Computational Techniques for Spatial Logistic Regression with Large Datasets

In epidemiological work, outcomes are frequently non-normal, sample sizes may be large, and effects are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. We focus on binary outcomes, with the risk surface a smooth function of space. We compare penalized likelihood models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation. A Bayesian model using a spectral basis representation of the spatial surface provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being more efficient computationally than other Bayesian approaches. One of the contributions of this work is further development of this underused representation. The spectral basis model outperforms the penalized likelihood methods, which are prone to overfitting, but is slower to fit and not as easily implemented. Conclusions based on a real dataset of cancer cases in Taiwan are similar albeit less conclusive with respect to comparing the approaches. The success of the spectral basis with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models.

Control algorithms for large scale adaptive optics

In this dissertation, the problem of creating effective large scale Adaptive Optics (AO) systems control algorithms for the new generation of giant optical telescopes is addressed. The effectiveness of AO control algorithms is evaluated in several respects, such as computational complexity, compensation error rejection and robustness, i.e. reasonable insensitivity to the system imperfections. The results of this research are summarized as follows: 1. Robustness study of Sparse Minimum Variance Pseudo Open Loop Controller (POLC) for multi-conjugate adaptive optics (MCAO). The AO system model that accounts for various system errors has been developed and applied to check the stability and performance of the POLC algorithm, which is one of the most promising approaches for the future AO systems control. It has been shown through numerous simulations that, despite the initial assumption that the exact system knowledge is necessary for the POLC algorithm to work, it is highly robust against various system errors. 2. Predictive Kalman Filter (KF) and Minimum Variance (MV) control algorithms for MCAO. The limiting performance of the non-dynamic Minimum Variance and dynamic KF-based phase estimation algorithms for MCAO has been evaluated by doing Monte-Carlo simulations. The validity of simple near-Markov autoregressive phase dynamics model has been tested and its adequate ability to predict the turbulence phase has been demonstrated both for single- and multiconjugate AO. It has also been shown that there is no performance improvement gained from the use of the more complicated KF approach in comparison to the much simpler MV algorithm in the case of MCAO. 3. Sparse predictive Minimum Variance control algorithm for MCAO. The temporal prediction stage has been added to the non-dynamic MV control algorithm in such a way that no additional computational burden is introduced. It has been confirmed through simulations that the use of phase prediction makes it possible to significantly reduce the system sampling rate and thus overall computational complexity while both maintaining the system stable and effectively compensating for the measurement and control latencies.

Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.

LARGE SCALE LANDSLIDE ON THE ONTONAGON RIVER, MICHIGAN

In 2003, a large landslide occurred along the Ontonagon River, located in the Upper Peninsula of Michigan, and adjacent to US-45 in Ontonagon County. The failure took place during the springtime, when the river reached a peak discharge that was the second highest on record. The volume of the slide has been estimated to be approximately 1,400,000 cubic yards. The colluvium blocked the river, forcing a new channel to be carved around the debris. The landslide consisted of a silt layer at its base, overlain by a coarsening upward sand sequence, and finally a varved glacio-lacustrine clay with sparse dropstone inclusions making up the upper section of hillside.

Changes in species composition in alpine snowbeds with climate change inferred from small-scale spatial patterns

Alpine snowbeds are characterised by a very short growing season. However, the length of the snow-free period is increasingly prolonged due to climate change, so that snowbeds become susceptible to invasions from neighbouring alpine meadow communities. We hypothesised that spatial distribution of species generated by plant interactions may indicate whether snowbed species will coexist with or will be out-competed by invading alpine species – spatial aggregation or segregation will point to coexistence or competitive exclusion, respectively. We tested this hypothesis in snowbeds of the Swiss Alps using the variance ratio statistics. We focused on the relationships between dominant snowbed species, subordinate snowbed species, and potentially invading alpine grassland species. Subordinate snowbed species were generally spatially aggregated with each other, but were segregated from alpine grassland species. Competition between alpine grassland and subordinate snowbed species may have caused this segregation. Segregation between these species groups increased with earlier snowmelt, suggesting an increasing importance of competition with climate change. Further, a dominant snowbed species (Alchemilla pentaphyllea) was spatially aggregated with subordinate snowbed species, while two other dominants (Gnaphalium supinum and Salix herbacea) showed aggregated patterns with alpine grassland species. These dominant species are known to show distinct microhabitat preferences suggesting the existence of hidden microhabitats with different susceptibility to invaders. These results allow us to suggest that alpine snowbed areas are likely to be reduced as a consequence of climate change and that invading species from nearby alpine grasslands could outcompete subordinate snowbed species. On the other hand, microhabitats dominated by Gnaphalium or Salix seem to be particularly prone to invasions by non-snowbed species.