Reformaation historian kertauskurssi lautapelinä

Peliarvostelu

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Dynamic ecosystems under anthropogenic stress : how does macrotidal sandy fauna respond to green tides?

Highly dynamic systems, often considered as resilient systems, are characterised by abiotic and biotic processes under continuous and strong changes in space and time. Because of this variability, the detection of overlapping anthropogenic stress is challenging. Coastal areas harbour dynamic ecosystems in the form of open sandy beaches, which cover the vast majority of the world’s ice-free coastline. These ecosystems are currently threatened by increasing human-induced pressure, among which mass-development of opportunistic macroalgae (mainly composed of Chlorophyta, so called green tides), resulting from the eutrophication of coastal waters. The ecological impact of opportunistic macroalgal blooms (green tides, and blooms formed by other opportunistic taxa), has long been evaluated within sheltered and non-tidal ecosystems. Little is known, however, on how more dynamic ecosystems, such as open macrotidal sandy beaches, respond to such stress. This thesis assesses the effects of anthropogenic stress on the structure and the functioning of highly dynamic ecosystems using sandy beaches impacted by green tides as a study case. The thesis is based on four field studies, which analyse natural sandy sediment benthic community dynamics over several temporal (from month to multi-year) and spatial (from local to regional) scales. In this thesis, I report long-lasting responses of sandy beach benthic invertebrate communities to green tides, across thousands of kilometres and over seven years; and highlight more pronounced responses of zoobenthos living in exposed sandy beaches compared to semi-exposed sands. Within exposed sandy sediments, and across a vertical scale (from inshore to nearshore sandy habitats), I also demonstrate that the effects of the presence of algal mats on intertidal benthic invertebrate communities is more pronounced than that on subtidal benthic invertebrate assemblages, but also than on flatfish communities. Focussing on small-scale variations in the most affected faunal group (i.e. benthic invertebrates living at low shore), this thesis reveals a decrease in overall beta-diversity along a eutrophication-gradient manifested in the form of green tides, as well as the increasing importance of biological variables in explaining ecological variability of sandy beach macrobenthic assemblages along the same gradient. To illustrate the processes associated with the structural shifts observed where green tides occurred, I investigated the effects of high biomasses of opportunistic macroalgae (Ulva spp.) on the trophic structure and functioning of sandy beaches. This work reveals a progressive simplification of sandy beach food web structure and a modification of energy pathways over time, through direct and indirect effects of Ulva mats on several trophic levels. Through this thesis I demonstrate that highly dynamic systems respond differently (e.g. shift in δ13C, not in δ15N) and more subtly (e.g. no mass-mortality in benthos was found) to anthropogenic stress compared to what has been previously shown within more sheltered and non-tidal systems. Obtaining these results would not have been possible without the approach used through this work; I thus present a framework coupling field investigations with analytical approaches to describe shifts in highly variable ecosystems under human-induced stress.