extremely low modulus, medium viscosity, room temperature curing), underfill materials (medium modulus, low viscosity, high temperature curing), and epoxy molding compound (EMC: high modulus, high viscosity, high temperature pressure curing), most notably, (1) zero-constraint mold for elastomers; (2) a two-stage curing procedure for underfill materials and (3) an air-cylinder based novel setup for EMC. For the CTE mismatch induced warpage, the temperature dependent CTE and the comprehensive viscoelastic properties are measured. The cured cylindrical specimen with a FBG sensor embedded in the center is further used for viscoelastic property measurements. A uni-axial compressive loading is applied to the specimen to measure the time dependent Young’s modulus. The test is repeated from room temperature to the reflow temperature to capture the time-temperature dependent Young’s modulus. A separate high pressure system is developed for the bulk modulus measurement. The time temperature dependent bulk modulus is measured at the same temperatures as the Young’s modulus. The master curve of the Young’s modulus and bulk modulus of the EMC is created and a single set of the shift factors is determined from the time temperature superposition. The supplementary experiments are conducted to verify the validity of the assumptions associated with the linear viscoelasticity. The measured time-temperature dependent properties are further verified by a shadow moiré and Twyman/Green test.

Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.

Explaining dinophysis cf. acuminata abundance in Antifer (Normandy, France) using dynamic linear regression

Classical regression analysis can be used to model time series. However, the assumption that model parameters are constant over time is not necessarily adapted to the data. In phytoplankton ecology, the relevance of time-varying parameter values has been shown using a dynamic linear regression model (DLRM). DLRMs, belonging to the class of Bayesian dynamic models, assume the existence of a non-observable time series of model parameters, which are estimated on-line, i.e. after each observation. The aim of this paper was to show how DLRM results could be used to explain variation of a time series of phytoplankton abundance. We applied DLRM to daily concentrations of Dinophysis cf. acuminata, determined in Antifer harbour (French coast of the English Channel), along with physical and chemical covariates (e.g. wind velocity, nutrient concentrations). A single model was built using 1989 and 1990 data, and then applied separately to each year. Equivalent static regression models were investigated for the purpose of comparison. Results showed that most of the Dinophysis cf. acuminata concentration variability was explained by the configuration of the sampling site, the wind regime and tide residual flow. Moreover, the relationships of these factors with the concentration of the microalga varied with time, a fact that could not be detected with static regression. Application of dynamic models to phytoplankton time series, especially in a monitoring context, is discussed.

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

EVALUATION OF NON-STATIONARITY IN ANNUAL MAXIMUM FLOOD SERIES OF MODERATELY IMPAIRED WATERSHEDS IN THE UPPER MIDWEST AND NORTHEASTERN UNITED STATES

United States federal agencies assess flood risk using Bulletin 17B procedures which assume annual maximum flood series are stationary. This represents a significant limitation of current flood frequency models as the flood distribution is thereby assumed to be unaffected by trends or periodicity of atmospheric/climatic variables and/or anthropogenic activities. The validity of this assumption is at the core of this thesis, which aims to improve understanding of the forms and potential causes of non-stationarity in flood series for moderately impaired watersheds in the Upper Midwest and Northeastern US. Prior studies investigated non-stationarity in flood series for unimpaired watersheds; however, as the majority of streams are located in areas of increasing human activity, relative and coupled impacts of natural and anthropogenic factors need to be considered such that non-stationary flood frequency models can be developed for flood risk forecasting over relevant planning horizons for large scale water resources planning and management.

Optimal control of non-linear systems through hybrid cell-mapping/artificial-neural-networks techniques

In this paper, a real-time optimal control technique for non-linear plants is proposed. The control system makes use of the cell-mapping (CM) techniques, widely used for the global analysis of highly non-linear systems. The CM framework is employed for designing approximate optimal controllers via a control variable discretization. Furthermore, CM-based designs can be improved by the use of supervised feedforward artificial neural networks (ANNs), which have proved to be universal and efficient tools for function approximation, providing also very fast responses. The quantitative nature of the approximate CM solutions fits very well with ANNs characteristics. Here, we propose several control architectures which combine, in a different manner, supervised neural networks and CM control algorithms. On the one hand, different CM control laws computed for various target objectives can be employed for training a neural network, explicitly including the target information in the input vectors. This way, tracking problems, in addition to regulation ones, can be addressed in a fast and unified manner, obtaining smooth, averaged and global feedback control laws. On the other hand, adjoining CM and ANNs are also combined into a hybrid architecture to address problems where accuracy and real-time response are critical. Finally, some optimal control problems are solved with the proposed CM, neural and hybrid techniques, illustrating their good performance.

Circadian Phase Control - Genetic Algorithm and Non-linear Control Approach

This paper deals with the phase control for Neurospora circadian rhythm. The nonlinear control, given by tuning the parameters (considered as controlled variables) in Neurospora dynamical model, allows the circadian rhythms tracking a reference one. When there are many parameters (e.g. 3 parameters in this paper) and their values are unknown, the adaptive control law reveals its weakness since the parameters converging and control objective must be guaranteed at the same time. We show that this problem can be solved using the genetic algorithm for parameters estimation. Once the unknown parameters are known, the phase control is performed by chaos synchronization technique.